Datasets:

oaimli

/

PeerSum

like 2

[ "nenWtQNbv4Z", "YCHzvtaQ1DL", "oo3YO3aaeVl", "2zYgcHn05M3", "9GstR2SWgcs", "v9qGHIwA0yp", "IJBSgzN6KzLH", "jZB4N35VlOM", "sL9Nu7Y5ZkR", "1tQIrAzVcbs", "jFfY0LcUH8l", "9FNazN9PkZZ" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I appreciate the authors’ thorough response to my questions. After reading the authors' response, now I think the paper’s contribution outweighs my initial concerns (especially regarding the significance). I still think the tackled problem of this paper is not very relevant to the general ML community, but seems to be sufficiently significant for physicists and engineers who are intersted in dealing with wave PDEs by using ML. I increased my review score (and contribution score) accordingly. ", " I appreciate the authors' detailed explanation. One thing that I'm still in doubt about is the comparison to the CPU versions. \nWhy writing a CUDA-based numerical solver for the proposed sparse linear system is \"fundamentally\" challenging, especially given that NeuRIPS is a computer-science conference? Are any special numerical operators we are missing in CUDA? The structure of the target linear system is particularly hard to be implemented in CUDA? I do understand the easiness of using Python-based frameworks such as Pytorch/Tensorflow, but it is hard to agree that this can be a reason to only compare to the CPU version. If this is the case, I think the related argument in the paper needs to be modified by toning down the speed claim.", " Thank you very much for your response and answers! I recommend this paper to be accepted. ", " Thanks so much for your appreciation of our paper and your valuable comments. This is a kind reminder of our responses to your review comments. If you have any further questions after reading our responses, please feel free to let us know during the rebuttal window. We wish that our response has addressed your concerns. Thank you very much! We will appreciate any follow-up suggestions!", " Thanks so much for your appreciation of our paper and your valuable comments. This is a kind reminder of our responses to your review comments. If you have any further questions after reading our responses, please feel free to let us know during the rebuttal window. We wish that our response has addressed your concerns. Thank you very much! We will appreciate any follow-up suggestions!", " Thanks so much for your careful reading of our paper and your valuable comments. This is a kind reminder of our responses to your review comments. If you have any further questions after reading our responses, please feel free to let us know during the rebuttal window. We wish that our response has addressed your concerns, and turns your assessment to a more positive one. Thank you very much! We will appreciate any follow-up suggestions!", " Thank you so much for your appreciation of our contributions and for providing valuable feedback on our work! Please see our responses below:\n\n**Q.1 Prior knowledge of PDE Encoder**\n\nThanks a lot for your comments. \n* In our target problem, i.e., optical field prediction for photonic device simulation, prior knowledge about the light propagation principle is very helpful in improving the model prediction performance. This specific prior knowledge in the PDE encoder part is actually customized for our target problem, which might not be readily applicable to other tasks. However, the following design concepts and contributions are generic and can be transferred to other tasks:\n * Our cross-shaped FNO model backbone is not limited to our problem but can be applied to other tasks for parameter-efficient PDE prediction. \n * Insights from our PDE encoder can be applied to other applications, i.e., PDE representation is very important when training neural operators. A compact and effective representation can significantly simplify the learning process and boost generalization compared to simply feeding raw PDE parameters to the model.\n * Data augmentation needs to be specially designed in PDE prediction tasks to mitigate the overfitting issues of pure data-driven neural operators.\n* We do not need to explicitly construct the Maxwell equation like physics-informed NNs, and we do not need to formulate complicated boundary conditions. We only need to inject the simplest and most effective prior knowledge into the PDE encoder, which is explained in Line 135-137. We find that the wave prior, light source hints, and the superposition property are the three most important prior knowledge to accomplish this field prediction task.\n* The PDE Encoder is not an NN model and thus does not have a model architecture. It simply translates the raw PDE parameters (Omega, epsilon, omega) into compact representations (epsilon, Pz, Px, H^J). The calculation of each term in the joint representation is described in each paragraph in Section 3.2.2. Our PDE encoder has a very compact and effective joint representation with negligible computational complexity. \n\n**Q.2 Average test error**\n\nThanks for your suggestions. Due to limited computation resources, We train F-FNO[33] and our NeurOLight 4 times with different random seeds and report the average test error below. We will add the average test error and the standard deviation to the Table in the revised manuscripts. Thank you.\n\n| Benchmark | Model | Avg. test err | Std. test err |\n|:-----------:|:----------:|:------------:|:------------:|\n| Tunable MMI | F-FNO[33] | 0.302 | 0.008 |\n| Tunable MMI | **NeurOLight** | 0.129 | 0.005 |\n| Etched MMI | F-FNO[33] | 0.521 | 0.005 |\n| Etched MMI | **NeurOLight** | 0.389 | 0.003 |\n\n", " Thank you so much for your appreciation of our contributions and for providing valuable feedback on our work! Please see our responses below:\n\n**Q.1 Evaluation of the overfitting**\n\nThanks for your comments. The overfitting issue is a major challenge for data-driven neural operators. In table 1, we show both the training error and test error to show the generalization gap. Since our model is parameter efficient and adopts dropout layers during training, our proposed method shows a good generalization. Also, our proposed superposition-based mixup method can effectively augment the training distribution to improve generalization, and we evaluate its effectiveness in Table 3. Figure 11 also shows that our method can generalize to unseen MMI sizes and frequencies. Due to the unavoidable domain gap between different photonic devices, direct inference on new devices will suffer from high prediction error out-of-distribution, as we show in Figure 12. We can resolve this issue with finetuning and quickly adapt to new devices with a few training examples.\n\n**Q.2 Evaluation is limited on the device scale**\n\nThanks for your comments. MMIs with different device scales (within a reasonable range) can be generalized by our trained model, as shown in Table 1 and Figure 11. However, a significantly larger device size will have a large data distribution shift, e.g., 5x5 MMI is much larger than 3x3 MMI. That is why we choose to apply finetuning to adapt our model to new device scales. However, if the device size is too large, we might need to increase the image size, otherwise the prediction granularity might become too coarse. Handling large devices or even challenging circuit-level simulation tasks will be our future work. We will add more discussion on this in the revised version. Thank you.\n\n**Q.3 Compare with CPU simulators**\n\nThanks to the highly optimized PyTorch APIs, NeurOLight can benefit from >200x speedup. We compare with CPU simulators with the following considerations:\n* Leveraging the massive parallelism of GPUs is our fundamental motivation to use NN for optical field prediction. \n* We enable multi-threading for the CPU-based numerical simulator for a fair comparison.\n* Solving Maxwell numerically is equivalent to solving a large-scale sparse linear system. Large-scale sparse linear system solving is currently not supported by PyTorch/Tensorflow. It requires considerable effort to write a CUDA-based numerical solver.\n\n**Q.4 Detailed form of A, X, b**\n\nThanks for your suggestions. This linear equation constructed for the Maxwell PDE is quite complicated [1,2]. The A matrix is a huge sparse matrix which is derived based on the PML and boundary conditions. The eigen light source vector b is different from light source J and is obtained by solving another linear equation to find the eigen mode of the input light source. The detailed form of those terms is out of the scope of this paper and can be found in the source codes of the simulator. We will try to add more introductions in the supplemental material.\n\nReference:\n\n* [1] Hughes, Tyler W. and Minkov, et al., “Adjoint Method and Inverse Design for Nonlinear Nanophotonic Devices,” ACS Photonics, 2018.\n* [2] Advanced Computation: Computational Electromagnetics FDFD, url: https://empossible.net/wp-content/uploads/2019/08/Lecture-4f-FDFD-Extras.pdf.\n\n**Q.5 Wave prior vs. Positional encoding**\n\nThis is actually a very interesting question. Previous attention-based NNs adopt linear or cosine positional encoding to inject spatial information into the attention operation. However, our wave prior is fundamentally different from a simple positional encoding. \n\nThe total electromagnetic field consists of the source field and the scattering field. Directly predicting the high-frequency total field is pretty challenging for NNs. We design this wave prior to explicitly integrate the high-frequency source field into the PDE encoder to help simplify this PDE prediction task, such that our model only needs to learn how that wave scatters and interferes within the device.\n\nOur wave prior not only encodes the position information (x and z) but, most importantly, embeds the wave propagation mechanism, as we illustrated in Fig. 4. If one just directly inputs the raw permittivity distribution to the model, the model will have a hard time learning its actual physical meaning, which is harmful for generalization. Since we already know how permittivities impact light propagation, we can feed that prior knowledge to the PDE encoder to boost generalization.\n\nIn Fig. 10(b), we compare various PDE encoding methods, including “positional encoding”. Comparing the first two rows, we can conclude that the pure positional information might not be useful, at least in our model. Actually, the most important thing is instead how to encode the physical meaning of permittivities into the model.\n\nWe will add more discussion on this topic in the revised manuscript. Thank you!\n", " Thank you so much for your appreciation of our contributions and for providing valuable feedback on our work! Please see our responses below:\n\n**Q.1 Relevance to NeurIPS**\n\nOur proposed learning framework is an important step in ‘AI for optics’ and focuses on novel learning-based methodologies for device simulation, which is aimed at pushing forward the application of next-generation photonic computing. Though photonics is a relatively new topic to NeurIPS, we believe our work will attract the interest of the NeurIPS audience due to the following reasons:\n* Photonic deep learning has gained much momentum in recent years, which is a promising technology for next-generation efficient AI. Prior NeurIPS and other machine learning conferences also have publications in the field of photonic/physics AI [1-5]. Fast and reliable device simulation is a critical step in the photonic AI chip design process. Our ultra-fast simulation enables accelerated photonic AI chip design closure and closes the loop of optics-AI synergy. \n* This paper is self-contained, and we have a clear problem definition, i.e., we want to learn parametric frequency-domain Maxwell PDEs. We try to simplify the photonics part so that readers could understand our ML contributions even without a deep understanding of the physical mechanism or advanced optics background to understand our ML contributions.\n* Solving Maxwell PDE using learning methods is a popular topic in the ML community, which shows significant performance improvement over conventional CNNs. Our customized NeurOLight framework has intellectual contributions to the ML community and shows several insights in this direction:\n * The importance of PDE encoding and representation in neural operator\n * Parameter-efficient neural operator design\n * Augmentation in the generalization of data-driven PDE learning\n * Domain adaptation for neural operator-based PDE model\n\nWe believe our work will inspire more follow-on investigations both in “AI for circuit design automation” and “efficient NN-based PDE solving”.\n\nReferences\n\n* [1] Julien Launay, Iacopo Poli, Kilian Muller, Igor Carron, Laurent Daudet, Florent Krzakala, Sylvain Gigan, “Hardware Beyond Backpropagation: a Photonic Co-Processor for Direct Feedback Alignment, “ NeurIPS workshop 2020.\n* [2] Jiaqi Gu, Hanqing Zhu, Chenghao Feng, Zixuan Jiang, Ray Chen, David Z. Pan, “L2ight: Enabling On-Chip Learning for Optical Neural Networks via Efficient in-situ Subspace Optimization,” NeurIPS 2021.\n* [3] Ruben Ohana, Hamlet J. Medina Ruiz et al., “Photonic Differential Privacy with Direct Feedback Alignment, “NeurIPS 2021.\n* [4] Sidharth Gupta, Remi Gribonval, Laurent Daudet, Ivan Dokmanic, “Don't take it lightly: Phasing optical random projections with unknown operators,” NeurIPS 2019.\n* [5] Jiaqi Gu, Chenghao Feng, Zheng Zhao, et al., “Efficient On-Chip Learning for Optical Neural Networks Through Power-Aware Sparse Zeroth-Order Optimization,” AAAI 2021.\n\n**Q.2 Limitations**\n\nThanks for your great suggestions. We discussed the current method's limitations and our future direction in Line 351-353. NeurOLight is currently designed to handle several key optical devices. In our ongoing work, we will extend our framework to handle more device types as well as challenging circuit-level simulation tasks. We will add a paragraph in the revision to discuss our limitations and future directions. Thank you.", " This paper proposes NeurOLight, a variant of neural operators that is suitable to emulate optical devices efficiently. While the core behavior of the proposed NeurOLight is similar to the Fourier neural operators (FNOs), the authors introduce several techniques for optical simulations, including the scale-adaptation for merging variant domains, wave priors for Maxwell PDE encoders, masked image modeling for the light source, cross-shaped FNO that separates the horizontal and vertical pattern predictions, and superposition-based data augmentations. These all techniques for NeurOLight can streamline the complexity of the model as well as generalize the predictive performance. The authors show the proposed NeurOLight outperforms other baselines such as U-Net and FNO. They also provide some ablation studies that can support the proposed techniques are indeed helpful. The paper has many merits: the introduced ad-hoc techniques are convincing for the targeted domain, the writing is clear, and the experimental validation is solid. The paper also demonstrates several interesting results including spectrum analysis and domain transfer learning. Without a doubt, it is a good application paper for optical device simulations.\n\nMy main concern is that the target domain seems to be a niche problem for NeurIPS audiences. Because the proposed techniques are generally applicable to such a niche domain, the relevance and significance of this paper are not entirely clear.\n\nOverall, I think this paper is worthy of publication at some venues (maybe a PDE-related workshop or computational physics journals), but the venue does not have to be NeurIPS main conference.\n The proposed method seems to be sufficiently solid and complete for its purpose. What prevents me from recommending the clear acceptance of this paper is that, as I mentioned in Strengths and Weaknesses, the main limitation of this paper is that the targeted problem is niche. The authors do not explicitly state the limitations of their proposed method.\n\nAs I mentioned in Strengths and Weaknesses, I think that the main limitation of this paper is that the targeted problem is less relevant to the NeurIPS audiences.", " This paper proposes a neural operator that jointly models multiple parameters of EM simulation. Given input light wavelength, permittivity, and domain/material properties, the goal here is to establish a parametric mapping from the inputs to the output EM field via a neural network. To this end, the input domains are first normalized in terms of spatial scales and resolutions. Then, the normalized inputs are encoded as wave prior similar to the Fourier positional encoding. Following the masked image modeling allows us to cast the challenging optics simulation problem into a synthesis problem for missing regions given the input light. The network architecture for doing that is inspired by the Fourier network with a separable modification applied to that: using two 1D FFT instead of having one 2D FFT. The authors also propose an augmentation method that uses a linear combination of input lights/output fields as additional inputs/outputs. Overall I like this paper. It tackles an important, but a challenging problem with novel solutions. Execution is also excellent. I hope below comments could be helpful to refine the paper.\n \nStrength\n- The paper tackles an emerging problem of learning-based optics simulation. The proposed method achieves SoTA performance on the device level simulation in terms of both accuracy and speed. \n- The paper is very well written with clear descriptions and figures. \n- Execution of the paper is of high quality. \n\nWeaknesses\n- There is no evaluation on the overfitting which often occurs in neural optical operators.\n- Evaluation is limited on a device scale as mentioned by the authors.\n- The comparison of the proposed method running on a GPU is done against FDFD method running on CPUs as described in Fig1.\n- L104: It would be helpful to write detailed forms A,x, and b in the main paper - The wave prior method reminds me of the positional encoding which has been extensively used in coordinate-baesd neural implicit functions. I wonder how these two could be related.\n\n- The authors compare the proposed method with FDFD solution that runs on CPUs instead of GPU. Is this because the FDFD on GPUs is challenging to be adopted for this problem? Discussion on this part would be helpful for general readers to understand the computational challenges in EM simulation.\n\n The authors adequately addressed the limitations.", " This paper proposed a physics-agnostic light field prediction framework, called NeurOLight, that consists of a joint PDE encoder and an efficient cross-shaped neural operator backbone. A superposition-based mixup technique is developed to dynamically boost the data efficiency and generalization during the training of NeurOLight. Evaluation results show that the proposed method significantly outperforms the existing methods. Strengths:\n[1] The idea is novel and interesting. It proposed a physics-agnostic light field prediction framework that can improve the efficiency and accuracy of learning parametric Maxwell PDEs. \n[2] It is the first AI-based framework that can learn the terahertz light propagation inside photonic devices that generalizes to different domains.\n[3] The proposed framework significantly outperforms the state of the arts with an average of 53.8% lower prediction error.\n\nWeakness:\n[1] It is not clear how much prior knowledge we should have for PDE encoder. If we do not have any prior knowledge in some applications, how does the proposed method work?\n[2] It is better to report the averaged results with multiple random seeds in Table 1. I am wondering if you could introduce the model architecture of the PDE encoder in more detail? Shall we know a PDE formula? Yes, they have." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 4 ]

[ "sL9Nu7Y5ZkR", "jZB4N35VlOM", "IJBSgzN6KzLH", "9FNazN9PkZZ", "jFfY0LcUH8l", "1tQIrAzVcbs", "9FNazN9PkZZ", "jFfY0LcUH8l", "1tQIrAzVcbs", "nips_2022_Il0ymeSnKyL", "nips_2022_Il0ymeSnKyL", "nips_2022_Il0ymeSnKyL" ]

[ "-tcekW8s7u0", "ERT3_NZctL6", "C6Ung6NWwPK", "56RWXgiNFLz", "GjO24kuKjoL", "2ZgkkaaVYrU", "L4et1Oq3FNj", "-fYcHoW1R4h", "2aPx5VYnvHo" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We are glad that your concerns have been addressed. Thank you for your valuable comments and for taking the time to respond to the rebuttal.", " All my concerns have been feedback by the authors. According to the authors' response and other reviewers' comments, I change my Rating of this manuscript as Accept. ", " We appreciate Reviewer PM1k's constructive and detailed feedback. We are glad that the reviewer acknowledges the contribution of our proposed method and likes our results. Below we address the concerns and questions.\n\n**Q: \"This is pretty close to HeadNeRF\"** \\\n**A:**\nFirst, our method is a generative model trained via a GAN loss, whereas HeadNeRF is trained via an image reconstruction loss with precomputed 3DMM parameters as input. As a result, our model produces much higher fidelity images than HeadNeRF, as shown in the supplementary material.\n\nMoreover, HeadNeRF enforces 3DMM conditioning simply via a reconstruction loss. We have demonstrated in our experiments that parameter reconstruction is an indirect conditioning approach and is ineffective for precise controllability, as shown in row 2 of Table 2 “$+ \\mathcal{L}_\\text{recon}$” (baseline). Our key technical contribution is **precisely a new effective conditioning mechanism** via a novel conditional Generative Occupancy Field (cGOF). It effectively conditions the NeRF on a given 3DMM mesh through a novel **Mesh-guided Volume Sampler** and a **Distance-aware Volume Density Regularizer**. Together with two losses (3D landmark and volume warping), our proposed method achieves significantly better 3D controllability, as shown in Table 1 & 2 and the supplementary material.\n\n**Q: \"I didn't see where or how you chose the different values for lambda's in (9)\"** \\\n**A:**\nWe start from the original Pi-GAN and add the proposed components one by one, as in Table 2 in the main paper. For each component, we first initialize the hyperparameter lambda as $1$, and empirically find a reasonable value before taking a fine-grained search. We have added these details to the updated version. \n\n**Q: \"Metrics: it would be nice to see a really proper human rater paired comparisons survey done\"** \\\n**A:**\nTo address this, we conduct a user study to add to the comparison. We follow the experiment setting of Table 1 in the main paper. Specifically, we provide the control results of five methods, and ask a total of $21$ users to rank the results according to their image quality and the controlling effects.\n\nTable C summarizes the results, where the \"Average Ranking / Average Score / Ranking 1st Ratio\" are reported for each method with respect to concerning factors. Our model achieves the highest average ranking and scores for all aspects, indicating our model produces more perceptually compelling results and achieves better 3D controllability than other counterparts. We have added the user study to the updated version.\n\n**Table C. User Study on the Disentangle Performance and Image Quality. Each cell contains \"Average Ranking / Average Score / Ranking 1st Ratio\".**\n| | DiscoFaceGAN | GAN-Control | Pi-GAN + $\\mathcal{L}_\\text{recon}$ | HeadNeRF | cGOF (Ours) |\n|:-------------:|:--------------------:|:-------------------:|:-----------------------------------:|:-----------------:|:-----------------------:|\n| Identity | 3.05 / 59.1 / 9.52% | 2.57 / 68.6 / 0.00% |3.33 / 53.3 / 9.52%| 4.67 / 26.7 / 0.0% | **1.38 / 92.4 / 81.0%**|\n| Expression | 2.29 / 74.3 / 19.1% | 3.81 / 43.8 / 9.52% |3.19 / 56.2 / 0.00%| 4.29 / 34.4 / 0.0% | **1.43 / 91.4 / 71.4%** |\n| Pose | 2.57 / 68.6 / 14.3% | 3.71 / 45.7 / 0.00% |3.81 / 43.8 / 4.76%| 3.67 / 46.7 / 0.0% | **1.24 / 95.3 / 81.0%**|\n| Image Quality | 2.10 / 78.1 / 9.52% | 2.86 / 62.9 / 4.76% |3.86 / 42.9 / 0.00%| 5.00 / 20.0 / 0.0% | **1.19 / 96.2 / 85.7%** |\n\n**Q: \"They limit the generated images to 64 x 64 during training. I am not sure I grokked the full ramifications and comparison issues due to this.\"** \\\n**A:** Due to the GPU memory limit, we train the model with 64 x 64 images. During inference, we render 128 x 128 images. With the super-resolution module [50], we are able to enhance the image quality and generate 512 x 512 images, without much damage to the controllability.\n\n**Q: \"Surprised that you don't need a conditional covariance matrix for that, does it just not matter much.\"** \\\n**A:**\nThanks for pointing out this mistake. In fact, we did calculate the covariance matrix and use it to normalize and denormalize the 3DMM coefficients, as shown in the submitted code (see \"parse\" function in the \"parse_recon.py\" and \"norm_coeff\" and \"denorm_coeff\" in the \"facerecon_model.py\"). We did encounter some problems when simply using the standard deviation in the beginning, but forgot to update the writing. We have fixed it in the updated version.\n\n**Q: \"I did not understand this sentence 'This allows us to incorporate a 3DMM parameter reconstruction loss that ensures the generated face images to commit to the input condition.'\"** \\\n**A:**\nEssentially, the baseline exploits a 3DMM reconstruction model that predicts 3DMM parameters from the generated images. We then enforce the predicted 3DMM parameters to be close to the ones given as input conditions to generate the images.", " As both reviewers and authors note, there are Inappropriate Potential Applications & Impact. Yes, the original conclusion of the paper notes that this technology could be used to generate fake facial images for imposture or\nto create synthesized facial images to hide the true identities of cybercriminals. It also suggests that future work focused on defensive algorithms for recognizing such synthesized facial images could help mitigate these risks. No recommendation. The authors already acknowledge potential inappropriate applications in the paper.", " \nWe appreciate Reviewer jXJ9’s constructive and detailed feedback. We are glad that the reviewer acknowledges the contribution of our proposed conditional Generative Occupancy Field, evaluation and ablation experiments, and well structured writing. We address the concerns and questions below.\n\n**Q: “originality of this proposed work is not enough… 3DMM conditioning idea is similar to the work in [8] and the cGOF idea is inspired from [53]”**\\\n**A:** Our baseline model is indeed inspired by DiscoFaceGAN [8] and HeadNeRF [17] leveraging a 3DMM parameter reconstruction loss. However, the baseline results in poor 3D controllability in the generated images as shown in Table 2 in the main paper (row 2).\nTo achieve effective 3DMM conditioning, we draw inspiration from GOF [53] and propose a **novel conditional Generative Occupancy Field (cGOF)**.\n\nNotably, unlike GOF [53], where the idea is simply to shrink the volume sample region to a narrow interval through a cumulative rendering process, our proposed **conditional GOF** involves a **Mesh-guided Volume Sampler** that gradually concentrates the samples on a conditional 3DMM mesh. Moreover, we further propose a **Distance-aware Volume Density Regularizer** that effectively suppresses the volume densities away from the conditional mesh.\n\nTo the best of our knowledge, this is the first paper to devise a **controllable NeRF-based generative model**. We believe this is a novel and significant attempt towards controllable 3D object synthesis. \n\n**Q: “It would be great to show that how the way the authors model the 3DMM conditioning in a normal distribution outperforms the VAE model in [8]”**\\\n**A:** \nBoth VAE models in DiscoFaceGAN [8] and the parameter normalization in our paper aim at mapping the normalized gaussian parameters to the 3DMM parameters. Empirically, we found simple normalization achieves good results without the extra complexity of training VAEs as in [8]. In fact, this is not the major difference between DiscoFaceGAN and our proposed method; rather, the key difference lies in the conditioning mechanism, ie., our proposed conditional GOF and the 3D landmark and warping losses.\nFurthermore, we additionally conduct a direct comparison between our method and DiscoFaceGAN [8]. Specifically, we constructed a “Pi-GAN + DiscoFaceGAN” model, by introducing the conditioning methods of DiscoFaceGAN, i.e. imitative loss and contrastive loss, into Pi-GAN. As shown in Table B, the “Pi-GAN + DiscoFaceGAN” model (Row 3) outperforms the Pi-GAN and DiscoFaceGAN baselines, but is still significantly worse than our proposed method. This further demonstrates the effectiveness of our proposed conditioning mechanism. We have added this result to the rebuttal revision paper.\n\n**Table B: Comparison with the \"Pi-GAN + DiscoFaceGAN\" model.**\n| Index | Method | CD | LD | LC | DS_s | DS_e | DS_p |\n|-------|-----------------------|----------|----------|-----------|-----------|-----------|-----------|\n| 1 | Pi-GAN | 1.09 | 5.04 | 2.04 | 2.13 | 2.54 | 7.16 |\n| 2 | DiscoFaceGAN | - | - | - | 5.97 | 15.70 | 5.23 |\n| 3 | Pi-GAN + DiscoFaceGAN | 1.32 | 2.40 | 32.55 | 6.16 | 7.63 | 12.13 |\n| 4 | Ours | **0.27** | **1.26** | **92.88** | **23.24** | **29.13** | **23.45** |\n\n**Q: \"It's not very clear what are the representations of the expression components. Is it also a PCA model or FACs based model? ”**\\\n**A:** Following [10], we adopt the widely-used Basel Face Model [37] for shape and texture bases, and use the expression bases of [a], built from FaceWarehouse [b]. The expression components are obtained from a PCA model of the offsets between the expression meshes and the neutral meshes of individual persons. We have added more details in the updated paper.\n\n\n**Q: “It's not clear how the authors handle these (invisible) landmarks.”**\\\n**A:** During training, we sample camera poses from a normal distribution, with a vertical standard deviation of 0.15 radian and a horizontal standard deviation of 0.3 radian, roughly estimated from the CelebA dataset. With such pose variations, inner 3D landmarks are in fact hardly occluded. We hence simply assume all landmarks are valid.\n\n\n**Q: “include the inference time”**\\\n**A:** With one GTX1080Ti GPU, it takes 0.5716s for cGOF to generate one 128x128 image, and 0.0550s for the neural renderer to upsample it to 512x512. We admit the point-by-point prediction of NeRF-based method is time-consuming. But the optimization of the inference time is not the key objective of this paper, so we leave it to the future work.\n\n**References:**\n- [a] Guo et al. Cnn-based real-time dense face reconstruction with inverse-rendered photo-realistic face images. TPAMI, 2018.\n- [b] Cao et al. Facewarehouse: A 3d facial expression database for visual computing. TVCG, 2013.\n\n", " \nWe thank Reviewer r2K4 for the constructive comments. We would like to address a few concerns and questions below.\n\n**Q: “The novelty of the proposed method is limited”**\\\n**A:** To the best of our knowledge, this is the first paper to devise a **controllable NeRF-based generative model**. We believe this is a novel and significant attempt towards controllable 3D object synthesis. To achieve 3D controllability, we incorporate priors from a 3DMM face model. However, conditioning a NeRF-based volumetric representation on a mesh-based 3DMM is not trivial at all. In order to achieve effective conditioning, we draw inspiration from GOF and propose a **novel conditional Generative Occupancy Field (cGOF)**.\n\nNotably, unlike GOF, where the idea is simply to shrink the volume sample region to a narrow interval through a cumulative rendering process, our proposed **conditional GOF** involves a **Mesh-guided Volume Sampler** that gradually concentrates the samples on a conditional 3DMM mesh. Moreover, we further propose a **Distance-aware Volume Density Regularizer** that effectively suppresses the volume densities away from the conditional mesh. Our proposed cGOF is not a trivial combination of pi-GAN, GOF and 3DMM, but rather a carefully designed framework for effective 3D controllable NeRF synthesis.\n\n**Q: “Please give the comparison results of the proposed method with the baseline model in section 3.2”**\\\n**A:** As explained in Sec 3.2, the baseline model consists of pi-GAN and a 3DMM parameter reconstruction loss $\\mathcal{L}_\\text{recon}$. The comparison with the baseline is provided in Table 2 in the main paper, of which we copy a part to Table A in the follow for reference. **Row 2** (‘+ $\\mathcal{L}_\\text{recon}$’) corresponds to the baseline (highlighted in the updated version).\nCompared to the baseline, the full model (**row 9**) achieves significantly better 3D controllability over the generated faces. For example, 3D Landmark Correlation 26.15 -> 92.88, and Disentanglement Scores 3.56 -> 23.24 (shape), 5.03 -> 29.13 (expression), 11.00 -> 23.45 (pose), as shown below.\n\n**Table A: Ablation Study extracted from Table 2 in the main paper.**\n| Index | Method | CD | LD | LC | DS_s | DS_e | DS_p |\n|-------|------------------------------|----------|----------|-----------|-----------|-----------|-----------|\n| 2 | + $\\mathcal{L}_\\text{recon}$ | 0.87 | 3.85 | 26.15 | 3.56 | 5.03 | 11.00 |\n| 9 | Ours | **0.27** | **1.26** | **92.88** | **23.24** | **29.13** | **23.45** |\n\n**Q: Typo**\\\n**A:** Thanks for pointing it out. $z_\\text{tex}$ denotes the component of the code that controls the texture, not the pose. We have fixed it in the updated version.", " The paper attacks the standard but hard problem of starting with a single-view 2D face shot and creating a 3D face model that can take expression and pose as inputs. Their approach is to meld pi-GAN with 3D Morphable Modeling (3DMM) of priors (based on PCA basis faces) and Generative Occupancy Field (GOF). I believe that they are also proposing the 3D Landmark Loss for this application, and a Volume Warping Loss which is a nice conservation type prior. Strengths: \n- The proposals seem totally reasonable: they bring together solid components and good ideas. \n- The comparisons to state-of-the-art seem fine, and I appreciated the additional results in the Supplemental\n- They show large gains to controllability\n- The ablation study was useful to see \n- I found the paper easy to read and mostly well-written\n\nWeaknesses: \n- This is pretty close to HeadNeRF but with the extreme case of just 1 input view, I would have appreciated more discussion of that\n- While it's nice their loss function in (9) balances many goals, they end up with 6 (5 free) hyperparameters lambda to set\n- Metrics: it would be nice to see a really proper human rater paired comparisons survey done (but yes I see the qualitative results in the Supplemental)\n- They limit the generated images to 64 x 64 during training (and then use another Neural Renderer to map it to 512 x 512... this seemed a bit iffy), and then Table 1 suggests their method without the extra Neural Renderer step). I am not sure I grokked the full ramifications and comparison issues due to this. - \"we assume that the 3DMM coefficients of all the training images follow a normal distribution\". Surprised that you don't need a conditional covariance matrix for that, does it just not matter much?\n\n- I may have missed it, but I didn't see where or how you chose the different values for lambda's in (9)? \n\n- I did not understand this sentence \"This allows us to incorporate a 3DMM parameter reconstruction loss that ensures the\ngenerated face images to commit to the input condition.\" Authors note the obvious problem in this field of creating fakes. In fact, it is hard to conceive of when you would want to do this other than trying to fake people out, but while I think this is not a really important problem to work on, I recognize that in general 3D from 2D is a popular set of problems and do not think the paper should be rejected for its choice of problem. ", " This paper aims the task of controllable 3D face synthesis based on a set of single-view real-world face images. The authors propose a solution based on the framework of pi-GAN and the widely used parametric 3D Morphable Model (3DMM). The key idea is that the conditional Generative Occupancy Field is employed to explicitly guide the volume sampling procedure of the 3DMM mesh. Meanwhile, for fine-grained 3D shape control, the 3D landmark loss and a volume warping loss is used. In the experiments, both qualitative evaluation and quantitative evaluation show the effectiveness of the proposed method. Strengths: The idea of combing pi-GAN and GOF as well as 3DMM for the task of controllable 3D face synthesis shows a certain novelty. \n\nWeaknesses: The novelty of the proposed method is limited. It can not be regarded as a new framework since all the related methods of pi-GAN, GOF and 3DMM are well-known. Meanwhile, the experimental results are not sufficient. The comparison of the proposed method with the Baseline method is missed in Table 1 and Table 2. Moreover, the presentation of the whole paper is not good. For example, in section 3.2, “where the shape, expression, pose and other factors of a face are modeled by a set of PCA bases and coefficients z = (z_shape, z_exp, z_tex, z_else)”, here, z_tex denotes the factor of pose or texture? \n 1. In section 3.2, “where the shape, expression, pose and other factors of a face are modeled by a set of PCA bases and coefficients z = (z_shape, z_exp, z_tex, z_else)”, here, z_tex denotes the factor of pose or texture? \n\n2. Please give the comparsion results of the propsoed method with the baseline model mentioned in the beginning of section 3.2. 1. The novolty of this paper is limited. \n2. The presentation of the whole paper is not smooth and well structured. \n3. The experimental results are not sufficient.", " This paper proposed a new NeRF-based conditional 3D face synthesis framework, which enables the control over head poses and expressions using a parametric 3D face model (3DMM). \n\nThe main contribution of this model is a conditional Generative Occupancy Field (cGOF) that effectively enforces the shape of the generated face to commit to the 3DMM model mesh. Besides that, novel loss terms such as 3D landmark loss and volume warping loss are proposed in the system. \n\nThe authors trained the model on the CelebA dataset and conducted both quantitative and qualitative comparisons to other methods. The results and comparisons showed that the proposed method outperforms the state-of-the-art methods. Meanwhile, the ablation study was also done to show the effectiveness of each proposed component.\n Strengths:\n\n1. This paper proposed a new NeRF-based 3D face synthesis framework, which allows controlling the large head pose change and expression changes of frontal face images.\n\n2. The core contribution is the usage of the conditional Generative Occupancy Field (cGOF) model. Other terms such as 3D landmark loss and volume warping loss terms all contributed to the effectiveness of the proposed framework.\n \n3. This paper is well structured and easy to follow. The authors clearly explained each term and did ablation study to show the impact of each proposed component.\n\n4. The authors further did quantitative and qualitative evaluations on the proposed method and some state-of-the-art methods such as PIE, StyleRig, DiscoFaceGAN, E2E, HeadNeRF, etc, showing that the proposed method outperforms. \n\nWeaknesses:\n1. I'm a little concerned that the originality of this proposed work is not enough. For example, the 3DMM conditioning idea is similar to the work in [8] and the cGOF idea is inspired from [53]. It would be great to show that how the way the authors model the 3DMM conditioning in a normal distribution outperforms the VAE model in [8].\n\n2. Some technical details are not very clear to me. Please see the following questions. \n 1. For the 3DMM conditioning, the authors mentioned that they assume the 3DMM coefficients of all the training images follow a normal distribution, while it's not very clear what are the representations of the expression components. Is it also a PCA model or FACs based model? The authors cited [37], which didn't mention about expression components. \n\n2. For the 3D landmark loss, the authors mentioned that they didn't consider the facial contour landmarks due to the impact of occlusion. However, in extreme head poses such as 90 degree left/right view, part of the inner facial landmarks are not visible as well. It's not clear how the authors handle these landmarks and be able to generate plausible results for side view head poses. \n\n3. It would also be great if the authors could include the inference time of the proposed framework. The authors addressed the limitations of the work that the proposed method couldn't handle precise texture and lighting control over the generated face. And also the model relies on 3DMM model, which could not generate high-fidelity shape details such as wrinkles and hair.\n\nFor societal impact, the authors mentioned that the work might be used to generate fake facial images. Defensive algorithms on recognizing these images should be developed. " ]

[ -1, -1, -1, -1, -1, -1, 7, 4, 5 ]

[ -1, -1, -1, -1, -1, -1, 3, 4, 3 ]

[ "ERT3_NZctL6", "-fYcHoW1R4h", "L4et1Oq3FNj", "nips_2022_Qq-ge2k8uml", "2aPx5VYnvHo", "-fYcHoW1R4h", "nips_2022_Qq-ge2k8uml", "nips_2022_Qq-ge2k8uml", "nips_2022_Qq-ge2k8uml" ]

[ "vFQkCjw9ZQd", "0Gy-0VHV4wE", "YxwfuhaUHhXB", "JlLzt33nj2G", "ttGPfy49lqE", "T8y-N-laYCH", "jruMAMhHrXG", "fdPZ8pPIiJ", "5dbaZDXjpA", "phcIQtW1zlH", "Jjtegx--3-O", "kw2kmnSp4AA", "DQselQsxbjK", "i4p8Bk5oUr", "DFTH9hF98FB", "g-B3jkpPsCW", "aCOPNMCshEq" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for your feedback and for taking the time to go through the revision, we appreciate it.", " Thanks for the additional experiments and further improvements.\n\nYour clarifications in Items 2, 3, 4 has well-resolved our concerns. Regarding Items 5 and 6, we have got your explanations. Thanks.\n\nIn our process of reviewing, one issue that concerns us is how to evaluate your contribution. We agree with what you have claimed on the performance of attack. However, such a successful attack seems not telling anything interesting for development/improvement of deep clustering models. Besides of the success of attacking, we fail to learn anything in-depth from your experimental results.\n\nWe appreciate your work while it is around the borderline of NeurIPS. So we keep the score of 5.\n", " Thank you for taking the time to go through the new results and response, and for updating the score. We will be sure to include the justifications and example in the final version.", " Thanks the authors for the detailed clarifications.\n\nThe response (including appendix E) has clearly addressed my concerns, and made the difference between classification attack and the proposed method clear. I it highly encouraged to incorporate the justifications in the manuscript, especially the '[1,2,3,4] v.s. [4,4,4,4]' example. This really helps readers to understand the difference.\n\nBased on these, my major concerns are well-resolved. And I'm raising the score to 5.", " Thank you for going through the additional experimental results and for your constructive feedback. We appreciate your time.", " Thank you for taking the time to go through the rebuttal/revision and for your constructive feedback, we appreciate it.", " Thanks for the additional experiments on the low-dimensional embedding space. The result seems interesting, and it satisfied my curiosity about what is happening in the low-dimensional representation. Considering the high impact on one sub-area of AI (area: adversarial ML, and sub-area: adversarial attack on clustering algorithms), I believe the evaluation of 7 is fair for this paper.", " Thank you for your detailed and well-prepared response to my concerns on differences between Vanilla GAN / Adv GAN, Face++ surrogate model details, epsilon values, clustering intuitions, and real-world threats, which clears up my concerns. I think a score of 6 remains fair, as a solid paper that provides an interesting study that applies to real-world black-box MLaaS systems with a novel but inspired by prior work technique. ", " We thank the reviewers for their comments and questions. We appreciate all the feedback and suggestions, which further improve our paper.\n\nFor easy reference, we have summarized the main changes made to the paper during the rebuttal phase:\n- Updated Figure 6 in the main paper to not have a 0 error bar (Reviewer c5rd).\n- Added Appendix G which contains new defense experiments (Appendices G.1 and G.2) using an older deep clustering method, t-SNE, and PCA (Reviewer c5rd and Reviewer hxny).\n- Added Appendix E which contains empirical results and comparison with SPSA attack (Reviewer sgLu).\n- Added subsection \"Attacks/Defenses Against Supervised Learning\" to Section 2, Related Works (Reviewer sgLu). \n- Added Appendix F which contains more discussion on why supervised attacks/defenses are not applicable to our setting (Reviewer sgLu).\n- Corrected the caption for Figure 1 (Reviewer sgLu).\n- Reworded footnote on line 35 to avoid ambiguity (Reviewer sgLu).\n- Changed subsection \"Adversarial Attacks Against Clustering\" to \"Training-time Adversarial Attacks Against Clustering\" to avoid ambiguity (Reviewer sgLu).\n- Reworded statement on line 138; this is line 153 in revised submission (Reviewer sgLu).\n- Added Appendix H which contains descriptions of 2 real-world practical attack scenarios for our attack setting (Reviewer sgLu and Reviewer 88S9).\n- Improved \"Limitations\" subsection in Section 7 (Reviewer sgLu and Reviewer 88S9).\n- Added footnote 2 on line 46 for threat model details (Reviewer 88S9).\n- Added lines 84-85 including footnote 4 detailing percentage performance changes (Reviewer 88S9).\n- Added footnote 6 on line 145 regarding distinction between score-based and decision-based attack (Reviewer 88S9).", " We thank the reviewer for their thorough reading of the paper and feedback. We have answered the questions below:\n\n- __Improvements over Vanilla GAN/AdvGAN:__ 1) We propose a novel loss function ($L_{attack}$) that aims to completely disrupt the deep clustering function by reducing the NMI/ACC/ARI of the models significantly. 2) The AdvGAN approach is designed for supervised learning, and the authors used distillation [1] for the blackbox attack which is invalidated by our threat model, further simplifying our approach. 3) Unlike AdvGAN, we implement adversarial image clipping [2] so values are within the appropriate range (0 to 255). This improves performance and generates more realistic adversarial images.\n- __Face++ Surrogate Model:__ We have provided training details for the CC [3] model that is used as the _surrogate_ for the Face++ attack in Appendix C. We train the CC deep clustering model on the Yale Face B dataset. Then, we use the GAN attack to generate attack samples for the CC model we trained on Yale Face B. The same set of benign and adversarial images (generated by GAN attack on CC) are provided to the Face++ API. We can then measure performance (NMI) pre-attack and post-attack to calculate the efficacy of our attack on Face++. \n- __Choice of $\\epsilon$:__ \n - Our experiments to determine the best $\\epsilon$ values were undertaken using grid search. However, the optimal perturbation found by the GAN might be much lower than $\\epsilon$. Thus, to report more precise $\\epsilon$ values we calculated the norm of the optimal perturbation and report that as $\\epsilon$ in the paper. We will refer to this here as $\\epsilon^*$. This is why the reported values seem somewhat arbitrary, and we apologize for not detailing this process in the original submission; we omitted it believing it is an implementation detail. In the final version we will include both and add a remark regarding this.\n - Using the reported values of $\\epsilon^*$ for the attack instead of $\\epsilon$ generates the same adversarial samples, as $\\epsilon^* \\leq \\epsilon$ and no extra clipping can occur. We confirmed this by re-running experiments before submitting. Note that for some models/datasets the GAN network converges much quicker, resulting in widely varying $\\epsilon$ and $\\epsilon^*$ values. \n - The images used for the attack are the ones visually reported in Appendix A.2 so it can be seen that the noise threshold is low from a visual perception sense. \n- __Regarding $\\epsilon$ values for the transferability table:__ While $\\epsilon$ can be fixed, for each model/dataset, the GAN attack might end up finding different optimal noise with different norm, i.e. different $\\epsilon^*$. Thus the adversarial perturbation norm values ($\\epsilon^*$) are different for the transferability matrix. We do not think this is a problem as previous foundational work on transferability also had different perturbation norm for different models (Section 3.3 in [4]).\n- __Possible reasons for clustering breakdown:__ We feel deep clustering models tend to be very over-/under-confident of certain classes when assigning cluster probabilities. Our $L_{attack}$ loss for the GAN attack is powerful as it aims to maximize the probability that the _least likely_ cluster label is assigned to a generated adversarial sample by maximizing the _distance_ between the _fixed_ pre-attack cluster probabilities and the cluster probabilities of the adversarial sample. Considering the above, the clustering breakdown effect seen in the paper possibly occurs because a) our loss is driving the model to pick the worst cluster label possible for the sample, and b) for deep clustering models the least likely classes/clusters are not equi-probable, i.e., one or a few cluster labels are generally the least likely cluster labels for a majority of samples. For e.g. consider 4 data samples with ground truth labels [1,2,3,4]. The clustering model outputs [1,2,3,4] pre-attack, giving NMI=1. For our attack the output will more likely be of the type [1,1,1,1] where NMI=0.\n- __Addition of real-world threat scenarios:__ We have added real-world threat vectors for our attack in Appendix H. We provide attack scenarios pertaining to 1) Malware Analysis, where clustering models are heavily used, and 2) Human Activity Recognition. We have also added more details to our limitations (Section 7).\n- __Minor comments:__ We have addressed the minor comments suggested by the reviewer in the main text. Please see line 46 (footnote 2) regarding threat model contribution, lines 84-85 (footnote 4) regarding % performance changes, and line 145 (footnote 6) regarding distinction between score-based and decision-based attack.\n\nReferences:\n1) G Hinton, et al. Distilling the knowledge in a neural network. 2015.\n2) N Carlini, et al. Towards evaluating the robustness of neural networks. 2017.\n3) Y Li, et al. Contrastive clustering. 2021.\n4) N Papernot et al., Transferability in Machine Learning. 2016.", " We thank the reviewer for their insightful feedback. We address the concerns in our response, and kindly request the reviewer to reconsider their score.\n\n__Inapplicability of supervised blackbox attacks:__\n- __Absence of ground truth labels:__ NES [1] and SPSA [2] cannot directly be used to attack deep clustering models since ground truth labels are not available to the adversary and assuming so invalidates our threat model. This is seen in the SPSA paper attack optimization [2] (Section 4.1) where $y_0$ is the ground truth label and in the suggested CVPR 2020 paper [3] (Section 2.1) where $y$ is the ground truth label. Moreover, deep clustering output labels may not map to actual ground truth labels and hence, the attack will be unsuccessful. In new experiments we did for all datasets (models: SPICE, RUC) using this setting, the SPSA attack was mostly unsuccessful and at times increased NMI (Appendix E, Table 11-13). \n- __Supervised attack loss with predicted labels and our proposed loss are different:__ \n - Even if we use a modified formulation for the supervised attack loss by replacing $y_0$ with the label predicted by the model, the SPSA margin loss and our loss $L_{attack}$ are very different. The margin loss aims to reduce performance by ensuring that $y_0$ is not predicted for the adversarial sample, i.e. $j\\neq y_0$ is predicted. Whereas our $L_{attack}$ loss aims to maximize the probability that the _least likely_ cluster label is assigned to a generated adversarial sample. I.e., it aims to maximize the _distance_ between the _fixed_ pre-attack cluster probabilities and the cluster probabilities of the adversarial sample. This leads to a more powerful attack. \n - We believe that deep clustering models tend to be very over-/under-confident of certain classes when assigning cluster probabilities. This possibly originates from the lack of labels during training. Hence, the least likely classes/clusters are not equi-probable. Further, minimizing the SPSA loss might not reduce performance of the deep clustering model at all. \n - Consider an example with 4 points. The pre-attack predicted labels and ground truth labels are both [1,2,3,4]. For SPSA, the attack will be considered successful for an output [4,3,2,1] since all labels are different post-attack and classification accuracy is 0. However, the NMI before and after the attack is still 1.0, which is the best possible clustering achievable. For our attack the output will more likely be of the type [1,1,1,1] where NMI=0, indicating _clustering breakdown_. \n - This failure of this supervised loss is shown in additional experiments (Appendix E, Table 11-13). For the same number of queries, we find that SPSA cannot reduce the clustering performance as well as our attack. \n\n__Concerns:__\n1. Thank you for the suggestions. We added two real-world attack scenarios to the paper (Appendix H) and improved limitations (Section 7).\n2. We corrected the Figure 1 caption.\n3. To avoid ambiguity, we re-worded line 35.\n4. We added a subsection \"Attacks/Defenses in Supervised Learning\" to Section 2, cited the relevant works (NES, SPSA, CVPR paper [3], etc.). We provide more details in Appendix F. As mentioned above (and Appendix E,F), classification attacks/defenses cannot be directly applied to deep clustering with good results.\n5. We changed it to \"Training-time Adversarial Attacks Against Clustering\" to remove ambiguity.\n6. Thank you for pointing out the oversight on line 138-- we have reworded it (line 153 in revised paper) so that it is correct. NMI/ACC/ARI require ground truth labels and are only used for evaluation so we cannot use them as the attack optimization target (even if they are non-differentiable). In the response above, we have detailed why supervised attacks still cannot be used successfully.\n7. As mentioned in the main text not all deep clustering models have latent spaces (earlier versions did). As we state in line 210, ALRDC can make the latent space robust to perturbations. However, the SOTA deep clustering models considered in this paper do not possess a latent space.\n8. We have hypothesized the reason for this trend in our response above. It seems that for SPICE/CC the model assigns a sample low probability w.r.t \"horse\"/\"cat\" unless it actually belongs to that cluster. Thus, these are usually the least likely cluster label (for SPICE/CC), and our attack moves samples to these labels, leading to very low clustering performance (NMI).\n9. We believe the word \"defenses\" in the title does not imply that we propose a new defense and we explicitly state that we use existing defenses throughout.\n\nReferences\n1) A Ilyas, et al. Black-box adversarial attacks with limited queries and information. 2018.\n2) J Uesato, et al. Adversarial risk and the dangers of evaluating against weak attacks. 2018.\n3) Y Dong, et al. Benchmarking adversarial robustness on image classification. 2020.\n4) P Huang, et al. Deep embedding network for clustering. 2014.", " We thank the reviewer for their insightful comments and suggestions, and hope to improve upon the weaknesses mentioned by doing some of the suggested additional experiments (Appendix G).\n\n__Additional Experiments:__ \n\nWe thank the reviewer for the excellent suggestion of using earlier deep clustering methods as an embedding approach. Based on this, we undertake the following experiments: 1) The first experiment (Appendix G.1) is based on utilizing an older version of a deep clustering method and attacking it using our GAN attack. The low-dimensional representations of benign and adversarial samples are visualized using t-SNE [2] and then analyzed using PCA as an anomaly detection approach. 2) The second experiment (Appendix G.2) uses a SOTA deep clustering model and decomposes its benign and adversarial samples using the same older deep clustering method to low-dimensional representations. We perform the same t-SNE visualizations and PCA anomaly detection analysis on the benign and adversarial samples' embeddings.\n\n__Design Choices For Experiments:__\n- Due to time constraints we cannot use SSD (the deep-learning based anomaly detection approach) for experiments since this model needs to be trained on the source/ground-truth data (i.e., all of CIFAR-10, or STL-10). To do this we would have to retrain the SSD model on the entire dataset of embeddings and there is no guarantee the SSD model would generalize well to these. Thus, instead of SSD, we use PCA for anomaly detection as it runs expediently and has a long history of being used for outlier/anomaly detection, especially on low-dimensional data [3]. \n- We undertook both experiments using the Deep Clustering Network (DCN) [1] as the low-dimensional embedding approach and the MNIST dataset. The size of the latent space for DCN is set to 10. We utilized DCN since its architecture improved upon previous approaches by opting for an autoencoder as opposed to just an encoder, resulting in better clustering performance. Using MNIST with DCN is a suitable choice because 1) the original DCN implementation expects grayscale images, and 2) experimentally, DCN does not tend to work that well with more complex datasets such as CIFAR-10/CIFAR-100 (the authors also consider _only_ MNIST in their paper). We use Contrastive Clustering (CC) as the SOTA deep clustering model to attack since it trains much quicker compared to other SOTA models.\n\n__Experiment on Attacking DCN:__\n\n- We train DCN on MNIST and attack it using the GAN attack in the paper. \n- We then use the low-dimensional representations obtained using the DCN network for both the benign and adversarial samples, and run t-SNE to visualize this low-dimensional space. These results are shown in Figure 48 (Appendix G.1).\n- As can be seen in Figures 48(b),(c), while t-SNE visualizations of the benign and adversarial samples look different visually, it is still hard to tell these apart unless the adversarial samples are known _a priori_ (Figure 48(a) shows both superimposed).\n- We then run PCA on these embeddings (60000 benign and 60000 adversarial samples) jointly as an anomaly detection approach to see how many adversarial samples are detected overall (Appendix G.1). While this direction as a possible defense seems promising, a large majority of samples are still not detected with only 20\\% (12000 out of 60000) being detected. \n\n__Experiment on Attacking CC:__\n\n- We train CC on MNIST and conduct the GAN attack on this model to obtain adversarial samples. \n- We then obtain embeddings of both these benign and adversarial samples using the DCN model trained on MNIST.\n- We carry out the same analysis by generating t-SNE visualizations for benign sample and adversarial sample embeddings. The results are shown in Figure 49 (Appendix G.2) and a similar trend follows from the previous experiment. It is hard to distinguish between adversarial and benign sample representations.\n- Then, we run PCA on the combined benign and adversarial samples for anomaly detection (Appendix G.2). Here too, the same trend holds. Approximately, slightly less than 20\\% of adversarial samples are detected (11981 out of 60000). Thus, while the suggested approach has potential as a defense strategy, it is unable to detect a large number of adversarial samples. \n- Our future aim is to train a SOTA anomaly detection approach on the low-dimensional embeddings and undertake the same experiments on the main datasets considered in the paper. \n\n__References:__\n1) B Yang, et al. Towards k-means-friendly spaces: Simultaneous deep learning and clustering. 2017.\n2) L Van der Maaten et al. Visualizing data using t-sne. 2008.\n3) C Aggarwal. An introduction to outlier analysis. 2017.", " We thank the reviewer for their insightful comments and questions.\n\n1. __Novelty of Attack Approach:__ \n - __Improvements from Vanilla GAN/AdvGAN:__ 1) We propose a novel loss function $\\mathcal{L}_{attack}$ that ensures the NMI/ACC/ARI of deep clustering models decreases significantly. 2) The original AdvGAN approach was designed for supervised learning; the authors used distillation [1] for the blackbox attack which is invalidated by our threat model, making our approach simpler. 3) Unlike AdvGAN, we implement adversarial image clipping [2] so that values are within the appropriate range (i.e. 0 to 255). This improves performance and generates more realistic adversarial images. 4) Despite its simplicity, our attack significantly reduces the performance of deep clustering models, showcasing its disruptive capability.\n - __The power of our loss function:__ We feel deep clustering models tend to be very over-/under-confident of certain classes when assigning cluster probabilities. Our $\\mathcal{L}_{attack}$ loss for the GAN attack is powerful; it aims to maximize the probability that the _least likely_ label is assigned by maximizing the _distance_ between the _fixed_ pre-attack cluster probabilities and the adversarial sample's cluster probabilities. Thus, the clustering breakdown seen in the paper possibly occurs because a) our loss is driving the model to pick the worst possible cluster label for a sample, and b) for deep clustering models the least likely clusters are not equi-probable across samples, i.e., one or a few cluster labels are the least likely cluster labels for most samples. E.g. consider 4 data samples with ground truth labels [1,2,3,4]. The clustering model outputs [1,2,3,4] pre-attack, giving NMI = 1.0. Based on the described ideas, our attack would likely label all samples in the same cluster (e.g. [4,4,4,4]) making NMI = 0.\n2. __Interpreting Norm of Adversarial Noise:__ The reviewer's recommendation is a great insight; one can define the _intensity_ of the noise $\\epsilon$ added as $\\frac{\\epsilon}{\\epsilon_{\\max}}$ to make it more interpretable. Here $\\epsilon_{\\max}$ is the maximum possible noise added after which the image starts deteriorating, revealing it is an adversarial sample. We will add this as a note in the final version and could update figures as well with this index. \n3. __Improving PCA:__ \n - We agree with the reviewer's suggestion. Our reason for undertaking the PCA analysis in the paper was to reinforce the results obtained via SSD (anomaly detection) and how it fails as a defense. However, based on the reviewers' suggestions, we improve the PCA analysis through a simple experiment using an older deep clustering model DCN [3] as a low-dimensional embedding approach. We obtain embeddings for both benign and adversarial samples for a SOTA model via DCN. We a) visualize the embeddings for benign and adversarial samples using t-SNE [4], and b) perform PCA based anomaly detection on the benign and adversarial sample embeddings to see if adversarial samples can be detected.\n - __Implementation:__ We conduct this experiment on the CC [5] deep clustering model and generate adversarial samples for it. After, we use DCN to obtain the low-dimensional embeddings for benign and adversarial samples.\n - __Results:__ a) The t-SNE visualizations show that while adversarial and benign samples look different visually (Figure 49(b),(c) in Appendix G.2) it is hard to tell these apart unless adversarial samples are known _a priori_ (Figure 49(a) in Appendix G.2). b) The PCA anomaly detection results on benign and adversarial sample embeddings show it cannot detect ~80% of adversarial samples (Appendix G.2 contains detailed results).\n4. __Error Bar:__ The value of the _best_ error bar is 0, which is why it doesn't have a _top_ or _bottom_. We kept it for consistency but have now removed it (Figure 6).\n5. __Anomaly Detection as Defense:__ Anomaly detection is an existing defense approach in unsupervised settings. We wanted to show that despite using SOTA deep learning anomaly detection models (SSD), this is not a good enough defense for adversarial attacks against deep clustering. We hope that through our work better defenses are proposed for deep clustering.\n6. __Queries Table:__ The query complexity table illustrates how costly the proposed attack is. Our goal was to demonstrate that query complexity for the attack is not large, even compared to attacks on non-deep clustering ML tasks. We can reword this to make it clearer in the final paper.\n\nReferences:\n1) G Hinton, et al. Distilling the knowledge in a neural network. 2015.\n2) N Carlini, et al. Towards evaluating the robustness of neural networks. 2017.\n3) B Yang, et al. Towards k-means-friendly spaces: Simultaneous deep learning and clustering. 2017.\n4) L Van der Maaten, et al. Visualizing data using t-sne. 2008.\n5) Y Li, et al. Contrastive clustering. 2021.", " This paper investigates the blackbox adversarial attacks against deep clustering models. It first proposes a blackbox adversarial attack using vanilla GAN. Then it evaluates the attacks against a number of SOTA deep clustering models and real-world images. It reveals that the proposed attack can significantly reduces the performance of these models, has minimal query complexity. Moreover, to further examine the robustness, it utilizes two unsupervised defense approaches, and observes unsuccessful defenses. And it also shows a successful attack on production-level API Face++.\n Strengths:\n\nThis paper, as the authors claimed, proposed the first blackbox adversarial attack against deep clustering models. And it performed multiple experiments to show its success on various SOTA models, real-world datasets, query complexity, transferability, resistance to defenses, and production-level API Face++.\n\nWeaknesses:\n\n1. The blackbox adversarial attacks seem a straightforward application of vanilla GAN to this problem. Although the authors mentioned the challenges in building GAN-based blackbox attacks in Sec.3, we did not see any novelty or smart operations in Sec.4.1 to build up blackbox attacks. And the most challenging part of the direct formulation of attack objective has been bypassed by practically choosing the indirect, and hence the ratio of successful attacks among total raises concerns. \n\n2. The norm of adversarial noise, epsilon, may not be an appropriately interpretable one in experiments (Fig.3), since its reasonable threshold can vary significantly for different datasets. Obviously a large enough epsilon can always lead to a \"successful\" attack, while it may not be a meaningful one (it should be reasonably small such that this attack does not completely overwrite datasets). One has to formulate an index that quantifies the intensity of attacking noises over data.\n Besides the major questions in the \"Weaknesses\" part, there could be more deserving the authors' attentions:\n\n3. The evidence of PCA might not be convincing. We assumes you perform PCA on the total datasets, including all classes. As a complicated clustering/classification task (not easily separable w.r.t. a few principle components), it is not supervising that all data mixed in PCA plot together with the adversarial ones (considering they are close to the original).\n\n4. In Fig.6, why the \"best\" plot also has an errorbar. Did it show multiple \"best\"? How did you define the \"best\"? Maybe we missed something.\n\n5. We failed to see the necessity or the supportiveness of the application of anomaly detection as a defense approach. Considering the adversarial attack samples are \"close\" to the original, it may be foreseen that they fail to be observed as anomalies.\n\n6. The query complexity of the attack (Tbl.2) may not be a fair comparison. These attack mechanisms are different and the attacks are imposed at different stages of learning process. Not sure whether this comparison could tell something.\n We do not see any potential negative societal impact of this paper.", " This paper proposes an effective attack method against deep clustering models. Specifically, the threat model and attack objective are newly defined, reducing the attack to an optimization problem. Then, by combining a common GAN training loss with the attack objective, the authors design a GAN-based blackbox attack so that the resulting GAN generates adversarial perturbations for a given input image.\n\nThe power of the attack–effectiveness, query complexity, and transferability–is demonstrated from thorough experiments. Also, the authors tested the performance of their attack against two standard defense methods (robust deep clustering and deep learning based anomaly detection), showing successful attack results against them. Finally, they tested a blackbox attack against an existing face clustering service. Since the actual cluster membership is unknown in this case, the authors trained an open-source surrogate model and attacked via the transferability of the attack.\n Originality: To the best of my knowledge, the paper contains novel ideas.\n\n[[Strength]]\n1. To the best of my knowledge, this is the first work about adversarial attacks against the deep clustering model.\n\nQuality: \n\n[[Strength]]\n1. The authors tested the attack against numerous clustering models and performance metrics. To explain, for the attack performance test, the authors prepare six different state-of-the-art models and three different clustering performance measures.\n2. Moreover, the authors also explore various aspects of the attack–query complexity and transferability–to better evaluate the attack’s value.\n3. The power of the attack is evaluated carefully against existing defense strategies.\n\n[[Weakness]]\n1. Visualization of the PCA patterns between adversarial examples and original samples may not be an effective way to analyze the reason. A better visualization should also show the difference in the PCA components between detected adversarial examples, undetected adversarial examples, and benign original samples. (The last two sets of samples should show similar patterns, while the first set should show visually different patterns.)\n\nClarity: The paper writing is clear, and there is no issue with the clarity of the paper.\n\nSignificance: \n\n[[Strength]]\n1. The power of attack looks to be very impressive. The attack significantly reduces the clustering performance for all 18 combinations (six different models, three different metrics).\n2. The proposed attack seems to be effective against existing defenses. The experimental results may imply the need for a new defense method to ensure the robustness of deep clustering algorithms.\n3. The authors experiment with the attack transferability and test it against an existing face clustering service (via an open-source surrogate model). This result shows an urgent threat of the attack in a practical setting.\n 1. While the paper demonstrated impressive performance against state-of-the-art deep clustering models, it would be interesting to attack some earlier deep clustering models. Since earlier models decompose the high-dimensional data to a low-dimensional representation, we can observe what happens in the low-dimensional space. (Those small perturbations in high dimensional may result in considerable differences in the low dimensional data.)\n2. A follow-up suggestion from Question 1 is to perform anomaly detection over the low-dimensional representations of adversarial samples. To explain, prepare an earlier version of the deep clustering model as an embedding method. (Even though earlier versions have low performance in clustering tasks, it is okay because we will use it only to create low-dimensional representations) Then, create adversarial examples against a state-of-the-art model and embed those adversarial examples in low-dimensional space. Using any anomaly detection method, check whether the embedded representations are outliers or not.\n The authors discussed limitations and potential negative societal impact in the paper appropriately.", " This paper presents a new black-box attack against deep clustering models. Specifically, the adversarial perturbation is computed by a generative model. It penetrates existing defense methods for clustering, and manifests transferrability which further make the proposed method practical. To further demonstrate the effectiveness of the proposed method, experiments are also conducted on a commercial API named Face++, apart from commonly used evaluation datasets in previous related works. # Strengths\n\n1. The manuscript focuses on run-time adversarial attack on deep clustering model, which is a less-explored area.\n\n2. The proposed attack method is simple and intuitive. Experiments demonstrate its effectiveness.\n\n# Weaknesses\n\n1. [minor issue: paper organization] The introductory part of the manuscript can be improved. Since the proposed attack and defense methods are all based on deep learning, it is no longer necessary to introduce the clustering task starting from traditional methods like k-means. Instead, it is suggested to briefly mention (1) how a deep learning-based clustering method works, (2) how does attack against such method work, and (3) the potential risk induced by the attack to practical applications. These will make it more worthwhile for this topic to draw attention from the community (line 40).\n\n2. [minor issue: unclear figure] In figure 1, it is unclear which picture correspond to which model mentioned on line 79 (SPICE, RUC).\n\n3. [minor issue: potentially misleading] On line 35, it is pointed out that “zero-th order optimization is intractable for deep models.” in foot note. However, zero-th order optimization is a common approach for black-box attack against supervised deep classification models. See survey paper “Benchmarking Adversarial Robustness on Image Classification, CVPR2020” for examples, including ZOO, NES, as well as SPSA. In this sense, the word “intractable” is ambiguous, and may possibly convey wrong information to the reader.\n\n4. [insufficient citations] This paper focuses on attack and defense problem on a specific domain other than classification. In section 2, the author should cite and discuss the main-stream attack defense works on the classification problem, and discuss how and why these ideas cannot be adapted for clustering.\n\n5. [misleading contents] In the field of classification, “black-box attack” usually refers to run-time attacks against a trained and frozen model. See “Benchmarking Adversarial Robustness on Image Classification, CVPR2020” for examples. The attacks happend during training-time are called Backdoor attack or Poisoning attack. So please avoid using “adversarial attacks against clustering” as paragraph title on line 90. To be less ambiguous, it should be “Training-time attacks against ...”.\n\n6. [important: relationship with classification attack] Based on the description on line 116. A frozen trained clustering model is a classification model to assign cluster labels from softmax probabilities. In this way the existing black-box (run-time) attacks should be compatible in the setting of this paper. However, comparison and discussion are missing. The aforementioned CVPR2020 survey paper can be used as a referece regarding this. Existing (black-box, run-time) classification attack methods can be used to attack the cluster assignment, e.g. based on the softmax scores. To be clear, score-based attacks like NES and SPSA in the mentioned CVPR2020 paper can do this. In this sense, the claim on line 138 is wrong. Score-based attack like NES and SPSA can optimize M (softmax scores) using estimated gradients even if the optimization target is completely indifferentiable.\n\n7. [minor issue: unconvincing claim] On line 210, the ALRDC approach makes the latent space robust to perturbations. A robust latent space is already very important for adversarial robustness, and it not clear why this restricts its use. That said, evidence provided on line 212 indeed makes comparison with ALRDC unnecessary.\n\n8. [confusing figure] Figure 2 shows an irregular pattern after attack. According to equation on line 148, the attack is untargeted, which means the objective does not care which would be the result class for misclassification. In this sense, shouldn't the confusion matrix be relative random instead of being concentrated on the “cat” or “horse” class?\n\n9. [misleading title] The title mentions “defense”. But the paper actually only involves attack and evaluated this attack against existing methods for defense. The paper does not propose any new possibility for defense. My questions are written in weaknesses 4, 5, 6, and 8. Limitations are not discussed in detail -- only several words in section 7.\nPotential societal impact is discussed in the last paragraph. I agree that in order to be able to defend, we first have to know how to attack.", " This paper proposes the first black-box test-time adversarial attack against deep clustering models. This work helps bridge the adversarial analysis from traditional clustering approaches (explored before) to deep learning-based clustering models, where only white-box supervised learning based attacks have been explored. The attack uses Generative Adversarial Networks (GAN) with just score-based query access to the deep clustering model, with a more clearly defined threat model. The authors evaluate this attack on SOTA deep clustering models, in a transferability study, and on the Face++ ML-as-a-Service (MLaaS) system. The authors also demonstrate that existing defense approaches fail to stop the attack. Strengths:\n- Attacks a real-world MLaaS\n- Evaluates against potential mitigation strategies\n- Strong attack results\n\nWeaknesses:\n- Limited technical novelty\n- Parts of the problem have been previously explored (e.g., traditional clustering, or white-box attacks on deep clustering), although the combination of factors is new\n- Ambiguous epsilon bounds\n The paper is well-written and explores an interesting problem (the adversarial robustness of deep clustering techniques along with some mitigation strategies). Overall, I think this is a good submission, and am encouraged to see work on black-box attacks on real MLaaS systems.\n\nOne aspect that could be improved is in making further distinctions between the authors' attack and AdvGAN, as it seems that there are many technical similarities between AdvGAN and the GAN formulation in this work. Although it is adapted somewhat to the clustering problem, the overall formulation with an adversarial, hinge, and GAN loss is very similar to AdvGAN, limiting its technical novelty.\n\nWhile generally well-written, there remain some things that could be further clarified in the paper. How is the surrogate to Face++ trained? Also, how are the epsilon bounds set for the table? It seems arbitrary given that the numbers in the Appendix are not consistent across datasets and it is unclear why they are different, so it seems some justification would help. Also in this case then, for the transferability studies, are the epsilons still unequal?\n\nDo you have any insight into: 1) why there seems to be common specific patterns in the noise and 2) why most attacks are clustered in the same class?\n\nFinally, I think more examples of specific real-world threat vectors could be included to better: 1) scope the societal impact of the work and 2) better motivate the need for robust deep clustering techniques.\n\nMinor comments:\n- Could clarify a bit what the specific threat model contribution is when brought up in the Intro (line 46)\n- Intro: could cite some specific numbers on percentage of performance changes with the attack\n- Could further distinguish between when a \"score-based\" black-box model is used vs. a \"decision-based\" black-box model\n The authors have provided clear descriptions on the level of access needed to data, models, etc. to pull off the attack, and several mitigation approaches are mentioned and studied. The authors also discussed their hope that this work leads to successful development of defenses. Specific examples of real-world motivations and consequences of attacks on deep clustering algorithms could be further discussed." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 5, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 5, 4 ]

[ "0Gy-0VHV4wE", "DQselQsxbjK", "JlLzt33nj2G", "Jjtegx--3-O", "jruMAMhHrXG", "fdPZ8pPIiJ", "kw2kmnSp4AA", "phcIQtW1zlH", "nips_2022_p62j5eqi_g2", "aCOPNMCshEq", "g-B3jkpPsCW", "DFTH9hF98FB", "i4p8Bk5oUr", "nips_2022_p62j5eqi_g2", "nips_2022_p62j5eqi_g2", "nips_2022_p62j5eqi_g2", "nips_2022_p62j5eqi_g2" ]

[ "lKdKGQxdbvq", "MkLuvgojwZl", "kToB4upS0cW", "0M4MESYbMdc", "pD2w9nlMh6T", "ZFi-KXJnrUH", "0WvRrBWe2uG", "MmxXJxtEq5P", "jaIxDCSdBA", "0KOx-SuGs5b", "6Bi-wMKptjV", "ewZ_imnEeUG", "pYSto1HDqHJ", "cW7mOZNm1K4", "xqwYSw_22Yh", "1gLerozHBti", "SbqTvje_PVx", "TYSMcKMS0GD", "r-SXRnmA5Uv", "ttKX6F0xP77", "rzVGMGlgGsK", "r_Q27chkcwr", "IIsUkLuVdB5", "bXKDDJv5nwV", "uUn8hgH91Si", "pVQ0YtFbeO", "8JM5Iv61AHX", "NnRZIov0Z3Q", "0Jj6A296Wvk" ]

[ "official_reviewer", "author", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I thank the authors for the extra details provided in the rebuttal. I appreciate the paper's contribution but believe it needs further work to be ready for publication.\n\n**Ensemble diversity**: The paper still needs a far more detailed discussion and results on the impact of ensemble diversity on attack success. The paper does not engage with the fact that when a new dataset comes along, the attacker is unlikely to have access to such a large number of good models, and may need to bootstrap from an ensemble of less effective models.\n\n**Other cloud APIs**: The fact that previous papers do not use other APIs does not preclude experiments with them in this paper.\n\n**Robust models**: A much more detailed discussion of this is needed. How many queries for targeted attacks are needed to approach the success of white-box attacks? What is the effect of adding robust models to the ensemble?", " Thank you very much for increasing your rating. \n\nCan we please request you to also revise your scores on soundness, presentation, and contribution. ", " Thanks for further clarification.\n\nAll my concerns are well addressed and I like to raise my score to weak accept.", " Dear Reviewer cKYU, \n\nWe hope you had a chance to look at our response to your question. Please let us know if you have any additional questions or concerns that we can address at this stage. \n", " We hope you had a chance to read our last response. Can you please tell us if we can provide any additional clarification. \nWe really appreciate your time, discussion, and all the questions you have asked so far. Thanks!", " Thank you for your response. We are glad to hear that your questions are clarified. \n\nRegarding your question if the generated adversarial noise was able to fool all the surrogate models. The answer is yes (almost always). In our perturbation machine design, we make sure that all the surrogate models are fooled simultaneously (see L150-151). We found T=10 iterations for the whitebox attack to be sufficient. In all our experiments, the average whitebox fooling rate of all surrogate models was 98–100%, across different surrogate sizes we tested. ", " Thanks for the detailed illustration of the confusing points.\n\nThe questions of 1,3,4 are well clarified. For question 2, I think i misunderstood the algorithm in the beginning. \nBut can I confirm two points?\n\na. Since T is set to a fixed number 10, so the generated adversarial noise is not necessarily able to fool all the surrogate models when finishing all the iterations?\n\nb. If it is true for point (a), I just think of another setting which may need investigation. How about we generate an adversarial noise in advance which could fool all the target models, regardless of the iteration T is, then we transfer once to the target black-box model, can you show or analysis the case with that in the paper?", " I appreciate the efforts from the authors and my raised concerns are well addressed. ", " We are grateful to you for acknowledging our work and increasing your scores. Thank you for your valuable suggestions, we will include the high-level summary as suggested. Please find the results for the combined attacks in our response above.", " 1. Thank you for your suggestions. We feel that we have already done a comprehensive literature survey. As we mentioned in our previous response, we focused on methods that require a small number of queries (less than 500) and achieve a high fooling success rate (close to 90%). This rules out several papers that combine the transfer and (pure) query based attacks but are not query efficient.\n\n2. We performed an experiment that combines [3*] and [4*] following your exact recommendations. We used the same (local) surrogate ensemble and images/labels that we used in our paper. For each image, we generate a perturbation using the surrogate ensemble and test transferability. If the attack fails to transfer, we deploy the Square-attack starting with the candidate perturbation. We use the official code from [4*]. Following the same setting in our Table 1 and Figure 2, we perform targeted attack on DenseNet121 with a perturbation budget of 16/255. The transfer rate of initial perturbed images is 75.5%. We attack the remaining 24.5% failed perturbed images using square attack by allowing a maximum query count of 500 (same setting as other baseline methods). On this subset of images, we observed a 33.9% fooling rate with query count (mean ± std): 238.2 ± 127.4. Overall, including the images that can initially transfer, the combination of [3*] and [4*] achieves a fooling rate of 83.8%, with query count (mean ± std): 24.5 ± 81.4. In comparison, our method achieves a 98.9% fooling rate with a query count of 1.7 ± 3.0. Similar trends appear for other victim models. Our main takeaway is that even though the surrogate ensemble provides highly transferable perturbation or perturbations that can be used as initialization for query-based optimization methods. The query-based methods lose their advantage by querying over a high dimensional image space. Our method searches over the weights of the ensemble loss, which is very low dimension and provides query efficiency. \n\nTable: Comparison of our method and [3*,4*] combination in terms of attack fooling rate and query count (mean ± std). Targeted attack settings are the same as used in Table 1 of our paper.\n| Victim model | Combination of [3*] and [4*] | Ours |\n|--------------|:----------------------------:|:-----------------:|\n| VGG19 | 64.7% ; 34.1 ± 99.2 | 93.2% ; 2.8 ± 5.1 |\n| DenseNet121 | 83.8% ; 24.5 ± 81.4 | 98.9% ; 1.7 ± 3.0 |\n| ResNext50 | 84.3% ; 24.7 ± 81.4 | 99.0% ; 1.8 ± 3.2 |\n", " I like the way the authors address my problems. Now, I am convinced that selection of target labels are not a factor here. Also, thanks for clarifying the misunderstanding on query=1 case. Since the attack success rate is quite high with limited queries, I suggest the authors may include a high-level summary in the paper and this may inform the readers better: the transfer attacks (given diverse enough local models) have the potential to achieve very high success rate, and we can unlock this potential by learning proper weight for each individual model using limited queries to the victim model. After the author rebuttal, I am now raising my score and the score can be further improved if the concerns on combined attack in part 1/2 can also be addressed. ", " I appreciate the efforts from the authors in addressing my concerns. A few more comments and some remaining concerns:\n1. I listed the four papers just as a sample list with a hope that the authors can properly position themselves in the related work by including more works (not just limited to the listed samples), especially the ones that attempt to combine the transfer and (pure) query based attacks in some forms. \n2. For the combination of works [3*] and [4*], I am not fully convinced that TREMBA can directly outperform their combination. The main reasoning is, TREMBA is still constrained on the gradient estimation attack form (as in the well-known NES attack), while (at least) for $\\ell_\\infty$ attacks, the random search methods seem to outperform the gradient estimation based attacks significantly. Also, directly mentioning extremely high query cost for [3*] might be unfair, as the experimental settings are different (i.e., local ensembles, selected target class). It will be ideal (and I will be fully convinced) if the authors can quickly run an experiment that combines [3*] and [4*], where the local ensembles are exactly the same as the ones used in this submission, and the for the failed transfers, the Square-attack is deployed to find successful adversarial examples. \n3. Direct comparison of a pure query-based attack and some form of combined attack cannot be used as a convincing argument here (e.g., comparison of LeBA, ODS and Square-attack) because the latter type has an additional access to local models.", " One more thing to add that we have included ablation studies on step size, learning rate, and other aspects in Section A of the supplementary material. ", " I am sorry to hear that you are confused. Let us try to clarify. \n\nOur proposed method is **NOT** a transfer attack method. We use queries from the victim model to adjust the weights of the ensemble loss to generate better attacks. \n\nThe response above was to the second question you asked on why the transfer attack success rate for a single surrogate model is so low. That question stemmed from your earlier comment that our method is 'guessing the model architecture'. We were talking about all the experiments we did with a single model-based surrogate models; which are **NOT** even part of the paper. We provided you the codes to verify that yourself. \n\nOur proposed method does not require any fine tuning of parameters. We are assuming a pure blackbox setting, where we use the same settings on surrogate ensemble side while attacking different victim models. That is the main point we were trying to convey. \n\nWe respect your opinion that you may want to see more ablation studies, but we assure you we are not 'cherry picking' the results. This comment is hurtful. We request you to revisit the earlier comments and our response for a complete context. ", " The updated author response actually makes me more confused.\n\nIf the transfer success rate heavily depends on so many factors (e.g., perturbation budget, bn, step size, number of iterations, initialization, just as claimed by the authors), then the experiment results shown in this paper are far from enough to verify the effectiveness of the proposed method.\n\nSeveral ablation studies should be include to make sure the proposed method is effective across different black-box settings, rather than a certain 'cherry pick' one (as claimed by the authors, 'we can change step size, number of iterations, initialization to get different success rates for the same surrogate/victim pair.')", " Let us label Su et al., “Is Robustness the Cost of Accuracy? – A Comprehensive Study on the Robustness of 18 Deep Image Classification Models”, ECCV 2018 as [9*] to make the references consistent across different posts. \n\nThere can be many possible explanations for this inconsistency. \nMost important one is that the attack settings in [9*] are different (easier) than our experiments in two main aspects: (1) perturbation budget and (2) evaluation metric. Figure 4 in [9*] has the closest setting to ours in terms of attack algorithm, but their perturbation budget is 5 times larger than ours; [9*] used $\\ell_\\infty = 0.3$, whereas we used $\\ell_\\infty$ = 0.06 (16/255). [9*] reports transfer rate using the top-5 success rate, whereas we report top-1 success rate (which is more commonly used and more challenging). In terms of the VGG family, [9*] evaluated the transfer rate between VGG16 and VGG19, which is different from our earlier response of transfer rate between VGG16_bn (VGG16 with batch normalization) and VGG19. All these differences contribute to the difference in our reported numbers. \n\nSeveral other factors influence transfer attacks, and any comparison without considering all those factors will be incomplete and unfair. For instance, we can change step size, number of iterations, initialization to get different success rates for the same surrogate/victim pair. In our experiments, we assumed a pure blackbox scenario in which we use the same attack settings to generate perturbations that we tested on different victim models. Our main finding was that targeted attacks generated by a single surrogate model have a really small success rate on other victim models (including those with the same architecture as the surrogate model). \n\nWe have uploaded an example code and table in an anonymous google drive below. Please feel free to run the script to reproduce the results for transfer attacks. \nCodes: https://drive.google.com/drive/folders/1ikYrhdWPqUrzcIHDdOf6ehVUonIGgQkE?usp=sharing\n\nTo summarize, our experiments on single-model based transfer attacks revealed that targeted attacks generated by a single model have a really small transfer success rate. In fact, these experiments motivated us to look into ensemble-based attacks and improve them. \n\nThank you very much for engaging in this discussion. We hope this explanation addresses your concerns. We are fairly confident about soundness and contributions of our work. We hope we have given you enough evidence to increase your individual and overall ratings. \n\nPlease let us know if you have other questions. ", " I appreciate the authors for the detailed response. As to the transfer success rates, the results reported by the authors (e.g., VGG13 to VGG19 is 17%, and the transfer rate from VGG16_bn to VGG19 is only 2%) are very low, which seem inconsistent with previous results [1*]. Could the authors further clarify on this point?\n\n[1*] Is Robustness the Cost of Accuracy? – A Comprehensive Study on the Robustness of 18 Deep Image Classification Models. ECCV 2018", " Dear Reviewers and Chairs,\n\nWe hope you have received our response and had a chance to read them. We eagerly await any additional question or comment you may have on our paper.\n\nBased on our understanding, main reviewer comments were about comparison and evaluation. We have provided detailed response to all the comments and provided additional evidence on why our method is superior to the current state-of-the-art. We hope our response has addressed the reviewer concerns. If we can provide any additional information, please let us know.\n\nWe also hope that you can review the ratings of the paper based on our response. We feel the current ratings do not match the contributions of this paper. \n\nThank you for your time and consideration. ", " Thank you for your thoughtful comments. We are glad you liked the presentation and found our paper clear and easy to understand. \n\n**(Novelty and analysis.)** We proposed and demonstrated with extensive experiments that potent adversarial examples can be generated for targeted and untargeted attacks by updating the weights of the ensemble loss. The simplicity of our approach is a feature and showcases the ease with which successful attacks can be generated. Our method requires a small number of queries (30x less than existing methods) because our search space is of very low dimension. We believe this is a significant contribution for one paper. \n\nIn terms of inspiration for future studies, our method not only outperforms existing blackbox attacks on classification tasks, but can also generate attacks for other tasks (such as object detection, segmentation, etc.). How does our ensemble-based method compare against hard-label attacks? We have provided preliminary results on these ideas, but they are important directions that require further research.\n\nOur method also raises several questions for future theoretical studies. For instance, what is the space of perturbations that can be generated by an ensemble as a function of the loss weights? how can we quantify and enhance the diversity of ensembles (also related to Reviewer vphn)? \n\n\n**Reply to questions:**\n\n1. **(Re-emphasize definition.)** Thank you for the suggestion, we will modify the text accordingly in the revision even though we have mentioned the notation of y* multiple times before eq (6), e.g. lines 129, 136, 159, algorithm1 input definition.\n\n1. **(Value of T)** In our experiments, T denotes the number of iterations that our perturbation machine uses to minimize the ensemble loss function in Algorithm 1. We fixed T=10 in all of our experiments, as mentioned on line 527 (we will include this in the main text). Each iteration involves calculating gradients of every surrogate model, which are then used to update a single adversarial perturbation. We do not view this as “transfering the consumed queries in black-box attack to white-box attack performed by a variety of surrogate models”, because whitebox attacks on surrogate models calculate the exact gradients and update a different loss than the one optimized for the victim blackbox model. We view this as a bilevel optimization problem where the blackbox model minimizes loss in Eq. 6 over w, and Algorithm 1 provides the perturbed image for a given w. We can view this overall process as an unrolled network, where we perform T backprops on each surrogate model per blackbox model query. \n\n1. **(Use of coordinate gradient descent.)** We use a gradient-free method to reduce the overall number of queries. In the coordinate descent approach, we update one coordinate of the weight vector (w) and generate one query for the blackbox. To estimate a full gradient over w, we would require 2N queries but that is not efficient for our method. N denotes the length of w (i.e., the number of surrogate models). \n\n1. **(Changes in datasets and labels.)** This question has two distinct parts. \nOne is different datasets; for instance, same distribution and labels but data split into different parts so that surrogate and victim models have little to no overlap. \nSecond is about different/unknown label sets, which raises additional questions about how we can generate specific targeted attacks. \n\n We used the pretrained models from Torchvision, all of which are trained on the ImageNet dataset. Using the same training data for surrogate and blackbox models is the common setting in previous works ([26,10,27,11,1*, 2*,3*,4*]). \n\n We also performed experiments on Google Cloud Vision (GCV), which suggest that our method can perform well even if training data and labels for surrogate and victim models are different or unknown, because we have no prior knowledge about training data or model architectures for GCV. \n\n We must add that the questions about data/label/domain mismatch are not specific to our method; they are generally applicable to all adversarial attack methods and require further research. \n \n (Please also see our response to Reviewer vphn and Ckyu on this question)\n\t\nWe hope our response has addressed your concerns, and you will consider increasing your ratings. If we can provide any other information, please let us know. \n", " First of all, thank you for your insightful comments. Thank you for summarizing the paper and its strengths. Our method uses fewer queries for two reasons: the first reason is, as you mentioned, our attacks are guided by perturbations generated via the fooling of a surrogate ensemble; the second reason is that we search over the weights of the surrogate loss function instead of the high-dimensional image space. \nWe discuss your comments and questions in detail below. \n\n1.\n**(Evaluation and experiments.)**\n 1. **(Single modality.)** To clarify, we have shown results on object recognition in the supplementary material. Please see Section C where we present our results for attacks on different object detectors using images from MS COCO dataset. \n **(Single dataset.)** ImageNet is one of the most comprehensive datasets in this area. Some previous papers may also use tiny images like MNIST and CIFAR10 for evaluation on some small models; however, they do not appear necessary given that the more comprehensive and complex ImageNet models are used. Recently, more and more papers only provide their evaluations on ImageNet (cite [26, 29, 1*, 3*]). Besides evaluations with ImageNet for classification tasks, we have also used the COCO dataset in the evaluation of object detectors.\n 1. **(Attacks on robustly trained models.)** We have performed experiments on Google Cloud Vision (GCV), and show that it is more challenging than subverting ImageNet models, and requires more queries. We expect that robustly-trained models will require more queries. We perform experiments on attacking the robustly trained model from [8*]. We follow the ensemble setting in our Table 1 but use their robust ResNet18 as the victim model, and observed an untargeted attack fooling rate of 92% with an average query of 2. \n 1. **(Different vision APIs.)** We mainly used GCV because it is widely used and acts as a strong blackbox model in our experiments. \nFor the purpose of mimicking a true blackbox setting, GCV seems sufficient thus we do not consider other APIs. In other papers such as TREMBA [10], the evaluation is also performed only on GCV.\n 1. **(Different model architectures.)** We select ensemble models to be as diverse as possible, given that we do not have knowledge of the victim architecture. The model selection process in our experiments can be seen in the supplemental material Line 532.\n**(Different datasets.)** We directly used the pretrained models from Torchvision, all of which are trained on the ImageNet dataset. A thorough study on the effect of the data distribution mismatch is an interesting topic, but it would require a long discussion and several experiments, which are beyond the scope of this paper. \n(Please also see our response to Reviwer vphn question 3.)\n\n1. **(Missing reference.)** Thank you for pointing it out. We will include the reference and discussion in the paper. (Please see our response to Reviewer vphn for a discussion on this paper). \n\n**Reply to questions:**\n\n1. Line 262-263: Yes, in the whitebox version we directly calculate gradients of the weight vector through backpropagation. We will clarify this.\n1. Line 267-268: Yes, for the ‘surrogate victim’ model, we use score access. We do not assume that the true victim is relevant to the ‘surrogate victim’. Figure 4 shows that using VGG as the ‘surrogate victim’ can transfer well to 6 models (ResNet, MobileNet, etc.). This result suggests that searching in the ensemble weight space can generate adversarial examples that are highly transferable across different models. \n1. **(Comparison with existing hard label attacks.)** Existing hard-label attacks [6*,7*] start with an exemplar image that is already misclassified and move towards the source image. Thus they use an evaluation metric of perturbation magnitude vs queries, which is different from score based attacks. Since hard label attacks are more challenging than score based attacks, they usually take thousands of queries to get close to the source image. Because of these key differences, we do not perform a direct comparison with hard-label attack methods.\n\n[6*] Chen et al. “HopSkipJumpAttack: A Query-Efficient Decision-Based Attack”, ISSP 2020\n\n[7*] Li et al. “Nonlinear Gradient Estimation for Query Efficient Blackbox Attack”, AISTATS 2021\n\n[8*] Salman et al. “Do Adversarially Robust ImageNet Models Transfer Better?”, NeurIPS 2020 \n", " **Reply to limitations:**\n\nHere we show a comparison of computational time across different methods for attacking densenet121 as the victim model, 20 surrogate models, evaluated on 100 images. \n\n\n| Method | TREMBA | GFCS | ODS | P-RGF | Ours |\n|-------------|--------|------|-----|-------|------|\n| Time (mins) | 8 | 10 | 30 | 45 | 37 |\n\nTREMBA generates adversarial examples by a forward and backward pass over a generator, which can be performed relatively quickly. It takes a significant time to train the generator (which we do not include here), and the inclusion of new surrogate models requires retraining. On the other hand, our method does not require any training but involves computing adversarial gradients through backpropagation on the ensemble models, which is the most expensive step in our method. Per-query time in our method is larger than query over high-dimensional image space. Since our attacks are more query efficient, the overall computation is still comparable with other methods. Furthermore, in adversarial attacks with limited queries, the computational time on the whitebox side may not be as critical as the number of queries used to defeat the blackbox model. \n\nWe hope our response has addressed your concerns, and you will consider increasing your ratings. If we can provide any other information, please let us know. \n", " Thank you very much for your thoughtful comments. Thank you for nicely summarizing the paper and its strengths. We are happy to hear that you found the paper very clear and easy to follow. We discuss your concerns about evaluation/comparisons below.\n\n1. \n**(Comparison with closely related work.)** Thank you for pointing out the 4 papers that we refer to as [1*,2*,3*,4*] below. We will be happy to cite and discuss them in the paper. As far as evaluation and comparisons are concerned, we believe that our experiments provide a comprehensive comparison with the current state-of-the-art methods in literature including these papers. We focused on methods that require a small number of queries (less than 500) and achieve a high fooling success rate (close to 90%). We compared our method against four strong baseline methods and showed advantages over all of them by a large margin. [1*,2*,3*,4*] are either already shown to be inferior to the baselines we use or they provide poor performance compared to our baselines in our preliminary studies. Below we discuss each of them in detail.\n\n[1*] Our experiments include comparisons with the most recent work GFCS [11] from ICLR 2022, which outperforms [1*] LeBA as shown in Table 1 and Figure 2 of [11]. Thus, it is reasonable to expect that our method will outperform [1*] as well.\n\n[2*] requires a large number of queries as it searches over the entire image (that is a high-dimensional space). As shown in Tables 6 and 7 of [2*], the method requires hundreds and thousands of queries for untargeted and targeted attacks, respectively for TinyImageNet images (64x64). This query count is orders of magnitude higher than our method. Another drawback of the approach in [2*] is that it requires the training of a simulator, which is computationally expensive (72 GPU hours for TinyImageNet images) and makes it difficult to scale to larger images like the ones in ImageNet dataset.\n\nWe have performed some experiments with our method using the models from [2*]. We use the same 16 surrogate models in Table 14 and use densenet121 as the victim model; all models are pre-trained on tinyImageNet, as provided by their code repository. We reuse their code to select tinyImageNet images at random and use incremental target label selection for targeted attacks (following [2*], target class is set to y_adv = (y+1) mod C, where y is the original label and C=200). We use the Linf norm = 8 as the constraint. We achieve a 93% attack success rate with an average query count of 11.1 (min = 1, max = 50, median = 8). For untargeted attack, our method achieves 100% fooling rate with an average query count of 3.65 (min = 1, max = 26, median = 1). In contrast, [2*] achieves a similar untargeted success rate with an avg query count of 811, which is 222 times more expensive than our method. Table 7 uses L2 constraint for targeted attack, which is an easier setting as shown in Table 3 and 4. Under the easier setting, their method still requires 1959 queries on average, while our method only requires 9.6 queries, which is 176 times more query efficient than their method.\n\n[3*] is one of the earliest works on hybrid attacks that uses surrogate models to generate the initial query, which is later updated using feedback from the blackbox model. Fine tuning the surrogate models shows slight improvements (as reported in Table 6 of [3*]). Furthermore, as reported in Table 3, [3*] suffers from extremely high query costs (over 10k queries). TREMBA has detailed experiments demonstrating that directly combining transfer and query based attacks will suffer from high query counts (see [10] Figure 1 & 2). The legend labels starting with “Trans-” are the methods that initialize query using transfer attacks. Since these methods are searching in a high-dimensional image space, the fooling rate vs query curve is almost flat (i.e., need a large number of queries to achieve a high fooling rate). Whereas the slope of (fooling rate versus query) curve with our method is much steeper compared to other methods (i.e., the fooling rate rapidly increases with a small number of queries).\n\n[4*] Square attack also searches in high-dimensional image and requires hundreds of queries for untargeted attack (Table 2 in [4*]) and thousands of queries for targeted attack (Table 9 in [4*]). This method underperforms [1*] as shown in Table 1 of [1*]. It also underperforms ODS [27] as shown in Table 5 of [27], especially in the targeted attack cases. Our method outperforms ODS by a large margin; thus, we expect our method to perform better than this method.", " Thank you very much for your insightful comments. Thank you for summarizing the paper and appreciating its strengths. \n1. \n**(Effectiveness of weight search.)** The fooling rate of our method keeps increasing as we update the weights of the ensemble loss function after every query. This effect is best illustrated in Figure 2. For example, in Figure 2 (a), the fooling rate starts at 54% for VGG-19 using a surrogate ensemble with equal weights (this can be viewed as transfer attack success rate, but we count it as one query). The success rate gradually improves and nearly 90% of images are fooled after 10 queries. 96% images are fooled by the time we stop after a maximum of 50 queries (i.e., 78% improvement over transfer attack). The number of queries reported in Table 1 are averaged over 1000 images. We provide some additional statistics on min, max, and median queries for the three blackbox models for completeness. \n\n| Model | Targeted | | | | Untargeted | | | |\n|--------------|:--------:|:----:|:----:|:-----:|:----------:|:----:|:----:|:-----:|\n| | Avg. | Min. | Max. | Median | Avg. | Min. | Max. | Median |\n| VGG-19 | 2.8 | 1 | 49 | 1 | 1.2 | 1 | 34 | 1 |\n| DenseNet-121 | 1.7 | 1 | 36 | 1 | 1.1 | 1 | 29 | 1 |\n| ResBext-50 | 1.8 | 1 | 47 | 1 | 1.2 | 1 | 44 | 1 |\n\nOur attack method provides a high transfer rate (with equal weights) in the beginning because we produce adversarial examples that fool all the surrogate models. The weights of our ensemble loss change quite a bit, and we illustrated this effect in Fig 1 and Fig 13-supplementary using real experiments over 3 surrogate models. \n\n\n2.**(Architectures of target model in ensemble.)** To clarify, we do not use any duplicates of blackbox models in our surrogate (whitebox) ensemble, but our surrogate ensemble can contain the models from the same architectural family of the victim model. This is a common setting in numerous papers (e.g., TREMBA [10], GFCS [11], [2*]). Since we have a limited number of architecture families, it is a reasonable assumption that the blackbox model would be related to some families of our surrogate models in practice. \n\nFurthermore, we do not gain much by guessing the architecture of the target model. Even for the models from the same family, the targeted attack direct transfer rate is quite low. For example, the transfer rate from VGG13 to VGG19 is 17%, and the transfer rate from VGG16_bn to VGG19 is only 2%. Other individual models from non-VGG families have 0% transfer rate. We can provide a detailed table for transfer attack success rates across different models that exhibit low transfer attacks success rate (similar results reported in ref [29] or arXiv:1611.02770). Our main advantage comes from attacking an ensemble and searching in the weight space of ensemble loss, which is more efficient than previous approaches in defeating unknown blackbox models. \n\nGoogle cloud vision (GCV) is an example of a pure blackbox target and it is highly unlikely that our ensemble contains a model with the same architecture as the GCV model. Our attacks on GCV show that our method can generate potent attacks for (unseen/unrelated) blackbox models. \n\n\n[2*] Ma et al., \"Simulating Unknown Target Models for Query-Efficient Black-box Attacks\", CVPR 2021 https://arxiv.org/pdf/2009.00960.pdf \n\nWe hope our response has addressed your concerns, and you will consider increasing your ratings. If we can provide any other information, please let us know. \n", " 2. \n**(Difficulty of target labels.)** We did not select the target labels in our experiments. We followed the procedure outlined in the NeurIPS17 competition. We choose the evaluation images and target labels from this competition because it is a well recognized test kit that many other papers have used [7,8,9,1*]. Note that the field of adversarial attacks has undergone rapid advancements in recent years, mainly due to the reduction of search space dimensions using surrogate gradients. The fooling rates recent methods [10,27,11] can achieve within tens or hundreds of queries would have taken previous methods tens of thousands of queries. (See Table 3 in [3*]). \n\nHaving said that, we appreciate the reviewer’s proposal for selecting the target labels. We performed an experiment to test the difficulty of three types of target labels and report our results below. Corresponding to Table 1 in our paper, we use DenseNet-121 as the victim model. We see that the original confidence scores of the NeurIPS17 target classes are already close to 0 (which means they are already challenging cases), for which our method requires an average of 1.64 queries to achieve a 100% fooling rate. The second most likely label has an average confidence of 0.08 (whereas top 1 is 0.8), and our method achieves a 100% fooling rate with an average of 1.02 queries. For the “hardest” setting of the least confident class label, our method shows a slight drop in fooling success rate and achieves 97% success using 2.20 queries on average. \n\n| Target classes | Avg. confidence | Fooling rate | Avg. count | Min. count | Max. count | Median count |\n|:---------------------------------------:|:---------------:|:------------:|:-----------:|:----------:|:----------:|:------------:|\n| “Easiest” (second most confident class) | 0.08 | 100% | 1.02 | 1 | 2 | 1 |\n| NeurIPS17 | 8.92e-06 | 100% | 1.64 | 1 | 13 | 1 |\n| “Hardest” (least confident class) | 1.74e-08 | 97% | 2.20 | 1 | 15 | 1 |\n\n\n#### 3. We respond to this comment in three parts.\n\n**(Impact of ensemble diversity.)** We studied the impact of ensemble diversity in Figure 3, where we show that query efficiency improves by adding more models (with different architectures) in the surrogate ensemble. Our results suggest that it is beneficial to leverage all available models for achieving the highest query efficiency. It is an interesting question and a promising future direction to quantify ensemble diversity for different tasks.\n\n**(Training data mismatch.)** Using the same training data for surrogate and blackbox models is the common setting in previous works ([26,10,27,11,1*, 2*,3*,4*]). Furthermore, our experiments on attacking Google Cloud Vision (GCV) show that our method can still handle data mismatch situations because most likely, training data for GCV and our surrogate ensemble are different. A thorough study on the effect of data distribution mismatches is an interesting topic, but it would require longer discussion and several experiments, which are beyond the scope of this paper. \n\n**(Availability of diverse ensemble architectures.)** In practice, we have access to a large number of models with diverse architectures, especially for the widely deployed scenarios like classification/object detection for natural images. For example, we have a huge number of publicly available models for classification, object detection, and segmentation. (See github repo of torchvision or mmcv https://github.com/open-mmlab/mmcv for a collection of more tasks and available models). Our approach offers strong attacks that directly benefit from a large and increasing number of available models. Since new models usually borrow good designs from previously published models, it would be difficult for a state-of-the-art blackbox model to completely avoid sharing any similarities with existing architectures. Our experiments on Google API shows that our attack performs well in a real blackbox setting without any knowledge of the victim model architecture.\n\n4.**(Equal weights.)** Thank you for bringing up this question. We have actually discussed the direct transfer rates when using equal ensemble weights from line 252 to line 254 and in our figures (see Figures 2, 3, 4, 6, 7, 8, 9), where Queries = 1. We observe a large improvement by updating the surrogate model weights; for example, in Fig2 (a) the direct transfer rate (equal weights) is 54%, which increases to 96% after weights update (this is a 78% improvement). Different experiments show similar results.\n\nWe hope our response has addressed your concerns, and you will consider increasing your ratings. If we can provide any other information, please let us know. ", " We thank all the reviewers for their careful and insightful comments. We very much appreciate that reviewers recognized our work as a simple and effective strategy that leads to significant improvements. \n\nThe main contribution and novelty of this paper is that we create potent adversarial examples using a perturbation machine (PM) that is defined as a weighted loss over an ensemble of surrogate models. To fool a victim blackbox model, we generate perturbations by searching over the weights of the surrogate ensemble loss. Since the search dimension is the same as the number of models in the ensemble, our method requires a small number of queries. This is in contrast to most of the existing approaches that query over the image space and require a significantly larger number of queries. For instance, we demonstrate that our method provides more than a 90% success rate using an average of 3 queries per image in most cases (which is at least 30x fewer queries than that required by state-of-the-art methods). \n\nThe main concerns brought up by the reviewers are about comparison with baseline methods, differences in model architectures and training data between the surrogate models used for training and the targeted blackbox models. \n\nWe believe that the paper presents a comprehensive set of experiments (and comparisons with state-of-the-art methods) using a large variety of model architectures, different tasks (classification and object detection), and real-life blackbox models (Google Cloud VIsion API). Our framework is generic and can be used for other tasks (e.g. segmentation, pose estimation);\n\nWe present our detailed responses to all of the concerns in individual comments. We hope that our responses will address the reviewers’ concerns, and they will consider increasing their ratings. We look forward to engaging in further discussions, and answering any further questions that the reviewers may have for us. \n", " This paper studies query efficient black-box attacks, which aims to generate black-box adversarial examples using least number of queries to the unknown victim model. The authors proposed to leverage ensemble of surrogate models to generate some candidate perturbations and then query the unknown model. The query feedback is then used to update the weights of individual surrogate models to produce better candidate perturbations for the next query. The empirical results demonstrate that the proposed approach can obtain reasonably high success with handful of queries. The presentation of the paper is very clear and easy to follow. However, the paper lacks comprehensive review of the related works and also the adopted baselines are not convincing enough. Further, the experiments should be designed to illustrate the importance of each module in the attack process. More specifically,\n1) many closely related works (especially attacks that combine transfer and query based attacks) are missing from the paper. A few samples are listed below [1], [2], [3], [4] and the authors are encouraged to conduct a more comprehensive survey on related works and include more recent baselines. For example, the listed baselines [1], [2] can be directly adopted as baselines for this paper and the combination method proposed by Suya et al. [3] might be coupled with the strong (should still be the state-of-the-art) query based attack [4] to form another strong baseline. The key is also to ensure that all baselines are using the same model ensembles. Since the nature of the proposed attack in this paper is \"adaptive\" transfer attacks using query feedback, it is really interesting to see if it is always advantageous over attacks that combine transfer and query based attacks directly. \n[1] Yang et al., \"Learning Black-Box Attackers with Transferable Priors and Query Feedback\", NeurIPS 2021.\n[2] Ma et a.., \"Simulating Unknown Target Models for Query-Efficient Black-box Attacks\", CVPR 2021\n[3] Suya et al., \"Hybrid Batch Attacks: Finding Black-box Adversarial Examples with Limited Queries\", USENIX Security 2020.\n[4] Andriushchenko et al., \"Square Attack: a query-efficient black-box adversarial attack via random search\", ECCV 2020.\n2) It is quite surprising to me that, targeted attacks even using the baselines only cost less than 100 queries in most cases. It may be because the selected target class for misclassification is still not hard enough. A more comprehensive way of evaluation might be to include three types of target classes: 1) easiest class (second highest class in original confidence scores), 2) random class and 3) hardest class (lowest class in the original confidence scores). \n3) at least the impact of ensemble diversity should be carefully measured. The current attack setup assumes the attacker has access to models that are trained on the exact same training data as the black-box model and also the ensemble set contains diverse enough architectures, which may not always hold in practice. \n4) In the attack results, maybe it is also better to report the direct transfer rates when different ensembles have equal weights. With this, we can see how much improvement is obtained by updating the surrogate model weights. Most of the suggestions for improving the paper are listed in the \"strengths and weaknesses\" section. Yes. ", " This paper proposes an ensemble search strategy for black-box adversarial attacks, which updates the weight of each ensemble member according to the queried feedback from target models. The empirical evaluation is done on the NeurIPS 2017 competition dataset (with 1,000 ImageNet-like images), using different model architectures. The results show that the query efficiency is largely improved. Strengths:\n- Clear writing and explanation of the proposed ensemble search strategy.\n- The ensemble search strategy is simple but effective, leading to a significant empirical improvement.\n- Commercial Google Cloud Vision API is also tested.\n\nWeaknesses:\n- My main concern is that in Table 1, the average query times of the proposed method (Ours) is around 1~2, which means the ensemble weights are only slightly updated. This makes me wonder if the effectiveness comes from the ensemble rather than the weight searching strategy.\n- The architectures of the target model (e.g., VGG, DenseNet, ResNext in Figure 2) are included in the substitute ensemble, thus the ensemble search strategy is more like 'guessing the architecture of the target model'. This is not the common case in practice, because the substitute ensemble usually may not involve the architecture of the target model. More ablation studies on this aspect would be helpful.\n Please answer the listed weaknesses. My final rate may depend on the authors' response. Yes", " This paper proposes a hybrid black-box attack on deep learning models that uses a combination of transfer and query-based attacks to reduce the number of queries while still maintaining a high targeted attack success rate. The main method involves creating a weighted ensemble of surrogate models, which is then used to generate local adversarial examples. These are tested against the victim model and the ensemble weights are updated using a form of coordinate descent based on the success of the locally generated adversarial examples. Experiments are carried out on non-robust models trained on the Imagenet dataset using standard Lp threat models. Both targeted and untargeted attacks are used. Real-world experiments on the Google Cloud Vision API also demonstrate the effectiveness of the method. **Strengths**\n+ The design of the proposed attack which involves optimizing over the weights in an ensemble of models to generate transferable adversarial examples ensures, by construction, that the number of queries used will be limited due to the significant amount of prior information leveraged to construct the adversarial examples. This is borne out by the empirical results, which use a small number of queries even for high-dimensional Imagenet data.\n+ The attack description is clear and well-written. The attack is easy to implement given a number of trained models with adversarial examples that transfer to the model under consideration.\n+ The attack is shown to be effective against different architectures.\n**Weaknesses**\n- My main concern with the paper is that the evaluation is rather thin. The experiments are carried out on a single dataset, and only models with non-robust training are considered. Also, only a single modality (image classification) and vision API (Google Cloud) is considered. For a more thorough evaluation, I would recommend that the authors do the following:\n - Attempt black-box attacks on another modality such as object recognition or segmentation. This will also enable the use of a different dataset such as MS-COCO.\n - Explore the space of attacks on robustly trained models. Does using robust models in the ensemble help or hinder the generation of effective adversarial examples? Does the number of queries needed to attack a robust model increase as the model's robustness increases (with respect to a specified threat model)?\n - Carry out a comparative evaluation of the attack's effectiveness on different vision APIs. This is also important to determine the relation between the chosen surrogate models and the target model.\n - Provide further explanations of the link between the models chosen in the ensemble and the target model. It appears that the models chosen to create the ensemble are very close to those targeted. What happens when the models in the ensemble are trained on a different dataset, for example, or a smaller subset of the same dataset?\n- The paper is missing a reference to very closely related work from Suya et al. (Hybrid Batch Attacks: Finding Black-box Adversarial Examples with Limited Queries). - Line 262-263: Does the whitebox version involve taking gradients with respect to the weight vector $\\mathbf{w}$? How is this gradient computed?\n- Line 267-268: For the hard-label attacks using a surrogate victim model, is score based access to the surrogate model assumed? What is the link between the architecture of the surrogate and true victim models?\n- Comparison with existing hard label attacks: Is there a reason there is no direct comparison to existing hard-label attacks such as the Hop-Skip-Jump attack (https://arxiv.org/abs/1904.02144)?\n - While I appreciate that the authors discuss the runtime of the perturbation machine as a possible source of computational expense, I would have liked to see direct timing comparisons between the proposed attack and existing black-box attacks. This is particularly important since the per-query time for this attack is likely to be higher than attacks using simpler queries.", " This paper proposes a new method in generating efficient adversarial examples by a set of surrogate models. They apply PGD over the losses computed by these surrogates and a group of weights to adjust the effect of different models. In the experiments, they can find the adversarial example for each input within only a few queries, which is 30x faster than previous methods.\n The paper is easy to understand and the structure is clear. Overall, the presentation is also good. \nThe idea of this paper makes sense and is straightforward.\n\nThe novelty of this paper or some analysis seems a little limited and not enough, which i mean, brings limited inspiration for our future studies. To solve this, a comprehensive theoretical analysis or more experimental analysis maybe needed.\n\n Here are some suggestions which may help improve this paper.\n\n1. In equation (6), the author actually uses the target label y*, which is different from previous expression trying to maximize the loss. It is suggesting that the definition of y* is re-emphasized here for clarification. Similar problem can be found in the expression of PGD optimization.\n\n2. The main idea or the advantage of proposed method is to leverage a variety of existing models to generate adversarial examples that could fool all the surrogate models. Such examples also intend to fool the targeted victim models in large probability. The trick of the method is to transfer the consumed queries in black-box attack to white-box attack performed by a variety of surrogate models. Thus, the number of T consumed by surrogate models should be well-studied and discussed. In experiments, for more comprehensive results, it is suggesting that an appendix column to show the number of T is added in the table to make it clearer or fairer.\n\n3. why use coordinate gradient descent for updating w instead of applying SGD over all elements in w?\n\n4. In the appendix, the authors also study the transferability of their generated adversarial examples in the task of object detection, which is good and convincing. I got another concern that, together the black-box classification task in the first phase, is data used for training surrogates the same as the data used in attack? I mean, for example, can the surrogate be trained in the CIFAR, and the attack is performed in the ImageNet. Can we assume the attacked data is unknown in advance and different from the data used in training surrogate? See above.\n" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 4, 4, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 5, 4 ]

[ "0M4MESYbMdc", "kToB4upS0cW", "ZFi-KXJnrUH", "NnRZIov0Z3Q", "1gLerozHBti", "0WvRrBWe2uG", "r-SXRnmA5Uv", "0KOx-SuGs5b", "6Bi-wMKptjV", "ewZ_imnEeUG", "bXKDDJv5nwV", "r_Q27chkcwr", "xqwYSw_22Yh", "xqwYSw_22Yh", "1gLerozHBti", "SbqTvje_PVx", "IIsUkLuVdB5", "nips_2022_lSfrwyww-FR", "0Jj6A296Wvk", "NnRZIov0Z3Q", "NnRZIov0Z3Q", "pVQ0YtFbeO", "8JM5Iv61AHX", "pVQ0YtFbeO", "nips_2022_lSfrwyww-FR", "nips_2022_lSfrwyww-FR", "nips_2022_lSfrwyww-FR", "nips_2022_lSfrwyww-FR", "nips_2022_lSfrwyww-FR" ]

[ "S71T3SdfM1Y", "_B1xJ5TFkA", "ICRn4sRPk3WJ", "fOqIqSYg-Jq", "k0t_nHxwFVv", "yLbctIH-uWg", "tqsWm659Uer", "1L3tk2cdOHo" ]

[ "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I do not think NeurIPS is markedly different from the SISC in expectations. The premise of the cited Call For Papers is \"We invite submissions presenting new and original research\". I already mentioned a concern on novelty.\n\nIf the paper would have been presented as suggested by Reviewer o4hv, or the library was written in such a way that overcomes limitations of the numpy or spicy with a good documentation, then that would be a welcome contribution to the community. I believe in the current form the paper does not fall into either category.", " The reviewer proposed an additional reason for the significance of the problem. We decided to add this point to the paper (see highlighted text in the introduction).\n\nThe reviewer raises the same questions as reviewer WidE regarding the relevance of a package presentation in NeurIPS. He then argues on the possibility of leveraging quadproj for comparison with state-of-the-art methods.\nThis is exactly the argument that drove us to submit here: offering to this large forum and audience that is NeurIPS a new tool that can be used in a variety of situations.\n\nFinally, the reviewer asks two questions. The first one has already been addressed in the answer to reviewer 47QC.\n\nAs far as the second question is concerned, the limited time constraint for this rebuttal prevents us to compare our method with state-of-the-art homotopy continuation method.\n\nIf we correctly understood the reviewer's suggestion, we could proceed as follows.\n\nConsider the problem (3) from the paper and directly compute the gradient of the Lagrangian, and then find its roots.\nThe main advantage of this method is that we do not need to diagonalize the matrix A.\nThis gives the following system of nonlinear equations to solve (for $x \\in \\mathbb{R}^n$ and $\\mu$ scalar):\n\n\n$$ 2(x - x^0) + \\mu (2 Ax + b) = 0 \\quad \\text{(A1)},$$\n$$ x^T A x + b^T x + c = 0\t\t \\quad\t\\text{(A2)}.$$\n\nLet $y = (x, 0)^T$, solving (A1)-(A2) is equivalent to solving $F(y) = 0$, for an appropriate vector-valued function $F$.\n\nAs we found no (easily installable) python library implementing homotopy continuation method, we decided to resort to scipy.optimize.fsolve.\n\nConcerning the execution time, the (new) Figure 1 shows that our algorithm is faster than fsolve for dimensions larger than 100.\n\nMoreover, this other method has the following drawbacks:\n\n- The method may converge to another root of (A1)-(A2) that is not the main solution of the projection (*i.e.*, a critical point that is not the global minimizer).\n\n- We have to choose a suitable starting point to ensure convergence. We decided to choose $[x^0 ; 0]$ as starting point (*i.e.*, $y^0 = (x^0, 0)^T$): it seems that we recover the correct solution (that is, the root of (A1)-(A2) corresponding to the optimal solution of (3)). If this choice seems reasonable, we have no theoretical guarantee.\n\n- In the degenerate cases, we still need to check the additional solutions (denoted as $x^\\textrm{d}_k$).\n\nThis last point is particularly troublesome because detecting that the case is degenerate (and computing these additional solutions) requires the eigendecomposition of A. This check is not considered in the execution time in Figure 1. We should add up the time of using fsolve (dashed orange line with star marker) and the time of the eigendecomposition (solid blue line with triangle down).\n\nUsing fsolve (or another solver of systems of nonlinear equations) is therefore slower, has no guarantee of convergence, and may return an incorrect solution (*i.e.*, not the optimal minimizer).\n", " This reviewer does not ask any questions but raises the novelty as a weakness.\n\nWe would like to point out that the NeurIPS Call For Papers (https://nips.cc/Conferences/2022/CallForPapers) markedly departs from the SISC editorial policy by explicitly mentioning \"implementations\" and \"libraries\". This policy motivated our submission to this conference.", " The reviewer mentioned the lack of computational performance study as a weakness.\nThe reason for this lack of study is twofold.\n\n- On the one hand, we were limited by the nine content pages.\n- On the other hand, because the main part of the execution time is spent in the eigendecomposition that is used for diagonalizing the matrix $A$.\nThis point is raised at the bottom of section 3: \"These computations are negligible with respect to the eigendecomposition, which is the bottleneck of the method. In particular, for 100 problems of size n = 500, we obtain a mean execution time of 0.065 s for the root-finding algorithm and a mean execution time of 0.66 s for the eigendecomposition\".\n\nStudying the (total) computation time of our package for large dimensions is equivalent to studying the computational time of the numpy.linalg.eig function.\n\nAs a way to support our claim, we added a small experiment (Figure 1 in the new version of the paper, see highlighted text at the end of section 3) that shows how the execution time evolves with $n$, but we decoupled the time needed for diagonalizing the matrix with the time needed for the projection *per se*.\n", " The paper describes a python package for projecting onto quadratic hypersurfaces. The basic problem it solves is to minimizing projection errors in Hilbert space subject to x^T A x + b^T x + c = 0. The authors show that with eigen decomposition of A, we can re-parametrize this problem and solve it with Newton's method. The paper also provides a number of example codes illustrating how to use the package. Strength\n\n* clarity of writing\n* the tool seems to have broader usage in practice\n\nWeaknesses\n\n* Some computational performance studies are missing. It would be nice to include statistics of how this package tool scales with the growth of problem size. \n\n Could you provide some studies about how this package tool scales with the growth of problem size. \n\nI would also like to see some high dimension application of the package. N/A", " This paper an introduction to a Python package implementing the method of projecting onto a central and non-cylindrical quadratic hypersurface (quadric) proposed in a recently posted arXiv manuscript [21]. Orthogonal projection onto a set is an important tool in machine learning as it is a basic building block of many learning algorithms. When the set onto which the projection is made is compact and convex the problem is relatively easy in the sense that the unique closest point exists and this point can be found using standard convex optimization algorithms. When the set is nonconvex, however, the problem needs to be tackled case by case. A quadric is a set of roots of a matrix quadratic equation characterized by the eigenvalues of the coefficient matrix $A$ of the quadratic term and the discriminant of the equation. This set is in general nonconvex. The recent manuscript [21, Proposition 2.20] provides characteristics of a projected point (there can be multiple closest points from the input point since the set is nonconvex) when the quadric is central (discriminant is nonzero) and non-cylindrical ($A$ is nonsingular), and also an algorithm [21, Algorithm 2] for computing it. This paper implements [21, Algorithm 2] in Python and build a package quadproj in order to democratize the algorithm. A review of the theory of [21] and exposition of how to use the quadproj package, with sample code snippets, are provided. A strength of the paper is in the \"democratization\" of the algorithm for projection onto a quadric by writing an easy-to-use Python package. The package is designed so that construction of a quadric object, projection onto the quadric, and visualization of the solution is straightforward. The sample code snippets are also easy to follow. Indeed, visualization (in 2D or 3D cases) is emphasized with a couple of figures. Also, the exposition is quite clear.\n\nA weakness is in novelty. All the theory and method in Sections 2 and 3 are treated in [21], so the contribution of this paper seems to be limited to Section 4, description of the quadproj package. I understand that careful and easy-to-use implementation of an algorithm is an important task, but for such an implementation is publishable to a premire conference and journal, I think more consideration is needed. For example, in the editorial policy of the SIAM Journal on Scientific Computing (https://epubs.siam.org/journal/sisc/editorial-policy), which I believe is closest in scope with the paper, states for the \"Software and High-Performance Computing\" category as follows.\n\n> ... For software in particular, submitted papers should not be limited to describing a new package but must present the algorithmic or technological innovations that made the development of the software possible.\n\nUnfortunately, I do not see either algorithmic or technological innovation in the exposition of the package in this paper.\n None. Please see \"Strengths And Weaknesses\" section. In the present form, this paper looks as if it is an appendix to [21].", " This paper is a short tutorial on a Python optimization package, which implements the method of the recent preprint [21], regarding the problem of projecting a given point of the Euclidean n-dimensional space onto a quadratic hypersurface. Strength:\n\nCertainly, being able to project efficiently and accurately onto a quadratic hypersurface is very important, and the present paper concerns a promising step in this direction. Here is an additional reason for the significance of this problem, not mentioned in the paper: It is a classical fact in algebraic geometry, that any variety defined by homogeneous equations is isomorphic, via the so-called Veronese map, to a variety defined by quadratic equations (e.g., see Exercise 2.9, page 25, in “Algebraic Geometry: A First Course” by Joe Harris). Thus being able to efficiently and accurately project onto a single quadratic hypersurface, is the beginning of being able to project onto any variety, since the latter can be viewed as an intersection of quadratic hypersurfaces. \n\nWeakness:\n\nWhile a tutorial presenting a Python package for projecting onto quadratic hypersurfaces is certainly nice to have, I am of the impression that NeurIPS is not the appropriate venue for it. Instead, I would have loved to see a short version of [21], with experiments or a case study highlighting the importance of the problem for the machine learning and data science community, and comparing with the state-of-the-art homotopy continuation methods for the same problem.\n\nBibliographic remark: I would like to bring to the authors’ attention the following papers and citations therein, regarding the problem of projecting onto hypersurfaces and varieties more generally:\n1. Draisma, Horobet, Ottaviani, Sturmfels, Thomas. “The Euclidean distance degree of an algebraic variety”. Foundations of Computational Mathematics.\n2. Breiding, Sottile, Woodcock. “Euclidean distance degree and mixed volume”. Foundations of Computational Mathematics.\n\n 1. What is the highest ambient dimension that the package can handle? Could the authors please report some indicative running times?\n\n2. How does this package compare to generic state-of-the-art homotopy continuation methods applied to the same problem? Yes.", " Presents a library for computing projections onto a range of surfaces defined by Quadrics. This paper does a good job of describing the problem it solves and illustrating examples of how the library can be used to solve instances of problems within the class of projection problems it considers. I am supportive of papers on software libraries, they are explicitly within the scope of NeurIPS and contribute directly to the ML community. I don't have any larger critiques, the examples are easy to understand and the visuals are simple and clear. N/A This paper addresses a very narrow problem, and does not illustrate any concrete applications. I would have liked to see some demonstration of applications of the library." ]

[ -1, -1, -1, -1, 7, 3, 3, 8 ]

[ -1, -1, -1, -1, 3, 4, 4, 4 ]

[ "ICRn4sRPk3WJ", "tqsWm659Uer", "yLbctIH-uWg", "k0t_nHxwFVv", "nips_2022_Qoow6uXwjnA", "nips_2022_Qoow6uXwjnA", "nips_2022_Qoow6uXwjnA", "nips_2022_Qoow6uXwjnA" ]

[ "pS7HwPjx11Bt", "rjRJR9_qp2v", "vJufpV1hb6J", "PmlUDntRTK9", "CuJi35zOOyW", "7MDD-D6ADOV", "lgZIwkuGZrK", "OqgxvONleaY", "Hs-fDAiHLi0" ]

[ "official_reviewer", "author", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Sorry, I am little late in the discussion. First, I want to point out that NeurIPS allows updating the paper as a rebuttal revision to include new/modified things. I see that some other comments also asked for some discussion, etc. I do expect the authors to update the paper instead of saying that will add the discussion. For this purpose, to make space for discussion both the proof of Prop 1 (a standard known result) and Prop 2 can move to appendix.\n\nNext, for the comments for me. I agree that [A] is a PAC analysis in the batch mode, but [20] is not - in [20] the defender strategy being chosen depend on the other defender strategies. I agree with the authors' claim that compared to SSG with quantal reponse, the follower utility is higher dimension (and linear) in Stackelberg game. But again, I am left wondering what difference does it make in the proof/proof technique with the change from x_i (dependence on one component) to x (dependence on all components). The authors claim this is a generalization but what was hard about this generalization, or is a simple extension?\n\nAlso, the claim that general utility leads to exponential sample complexity in [A] is informal. That exponential complexity is when the class of functions in the exponent is Lipschitz functions, whereas the class of functions here is linear. Please provide a more nuanced comparison - it is important to point out precisely how the active learning set-up helps.", " Thanks for the followup comment here. We fully agree with this suggestion and will make sure to clarify on these nuances. We note that, though the paper uses a simplified definition of SSGs, the optimization program (4.2) can be extended for learning in general SSGs, since it only relies on the linearity of the payoff structure $V(x,j) = w_j x_j + b_j$. However, the caveat here is that we shall carefully query defender strategies that satisfy the additional resource allocation constraints of general SSGs. This turns out to only be a small adjustment to our active learning algorithm, e.g., to pick strategies on the vertices of constrained simplex space. We will include additional descriptions and experiments on this setting in the appendix.", " > Exactly as the reviewer commented, our choice of the simpler definition is to make our structured learning approach easier to understand, since section 4.3 is just to demonstrate the flexibility of our framework for accommodating these structure constraints.\n\nIt's perhaps a bit misleading to claim in the paper that you are applying it to SSG when you are actually applying it to a simplified version; for one your formulation removes the usual difficulty of SSGs which is dealing with the combinatorial space of possible allocations. I think this should at the very least be discussed. If you want to claim that this is done in the name of presentation then it would probably be best to show in the appendix that the more general version also works. Otherwise I would suggest that a phrasing more along the lines of \"while we study a simplified SSG model here, we expect our framework to apply to standard SSGs as well, for XYZ reasons.\"\nThis is made worse by the fact that the paragraph itself talks about \"security resources\" in plural, but then implicitly simplifies to a single resource by stating $x\\in \\Delta^n$, with no comment that this simplification was made.", " We thank the reviewer for the encouraging feedback and valuable suggestions! We will make sure to improve our citation and notations in the next version. Below we respond to the few technical questions:\n\n- Regarding Alg.1 line 7: \n\nYes, it is an uniformly random perturbation, just like the popular $\\epsilon$-greedy, DBGD algorithms. \n\n- Regarding Alg.1: \n\nThe $\\mathcal{X}$ is initialized to contain a list of simplex vertices. The algorithm is designed to search and replace the existing leader strategies in the list with which the induced follower response distributions are easier to estimate. \n\n- p.8 L355 regarding utility generation in experiments: \n\nThis way of generating utility matrices is intended to capture fully random payoffs (\\alpha=0), fully structured payoffs (\\alpha=1), as well as those in-between. Besides random payoffs, we are not aware of any other systematic way to generate representative payoffs for general Stackelberg games. Our experiments were actually designed to go beyond purely random cases and fully structured cases and thus used the above interpolation. However, if the reviewer may have any other suggested utility generation approach, we are more than happy to test on that as well!\n", " We thank the reviewer for the encouraging feedback and valuable suggestions! We will make sure to fix the typos in the next version. Below we respond to the technical questions: \n\n- Regarding generalizability to variants of quantal response models.\n\nWe expect our framework to generalize to other bounded rationality models. Moreover, we believe the key insight of this paper will still hold, i.e., boundedly rational behaviors can help to ease the estimation of agents' utility parameters due to the \"smoothed\" agent response function. However, the rigorous theoretical analysis is likely to depend on the specific model at hand and, in some cases, may require different parameter estimation approaches other than the maximum likelihood. Our algorithm hinges on the nice mathematical structure of this original and popular quantal response model.\n\n- Regarding the definition of SSGs in section 4.3:\n\nYes, our SSG definition in section 4.3 is slightly simplified, and we are fully aware that there is a more general framework for SSG with multiple resources and scheduling constraints. Exactly as the reviewer commented, our choice of the simpler definition is to make our structured learning approach easier to understand, since section 4.3 is just to demonstrate the flexibility of our framework for accommodating these structure constraints. Notably, such simplification is used in several other recent works as well [7,9,20,29,37]. And yes, we expect our framework to accommodate the general SSG model as well, given the resources and scheduling constraints can be formulated into additional linear constraints.\n\n- Regarding the usage of PURE-EXP:\n\nYes, PURE-EXP becomes a better approach, when the agents tend to be strictly rational (i.e., best responding), and empirically when the $\\lambda$ gets unusually large (e.g., >100). This is of course an extreme case, given $\\lambda$ is measured to be around 8 in practice [28, 32, 36, 38, 40]. \n\n- Regarding the computational time complexity:\n\nThe sampling procedure takes $O(T)$ time. And once the distribution estimation is obtained, the complexity to compute optimized parameters is a polynomial function of the size of the utility matrix $(m,n)$. \n\n- Regarding the generalization to sequential games:\n\nGeneralizing to sequential games could be challenging, as it might require learning arbitrary utility functions and the agents could have long-term objectives. The only work in this domain that we are aware of is, *Learning in Stackelberg Games with Non-myopic Agents, By Nika Haghtalab, Thodoris Lykouris, Sloan Nietert, Alex Wei. EC 2022*. So they are indeed exciting future directions for our study.\n\n- Regarding the time complexity of solving the optimization program in Theorem 2:\n\nThe mathematical program in Theorem 2 is a well-known optimization problem with a convex objective and linear constraints. So not only theoretically there are polynomial time algorithms to approximate the optimal solution, but also in practice there are matured solvers to compute the solution efficiently. And there is our implementation in the supplementary materials.\n", " We thank the reviewer for the critical feedback and valuable suggestions. **However, we notice several important conceptual misunderstandings in the reviewer’s comments and thus respectfully ask the reviewer to re-evaluate the merit of this work.** Below are our clarifications and responses.\n\nFirst and foremost, we disagree with the reviewer's comments that our work is \"incremental\" and “lacking sufficient novelty”. The reasons are elaborated below:\n\n1. Reference [A] studies a completely different learning setup from ours. Specifically, [A] is in the offline learning setup under PAC framework, so all their samples are i.i.d. drawn from a fixed distribution. Our learning setup is the active learning setup, in which the leader/learner can choose the queries (i.e., the mixed strategy), possibly based on previous feedback. We do appreciate the reviewer for pointing out this related reference (and will add a discussion on it), but we do not see how the PAC-learning results from [A] can \"cover\" (in fact even be comparable to) our results. And this is probably why the reviewer questioned how the leader can learn the follower's payoff matrices. In PAC learning, the leader is not guaranteed to learn the follower’s payoffs, since the small learning error in PAC only means the learned model is good under the given $(\\mathcal{X},\\mathcal{Y})$ distribution (e.g., an offline dataset). However, under active learning setup, the leader can indeed learn the payoffs due to the flexibility of choosing strategies in order to \"probe\" the uncertain directions. In fact, previous work [9,37] on active learning under perfectly rational follower responses can also learn follower's payoffs, up to some linear transformation.\n\n2. [20] and [A] are limited to Stackelberg security games; their efficient learning algorithms heavily rely on the special structure of security games. More specifically, they exploited the fact that the attacker's utility at each action/target $i$ is a one-dimensional function mapping protection probability $x_i \\in \\mathbb{R}$ to a utility. In our problem, however, the follower's utility for each action is a high-dimensional function. Generalizing one-dimensional function learning to high-dimensional function learning is a well-known non-trivial learning task due to the curse of dimensionality. For example, [A] does have a result for general follower utility function (their Thm. 3), but [A]'s sample complexity becomes EXPONENTIAL in the number of follower actions; in contrast, our sample complexity is almost linear. Therefore, we disagree with the comment that these previous results can \"cover\" our results.\n\n3. Regarding comparison to [9,37], indeed they prove polynomial sample guarantees for learning optimal defender strategy from interacting with perfectly rational attackers. However, their best sample complexity (achieved in [37]) is $O(m^3)$, whereas instantiating our Thm 2 to the special case of security games already leads to an improved $O(m^2\\log(m))$ complexity. Moreover, in general Stackelberg games, our $O(mn\\log(mn))$ sample complexity is significantly better than the exponential sample complexity of [37]. Such accelerations are due to our learning from boundedly rational followers; this is precisely the key conceptual message our paper wants to convey, i.e., the \"blessing of bounded rationality\" as in our title. \n\nRegarding Prop 1 and Thm 1:\n\nWe agree that Prop 1 is intuitive to experts of the game theory field. We did not mean to view it as a main result any way -- it is formalized as a proposition only for the sake of readability to the general audience since it is used later to introduce logit distance and thereby to characterize the solution set of recovered follower utilities used in Thm 1 and 2. In the revision, we will emphasize its connection to prior results and are happy to make it an *observation* if the reviewer prefers.\n\nHowever, our Thm 1 is presented to be a strengthened result over Prop 1, that is, how the learnt follower’s payoff (with potential errors) can be converted to an approximately optimal leader strategy. To our best knowledge, this result is novel and unknown in any prior work on learning Stackelberg equilibrium. In particular, this theorem introduces a new notion of \"inducibility gap\" that captures how difficult it is to convert the learned approximate payoff matrix to an approximately optimal leader strategy.\n\nRegarding Prop 2 and [20]:\n\nWe do not view Prop 2 as our main result. This is why it is a *proposition* and why we intentionally draw a parallel to the established result in [20] (i.e., from 3 strategies to m strategies). We nevertheless stated it as a proposition since (1) it generalizes the main result of [20] to handle high-dimensional utility functions and thus has some merit (including generalizing their distance condition on query strategies); (2) more importantly, it prepares the reader with the intuitions for Thm 2, which is one of our main results.\n", " This paper analyzes the problem of identifying follower utility in Stackelberg games, under the assumption that the follower *quantally* responds via softmax rather than playing a strict best response. Remarkably, this turns out to be an easier problem. The paper analyzes the sample and query complexity of identifying follower utility first under the toy assumption that the follower's full mixed strategy is observable, and then under the more realistic assumption that only actions realized from this strategy will be observed. A specific algorithm is specified and used to validate the theoretical results empirically in experiments. The Stackelberg setup is commonly used in security work, including with the assumption of quantal follower response, but it typically makes the assumption that follower utilities are known. This paper studies the extension of this well-studied setting to a more realistic setting in which follower utilities must be inferred from their behavior. These results are both novel, and likely to have significant impact on the security games literature.\n\nThe paper is well-written; the motivation, results, and proofs are all very clearly stated. There are a few notational inconsistencies that I have noted below, but overall the paper was a pleasure to read, and did an excellent job of expressing some subtle distinctions.\n\n\n__Minor issues__\n- p.4: \"And we know the close form of follower's optimal strategy... [33]\": [Luce 1959] \"Individual Choice Behavior\" or [Train 2009] \"Discrete Choice Methods with Simulation\" would be more standard references for this equivalence.\n- eqn (4.1): Why does the optimization use $\\hat{y}$ instead of $y$? This section assumes that we are able to observe the full mixed strategy, no?\n- p.6 L251: \"the strategy $x^{j^*}$\": Shouldn't this be $x^{\\tilde{j^*}}$?\n- also L251: \"for all $j' \\ne j$\": Should this be $j' \\ne j^*$?\n- p.7 L281: The empirical distributions are introduced as $\\tilde{y}(t)$, but the program in equation (4.2) seems to use $\\hat{y}(t)$, are these the same thing?\n- The empirical distributions $\\tilde{y}(t)$ (and/or perhaps $\\hat{y}(t)$) in this section will all be deterministic/one-hot distributions, right? Might not hurt to say so explicitly.\n- Alg.1 line 7: \"Sample a random perturbation $\\tilde{x}$ from simplex $\\Delta_m$\": Does the sampling distribution matter here? Should I just imagine a uniform sample?\n- Alg.1: The description (lines 2--5) of how the $\\mathcal{X}$ and $\\mathcal{Y}$ lists are generated is kind of confusing; the initialization section makes it seem like they are generated up front, but it looks like $\\mathcal{Y}$ at least is generated \"on the fly\" on line 5. 1. p.8 L355: \"We generate the follower's utility matrix $V=\\alpha I + (1-\\alpha)\\Xi$\": This seems like a very special kind of structure for the utility; should I be worried that the empirical results depend upon it? I don't forsee any serious negative impact from this work.", " Leader-follower games are among the most studied classes in the field of algorithmic game theory. The reason is simple: the corresponding solution concept – the strong Stackelberg equilibrium – proved to have many real-world applications. One of the central issues of Stackelberg equilibrium is its lack of robustness with respect to utilities. More specifically, it is imperative to correctly estimate the players’ priorities, represented through their utilities, otherwise the solution may force the leader to commit to a strategy that will eventually harm them.\n\nIn this paper, the authors present an approach that guarantees to uncover the follower’s true utilities in two-player leader-follower games through repeated interaction with the follower. The key appears to be the assumption of the follower’s bounded rationality. More precisely, the follower’s behavior needs to comply with the logit quantal response model of subrationality, playing each action with non-zero probability. Using this property, the authors are able to determine the number of interactions needed to estimate the follower’s utilities to a sufficient precision. Such characterization is possible not just when the leader observes the follower’s entire quantal-response strategy, but also in a more realistic setting, when they observe only samples from the strategy. Once the observations are collected, the follower’s utility is calculated as a solution of a particular mathematical program. The authors further show how to tailor their method to specific utility structures or when the follower’s quantal responses begin to approach best responses. The last part of the paper is dedicated to empirical analysis, depicting differences between true and estimated utilities over games with diverse sizes, players with different degrees of rationality, and utility matrices with varying levels of randomness.\n I enjoyed reading the paper. Its motivation is clear and the authors describe well how their work fits into the literature on the topic. The results appear to be original and novel. The notation is not excessively complex and all notions are sufficiently well described. The arguments presented throughout the paper seem reasonable, facilitating the understanding of the exposition. I went through some of the proofs in the appendix and even though I did not go into all the details, as far as I can tell, they give an impression to be correct to me. Moreover, the results the authors present in the experimental section seem to corroborate the authors’ theoretical claims, even though at times the error bars happen to be rather larger (e.g., in the right graph of Fig. 3, for pure-exp and larger lambda), which would suggest averaging over more seeds might be a good idea. \n\nOtherwise, I found it a bit confusing to refer to this setting as to a “sequential game”, which is a term commonly reserved for non-trivial extensive-form games, rather than a repeated Stackelberg (or leader-follower) normal-form game, which seems to be the case studied by the authors here.\n\nFor some of this work’s (possible) weakness, please see the next section.\n\nOverall, I believe this is a nice work that may profit from some more detailed discussion regarding its limitations, but is worth publishing.\n\nNits:\nLine 10: this work relax -> relaxes\nLine 243: the equation in Def2 is missing a period at the end of the sentence\nLine 259: we defer to the full statement -> we defer the full statement\n The authors of the original Quantal Response paper later introduced also other possible quantal-response models besides the logit one, e.g., probit, Luce, etc. Would this approach generalize to those models as well?\n\nThe definition of SSGs in section 4.3 appears to be a bit simplified for the sake of arriving at linear utilities. If I am not wrong, it is much more common to define defender strategies in SSGs using limited resources allocated to a subset of possible targets, expressing utilities using marginal coverage probabilities of the targets. Would this definition of SSGs lead to a similar result?\n\nI liked how explicitly the experimental section compares PURE and PURE-EXP algorithms. Still, I am missing some intuition on when exactly it becomes beneficial to resort to PURE-EXP. Could the authors construct some explicit example when it is to? For example, on some fixed 2x2 game, what would be the follower’s rationality parameter (and the corresponding expected utilities of actions and quantal-response strategies) when the quantal responses approach best responses too closely to use PURE efficiently?\n\nCould the authors comment on how do the computational times scale with the game size, i.e., how large games and datasets are solvable within some reasonable time limit?\n\nCould the authors mention some possible applications of this exact learning method they propose? In which settings could the leader afford to practically iterate over their own strategies, when some could arguably lead to terrible outcomes?\n\nDo the authors foresee how difficult it would be to generalize their approach into sequential games? More specifically, do they see some way how to deal with the problems associated with sequential reasoning, e.g., the existence of non-credible threats, in their learning framework?\n\nCould the authors state if or when is the mathematical program from Theorem 2 solvable/approximable in polynomial time?\n The authors did not include an explicit section about limitations, but they do mention some shortcomings in the introduction. Still, there are some limitations which most readers recognize when reading the text the authors may consider discussing. For example, how realistic is it to assume the follower’s model is fully known and what to do when it is not (perhaps something akin to playing a game with known utilities?)? \n", " This paper studies learnability of approximate Stackelberg games in rational and quantal response follower setting. Results are mostly positive relying of ceratin properties of the utilities. The result explores sample complexities and performs experiments in simulation. This content of this paper is incremental and to some extent covered in few related works, one of which[A] the authors do not include in references. The writing should provide more explanation and comparison to prior results.\n\nFirst, the m strategies proof (Prop 2) is a minor extension of the work in the paper [20], same style of proof also except the utility function is slightly different.\n\nProposition 1 really does not deserve the importance given in the paper; it is a well-known fact for rational player games and for quantal response (stated in text in [A],[20]). That invariance can actually be easily handled by fixing one utility parameter to be 0, again as in [A], [20].\n\nThe paper [9, 37] gives an explicit best response sample complexity for computing approximate SSE in security games (with one resource, a security games is essentially a standard Stackelberg game with m=n). So, I do not understand how Thm 1 compares to this, I do not understand why Thm 1 assumes a given learned tilde(V) with a certain property? How can this be learned from best response samples? Thm 1 also refers to leader optimal strategy - should it be explicitly called SSE as written in the proof - this is important as the paper deals with both SSE and QSE.\n\nIn the same vein, [A] gives an explicit sample complexity for the quantal response case in achieving the same (m log m) term. How does this compare to Thm 2? In fact, that paper [A] present a more general result in terms of the capacity of the function class used in the exponent, making those result more applicable than the result here for bimatrix games.\n\nOverall, I find the paper lacking sufficient novelty over prior work and also a lack of in-depth comparison with prior work.\n\nSome citations are missing venue: e.g., [20].\nSome citations seem irrelevant for Stackelberg games such as [24,25]\n\n\n[A] Arunesh Sinha, Debarun Kar, Milind Tambe. Learning Adversary Behavior in Security Games: A PAC Model Perspective, in International Conference on Autonomous Agents and Multiagent Systems (AAMAS), May 2016\n\n[9] Avrim Blum, Nika Haghtalab, and Ariel D Procaccia. Learning optimal commitment to overcome insecurity. Advances in Neural Information Processing Systems, 27, 2014.\n\n[20] Nika Haghtalab, Fei Fang, Thanh Hong Nguyen, Arunesh Sinha, Ariel D Procaccia, and Milind Tambe. Three strategies to success: Learning adversary models in security games. 2016.\n\n[37] Binghui Peng, Weiran Shen, Pingzhong Tang, and Song Zuo. Learning optimal strategies to commit to. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pages 2149–2156, 2019 I have none, but authors can respond to my comments above. Not really applicable here." ]

[ -1, -1, -1, -1, -1, -1, 8, 7, 3 ]

[ -1, -1, -1, -1, -1, -1, 4, 4, 5 ]

[ "7MDD-D6ADOV", "vJufpV1hb6J", "CuJi35zOOyW", "lgZIwkuGZrK", "OqgxvONleaY", "Hs-fDAiHLi0", "nips_2022_ymAsTHhrnGm", "nips_2022_ymAsTHhrnGm", "nips_2022_ymAsTHhrnGm" ]

[ "1sCOOudUFdf", "6ezUyvW-51a", "0BpMt3MuY_i", "kdzXsvQaeut", "v0j2XMKTm-r", "X4bxTntZ3U0", "P45bYGgRViH", "GMO4KBkmh58", "BZAr-5CbXVh", "VL4P_W_FLdw", "fQ0VPbqPdoB" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for the revision! The newly added figure 2 does explain the concept in much simpler terms. My apologies for not having found the supplementary material before, thank you for pointing it out. Including all these details in the appendix is indeed much appreciated!\n\n", " Thank you to the authors for the responses. I still think the manuscript will benefit from more thorough empirical analysis. Having said that, I believe it is still a nice work. I am increasing my score to 5.", " Thanks for your response!", " We thank the reviewer for their encouraging comments! We do have other mappings in mind, but they all require much more computation than the simple one presented in the paper, so we decided not to pursue them for the current paper. In regards to other methods, it depends. It is difficult to beat the performance of large autoregressive models on discrete data, especially since they are universal models on discrete data. However, we are excited to see how this approach can be further improved for the disjoint mixture modeling direction, and can envision that it may become a cost-effective approach with tractability guarantees.", " We thank the reviewer for their encouraging comments! We agree the paper is rather dense due to the amount of information and number of equations. We’ve updated the paper to include a new illustration of the technical method (Figure 2), and also simplified some of the exposition in the paper.\n\n> Could it be that no Appendix was present with the submission, even though it was referred to?\n\nThe Appendix is in the supplementary materials, as we are not sure if NeurIPS allows appendices to be included in the main PDF. Mainly proofs and experimental details are provided there.\n\n> In Figure 5, the caption could directly explain what \"Samples\" refers to. \n\nThese are samples obtained from the model. Mainly shown to verify correctness of the implementation, that the density evaluation correctly corresponds to the sampling process of the model.\n\n> Line 325 also mentions how the method could potentially make gradient-based optimization difficult, has this been tried in any experiments? It would be interesting to see such results, or these kinds of applications with the framework.\n\nThese discontinuous gradients were a concern a priori and during experimentation; however, we never really encountered any problems. To clarify, we believe that while the density (i.e. training loss) of the model is continuous, its gradient is not. But this is a fairly common phenomenon within deep learning, e.g. when using ReLU neural networks. Nevertheless, since adaptive optimizers estimate second-order information, it’d be interesting to see if there are any meaningful improvements by making the density of the model smoother in future works.", " We thank the reviewer for their encouraging comments! We started exploring this tessellation approach for its ability to learn the boundaries themselves, whereas---to the best of our knowledge---prior dequantization approaches all had manually designed boundaries. In the future, we’re excited about using tessellation to build scalable disjoint mixture models. Most generative models do not tend to perform well on multimodal distributions or distributions with holes as the mapping from noise to data is necessarily continuous, while combining them via mixtures naively increases computational cost. At this time, we do not yet have a tractable method of building *deep* disjoint mixture models, but we believe a tessellation-based approach (not necessarily Voronoi however) can lead us there. In regards to building more intuition, we've added an illustration (Fig 2) to help readers better understand the method itself.", " We thank the reviewer for their candid comments, especially for their concrete suggestions for improving presentation. We have improved the paper in light of these comments.\n\n> Unfortunately, the paper is not clear on technical details. Important concepts are assumed to be known by the reader instead of properly introducing them e.g. tessellation, anchor points, Voronoi tessellation etc. The paper will greatly benefit from having a brief notations and definitions section. I also believe the paper will benefit greatly from having intuitive explanations accompany technical details to make it easier to follow.\n\nWe defined anchor points and Voronoi tessellation in Eq 4. However, we agree we did not define tessellation succinctly, and appreciate the reviewer bringing this up. We have now included an English description in the introduction, right after the first mention of tessellation, as well as a more technical definition of Voronoi tessellation after Eq 4. If these definitions are unsatisfactory, we can make further adjustments.\n\nFurthermore, we’ve added an example illustration (Fig 2) to accompany technical details when discussing the invertible mapping. We hope this will make the paper easier to follow.\n\n> Similarly, several appropriate references are missing e.g. for dequantization, the paper by Uria, 2013 needs to be cited. \n\nIf the reviewer believes that more appropriate papers should be referenced, we can certainly update our paper.\n\nWe’ve added the reference to Uria 2013; however, this paper only adds uniform noise without discussing the implications. Our choice of citation on dequantization (Theis 2016) is mainly due to their specific discussion on dequantization and the relation between the original discrete distribution and the dequantized continuous density (as an ELBO), though it is easy to see the connection in hindsight.\n\n> Similarly, statements/claims as in line 46-48 need to be supported with relevant references.\n\nIt is difficult to find a citation to support a statement about how something does not exist. However, we agree that such a statement may be too strong. We’ve added some clarifications and weakened this statement.\n\n> It was not immediately clear to me why is it useful to go from continuous case to the discrete case? What applications will this be important in? Apart from testing this on simple UCI datasets, I do not see any specific experiments for this.\n\nThe main argument for disjoint mixture models is the ability to scale without extra computation costs. Our models on the UCI data set are effectively disjoint mixtures of normalizing flows. This approach is simple and does not increase compute cost by much. Whereas a naive method of constructing a mixture of normalizing flows would quickly become intractable as it requires a much larger compute/memory cost (costs increase linearly with respect to the number of components).\n\nGranted, the UCI experiments are not very exciting; we agree. We tried scaling up to higher dimensions, and building deep disjoint mixture models, but found that the choice of Voronoi tessellation did not lead to better performance. Our hypotheses for the reasons behind this are discussed in the limitations section, and we plan on improving this general direction in the future.\n\n> I also found the experiments fairly limited in scope. There are no experiments to show the capability of the model on modeling categorical data with large number of classes. The language modeling task have small vocabularies. I'd recommended to evaluate the model on word-based language models with large vocabularies.\n\nThe itemset modeling experiments contain vocabulary sizes of 200-800, and are used to test the ability to model larger vocabularies. While the baseline methods with fixed dequantization require binarizing the data beforehand—this is a manual way of working with a large vocabulary since otherwise the embedding space would be just as high—our method with learnable dequantization boundaries works automatically without needing this binarization trick, which can create many empty classes if the original number of the classes is not a power of 2. \n\nWe mainly used language modeling as an experiment since it has been used by prior works and has reproducible code. We showed that by simply changing the dequantization method we obtain meaningful gains over the prior work. This result is shown for a variety of data modalities.\n\n> Similar to RAD flows, I believe the method will suffer from exploding gradients near the boundaries. How is the training stabalised to address this behaviour?\n\nThe gradients theoretically do explode, but we did not find this to be a huge problem in practice. We believe this is because the density itself is still continuous and differentiable almost everywhere, and that most samples will appear in the interior rather than on the boundary. We also do gradient clipping, so in the rare cases where a sample is extremely close to the boundary, it would get clipped.", " The paper presents a tessellation based approach to mapping between continuous and discrete distributions which learns quantization boundaries in continuous space. The approach has several desirable mathematical and computational properties that give rise to more efficient scaling in dimensions than previous approaches. The approach is used in two ways--Voronoi dequantization and Voronoi mixtures--which are demonstrated on data and shown to be competitive with baselines. The authors concluded by noting some limitations and directions for extension. The paper is a mostly clear and interesting presentation of an interesting approach to bridging discrete and continuous distributions. Strengths include: clear mathematical and general exposition, an interesting mix of mathematical and computational considerations, and interesting empirical tests. There are not many weaknesses, though I found myself wanting to understand the advantages of the Voronoi approaches better. The experiments did what the authors proposed (show competitiveness), but it would have been nice to have stronger intuition. Following the above discussion, I would be interested in understanding the advantage of the Voronoi approaches. The authors do mention a couple limitations and directions for future work, which I applaud. There is no reason to discuss social impact for this work. ", " A dequantization method is presented that is able to map between discrete and continuous distributions using continuous, invertible normalizing flows. Two applications are presented, namely Voronoi dequantization and Voronoi mixture models. The results are well founded, and figures visually explain the concepts well. Though the text is often a bit convoluted, where the text explanation tends to be over-complex and hard to understand for non-experts in the field.\n\nAlthough it is great how much space is given to explaining the background and catching the reader up, more results and experiments would perhaps be even more intriguing. \n\nCould it be that no Appendix was present with the submission, even though it was referred to? In Figure 5, the caption could directly explain what \"Samples\" refers to. Line 325 also mentions how the method could potentially make gradient-based optimization difficult, has this been tried in any experiments? It would be interesting to see such results, or these kinds of applications with the framework. The limitations are clear.", " The paper proposes a new method for modelling discrete data using normalizing flows by extending previous works on dequantization based method (like argmax flows) using a \"tessellation\" (not introduced or defined in the paper) based approach that automatically learns the boundaries for quantization. This is explore both for discrete to continuous and continuous to discrete. **Strengths:**\n- The paper describes sound extensions to normalizing flows for modelling discrete data and explores novel ways of incorporating tessellation based approaches in this context.\n- The experiments are done on a variety of datasets including language modelling etc to study the empirical performance of the method. \n- Significance: Getting good performance of generative models on discrete data is challenging and thus the problem is quite hard. This paper explores an interesting extension to previous methods to tackle this problem.\n\n**Weakness:**\n- Unfortunately, the paper is not clear on technical details. Important concepts are assumed to be known by the reader instead of properly introducing them e.g. tessellation, anchor points, Voronoi tessellation etc. The paper will greatly benefit from having a brief notations and definitions section. I also believe the paper will benefit greatly from having intuitive explanations accompany technical details to make it easier to follow.\n\n- Similarly, several appropriate references are missing e.g. for dequantization, the paper by Uria, 2013 needs to be cited. Similarly, statements/claims as in line 46-48 need to be supported with relevant references. \n\n- It was not immediately clear to me why is it useful to go from continuous case to the discrete case? What applications will this be important in? Apart from testing this on simple UCI datasets, I do not see any specific experiments for this.\n\n- I also found the experiments fairly limited in scope. There are no experiments to show the capability of the model on modeling categorical data with large number of classes. The language modeling task have small vocabularies. I'd recommended to evaluate the model on word-based language models with large vocabularies.\n\n- Similar to RAD flows, I believe the method will suffer from exploding gradients near the boundaries. How is the training stabalised to address this behaviour? Please see in the strengths and weakness section. Limitations have been discussed.", " The paper applies Voronoi tessellation to allow the application of normalizing flows on discrete data. The main contributions are Voronoi dequantization, which is a new mapping method between discrete values and continuous space, and a disjoint mixture model, which uses an invertible mapping between unbounded support and convex polytopes. Experimental result on a variety of datasets shows that the proposed method outperforms existing baselines. Strengths:\n- The Voronoi tessellation idea is simple, novel, and intuitive. Additionally, it addresses an important problem of modeling discrete data with normalizing flows.\n- The writing is very clear. All mathematical details are concise yet complete. The authors also provide enough context to distinguish their contribution from related works. \n- The proposed method for dequantization and disjoint mixture modeling significantly improves performance with little additional computational cost. \n\nWeaknesses:\nThere are no major flaws that I can think of. The paper can be further improved if the authors can provide a few alternatives to the current invertible mapping to convex polytopes and compare performance and computation costs. Other design choices can be explored as mentioned in the conclusion section, but the current content seems sufficient for a paper.\n - Since the experiments mainly compared with other flow models, it would be interesting to see how the proposed methods compare with state-of-the-art methods. Is normalizing flow outperformed by other methods even with the Voronoi dequantization and mixture modeling, or can it actually have better performance?
 The authors have discussed limitations, along with possible ways to address them, in the conclusion. \n" ]

[ -1, -1, -1, -1, -1, -1, -1, 7, 8, 5, 8 ]

[ -1, -1, -1, -1, -1, -1, -1, 3, 3, 4, 3 ]

[ "v0j2XMKTm-r", "P45bYGgRViH", "X4bxTntZ3U0", "fQ0VPbqPdoB", "BZAr-5CbXVh", "GMO4KBkmh58", "VL4P_W_FLdw", "nips_2022_NMTSIY6ykw7", "nips_2022_NMTSIY6ykw7", "nips_2022_NMTSIY6ykw7", "nips_2022_NMTSIY6ykw7" ]

[ "0ubEhA6PoRW", "4vb23U_8cQD", "hF8AukSVVhC", "yJnihRN_f1", "wXlaLnYHYuD", "RpjDCvxR0TZ3", "-yA5D3XP2cp", "MqAzhRGTk_", "wZnxLIBig9j", "GC8VijXwuTW", "tlkfOggzNWF", "yFiPDClknly", "7n9NJZMUYog", "2M-nOu6hYDc", "FoEeqR18HW", "P9plx6Juyd", "I7AxjeXhHjz", "CTYXlMwAKtx" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for addressing the questions and weaknesses in my comment. I have raised the score according to the responses.", " Thanks for addressing questions in my original review and thanks for the clarification.", " Thanks for the explanation! It makes perfect sense to me, and I can imagine that this enjoys certain degrees of universality.", " We really appreciate the reviewer's feedback and we will make the model assumptions appear earlier in the paper. \n\n**Related to the $A^TP_kA$**\n\nYes, we were referring to the $A^TP_kA$ part in Eq (4). In order to get the dynamics with the Volterra equation, it roughly requires the variance of the mini-batch to also have a specific interpretation. For this, we require the data matrix $A$ to have some \"delocalization of eigenvectors of AA^T\", which many natural distributions of random matrices satisfy. We chose the strongest form of this delocalization, which is the left-orthogonal invariance condition. Some future work is to remove this condition to satisfy more random matrix ensembles. \n\nAs the reviewer might know, delocalization of the eigenvectors does not directly imply anything about the spectral measure. It is possible to create random matrices $A$ with arbitrary spectra (e.g., as non-concentrated as you want), but have left-orthogonal invariance. But, it is true that eigenvector delocalization and concentrated spectral measure tend to ``happen at the same time'' for random matrices. \n\n----\n\nAgain, we thank the reviewer for the questions and the general interest in the results. We are happy to continue answering any questions the reviewer has. \n\nWe also want to make aware to the reviewer that they have not yet clicked the *Author Rebuttal Acknowledgement* button on the top of the page. We want to make sure that the reviewer is acknowledged for their contributions to the author-reviewer discussion period. ", " I would like to thank the authors for their efforts in explaining everything! Now the results make sense to me and I have adjusted the rating.\n\nYes, please clarify the model assumption earlier in the paper when preparing future versions.\n\nThe comments on the high-dimensionality effect seem interesting. Previously my impression was that it reflects the limiting spectral distribution of A as the law of A is assumed to be orthogonally (left) invariant. By 'simplify the noise generated from uniformly choosing indices of A', I guess what you are saying is related to the $A^\\top P_k A$ part in Eq. (4)? I thought this form of update is crucial and somehow limited to the linear setting.", " *First, we are happy to move the generative model assumption up further in the paper in order to make the paper more reader friendly; we will have to do this after the rebuttal, if accepted, because of the 9 page space limitation.*\n\nWe thought the reviewer might also be interested in how to remove $R$ and $\\tilde{R}$ or at least give a different interpretation especially in the setting when $d$ is fixed and $n \\to \\infty$. \n\n**1. Removing $R$ and $\\tilde{R}$ and linear model** \n\nA way to remove $R$, $\\tilde{R}$, and linear model (which we did not directly state in the paper, but it is hidden in the proof) is to view the whole forcing term $F(t) = \\frac{R}{2} h_1(t) + \\frac{\\tilde{R}}{2} h_0(t)$ as the loss function $f$ applied to full-batch gradient descent with momentum but with learning rate $\\gamma \\cdot \\zeta$, $f(x_k^{\\text{full batch gd+M}})$. We note the forcing term is the only place where $x_0, \\tilde{x}$, and $\\eta$ are used. They do not appear in the kernel. \n\n**Our assumptions on $x_0, \\tilde{x},$ and $\\eta$ involving the $R$ and $\\tilde{R}$ only help simplify $f(x_k^{\\text{full batch gd+M}})$, where $x_k^{\\text{full batch gd+M}}$ is the $k$th iterate generated from full batch gradient descent with momentum and stepsize $\\gamma \\zeta$.** If you want to run simulations and have exact predictions without having to run GD+M, it is nice to have a simple form for $f(x_k^{\\text{full batch gd+M}})$, but you could also leave it as is. \n\nYou do need some mild assumptions on $x_0$ and $b$ (such as $\\||x_0\\||^2 \\le C$ and $\\||b\\||^2 \\le C$ independent of $n$ and $d$ plus a little more) to make everything work even in this case. For instance, you need this quantity $f(x_k^{\\text{full batch gd+M}})$ to be defined for large $n$ and $d$. \n\nThe dynamics would be\n\n$$ \\psi(t+1) = f(x_k^{\\text{full batch gd+M}}) + \\gamma^2 \\zeta (1-\\zeta) \\sum_{k=0}^t H_2(t-k) \\psi(k), $$\nwhere $x_k^{\\text{full batch gd+M}}$ is the $k$th iterate generated from full batch gradient descent with momentum and stepsize $\\gamma \\zeta$.\n\nThis has the nice view of showing exactly that the loss under SGD+M is the loss under GD+M plus a noise term which is generated by the stochasticity in algorithm and we give explicit expressions for the noise. \n\n**2. High-dimensionality effect**\n\nWe also wanted to point out the \"high-dimensionality\" effect is really not due to the linear model $b$. It's more subtle than this. The high-dimensionality allows us to simplify the noise generated from uniformly choosing indices of $A$ (or the noise generated by the stochastic algorithm). This is a nice reason why to assume high-dimensionality. \n\n**3. Interpretation of $R$ in Theorem 1**\n\nIf you assume some mild assumptions like $||x_0||^2 \\le C$ and $||b||^2 \\le C$ independent of $n$ and $d$, Theorem 1 will change to the equation above in (1). The limiting loss value would become:\n\n$$\\psi(\\infty) = \\frac{f(x^{\\text{full batch gd+M}}_{\\infty})}{1-||K||}$$\n\nwhere $f(x^{\\text{full batch gd+M}}_{\\infty})$ is the limiting value of the loss of full batch gradient descent with momentum but with stepsize $\\gamma \\zeta$. This quantity is well defined for any $x_0$ and $b$ set-up. \n\n*We hope the reviewer finds this an interesting avenue of research.*\n\n", " Thanks again for the clarifications! \n\n- Regarding the limitation of $b = A \\tilde x + \\eta$, I think it should be emphasized that the setting in this paper is a _linear model_, in the introduction or abstract. In the latest response, the authors mentioned that 'as mentioned below, we can eliminate this assumption', but I don't see where this is explained. Did I miss anything?\n\n- Yes, I totally agree that the regime where $n$ is growing proportionally to $d$ is preferable.\n- I get that due to the stochastic noise, the SGD+M iterates will oscillate around $\\tilde x$ even if it's initialized exactly at $\\tilde x$. This resolves my previous question. \n- Regarding $R$ in Assumption 1, do you mean that $R$ can depend on $d$ and $n$, instead of being a universal constant? If so, then I have misunderstood this previously and I think this should be clarified in the paper because in Theorem 1, we are talking about the limit of large $n$ and $d$.", " **Limitation of $b= A\\tilde{x} + \\eta$**\n\nIn the current set up of the paper, we do assume that $b = A\\tilde{x} + \\eta$; a generative model, that is, the targets come from a true signal plus noise. The set-up is widely used (see [1,2] to name a few). We *explicitly* state this in **Eq 3** in the set-up section of the paper. Moreover as mentioned below, we can eliminate this assumption. \n\n[1] Mei, S. and Montanari, A. *The generalization error of random features regression: Precise asymptotics and double descent curve*, 2019\n\n[2] Adlam, B. and Pennington, J. *The Neural Tangent Kernel in High Dimensions: Triple Descent and a Multi-Scale Theory of Generalization*, 2020\n\n**Response to $d$ fixed and $n \\to \\infty$** \n\nFirst in order to take $d$ fixed and $n \\to \\infty$, as mentioned in our rebuttal, one would have to change Assumption 1.1 because, as you mentioned, this would imply that $E[\\||x_0-\\tilde{x}\\||^2_2] \\to 0$. However you can reinterpret what the $R$ and $\\tilde{R}$ mean in Assumption 1.1. A better way (which we did not state in the paper, but can do so), is to view the whole forcing term $F(t) = \\frac{R}{2} h_1(t) + \\frac{\\tilde{R}}{2} h_0(t)$ as the loss function $f$ applied to full-batch gradient descent with momentum but with learning rate $\\gamma * \\zeta$. We note the forcing term is the only place where $x_0, \\tilde{x}$, and $\\eta$ are explicitly used. In this way, you can start with any $x_0$ and $b$ under some mild assumptions (i.e., $\\||x_0\\||^2 \\le C$ and $\\||b\\||^2 \\le C$ independent of $n$ and $d$). Then the dynamics would be \n\n$$ \\psi(t+1) = f(x_k^{\\text{full batch gd+M}}) + \\gamma^2 \\zeta (1-\\zeta) \\sum_{k=0}^t H_2(t-k) \\psi(k), \\text{where full batch gd+m is with stepsize $\\gamma \\zeta$.}$$\nIf the reviewer prefers this interpretation, we can add it to the paper. This has the nice view of showing exactly that loss under SGD+M is loss under GD+M plus a noise term which is generated by the stochasticity in algorithm and we give explicit expressions for the noise. \n\nOne nice reason to state with $R$ and $\\tilde{R}$ is that $R/\\tilde{R}$ represents the signal-to-noise ratio. Often many high-dimensional asymptotic results use this quantity. \n\nWe also want to point out that most ML architectures are in the regime where $d$ is proportional to $n$. [3]\n\n[3] Martin, C. and Mahoney, M. *Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory\nand Implications for Learning*, 2021\n\n**Confusion about $x_0$ close to $\\tilde{x}$ and kernel** ($||K||$ not necessarily $0$ and no contradiction). \n\nWe are not assuming that the step size $\\gamma \\to 0$. Therefore because we are running a stochastic algorithm, we always move away from $x_0$ in one step provided the step size is not $0$. This is the noise created by running any stochastic algorithm such as SGD+M (i.e., you always take a step away from the optimum even if you are at the optimum since the *stochastic gradient* is not $0$). The $1-\\||K\\||$ is capturing the cumulative effect of this noise as $k \\to \\infty$. \n\nWe note that if the step size goes to $0$, then $\\||K\\|| \\to 0$ as $k \\to \\infty$ (see Eq. 11). You expect this because it is known that SGD with step size $\\to 0$ converges to the noise in $b$. We agree with the reviewer, in this setting with $\\gamma \\to 0$, that the loss value does not change much from initialization. \n\nOn the other hand, if the step size does not go to $0$, there is persistent noise from the algorithm (i.e., you always take a step away from the optimum even if you are at the optimum). The effect is that $0< \\||K\\|| < 1$. The value at $\\infty$ reflects the cumulative noise of always having to take a step because $\\gamma > 0$. Our model captures both when stepsize goes 0 and when stepsize is bounded away from $0$. \n\n*Is this what the reviewer is concerned about? Could the reviewer elaborate more on the \"contradiction\" part?*\n\nThere is also **no warm start needed** because $R$ is arbitrary. For instance, fix any dimension (say $n> d$) and chose an $x_0$ and assume that $b = A\\tilde{x} + \\eta$. Then there exists an $R$ such that $\\||x_0-\\tilde{x}\\||^2 = R d/ n$. We then give you exactly how that value $R$ (or distance to signal) effects the performance of the algorithm through our dynamics equation. Intuitively, the distance that you start from the \"optimum\" (that is denoted by essentially $R + \\tilde{R}$) should mean that the algorithm takes longer to converge, which it does!\n\n", " First I thank the authors for the explanations. I have read other reviewers' reviews and the corresponding rebuttal. \n\nI find one thing confusing: The authors mentioned in the response that 'one can take $d$ fixed and $n \\to \\infty$ and all propositions and theorems hold'. Let's say $d$ is fixed, then as $n \\to \\infty$, Assumption 1 tells us that the initialization $x_0$ is arbitrarily warm as $E[||x_0 - \\tilde x||_2^2] = \\frac{Rd}{n} \\to 0$. However, Proposition 1 instead tells us that $\\psi(\\infty) = \\frac{\\frac{\\widetilde R}{2} (\\max(1-\\frac{d}{n}, 0))}{1-||K||} \\to \\frac{\\widetilde R}{2(1-||K||)}$. Is this a contradiction? When $x_0$ is very close to $\\tilde x$, then basically $f(x_0) = \\frac{1}{2} ||\\eta||_2^2 = \\frac{\\widetilde R}{2}$ So $||K||=0$ in this case? In other words, the case of $d$ being fixed degenerates due to Assumption 1, which requires an arbitrarily warm start.\n\n\nAlso, it seems to me that the analysis is limited to the case of linear model where $b = Ax + \\eta$. Otherwise it is not clear to me how the high-dimensional effect kicks in, which crucially relies on the property of matrix $A$ in the current setting. If this is true, I think the limitation should be stated clearly somewhere early in the paper.", " We thank the reviewers for their comments and suggestions. We encourage the reviewers to look at the **newly uploaded main paper and Supplementary Materials as well as the new experiments** of Figure 4 on MNIST data and convergence behavior near the ICR on the MNIST data set and simulated data **([see here for ICR near crossover regime](https://anonymous.4open.science/r/predicted_ICR-C2F8/figure7.pdf) and [here for Figure 4 on MNIST data](https://anonymous.4open.science/r/heat_maps-B391/figure6.pdf))**. In the new version of the paper, we have implemented suggestions by the reviewers including \n\n1. Formatting changes (e.g., removed the figure wrapping and fixed typos)\n2. Adding the definitions of $h_0, h_1$, and $H_2$ in Theorem 1\n3. Rewriting parts of Section 2 to add more clarifications. \n4. Adding new experiments showing parameter selection and convergence rate on real data. Particularly we redid Figure 4 with the MNIST data set (**[see Figure 6 in newly uploaded Supplementary Materials or here](https://anonymous.4open.science/r/heat_maps-B391/figure6.pdf)**)\n5. Adding new experiments showing convergence rate near the ICR for simulated data and for MNIST data (**[see Figure 7 in newly uploaded Supplementary Materials or here](https://anonymous.4open.science/r/predicted_ICR-C2F8/figure7.pdf)**). The ICR exactly predicted the transition in convergence rates. ", " We thank the reviewer for their suggestions about further experiments, which we added to the newly uploaded Supplementary Materials. In particular, we did the following:\n\n* Reran Figure 4 – Convergence rate for various momentum and stepsizes on MNIST data. The figure is found in Supplementary Materials, Appendix D (Figure 6) **[see here](https://anonymous.4open.science/r/heat_maps-B391/figure6.pdf)**.\n* Added Figure 7 -- Convergence behavior near batch fraction equal to ICR on simulated data and MNIST **[(see here)](https://anonymous.4open.science/r/predicted_ICR-C2F8/figure7.pdf)**. The ICR *exactly* predicted the transition. \n* Added the definitions of $h_1, h_0, H_2$ into the main text. \n\nWe appreciate that the reviewer likes the contributions of the paper. We clarify below the reviewer’s questions and concerns. \n\n**Response to Weaknesses**\n\n*1. The organization of the paper is not reader-friendly. The figures of experiments are located in different places on paper and the setting of the experiments is in the supplementary documents. It's quite hard to follow when reading the paper.*\n\nWe fixed the figure placement in the revision and hopefully the placement is better in the updated version of the paper which we encourage you to look at. Unfortunately due to space limitations, we can not fit the experimental set-up into the main 9 pages without removing some of the important theoretical results. \n\n*2. There are several functions in the paper, such as $h_1, h_0, H_2$, which are defined in the supplementary documents. But in the main text, the authors use the conclusion from the function that $F(t)-O(\\lambda _{2,max}^t$). This may confuse readers.*\n\nWe have added the definitions of $h_1, h_0, H_2$ into the main text. \n\n*3. Since there are several constants in the paper, it may be better to have a table for the definition of constants.*\n\nDue to space limitations, we do not have the room to place a table into the main 9 pages.\n\n*4. There is not enough related work discussed in the related work section.*\n\nWe will add the following references if accepted; we were limited on space but will add if we are given the extra 1 page to the main text. (If the reviewer has more suggestions, we would be grateful.) \n* In Gitman, et al [2019], the authors use an analysis of SGD+M which breaks down the rate in two: a deterministic part and a part governed by the noise. They derive an exact formula in the most general quadratic setting, but do not analyze the rates to show if SGD+M achieves $O(1/\\sqrt{\\kappa})$. \n* Other works have shown that worst-case SGD+M does not achieve acceleration (see e.g., Kidambi et al. [2018], Sebbouh et al. [2020], Zhang et al. [2019], Liu et al [2020]). \n* The lack of general convergence guarantees showing acceleration for existing momentum schemes, such as heavy-ball, in the stochastic setting, has led many authors to design alternative acceleration schemes [Allen-Zhu, 2017, Ghadimi and Lan, 2012, 2013a, Kidambi et al., 2018, Kulunchakov and Mairal, 2019, Liu and Belkin, 2020].\n\n**Response to Questions**\n\n*1. In Assumption 1.1, there is an assumption about the initialization x_0, which is not normal for the problems. It is hard to check this assumption since the signal \\tilde{x} is not known in practice.*\n\nThe condition in Assumption 1.1 says that $||x_0-\\tilde{x}||^2$ is bounded, which is a common assumption in theory. The $d/n$ appearing was for convenience in the analysis. The assumption is simply that $\\||x_0-\\tilde{x}\\||^2$ is bounded (or the distance to optimality) does not grow in dimension, that is as $n \\to \\infty$ or $d \\to \\infty$. We do not want this quantity to grow in $n, d$ because we are varying the dimensions $d$ and $n$, and so we need to ensure that as $d$ and $n$ grow the distance to optimality $\\||x_0-\\tilde{x}\\||^2$ is constant so that we don’t start further away from the optimum (e.g., if $x_0 \\sim N(0,I_d)$ then as $E[||x_0||^2]$ grows like d). \n\nNote one does not actually need to know $R$ and $\\tilde{R}$ in order to compute $\\psi$ (see Reviewer n1XZ, Question 3).\n\n*2. In the experiment part, Figures 4 and 6 are based on Gaussian random least squares problems. They are based on calculating the analytic expression for convergence rate. Is it possible to plot the figure based on an empirical experiment?*\n\nWe have added in Appendix D, Supplementary Materials (see new revision of paper) a **[new figure, Figure 6 (see here)](https://anonymous.4open.science/r/heat_maps-B391/figure6.pdf)**, which is Figure 4 but on the MNIST dataset. \n\n*3. In section 4, the authors mentioned the two batch size regimes. Providing experiments comparing these two regimes will be great to validate this claim.*\n\nSee **[Figure 7 in Appendix D of Supplementary Material or here](https://anonymous.4open.science/r/predicted_ICR-C2F8/figure7.pdf)** showing behavior near the ICR. The batch fraction equal to the ICR *exactly* predicted this crossover behavior.", " We thank the reviewer for the careful reading of our paper and the reviewer's appreciation for our contributions and general approach to analyzing SGD+M. \n\nWe have implemented the following in the **newly uploaded version of the Supplementary Material and main text** as suggested by the reviewer. We encourage the reviewer to look at these in the new versions. \n\n* Figure wrapping changes. \n* Added experiments showing behavior near the **[crossover batch fraction point for simulated data and MNIST in Appendix D of Supplementary Materials (see here as well)](https://anonymous.4open.science/r/predicted_ICR-C2F8/figure7.pdf)**\n* Removed $\\mathcal{K}$ to represent the kernel\n* Rewrote beginning of Section 2 to help with clarification. We would like more feedback from the reviewer on this.\n\n**General comments**\n\n*“I don't know of any papers using large-batch training where acceleration-like improvements are observed when using momentum, I wonder if the authors are aware of any?”*\n\nThere are two concurrent works of ours [1,2] that have shown some degree of acceleration. These were released after and right before (~1.5 months) our submission to NeurIPS (thus making them concurrent works according to NeurIPS). \n\n* In [1], the authors showed that SGD+M (and other related stochastic accelerated algorithms such as stochastic Nesterov’s accelerated method) achieve the $O(1/\\sqrt{\\gamma \\sigma^2_{\\min}} )$ rate where $\\gamma$ is the learning rate, but require $\\gamma$ small so one may not see the acceleration. \n* In [2], the authors, using a finer analysis of products of random matrices, show that mini-batch SGD+M achieves the desired $1/\\sqrt{\\kappa}$ rate provided that the mini-batch is sufficiently large; a similar ideas as us. To achieve this acceleration, the authors require that their batch fraction be an order $\\kappa$ bigger than the ICR we propose. This extra condition number can be quite large which in turn means they need huge batch sizes to achieve acceleration. Moreover in their experiments they show that our batch fraction is sufficient. This said, they work in a more general setting. **Moreover in [our new figure (see here)](https://anonymous.4open.science/r/predicted_ICR-C2F8/figure7.pdf), you can see that when the batch fraction equals the ICR, it *exactly* finds the transition point.** \n\n[1] Can, B. and Gurbuzbalaban, M. *Entropic Risk-Averse Generalized Momentum Methods*, arxiv preprint: 2204.11292\n[2] Bollapragada, R., Chen, T., and Ward, R. *On the fast convergence of minibatch heavy ball momentum*, arxiv preprint: 2206.07553\n\n*Some further plots showing the behavior in and around the cross-over region would be nice.*\n\nWe have added in the Supplementary Materials, Appendix D a new experiment showing the behavior near the ICR region for simulated data and on MNIST **[(see Figure 7 or the link here)](https://anonymous.4open.science/r/predicted_ICR-C2F8/figure7.pdf)**. The results show that the ICR *exactly* predicts the crossover behavior even on real data such as MNIST. \n\n*Removing text-wrapping of figures.* \n\nWe implemented the reviewer’s suggestion in the new revision of the paper for some of the figures. Unfortunately for one figure we could not remove the text-wrapping without causing us spacing issues. If the reviewer has another suggestion to fix this, we would gladly implement it.\n\n**Response to Questions**\n\n*1. It's confusing to use \\kappa as a constant and capital kappa for kernel, the symbols are almost the same, perhaps change the notation for the kernel to just K? a lot of papers use that.* \n\nWe thank the reviewer for their feedback and we have made the revision in the new version of the paper. \n\n*2. The beginning of section two doesn't make much sense without reading the appendix, it leaves too much out.*\n\nWe have rewritten the beginning of Section 2 and added some of the equations from the Appendix to clarify the forcing term in the new version of the paper.\n\n*3. Are the eigenvalues of H σ or σ2? Using σ2 is a little odd.*\n\nThe $\\sigma^2$ are the eigenvalues of $AA^T$; we used this notation so that $\\sigma$ would represent a singular value of $A$. As far as we are aware, there is no $H$ in the paper. Could the reviewer clarify what $H$ they are referring to? \n", " We would like to clarify some concerns of the reviewer. We hope that the reviewer will reconsider their rating and carefully read our response on how to interpret Theorem 1 and, for instance, obtain convergence rates. \n\n**Response to Weaknesses**\n\n*“…gap between the actual convergence of SGD+M and the presented equivalence between SGD+M and the discrete Volterra equation, which makes some claims a bit misleading…Addressing Theorem 1 characterizes the closeness between the SGD+M iterates and the discrete Volterra equation iterates, but only for finite T and the error does not decrease with T...Thus it is misleading to make claim about the convergence of SGD+M based on the convergence of ψ, as in Theorem 2.”*\n\nThe subject of this article is high--dimensional analysis: we assume that the number of samples $n$ is large (and are interested in cases when both $n$ and $d$ are large), and we look for ways in which the problem simplifies over low dimensions. As it is typically the case in machine learning problems that these are large (in the hundreds is already enough for good numerical agreement), this assumption is usually desirable.\n\n**The Volterra model that we derive is the explicit high-dimensional ($n$ is large) equivalent of the minibatch suboptimality.**\n\n**In our theorem formulation, the quality of the agreement is high when $n$ is large,** and as you observe it does not improve with iteration count. Formulating a statement that holds on an **infinite time horizon is possible**, and could be an interesting future direction.\n\nBut the convergence can not already be determined from our theorem, although the formulation is different from non-high-dimensional optimization. You should rather use the following approach.\n\nTo reach $\\varepsilon$-suboptimality in the minibatch SGD+M, you would first use the Volterra equation to derive the number of iterates T required to reach this suboptimality. Our theorem then tells you a dimensionality in which you should work (although we do not quantify it), and then it says with overwhelming probability the random algorithm reaches suboptimality $2\\varepsilon$ in $T$ steps.\n\nSo as a consequence, our theorem shows that the trajectory of the minibatch training loss is contained in a tube around a particular path, which implies neighborhood convergence. Of course in the non-interpolation regime, with a stochastic algorithm and without iterate averaging and with constant step size, this is the best you can hope for anyhow. Studying those alterations is also possibly interesting future work.\n\nWe would like to emphasize that while our convergence is 'neighborhood' type, it is substantially sharper than any other convergence result you will find in the literature in high dimensions. The Volterra equation is **actually the high--dimensional limit**. This means that to reach a given $\\varepsilon$-suboptimality, there is a number $T_{\\varepsilon}$ (determined by the Volterra equation) so that mini batch-SGD+M requires *exactly* $T_{\\varepsilon}$ steps to reach this suboptimality with overwhelming probability, for all dimensions sufficiently large.\n\n**Response to Questions**\n\n*1. The paper title suggests that the dimension d is high, but this is not clear from the results. In Theorem 1, is it true that the result holds for a fixed d as n goes to infinity? If d is fixed and n is large, then basically each SGD step corresponds to an over-determined linear regression? I'd like the authors to clarify the relationship between n and d.*\n\nThe results hold for any $n$ and $d$ provided $n$ is large (and, as suggested by the title of the paper, we are interested when both $n$ and $d$ are large as the “over-parameterized, high-dimensional” setting is common in machine learning settings) . This means that one can have $d \\ge n$ or $n \\ge d$; both the over- and under- determined settings are represented by all the theorems and propositions. The only place large $d$ enters is the concentration related to the signal R (Assumption 1.1), but if we condition on $x_0$, $\\tilde{x}$ and set $R = ||x_0-\\tilde{x}||^2$, there is nothing else regulated by $d$. Thus one can take $d$ fixed and $n \\to \\infty$ and all propositions and theorems hold. \n\n*2. In Theorem 1, it is said that Eq.(12) holds for sufficiently large n. What is the threshold for being 'sufficiently large'?Definition/properties of the function H in Eq.(13) should be specified in the theorem statement*\n\nThe “sufficiently large n” is to suppress a constant that appears in Thm 1. For exactly how large an $n$, it should satisfy Line 549 in Lem. 1 in the Appendix. \n\nAdded the definitions of $h_1, h_0,$ and $H_2$ (and their dependencies on $\\gamma, \\Delta, \\zeta$, $A A^T$) to the statement of Theorem 1 in the new version of the paper. \n\n*3. What is K in Eq.(15) when translating Eq.(13) into the form of Eq.(15)?*\n\nK in Eq. (15) is $K(t) = \\gamma^2 \\zeta (1-\\zeta) H_2(t)$ where $H_2(t)$ is defined in Eq. 9, see Appendix A for details. ", " We thank the reviewer for their careful reading of our paper and thoughtful questions. We appreciate that the reviewer identified many contributions of this work. We fixed the typos and added in Appendix D an explanation of our hyperparameter tuning $R$ and $\\tilde{R}$ in the *newly uploaded version of the paper and Supplementary Materials*. \n\n**Response to Weaknesses**\n\n*1. When the number of samples (n) is small, the function ψ cannot accurately approximate the training loss.*\n\nYes, your discussion is exactly correct. When the problem size is small (say d = 30, n = 20), we have nothing to say. On the other hand, we would argue there is quite a bit of interest in large parameter and large sample settings with respect to the machine learning community.\n\n*2. Factors $R$ and $\\tilde{R}$, should be predefined.*\n\nThe value $\\frac{R}{\\tilde{R}}$ represents the signal-to-noise and indeed they can not readily be computed. However we note that the forcing term in Eq. 10, $F(t) = \\frac{R}{2} h_1(t) + \\frac{\\tilde{R}}{2} h_0(t)$ has another interpretation as it equals the loss function $f$ under full-batch gradient descent with momentum with step size $\\gamma \\cdot \\zeta$ (scaled by the batch fraction). Since the loss under full-batch gradient descent with momentum on a least squares problem is completely determined by the spectrum of the Hessian and the targets $b$ one does not actually need to compute the values of $\\tilde{R}$ and $R$ [1]. \n\n[1] C. Paquette, et al, Halting Time is Predictable for Large Models: A Universality Property and Average-Case Analysis, Found. of Computational Mathematics, 2022\n\n**Response to Questions**\n\n*1. When do we say the number of samples (n) is large? n = 1000?*\n\nIn practice, we get good agreement with our theory when $n$ is in the hundreds. We note that the results hold for any $n$ and $d$. The statement of Theorem 1 says that as $n \\to \\infty$ the loss of mini-batch momentum concentrates around the deterministic function $\\psi(t)$, meaning as the number of samples $n$ grows, the better the approximation of $\\psi$ gets to the actual SGD+M. \n\n*2. Why does the author add $P_k$ in Eq. (4)?*\n\nThe $P_k$ is a random projection matrix and its introduction was for notational convenience. Also it is convenient in the proof to think of the mini-batch as a random projection so that one can use results from high-dimensional probability. Note the $P_k$ is equivalent to randomly selecting rows of $A$ (or indices $i \\in [n]$) as one would do in a mini batch stochastic algorithm. \n\n*3. Since the author uses the function $\\psi$ to approximate the training loss trajectory, how do you select the factors, $R$ and $\\tilde{R}$ such that $\\psi$ can approximate the training loss trajectory accurately?*\n\nWith generated data, such as $x_0 \\sim N(0,I_d)$, $\\tilde{x} \\sim N(0, I_d)$, and $\\eta \\sim N(0, I_n)$, one can compute exactly $R$ and $\\tilde{R}$. This was done to show proof of concept in Figure 1, for instance. On real data (e.g., Fig. 3), we grid searched through various values of $R$ and $\\tilde{R}$. We added an explanation in Appendix D: Numerical Simulations explaining our hyperparameter tuning of $R$ and $\\tilde{R}$. Alternatively, see Weakness point 2 above, $\\frac{R}{2} h_1(t) + \\frac{\\tilde{R}}{2} h_0(t)$ has another interpretation as it equals the loss function $f$ under full-batch gradient descent with momentum with step size $\\gamma \\cdot \\zeta$. One could run full-batch gradient descent with momentum (which is not stochastic) and get an expression for the $\\frac{R}{2} h_1(t) + \\frac{\\tilde{R}}{2} h_0(t)$. ", " The author analyzes the dynamics of large batch stochastic gradient descent with momentum and shows that the dynamics of SGD+M converge to a deterministic discrete Volterra equation as dimension increases. The author also identifies a stability measurement, the implicit conditioning ratio (ICR), for the stability of SGD+M and gives explicit choices for the learning rate and momentum parameter. Strengths:\n1. The author provides a non-asymptotic comparison for the behavior of the training loss under SGD+M to a deterministic function $\\psi$.\n2. The exact loss trajectory gives a rigorous definition of the large batch and small batch regimes.\n3. The author introduces a stability measurement that exactly captures the transition of SGD+M to an accelerated method.\n4. The author finds that the dynamics of SGD+M and of SGD are truly non-equivalent.\n\nWeaknesses\n1. When the number of samples (n) is small, the function $\\psi$ cannot accurately approximate the training loss.\n2. Factors $R$ and $\\tilde{R}$, should be predefined.\n 1. When do we say the number of samples (n) is large? n = 1000?\n2. Why does the author add $P_k$ in Eq. (4)? \n3. Since the author uses the function $\\psi$ to approximate the training loss trajectory, how do you select the factors, $R$ and $\\tilde{R}$ such that $\\psi$ can approximate the training loss trajectory accurately?\n\nTypos\n\nLine 86 used a -> used\n\nLine 91 do -> does\n\nLine 191 discussed -> are discussed\n\nLine 211 a produce?\n\nLine 303 benefit -> a benefit\n\nLine 306 achieved -> be achieved\n\netc.\n Yes", " This paper studies large batch stochastic gradient descent with momentum, where the setting is specialized to the least square problem with large sample size and dimension. It is shown that the dynamics of SGD with momentum will converge to deterministic dynamics described by the discrete Volterra equation, as the sample size increases. Based on this, a quantity called implicit conditioning ratio is identified to characterize when SGD with momentum can achieve acceleration. This further yields suitable choices for the learning rate and momentum parameter. This paper is clearly written and easy to follow. The problem setting and assumptions are clarified, and the discussion on the results yields interesting observations about the behavior of SGD with momentum. However, there is still a gap between the actual convergence of SGD with momentum and the presented equivalence between SGD with momentum and the discrete Volterra equation, which makes some claims a bit misleading. See details below. Some comments and questions are as follows:\n\n1. The paper title suggests that the dimension $d$ is high, but this is not clear from the results. For example, in Theorem 1, is it true that the result holds for a fixed $d$ as $n$ goes to infinity? This also concerns the paragraph from line 220 to 225. When $d$ is fixed, it is an over-determined linear regression for large $n$. The same problem exists in the statement of Proposition 4. If $d$ is fixed and $n$ is large, then basically each SGD step corresponds to an over-determined linear regression? I'd like the authors to clarify the relationship between $n$ and $d$.\n\n2. In Theorem 1, it is said that Eq.(12) holds for sufficiently large $n$. What is the threshold for being 'sufficiently large'? Also, the definition/properties of the function $H$ in Eq.(13) should be specified in the theorem statement, otherwise it is not clear what is its dependence on the problem parameters.\n\n3. What is $\\mathcal{K}$ in Eq.(15) when translating Eq.(13) into the form of Eq.(15)?\n\n4. Theorem 1 characterizes the closeness between the SGD+M iterates and the discrete Volterra equation iterates, but only for finite $T$ and the error does not decrease with $T$. This suggests that there is a gap between the convergence of SGD+M and that of $\\psi$. Thus it is misleading to make claim about the convergence of SGD+M based on the convergence of $\\psi$, as in Theorem 2. I'd like the authors to discuss how to resolve this gap, otherwise the claims about the convergence of SGD+M is problematic. The authors have adequately addressed the limitations and potential negative societal impact of their work.", " In this paper, the authors analyzed the dynamics of stochastic gradient descent with momentum based on the linear regression (least-squares) problems. They used the deterministic discrete Volterra equation to approximate the dynamics of stochastic gradient descent with momentum. They provided proof of convergence of the iterates of stochastic gradient descent with momentum to the discrete Volterra equation in Theorem 1. They proposed the Implicit conditioning ratio (ICR) and claimed that there are two regimes. For large batch sizes, the SGD+M performance matches the performance of the heavy-ball algorithm with Polyak momentum parameters, while there is no gain in convergence rate by increasing the batch fraction. For small batch sizes, there is still a benefit in increasing the batch fraction. Strengths:\n1) The paper has solid mathematical proof and contributions.\n2) The figures in the paper are well-presented.\n3) The idea of the paper has been written in a clear and reader-friendly way.\n\nWeaknesses:\n1) The organization of the paper is not reader-friendly. The figures of experiments are located in different places on paper and the setting of the experiments is in the supplementary documents. It's quite hard to follow when reading the paper.\n2) There are several functions in the paper, such as h_1, h_0, H_2, which are defined in the supplementary documents. But in the main text, the authors use the conclusion from the function that F(t)-\\bigO(\\lambda _{2,max}^t). This may confuse readers.\n3) Since there are several constants in the paper, it may be better to have a table for the definition of constants.\n4) There is not enough related work discussed in the related work section. 1) In Assumption 1.1, there is an assumption about the initialization x_0, which is not normal for the problems. It is hard to check this assumption since the signal \\tilde{x} is not known in practice.\n2) In the experiment part, Figures 4 and 6 are based on Gaussian random least squares problems. They are based on calculating the analytic expression for convergence rate. Is it possible to plot the figure based on an empirical experiment?\n3) In section 4, the authors mentioned the two batch size regimes. Providing experiments comparing these two regimes will be great to validate this claim.\n4) Figure 4 and 6 are based on least-squares problems, are there similar figures for MNIST experiments? Yes", " Analysis and characterization of two regimes for SGD on quadratic problems. Large batch setting where accelerated rates occur and small batch setting where non-accelerated rates occur. I generally like the approach this paper takes and the theoretical outcomes. The separation of the convergence rates into two regimes makes a lot of sense and matches my personal intuition about the behavior occurring in practice. Although momentum helps stochastic optimization in many practical settings, in my experience it doesn't appear to provide \"acceleration\", but rather robustness and generalization advantages, and I think the behavior in practice is very much what the theory in this paper describes in the small batch setting. I don't know of any papers using large-batch training where acceleration-like improvements are observed when using momentum, I wonder if the authors are aware of any?\nI'm not familiar with discrete Volterra equations, as I expect would be the case for most readers. I'm still able to largely follow the arguments presented. The results are surprisingly precise regarding the $\\zeta$ and its relation to the spectrum. Some further plots showing the behavior in and around the cross-over region would be nice.\n\nThe use of text-wrapped figures here doesn't make sense to me, given that in both cases two figures are stacked, they could easily be instead stacked side-by-side and floated at the top of the pages without losing any space, I would suggest the authors do that for the camera ready. It's more readable. It's confusing to use \\kappa as a constant and capital kappa for kernel, the symbols are almost the same, perhaps change the notation for the kernel to just K? a lot of papers use that.\n\nThe beginning of section two doesn't make much sense without reading the appendix, it leaves too much out.\n\nAre the eigenvalues of H $\\sigma$ or $\\sigma^{2}$? Using $\\sigma^{2}$ is a little odd. A theory paper is always limited by its assumptions. The assumptions are very very strong here, almost the strongest possible given the setting. However, the results are correspondingly concrete and specific, so strong assumptions are ok." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 8 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 3 ]

[ "tlkfOggzNWF", "2M-nOu6hYDc", "yJnihRN_f1", "wXlaLnYHYuD", "RpjDCvxR0TZ3", "-yA5D3XP2cp", "MqAzhRGTk_", "wZnxLIBig9j", "7n9NJZMUYog", "nips_2022_z9poo2GhOh6", "I7AxjeXhHjz", "CTYXlMwAKtx", "P9plx6Juyd", "FoEeqR18HW", "nips_2022_z9poo2GhOh6", "nips_2022_z9poo2GhOh6", "nips_2022_z9poo2GhOh6", "nips_2022_z9poo2GhOh6" ]

[ "aZJcKrJEhp_", "jUDFjrfXOU", "LQpkXag3gs-s", "YtA-_fcS2_W", "xe3yTODkPa-", "miLSpwuulc-V", "bkCD7i-IK-2", "c12kofOJOq1", "TF1fgmh4Q0m", "RGDVWZvN2sD", "pc6ctyDbGqI", "QApnguVYFQ_", "hr_MSjlnYA", "ALpOS9tyQAh", "tiLq31jU05t", "WccGVGVEqyR", "UbQLuPm983y", "U6BsKTxwCx", "WlNgoi5cjNx", "mFWqHg5VHYm" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We sincerely thank all reviewers for the thoughtful responses and constructive feedback. We truly believe they improved the quality of the paper overall.\n\nWeakly-supervised audio-visual source localization is a challenging task that aims to predict the location of visual sound sources for enhanced audio-visual perception, while relying on minimal human annotation.\nThis is critical for many applications in the community, such as robotic perception and egocentric video understanding. We thus believe that advances in visual source localization will have many downstream benefits.\n\nOur paper makes significant advances in both how to learn and how to evaluate weakly-supervised visual source localization.\nWe propose “Simultaneous Instance Discrimination and Localization” - a novel contribution of this work with clear benefits, as it demonstrably improves both precision and false positive rates.\nWe also extended Flickr-SoundNet and VGG-SS to address a critical limitation of these established benchamark datasets, and provide a new and effective way to assess a model in a more realistic scenario.\n\nReviewers played an important role in improving our paper. It was pointed out the misuse of the term “unsupervised” and the existence of relevant works on identifying silent objects.\nIn rebuttal, we addressed these concerns. To clarify the different levels of supervision that can be used to train VSL model, we formally defined unsupervised, weakly supervised, semi-supervised, and fully supervised VSL.\nWe also explicitly indicated that we (as well as other prior work) are addressing the Weakly Supervised setting.\nRegarding prior work on silent objects, we clarified how our work stands in relation to DSOL (NeurIPS’2020) and IEr (AAAI’2022), and gave them proper credit for their contributions. We also added DSOL to the list of methods that we benchmarked using the new evaluation protocol.\n\nWe appreciate that all of the reviewers recognized our contributions and believe that our study has the potential to inspire more audiences attending NeurIPS.", " I thank the authors for the detailed reply and the corresponding polishments in the draft. I hence increase my score from 2 to 7. Hope to see a better final version of this paper!", " We’d like to prompt the reviewer whether the later revisions properly addressed the reviewer concerns.\n\nWe sought to clarify in our revision the contributions of DSOL and IEr and how they relate and differ from our work.\n\nPlease let us know if you have further suggestions or concerns.", " As promised, 2->7. Thanks for addressing my comments.", " We are glad that the reviewer took our rebuttal into consideration and appreciate the thoughtful response. Our first revision focused on offering proper experimental comparisons to these works. We have now tried to correct inaccurate statements in the intro and related work. We point the reviewer to lines 45-49 (intro) and 90-101 (related work) of the revised manuscript. We’ve also searched for other places where the claim had to be softened. We quote below the two main additions:\n\n**Intro (ln45-49)**\n>It should be noted that false positive detection is closely related to the silent object detection problem highlighted in recent works [7, 8].\nAlthough these works introduce methods to suppress the localization of silent objects, they require the collection of a clean dataset containing a single source per video. Instead, we aim to tackle this issue without assuming knowledge of the number of sources.\n\n**Related work (ln90-101)**\n>Although understanding when sources are not visible is important to several audio-visual tasks, like in open-domain audio-visual source separation [35, 36], this issue still poses significant challenges. DSOL [ 7] and IEr [ 8] proposed a method to suppress localization of silent objects, and an evaluation metric that measures the ability of a model to ignore visible silent objects. These methods, however, rely on the knowledge of the number of sound sources, not available in most large scale datasets. In contrast, we tackle visual source localization without assuming knowledge of the number of sources. Specifically, we propose a novel Simultaneous Instance Discrimination and Localization framework for weakly-supervised visual source localization with clear benefits, as it demonstrably improves both precision and false positive rates. We also annotate real world test samples that may lead to false positives (beyond silent objects), and propose new metrics for comprehensive evaluation.\n\nWe hope this clarifies how our work stands in relation to DSOL and IEr, and provide these works proper credit for their contributions. Please, let us know if you (or other reviewers) have further suggestions on how to be more precise in addressing this issue.", " I thank the authors for the feedback. Part of my concerns are addressed, e.g., no code and no demo video. Besides, the additional analysis on the novelty generally makes sense. \n\nOverall my biggest concern remains that the initial version of the paper ignores DSOL [a] (NeurIPS'20), which makes so many claims in the introduction and related work parts inaccurate. I could understand that IEr (AAAI'22) is recently proposed, so missing this work should not be over-criticized. However, DSOL [a], which targets exactly the same problem of solving silence, ought not to be ignored. Even though I agree with the authors that both DSOL and IEr all require a more demanding single-source dataset for pre-training, the authors could explain the difference between these works' settings. Besides, some of the compared baselines in this work [b] also mention and discuss DSOL. \"Unfortunately, at the time of writing, we were unaware of these two papers, DSOL (NeurIPS'20) and the recently released IEr (AAAI'22).\" makes me disappointed. The initial rating was mostly derived from the doubt about the authors' efforts in surveying this area, since this is always the first step in doing research. \n\nBesides, multiple parts of the claims on the introduction should be revised. For example, in L44 it is incorrect to say that all previous works ignore such problem. The authors are encouraged to highlight the discussions on these works in the introduction, since the title itself contains 'tackle the silence'. \n\nOverall, I thank the authors for the rebuttal and your efforts in polishing the manuscript. I will consider raising my score after these revisions.\n\n[a] Discriminative Sounding Objects Localization via Self-supervised Audiovisual Matching, Hu et al., NeurIPS 2020.\n\n[b] Learning Sound Localization Better From Semantically Similar Samples, Senocak et al., ICASSP 2022.", " Good catch, we missed the caption. It has now been corrected. Thanks again for the thoughtful review!", " Thanks, your paragraph seems a very good candidate for placing the work of this paper and fixing the issues of the terminology issues by prior work. I will increase my score 2 -> 7 given that the paragraph above goes in the final manuscript. Table 1 still has a wrong unsupervised term in there, please fix and let me know to increase my score.", " We appreciate the prompt and thoughtful response to our rebuttal.\n\nAfter reflecting on R2's comments, we completely agreed and decided to address this misconception of prior work more proactively. To this end, we 1) defined the different levels of supervision (unsupervised, weakly supervised, semi-supervised, and fully supervised) that can be used to train VSL models. 2) We explicitly indicated that we are addressing the Weakly Supervised setting, and 3) pointed out that prior works (mistakenly) refer to the problem as unsupervised VSL, as they use supervised pre-trained models. Finally, 4) we edited the rest of the document (including the title) accordingly.\n\nQuoting from the new revised manuscript (starting at Ln 105):\n>**Section 3.1: Preliminaries: Weakly Supervised Visual Source Localization**\n>\n>Given an audio-visual paired dataset $\\mathcal{D}=\\{(v_i, a_i): i=1, \\ldots, N\\}$, visual source localization (VSL) aims at predicting the location of the sources present in sound $a_i$ within the visual frame $v_i$.\n>VSL models can be learned from various levels of supervision:\n>*Unsupervised VSL* learn to localize without any form of human annotations;\n>*Weakly-supervised VSL* forgo bounding-box supervision but may leverage categorical information. This categorical information can be in the form of object labels for visual encoder pre-training, or audio event labels for audio encoder pre-training;\n>*Semi-supervised VSL* learns from a small number of bounding-box annotations, together with a large unsupervised or weakly-supervised dataset;\n>*Fully supervised VSL* models can learn from large amounts of fully annotated datasets.\n>In this paper, we tackle the Weakly-Supervised VSL problem. We note that equivalent prior work, such as [1, 4, 2, 3, 35, 6, 7, 5], often refer to this problem as unsupervised VSL, despite actually addressing the weakly supervised problem, as they use vision models pre-trained on ImageNet for object recognition.\n\nPlease let us know if R2 (or any other reviewers) has further suggestions on how to be more precise in defining or addressing this issue.", " I thank the authors for their effort to answer all my answers and most of my criticisms. However, there is still the most important criticism which still has not been fully addressed by the authors. Pre-training a CNN on a fully labeled image dataset with multiple images of the same object with a different background is by **any** means a model that can be used for a downstream **unsupervised** approach. The approach of this paper and all others cited [1,2,5,6,7] are **weakly supervised** since they are using class labels which helps significantly in understanding class-discriminatory features and drive the model towards picking up the most salient pixel-level features for each class in a much easier way than not having those class labels. If the authors still think that this distinction between *unsupervised* and *weakly supervised* is not so important for their paper, I challenge them to rerun their models with their ResNet trained from scratch and see if there is a difference between a true \"unsupervised\" and a \"weakly supervised\" approach as the one proposed here.\n\nIt is really disheartening that the authors acknowledge that the **unsupervised** terminology is actually wrong (quoting from the response above: \"We completely agree with this observation... We nevertheless agree with the reviewer, and will try to make this clear in the manuscript.\") and then the authors prefer to continue this misuse of the term simply because other works have done the same mistake (quoting from above: \"we felt the need to use the term \"unsupervised\" to follow the terminology used in prior works (see [1,2,5,6,7]).... To link to prior work, we will still introduce the problem as \"unsupervised visual source localization\" but add the proper context\"). The authors should explicitly state that (or a similar sentence): *In multiple previous works have stated this task as unsupervised sound localization but they actually perform weakly supervised methods which are pre-trained on large image-labeled datasets. Thus, our approach is also weakly-supervised since it is based on strong image priors but we hope that we can extend it to unsupervised approaches where our image encoder will not require labels for pre-training.*\n\nOur goal as researchers is not to conceal the truth simply because it is more convenient \"*to follow the terminology used in prior works*\". Our goal is to write papers that help the community go forward and point out mistakes that prior work has, if need be, to reconsider problems and solutions. At some point there is going to be a work which performs **truly unsupervised** sound event localization and the authors will need to explain how their work is different from the previously wrongly claimed *unsupervised* sound event localization papers, I am betting that the authors would be far better off by pointing this difference right now and help the community and themselves in the long term. \n\nMy suggestion will be a strong rejection for this very good overall paper until the authors remove all wrongly used **unsupervised** terms from the paper and replace them with **weakly supervised**.\n", " I thank the authors for the clarification, I had indeed missed that the precision would not be affected by the addition of negative samples. I would recommend to make an explicit note on this in the paper, as I believe other people than me could get confused as well.\n\nAs promised, I hence change my overall score from 5 to 8.", " **The paper ignores some very important and relevant works, DSOL [1] and IEr [2]. These two methods successfully solve the silence problem in the sound localization. However, the authors claim that this is an unsolved problem.**\n\nUnfortunately, at the time of writing, we were unaware of these two papers, DSOL (NeurIPS'20) and the recently released IEr (AAAI'22). Despite significant differences (which we highlighted below), we agree they are relevant, and should have been cited, discussed and compared with. We added a proper discussion and experimental comparison in the revised manuscript, and hope the reviewer considers this effort. We believe, and support with empirical evidence, that DSOL and IEr do NOT solve the false positive rate problem, as they still tend to overdetect sounding objects when none are visible. We summarize this discussion below.\n\nWhile both DSOL and IEr propose a method to suppress localization of silent objects, they address a less general problem (ie, with access to more supervision) than ours. Both DSOL and IEr require a clean dataset containing a single source per video, which require a fair amount of human annotation in order to ensure that the training data does NOT contain sound mixtures and that the sound source is on screen. This type of annotation is particularly important to obtain high quality audio/visual prototypes, which in turn are critical for the second learning stage. In contrast, we tackle the problem of visual source localization without assuming knowledge of the number of sources, allowing training to be scaled easily.\n\nAs pointed out by the reviewer, DSOL also proposes an evaluation metric (NSA) that measures the ability of a model to ignore visible silent objects. This metric however is computed using an artificially generated 2x2 grid of images, and so it is unclear how it extends to natural images. In contrast, we actually **annotate** real world test samples, where 1) objects are visible but silent, 2) the sound source is active but not visible, or 3) no visible or active sound sources are present. Note that some of these situations are not considered in the NSA metric. We believe the test set we provide will lead to a more realistic and thorough assessment of VSL approaches.\n\nFinally, to compare to our approach, we trained DSOL on the **full VGG-SS** dataset using the code released by the authors (VGG-SS results in the DSOL paper only used a small subset of VGG-SS). We've added the results to Tables 2 and 3 of the paper (see revised manuscript). From Table 2, we see that DSOL still suffers from overfitting issues, with a drop of 3\\% if early stopping is not used. Table 3 also shows that DSOL is significantly worse than our method (about 13\\% worse precision, 14\\% worse max-F1 and 17\\% worse AP!). We did not compare on Flickr-SoundNet as this dataset does not have audio label annotations, and thus the audio event model could not be trained. We also do not report results with IEr, as their code has not been released yet.\n\n\n**Lack of Novelty. Dropout and EMA updates are very basic tricks and couldn't independently serve as a novelty or contribution to the community.**\n\nOur paper makes significant advances in both how to learn and how to evaluate unsupervised visual source localization. Simultaneous Instance Discrimination and Localization is a novel contribution of this work with clear benefits, as it demonstrably improves both precision and false positive rates. The extended Flickr-SoundNet and VGG-SS provide a new and effective way to assess a model in a more realistic scenario. We agree that dropout and momentum encoders are basic regularization techniques, but the negative impact of overfitting has clearly been overlooked even after a large number of papers being published on the topic (otherwise, regularization techniques would already be part of prior works). We hope the reviewer takes these contributions into consideration when judging our papers' contributions and novelty.\n\n\n**Why dropout works?**\n\nRegarding visual dropout, it works by encouraging higher spatial redundancy, as the model needs to prevent loss of information when features are dropped (ie it leads to spatially smoother feature maps). This reduces the likelihood of spurious audio-visual alignments.\n\n\n**Demo Video**\n\nWe’ve shown several examples of model predictions in Supplementary Material. We’ve also created a demo video. See the following anonymized link: \nhttps://drive.google.com/file/d/1SDJj1JoZxRIJBcTJL4pKbmcHs3T1DRdm/view\n\n\n**No code**\n\nUnfortunately, we were not able to provide code in supplementary, as we planned. We are however ready to share the code and pre-trained models with the community, as can be seen here: https://anonymous.4open.science/r/MoVSL-1021.\n", " **Model components could be explained better. In most cases, I do not see a direct connection between a specific problem and how these ideas should be expected to help.**\n\nWe summarize below the motivations of each component and how they can help with the issues identified in the paper.\n\nFirst, to combat overfitting, we adopt 1) visual dropout and 2) slow-moving momentum encoders. Visual dropout is of course a common regularizer. An interesting insight is that to properly address overfitting unusually high visual dropout rates are required. We describe a potential reason for this in lines 133-135. As for the momentum encoder, it prevents overfitting as they provide more stable targets. As mentioned in Ln 140-141: \"Since updates to the audio-visual encoders are slowly incorporated into the momentum encoders, the target representations display a smoother behavior during the training process.\"\n\nTo reduce false positives, we explicitly force the model to perform audio-visual instance discrimination in addition to localization. Note that prior works only ask the model to perform instance discrimination through the loss function, and not as a part of the model architecture itself. In our case, the localization module highlights which image regions are most associated with a particular audio, while the instance discrimination module downplays regions that can be better described by the audio of other samples. The key insight is that the model can prevent false detections more effectively, when selecting regions that are simultaneously highlighted in both terms.\n\n\n**There are numerous \"dimensions\" in which momentum could reasonably be applied here—time, visual extent, training iteration. Which one do we use?**\n\nWe use momentum encoders, as commonly used in self-supervised frameworks like MoCo [34]. This means using momentum (over training iterations) to update the encoders used for the target representations (see footnote 3 in Ln139).\n\nWe also find the idea of using momentum along other \"dimensions\" like time or space to be interesting directions for potential future improvements. It is however beyond the scope of this work.\n\n\n**SLID motivation. Shouldn't most images have regions that correspond to no audio at all? Why incentivize all image regions to be matched to a particular audio (through the “xid” branch)?**\n\nWe agree that most images have regions that correspond to no audio at all. However, it is NOT true that the \"xid\" branch requires every visual region to be matched to the corresponding audio. Note that the loss of eq. (4) only operates on the spatial location that is most aligned with the audio (not all locations). That means that, even if some regions are not associated to any audio (eg the softmax outputs a uniform distribution over all audios in the batch), as long as the representations of some visual regions do get aligned with the corresponding audio, the loss can still be minimized.\n\n\n**What are the definitions for \"small, medium, large, huge\"?**\n\nThese categories refer to the different sizes of the ground-truth bounding boxes *as measured by the pixel area*. We clarified the definition of these groups in the revised manuscript. The cutoff between categories is defined in Table 1.\n\n\n**What is the audio sampling rate?**\n\nThe audio sampling rate is 22050Hz. We've added to the paper.\n\n\n**What is the criterion for determining \"best\" (bold) in tables 2 and 3?**\n\nWe bolded the best results with and without OGL. OGL is an object prior that can be added to any audio-visual localization method for improved performance. As such, we believe that comparing the pure audio-visual performance (without OGL) is still important. We clarified in the paper.\n\n\n**Several answers to the author checklist are incorrect or left as \"N/A\"**\n\nWe apologize for the incorrectly filled form. We have fixed it.\n\n\n**Societal implications are not mentioned. The problem being studied here has obvious applications in surveillance that could be mentioned.**\n\nWe mention that the fairness of current models heavily depend on the biases of the datasets in use, and that a more thorough curation of the datasets against nefarious bias should be conducted before deployment in real world settings. We added a sentence regarding surveillance applications.\n\n\n", " **A similar problem has been addressed in open-domain audio-visual sound source separation (AudioScope).**\n\nWe appreciate the reference to open-domain audio-visual source separation and added it to related work. Indeed, being able to understand when sound sources are not visible is of interest to many audio-visual tasks. \n\n\n**Why the authors did not try to optimize a straightforward loss on the mask of hard negative examples?**\n\nSeveral methods already seek to suppress localization for nonaligned audio-visual pairs. For example, EZ-VSL (ECCV22) uses a contrastive objective that reduces the likelihood of localization when the visual frames and the audio belong to different videos. LVS (CVPR21) finds hard negative regions within a frame, and minimizes a loss that suppresses localization within them. We agree that these more straightforward approaches could potentially address the false localization issue. However, as evidenced by the relatively low AP and max-F1 scores in Table 3, they do not fully address the problem.\n\n\n**This approach needs supervised data to fine-tune the confidence threshold in order to select the desired operating point of the model.**\n\nTechnically, the proposed evaluation procedure does not select an operating point, as both max-F1 and AP metrics summarize the performance across all operating points. A higher AP score indicates a higher operating curve on average, and a higher max-F1 score indicates a higher max performance. Having said that, this is a good observation, as deploying the model would require us to choose an operating point. Without validating the chosen confidence threshold on a supervised set, we may not be operating at the highest possible performance. However, given the higher max-F1 and AP scores, our method is still likely to perform better than competing methods regardless of the chosen operating point.\n\n\n**ResNet weights are supervised on image classification tasks. Remove the unsupervised terminology or show results without supervised pre-training. This is “the only reason that in the current state I vote in favor of NOT accepting this great paper.”**\n\nWe completely agree with this observation, but we felt the need to use the term \"unsupervised\" to follow the terminology used in prior works (see [1,2,5,6,7]).\n\nIn the literature, \"unsupervised source localization\" refers to the fact that the model is trained to perform *localization without using ground-truth bounding box annotations*. Since the main goal is to learn to localize (and not visual representation), all prior approaches still use ImageNet pre-trained weights (while still referring to the task as unsupervised localization).\n\nWe nevertheless agree with the reviewer, and will try to make this clear in the manuscript. We removed the term \"unsupervised\" from spotlight locations like the title. To link to prior work, we will still introduce the problem as \"unsupervised visual source localization\" but add the proper context (see for example new footnote 1 on page 4).\n\n**How can the proposed method be extended towards removing the dependencies on object detection models and object saliency maps?**\n\nWe agree that, in principle, audio-visual localization does not need to depend on pre-trained object priors, as the model could learn them if necessary. However, these object priors still seem to be highly effective during inference, as most sound sources are objects.\n\nTrue large-scale training and further technical advances may reduce the benefits of pre-trained object priors. One may also seek to learn object priors in an unsupervised fashion instead. One potential approach would be to learn from video tracking (ie learn to identify which pixels are likely to move together in a video).\n\n\n**Remove the gray background in Figures 2 and 3.**\n\nThanks for your suggestion. See manuscript.\n\n", " **Mistake: Precision in Table 3 copy-pasted from Table 2.**\n\nThis is not a mistake. The two metrics (columns \"LATEST\" in Table 2 and \"Precision\" in Table 3) are indeed the same. They both represent the precision using the latest checkpoint. So, all the discussion and conclusions of the paper are indeed valid.\n\nNote that, in Table 3, both Flickr and VGG-SS test sets are extended by introducing only negative samples. Thus, this extension of the test sets does NOT affect the computation of Precision (defined as the portion of *actual* sound sources that are correctly localized). In fact, this is why we believe that solely relying on Precision (often called CIoU in the literature) to assess performance is not enough, thus motivating our broad comparative study using metrics that also assess the ability to reject samples without visible sounding sources.\n\n**In equation (1) and equation (4), the loss function should be denoted $\\mathcal{L}_i$ to improve clarity.**\n\nThanks for the great suggestion. We made the change in the revised manuscript.\n\n**Is the final loss the sum of sample losses over a mini-batch?**\n\nThe model is trained on the *average* per sample loss: $\\mathcal{L}=\\frac{1}{P}\\sum_{i=1}^P\\mathcal{L}_i$. We clarified in the paper.\n\n\n**In eqs (1) and (4), is the sum over j taken over $j \\neq i$?**\n\nNo, we use the InfoNCE loss [A], where the positive score also takes part in the sum in the denominator. We will use $\\sum_{j=1}^P$ instead of $\\sum_j$ to make this clear.\n\n[A] Oord, Aaron van den, Yazhe Li, and Oriol Vinyals. \"Representation learning with contrastive predictive coding.\" arXiv:1807.03748, 2018.\n\n\n**Typo in eq. (4): $P_{ji}$ instead of $P_{ij}$.**\n\nThanks for spotting the typo. We have updated it in the revision.\n\n**How are the categories \"small, medium, large and huge\" defined?**\n\nThese categories refer to the different sizes of the ground-truth bounding boxes *as measured by the pixel area*. We clarified the definition of these groups in the revised manuscript. The cutoff between categories is defined in Table 1.\n\n**Term \"(usually set at $\\gamma$)\" is confusing.**\n\nThis is a typo. We meant to say \"(usually set at $\\gamma=0.5$)\".\n\n**How the (x,y) locations are selected inside each image to compute local visual features?**\n\nTo compute localized features, we follow prior work like LVS and EZ-VSL, and use the output feature map from a fully convolutional backbone (ResNet-18 w/o the final average pooling and classifier). Thus, the (x,y) locations are indeed selected on a regular grid and are computed from the full receptive field of the last convolutional layer.\n", " We thank all reviewers for the insightful feedback. We believe that it already improved the overall quality of our paper. We will address each reviewer in a separate thread. When appropriate, we made changes to the paper directly. See the revised manuscript for reference (all changes in the manuscript are shown in red). We encourage the reviewers to reach out during the discussion period, if you have any remaining questions.", " The authors propose a new method for the self-supervised localization of sounding objects in image. The paper focus on two important limitations of current methodologies 1) they do not handle well sample with no visible or audible sound sources and 2) they are prone to overfitting due to using early stopping criteria on test sets. To address these issues, the main methodological contributions of the paper are - - the introduction of slow-moving momentum audio and visual encoders\n- the use of extreme dropout on visual encoders\n- the introduction of a loss function that jointly enforces sounding region selection and cross-modal instance discrimination, using different projections for each tasks.\n\nExperiments reveal that the propose method establishes a new state-of-the-art on standard datasets as well as on newly designed datasets that include negative samples. Careful ablation studies on the components of the proposed approach and on the metric parameters are also conducted. ## Strengths\n- The paper is clear and pleasing to read. The formalization of the method and chosen notations are sound and easy to follow.\n- Beyond establishing a new state of the art, it is also a welcome contribution to research reproducibility in this field.\n- Experiments are convincing and are rigorously designed to avoid biases, in particular in the choice of metric threshold.\n\n## Weaknesses\n- **There is unfortunately a potential fatal mistake in the paper: the precision results of Table 3 seem to have been copy-pasted from Table 2. It is not clear whether the discussions and conclusions drawn by the authors throughout the paper will still hold after fixing this. This must be discussed during the rebuttal phase. Hence, I give the paper a grade of 5, which would become an 8 if this issue is satisfyingly fixed.**\n- There are several points in the paper that deserve to be clarified, see next section. - In equation (1) and equation (4), the loss function depends on the index i. It should be denoted \\mathcal{L}_i to improve clarity. Is it the case that over a mini-batch containing several audio-visual pairs (a_i,v_i), i=1...P, the minimized loss is actually the sum of \\mathcal{L}_i for i=1...P ? Moreover, are the sum over j in the loss actually taken over $j\\ne i$ ? Please make this precise.\n\n- In eq. (4): typo: I guess the denominator of the second term should contain P_ji instead of P_ij, otherwise it doesn't make sense (the two terms are identical).\n\n- L182: while this is probably obvious to the authors, it is not entirely clear to me what the categories \"small, medium, large and huge\" refer to. The total image size? The sounding object size? How is this defined?\n\n- L187: the bracketed term \"(usually set at γ)\" is confusing and should probably be removed.\n\n- Section 4.1: Maybe I missed it but I do not see how the (x,y) locations are selected inside each image to compute local visual features. At random? On a regular grid? And from how many pixel are the visual features are computed?\n The authors have correctly addressed the limitations of their work, mostly the poor performances on small objects.", " This paper proposes new metrics and training recipes in order to avoid problematic behavior of sound localization methods which tend to overfit to predicting correctly masks for sounding objects which appear on-screen but completely neglect input images with not on-screen sounding objects. The authors also propose a momentum audio-visual approach which shows state-of-the-art results on widely used benchmark datasets.\n ***Pros:***\n- The approach is simple and well described so researchers can reproduce the results.\n- The paper discusses a really important problem of rejecting regions with not on-screen sounding objects which is beneficial for the community. The paper also extends benchmark datasets with well detailed evaluation dataset extensions to include the capability of models to reject off-screen sounds.\n- The results on widely used benchmark datasets are robust and the paper is clearly written.\n\n***Cons:***\n- The paper addresses the problem of the models in the literature to overfitting, whereas the main problem is that one could also use hard-negatives and negative samples during training directly (e.g. using a loss function that tries to make the predicted audio-visual mask zero for frames which are not aligned with the input audio). A similar problem (videos with no on-screen sounds) has also been addressed in open-domain audio-visual sound source separation [A] using a multi-instance loss and measuring the off-screen power suppression for sounds which do not appear on-screen. It is not so straightforward why the authors did not try to optimize a straightforward loss on the mask of hard negative examples.\n- Picking the confidence threshold also depends on the dataset and thus, although there is no strict dependence on supervised data to train a model with the proposed methodology, this approach also needs supervised data in practice to fine-tune the confidence threshold in order to shift the operating point of the model towards a desired one.\n- The ReNet weights which are used come from supervised training on image classification tasks (Line 222: “we initialize the visual encoder with ImageNet [39] pre-trained weights”), please correct me if I am wrong. In this case, the authors either need to remove the terminology about “unsupervised” and replace it with partially/semi/less - supervised or they can show results where their method does not need supervised pre-training to work. \n\n[A] Tzinis E, Wisdom S, Jansen A, Hershey S, Remez T, Ellis D, Hershey JR. Into the Wild with AudioScope: Unsupervised Audio-Visual Separation of On-Screen Sounds. In International Conference on Learning Representations 2021.\n\nI am more than happy to increase my score if the authors address my concerns. To be honest, the only reason that in the current state I vote in favor of NOT accepting this great paper is the misuse of the term “unsupervised” when in all the experiments the backbone image encoder was pre-trained on the whole ImageNet (and this is the reason that I used this rating on the soundness axis). - How can the proposed method be extended towards removing the dependencies on object detection models and object saliency maps? \n- The authors can remove the gray background in Figures 2 and 3. In my opinion, the authors aptly address several limitations of their work in the main text (see Section 4.5).\n", " This paper describes two contributions to audio-visual source localization: 1) an evaluation protocol designed to explicitly include negative example cases (where no sound source is visible in the image), and 2) model components designed to address shortcomings in prior work.\nThe authors compare the proposed model extensions to prior work, using both the proposed evaluation (and extended datasets) and previous evaluation schemes.\nAblation studies quantify the relative contributions of each modeling component across the new metrics. Strengths:\n\nThe explicit inclusion of negative examples for this task makes a great deal of intuitive sense, and addresses a real shortcoming of previous work in this area.\n\nThe evaluation appears to be carefully done, and the proposed modeling components do seem provide a substantive improvement for localization.\n\n\n\nWeaknesses:\n\nThe proposed model components (section 3.2) could be explained better.\nIn most cases, I do not see a direct connection between a specific problem with prior models and how these ideas should be expected to help.\n I found the description of momentum confusing and lacking context. There are numerous \"dimensions\" in which momentum could reasonably be applied here—time, visual extent, training iteration—and a reasonable case could be made for any of them. (E.g., one should expect smooth variation in the visual extent if sound sources are compact visual objects, and sound activation should be piecewise constant in time for most types.) I *think* you mean momentum in the training iteration sense, but I'm not 100% certain and could not find any definitive statement to this effect in the text. Could you please clarify, and explicit about what you're doing?\n\nSimilarly, I don't think I fully understood the motivation for SLID. It seems like the \"xid\" branch is incentivized to match every visual region to audio from some example in the batch (by virtue of maximizing a softmax, eq 3), but why is this reasonable? Shouldn't we expect most images to have regions that correspond to no audio at all?\n\nWhat are the definitions for \"small, medium, large, huge\" in line 182?\n\nSection 4.1 omits the audio sampling rate, without which the numbers describing the audio encoder are meaningless. Please clarify.\n\nWhat is the criterion for determining \"best\" (bold) in tables 2 and 3? Of course the \"ours\" method is bold, but in both tables, there are prior examples (EZ-VSL+OGL) that achieve higher/comparable scores (eg 37.86 vs 37.79). The authors do state that the experiment is too expensive to support error bars, but some statement of a meaningful difference should be provided.\n\nSeveral answers to the author checklist are incorrect or left as \"N/A\". Specifically:\n- 1.c, broken reference (no such text exists)\n- 3.d, section 4.1 does not include the specified details\n- 4.a, does not appear to cite all tools used (i.e. software), only prior papers describing models\n- 4.c, 4.e: answer should be \"no\", not \"N/A\" (you are using existing assets, and did not address these points)\n Some technical limitations are discussed, but no societal implications are mentioned. The problem being studied here has obvious applications in surveillance that could be mentioned.", " The authors propose a new Momentum-based approach for Visual Sound Localization, termed as MoSVL. It focuses on two key audio-visual sound source localization problems: 1) previous studies are not truly un-supervised and have overfitting problems easily when scaled up to large datasets. 2) the authors claim that all baseline methods fail to consider the silence in the sound localization problem, hence a new mechanism with evaluation protocols is proposed. Strengths:\n\n- [minor +] The audio-visual learning is on the surge and is of great importance. Hence the focused problem has good practical impacts.\n\n- [minor +] The paper is generally easy to follow.\n\nWeaknesses:\n\n- [major -] My biggest concern is that the paper **directly ignores some very very important and relevant works**, DSOL [1] and IEr [2]. They are neither compared nor even discussed/cited in the paper. In particular, DSOL [1] targets to solve the discriminative sounding object localization in multi-sound scenarios **as well as coping with the silent objects**. They suppress those silent but visible objects by multiplying the audio category probability distributions to the visual object distributions, hence those silent objects will not take effect. Besides, DSOL **also propose a manner to effectively evaluate the sound localization performance**. They create a 2x2 grid, with two sounding objects and two silent objects to evaluate cIoU and NSA (Non-Sound Areas). If the model mistakenly localize the sounds to the silent regions, both the cIoU and NSA will perform poorly. In IEr [2], the authors propose to not only deal with the in-the-scene silent objects, but also suppress the off-screen background noise by cross-modal matching. All these two methods are proved to successfully solve the silence problem in the sound localization. However, the authors claim that this is an unsolved problem and it constitutes a very important observation and contribution of this paper.\n\n- [major -] Lack of Novelty. To solve the overfitting problem, the authors propose to add more dropout to the visual features and perform the EMA update on the encoders. However, these are all very basic tricks and couldn't independently serve as a novelty or contribution to the community. Besides, the authors fail to very carefully analyze the effect of dropout or ways to prevent overfitting. Why the dropout works? Why other tricks that help to prevent overfitting won't work, like data augmentation, network parameter normalization, etc.\n\n- [major -] Lack of Demo Video. The lack of demo video weakens the qualitative results of this paper. I could not straight judge the performance when silent objects exist. \n\n- [minor -] No code. As promised by the authors in the checklist, they will include code or data in the supplementary material. Although the authors say that the dataset is too large to submit. The code is not included, which makes doubt the answer [YES] in the checklist and the re-producibility of this paper.\n\n[1] Discriminative Sounding Objects Localization via Self-supervised Audiovisual Matching, Hu et al., NeurIPS 2020.\n\n[2] Visual Sound Localization in-the-Wild by Cross-Modal Interference Erasing, Liu et al., AAAI 2022.\n\nOverall, the ignorance of very relevant works makes the claim, contribution and novelty of the paper poor. The focused problem has already been solved, and the corresponding evaluation protocols have already been proposed, while they are not even discussed in the paper. This makes the main body of the paper meaningless. The left part is the method to solve the overfitting problem, which are quite trivial tricks to me. The authors fail to make their best efforts to delve into the phenomenon and analyze why such methods could alleviate the overfitting problem. My concerns are elaborate in the above weaknesses field. The lack of comparison and discussions with important related works makes the majority of the paper meaningless. They are discussed in the supplementary material, but it shows up as Section ?? in the checklist. I recommend the authors to pay more attention to the checklist, since this is a very important and useful part in NeurIPS submission." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 7, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 5 ]

[ "nips_2022_pn5trhFskOt", "LQpkXag3gs-s", "miLSpwuulc-V", "bkCD7i-IK-2", "miLSpwuulc-V", "QApnguVYFQ_", "c12kofOJOq1", "TF1fgmh4Q0m", "RGDVWZvN2sD", "ALpOS9tyQAh", "tiLq31jU05t", "mFWqHg5VHYm", "WlNgoi5cjNx", "U6BsKTxwCx", "UbQLuPm983y", "nips_2022_pn5trhFskOt", "nips_2022_pn5trhFskOt", "nips_2022_pn5trhFskOt", "nips_2022_pn5trhFskOt", "nips_2022_pn5trhFskOt" ]

[ "Bd3ybizhtIV", "g48dVxlFvW_", "F6T51b7yF-dq", "8Jfmw8RsJW_", "Ll7aJdQz7oe", "nFZ3685pCVu", "9Wo4XGd4LA2", "8_cG-74A4Om", "-hNZGQ4AAQh", "6h8nVNvyfnG", "j_HThPtGF1h", "ELLD1V0c9mL" ]

[ "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for the response. I will keep my score unchanged", " Thank you for answering my questions. I decide to increase my score to a 6.", " Dear reviewer, \n\nPlease let us know if our response has addressed the issues raised in your review. We hope that our corrections, clarifications, and additional results address the concerns you've raised. We are happy to address any further concerns.", " Thanks for the answers/comments! I continue to think that this is a good paper.", " We thank the reviewer for the thorough and detailed comments.\n\nRegarding the weakness and typos you posted: we have fixed the typos and revised the pictures within the paper to reflect your concerns and suggestions, please see our revision.\n\nRegarding your questions: yes, you are right. The learned execute-policy enables generating correct actions to reach the desired state via the generalization ability of neural networks. It may fail to generalize due to limited data size or narrow data distribution, we theoretically give the generalization bound with respect to the guide-policy in Theorem 1, and we show empirically that by using a proper guide-policy, the execute-policy can achieve good results.\n\nRegarding the limitations you posted, we think our method can still work on discrete control tasks. The execute-policy may be easier to learn if the action only has several choices. We will consider adding some discrete control tasks in the latter revision.\n", " Thank you very much for your kind suggestions and detailed review, you are one of the most responsible reviewers we have encountered! \n\nWe especially appreciate for minor writing comments you posted, we have made several writing adjustments within the paper to reflect some of your concerns and suggestions, please see our revision. There are still some we haven't solved, we will definitely solve it all in the latter version.\n\n>\"Since the guide policy is predicting the next state, it's output could be very high dimensional, right? Does this pose a problem?\"\n\nYes, we agree that this is one weakness of POR. Fortunately, the state space of antmaze is 29, it is not super large, and we may need to use representation learning to reduce the dimension in those high-dimensional tasks.\n\n>\"How does network capacity affect the performance of the guide policy?\"\n\nWe compare the used guide-policy network size ($(256, 256)$ in the paper) to a smaller one $(128, 128)$ and a larger one $(1024, 1024)$, and the results are listed as follows. We found that using a small network size is insufficient for learning in some datasets but a much larger network size didn't guarantee higher scores.\n\n| Dataset | (128, 128) | (256, 256) | (1024, 1024) |\n| ----------- | ----------- | ----------- | ----------- |\n| antmaze-m-p | 64.6+7.8 | 84.6+5.6 | 80.2+3.3 |\n| antmaze-m-d | 70.5+9.2 | 79.2+3.1 | 80.4+6.5 |\n| hopper-m-r | 40.6+14.2 | 98.9+1.6 | 99.5+3.2 |\n| walker2d-m-r | 36.4+15.2 | 76.6+6.9 | 76.4+7.2 |\n\n\n>\"Eq. 4 -- How carefully does $\\alpha$ have to be tuned?\"\n\nWe set it to 0.2 in AntMaze tasks and 0.5 in MuJoCo tasks.\n\n>\"For the experiments in Fig 3, I suspect that most of the benefit from the \"mixed\" approach is that learning the execute policy on the expert data effective amounts to behavioral cloning (e.g., see analysis in [3]). If so, this benefit can be injected into the TD3+BC and CQL methods, too. For example, for TD3+BC, we could learn the Q-function on the combined dataset and train the actor on just the expert data. How would these \"mixed\" versions of TD3+BC and CQL perform?\"\n\nThis is a good question. First, we want to apologize that we didn't make the description of the setting in Section 5.3 clear enough, and we have revised the paper to make it more clear. We want to study the setting where we already have a policy learned from a small yet high-quality dataset $\\mathcal{D}_e$, and now we get a supplementary large dataset $\\mathcal{D}_o$. $\\mathcal{D}_o$ may be sampled from one or multiple behavior policies, it provides higher data coverage but could be suboptimal. We are interested to see whether we can use $\\mathcal{D}_o$ to obtain a better policy.\n\nSo in this setting, only POR is able to keep the execute-policy learned from $\\mathcal{D}_e$ unchanged but use the combination of $\\mathcal{D}_e$ and $\\mathcal{D}_o$ to re-train the guide-policy (i.e., the \"mixed\" training scheme) due to the decoupled training procedure, that's the reason why initially we didn't include the \"mixed\" version of TD3BC and CQL. After reading your review, we immediately try the \"mixed\" version of TD3BC and CQL, the results are listed as follows.\n\n| Dataset | TD3BC-main | TD3BC-more | TD3BC-mixed | CQL-main | CQL-more | CQL-mixed |\n| ----------- | -----------| -----------| -----------|----------| ---------| ---------|\n| hopper-medium-replay-v2 | 39.1 | 38.7 | 37.5 | 50.5 | 30.1 | 55.6 | \n| walker2d-medium-replay-v2 | 53.6 | 62.4 | 69.7 | 56.8 | 57.4 | 66.1 | \n\n\nThe results show that the \"mixed\" version of TD3BC and CQL perform inferior to the \"mixed\" version of POR. We have not figured out why, one reason we suspect is that when computing the target $Q$ value, the policy may generate some OOD actions since $Q^{\\pi}$ is trained on $\\mathcal{D}_e$ and $\\mathcal{D}_o$ while the policy is trained only on $\\mathcal{D}_e$, the actions produced by the policy may have a large discrepancy from actions in $\\mathcal{D}_o$, causing large policy evaluation errors.\n\n\n>\"Can the method be used to perform transfer across agents with different action spaces? E.g., learn a guide policy for one robot and an execute policy for another robot, and then mix and match them.\"\n\nThanks for pointing out that! A really good point. We think our method could do this since the guide-policy only indicates which state is more optimal, we will add some experiments to verify that in the latter revision.", " We thank the reviewer for the thorough and detailed comments.\n\n>\"The description of some references is inaccurate. For example, the authors state that One-step RL [3] and IQL use different weights to do behavior cloning. Is that true?\"\n\nWe have included a whole section to discuss this, please see Appendix A for details. \n\n>\"What is the direct benefit of using expectile regression to learn g_\\omega rather than \\pi(a|s).\"\n\nIf we understand correctly, the question you want to ask is that \"what is the benefit of using expectile regression to learn the state value function in POR against to learn the state-action value function in IQL?\".\n\nThe high-level idea of IQL and POR is different in that IQL is doing action-stitching while POR is doing state-stitching.\n\nIQL uses expectile regression to approximate the expectile of $Q$ with respect to the action distribution given a state. To extract the policy, IQL maximizes this objective, $L(\\pi)=\\mathbb{E}_{(s, a) \\sim \\mathcal{D}}\\left[\\exp \\left(\\beta\\left(Q(s, a)-V(s)\\right)\\right) \\log \\pi(a|s)\\right]$, which can be deemed as using dataset actions to do weighted behavior cloning.\n\nCloning dataset actions can only do action-stitching, which loses the ability to surpass the dataset by out-of-distribution (action) generalization. In POR, we learn an out-of-distribution state indicator, i.e., the guide-policy $g$, to guide the policy to the optimal next state. If the execute-policy can generalize well, it will output a different yet optimal action $a=\\arg \\max_{a} \\pi(a | s, g(s))$.\n\n>\"The authors state that \"we only need to learn a value function while IQL needs an additional Q-function to extract the policy\".\"\n\nWe apologize for the misleading statement here. We want to discuss the difference between learning $V$ in POR and learning $Q$ in IQL, not to mean that the benefit of POR is only need to learn one value function rather than two. We have revised our statement in the paper to make it more clear.\n\n\n>\"Intuitively, the expectile regression can sometimes eliminate the OOD issue in offline RL, but the authors additional introduce a behavior cloning term in Equation 4. My question is, if we replace the expectile regression in Equation 3 with the standard regression loss and then adopt the behavior cloning loss in Equation 4, what will be the difference in performance. More ablation experiments are required.\"\n\nThe expectile regression technique and behavior cloning loss are two orthogonal term. Yes, expectile regression can eliminate the OOD issue because it uses only dataset samples, but only when we are learning the value function. When we use the value function to extract the policy, it will still query the value function about actions (states in our case) that generated by the policy, which are out of distribution. So we need the behavior cloning loss in Equation 4. \n\nWe add a ablation study that replaces the expectile regression in Equation 3 with the standard mse loss. The results are listed as follows, as expected, the standard mse loss performs worse than the expectile regression loss.\n\n| Dataset | Expectile regression | Mean-squared error |\n| ----------- | ----------- | ----------- |\n| antmaze-m-p | 84.6$\\pm$5.6 | 25.0$\\pm$18.4 |\n| antmaze-l-p | 58.0$\\pm$12.4 | 15.2$\\pm$7.0 |\n| hopper-m-r | 98.9$\\pm$2.1 | 30.7$\\pm$2.4 |\n| walker2d-m-r | 76.6$\\pm$6.9 | 70.5$\\pm$3.4 |\n\n\n>\"The authors use both expectile regression and BC loss for learning the guide-policy. Doesn't this make learning too conservative?\"\n\nAs we discussed above, these two term are orthogonal, it won't make learning too conservative.\n\n>\"In essence, the proposed method requires learning addition execute-policy. I do not see why there would be an added advantage over IQL on the D4RL tasks.\"\n\nAs I discussed above, POR is doing state-stitching rather than action-stitching, which reduces conservatism and allows more out-of-distribution generalization.\n\n>\"However, the toy example assumes that offline data includes transitions of taking random actions at random states. So, is there any OOD action in this motivating example?\"\n\nIn the motivating example, the dataset is colored green, we do not generate random actions at every state, so there are plenty of OOD actions. \n\n>\"Further, does the learned execute-policy enable the output of the so-called \"logical\" out-of-distribution actions?\"\n\nThis is a good question. The learned execute-policy enables generating correct actions to reach the desired state via the generalization ability of neural networks. It may fail to generalize due to limited data size or narrow data distribution, we theoritically give the generalization bound with respect to the guide-policy in Theorem 1, we show empirically that by using a proper guide-policy, the execute-policy can achieve good results.\n\n\n\n\n\n\n\n", " Thank you for your review and for providing relevant references that we had overlooked. \n\n>\"so it would be more relevant to cite references to prior work on those\"\n\nThanks a lot for pointing out that! We have included a section to discuss more related work about the inverse dynamics model, see Appendix B for details.\n\n>\"The experiment in Sec. 5.3 is quite interesting, but it is unclear why the execute policy is not trained on $\\mathcal{D_{o}}$. If I understand correctly, the execute policy is not a typical policy but an inverse dynamics model as mentioned above, and it can be trained on data from any policy.\"\n\nWhile in principle the execute-policy can be trained on any data, we find in practice that there's a trade-off between the data coverage and data quality used to train the execute-policy. We conjecture the reason is that the neural networks we used are still not powerful enough to capture all different modes, those low-quality data may affect the network learning, especially when the size of high-quality data is small. Using more powerful network architecture/representation learning/more advanced supervised learning techniques might help.\n \n>\"The paper contains a large number of spelling mistakes, which feels unprofessional\"\n\nWe are very sorry for this, we have checked and corrected all spelling mistakes in the revision.", " This paper proposes a new algorithm for the offline RL problem (learning a high-performing policy from a fixed dataset instead of directly interacting with an environment). The main idea is to decompose the agent into a *guide-policy* —— which suggests the highest value next state to transition to given the current state —— and an *execute-policy*, which produces the action that is likely to transition the agent to a given state in one step. By using this decomposition, the paper claims to avoid the pitfalls of methods that use an action-value function, while retaining the stability of imitation learning methods.\n \nStrengths:\n- The proposed decomposition of the agent and training process into guide and execute policies is a new and interesting contribution. \n- The main contributions of the paper are communicated clearly, with motivating examples and discussions to make the ideas understandable.\n- The experiments are reasonably well designed and explore interesting properties of the proposed POR algorithm beyond benchmark scores. I particularly like Sec. 5.3 for giving readers an interesting insight into how POR can be useful in certain situations.\n\nWeaknesses:\n- The proposed execute-policy is presented as an instance of RL via supervised learning popular more recently (citation to UDRL [1] is missing here), and this framework is discussed multiple times, but what is actually learned is in fact known as an \"inverse dynamics model\", so it would be more relevant to cite references to prior work on those. [2] is a nice paper from 2016 that learned one using neural networks, but the concept is older and more general.\n- The experiment in Sec. 5.3 is quite interesting, but it is unclear why the execute policy is not trained on $\\mathcal{D}_o$. If I understand correctly, the execute policy is not a typical policy but an inverse dynamics model as mentioned above, and it can be trained on data from any policy.\n- The paper contains a large number of spelling mistakes, which feels unprofessional. A spelling checker would easily find these.\n\n[1] Srivastava, R.K., Shyam, P., Mutz, F., Jaśkowski, W. and Schmidhuber, J., 2019. Training agents using upside-down reinforcement learning. arXiv preprint arXiv:1912.02877.\n\n[2] Christiano, P., Shah, Z., Mordatch, I., Schneider, J., Blackwell, T., Tobin, J., Abbeel, P. and Zaremba, W., 2016. Transfer from simulation to real world through learning deep inverse dynamics model. arXiv preprint arXiv:1610.03518.\n Please address the weaknesses listed above (and fix spelling). $\\alpha$ is a new \"conservative-ness\" hyperparameter similar to other offline RL algorithms, and it is not clear how to set it for a new use problem. If the authors have any algorithmic or practical suggestions for this, it would be great to have them included in the paper.\n", " The paper studies offline reinforcement learning (RL) and proposes to decouple the reward-maximizing objective in RL into learning a guide-policy and an execute-policy. For learning the guide-policy, the authors adopt the expectile regression and an additional BC loss. For learning the execute-policy, the author performs supervised learning by maximizing a likelihood. During the test, the guide-policy tells the execute-policy where it should go, and then the execute-policy conditioned on the current state and goal-state outputs the action. The authors also show the effectiveness of the method on a range of tasks (including the standard D4RL tasks and some transfer tasks). Strengths:\n+ The presented method is simple and well-motivated.\n+ The paper is overall well-executed. \n+ Experiments cover various scenarios, showing the effectiveness on D4RL tasks and the generalization ability of the execute-policy.\n\nWeaknesses:\n+ The proposed method is somewhat incremental, which combines the expectile regression (and a BC loss in Equation 4) for eliminating the OOD issue in offline setting and supervised goal-reaching execute-policy learning. \n+ The authors adopt the expectile regression from IQL, but do not explain the direct benefits of using expectile regression to learn g_\\omega rather than \\pi(a|s). \n+ Some references are misquoted, eg. seeing Line 264.\n+ The description of some references is inaccurate. For example, the authors state that One-step RL [3] and IQL use different weights to do behavior cloning. Is that true? \n+ The representation of some formulas is not rigorous enough. For example, a_0 in Equations 1 should be a_0 \\sim \\pi(a_0|s_0). a_t and s_t in Equation 2 should be given a clear description, eg. the relation to \\tau. 1. What is the direct benefit of using expectile regression to learn g_\\omega rather than \\pi(a|s). The authors state that \"we only need to learn a value function while IQL needs an additional Q-function to extract the policy\". However, the authors also introduce an additional guide-policy, as well as the execute-policy. \n2. Intuitively, the expectile regression can sometimes eliminate the OOD issue in offline RL, but the authors additional introduce a behavior cloning term in Equation 4. My question is, if we replace the expectile regression in Equation 3 with the standard regression loss and then adopt the behavior cloning loss in Equation 4, what will be the difference in performance. More ablation experiments are required. \n3. The authors use both expectile regression and BC loss for learning the guide-policy. Doesn't this make learning too conservative?\n4. In essence, the proposed method requires learning addition execute-policy. I do not see why there would be an added advantage over IQL on the D4RL tasks. \n5. In Section 4.1, the authors state that \"to generate better-than-dataset trajectories, the agent needs to take logical out-of-distribution actions\". However, the toy example assumes that offline data includes transitions of taking random actions at random states. So, is there any OOD action in this motivating example? Further, does the learned execute-policy enable the output of the so-called \"logical\" out-of-distribution actions? \n6. In Equation 4, are sampled states s and s' at two adjacent time steps? If so, I think the execute-policy will not output the (logical) out-of-distribution actions, given the current state s and goal-state s' are two adjacent states. yes", " This paper proposes an approach to offline RL that first learns a policy $\\pi(s' \\mid s)$ for predicting the next *state*, and then learns another policy for extracting the corresponding action. The next-state policy (\"guide policy\") is trained to maximize a learned value function while staying close to the next states in the dataset. The action policy (\"execution policy\") is trained using a standard inverse action loss. Empirically, the proposed method outperforms prior methods on many benchmark tasks, especially ones involving sub-optimal data. Additional experiments show that the method affords efficient transfer to new tasks by finetuning just one of the two policies.\n\n--------------------\n**After author response**: The authors did a great job addressing my questions and concerns. I continue to think that this is a strong paper and should be accepted. Strengths\n* The idea is novel and makes intuitive sense.\n* The experimental results are strong, with a lot of care put into making them reproducible.\n* The additional experiments were good for building intuition into the method.\n* Fig 1 is great for building intuition (though the description could be clarified).\n* It's great that the paper provides theoretical results relating the policy learning losses to the performance of the resulting policy.\n\nWeaknesses\n* It's not entirely clear *why* the proposed method should work, especially since the guide policy's job of predicting the next state seems onerous in high-dimensional tasks (e.g., AntMaze).\n* The writing is legible, but grammatical and spelling errors are frequent.\n\n\nMinor writing comments:\n* Abstract -- I didn't understand the method after reading the abstract (but the last two paragraphs of the intro do provide a good succinct description)\n* L12 \"Prophet\" -- I found this pretty confusing, as it was unclear how this relates to the execute and guide policies. I might recommend renaming everything to refer to its inputs and outputs (e.g., inverse action policy, next state policy)\n* L16 \"we highlight\" -- Great contributions!\n* L25 \"requires\" --> \"often entails\" (this isn't a strict requirement)\n* L29 \"can not ...\" -- Cite.\n* Introduction -- At some point, it would be useful to more formally characterize the difference between the IL and RL methods being discussed (e.g., \"We use imitation learning to refer to methods that do not learn a value function.\")\n* L49 \"optimal next state ... \" -- Great explanation.\n* L55 \"which owns logical\" -- I didn't understand this.\n* L60 \"We also show ...\" -- Great description of the contributions.\n* L64 \",\" --> \".\"\n* L140 \"second method\" -- Does this second method implicitly assume access to an oracle execute policy? If the action has never been taken before, then how would the agent know which action to take?\n* L141 \"acction\" --> \"action\"\n* L164 \"orronumously\" --> \"erroneously\"\n* L170 -- L179 -- It would be good to clarify that none of this material is novel, but instead is taken from IQL. This will help the reader distinguish the contributions of the paper.\n* Sec. 4.3 -- Cite many other papers that use inverse action models [1, 2], which are more relevant than RvS.\n* L206 \"conditioning variable can be automatically generated\" -- Great point.\n* Assumption 1 -- Is $(s_1, s_1')$ treated as a big, concatenated vector when taking the norm? Which norm is this?\n* Assumption 2 -- It seems like this can be made to hold by simply restricting the policy class. That is, this is not an assumption on the problem, and instead could be treated as part of the algorithm.\n* L224 -- L229, \"meaningless\", \"in vain\", \"plenty of worls\" -- Too colloquial for technical writing.\n* Eq 7 -- Precisely, how is $a^*$ defined?\n* Theorem 1 -- Does this suggest that $\\pi$ should be trained with the $\\ell-\\infty$ norm used for $\\epsilon$, or that $\\alpha = L_1 + L_2$?\n* Theorem 1 -- It would be good to acknowledge the limitation that computing the $\\ell-\\infty$ norm for $\\epsilon$ is quite hard, and its value will be quite large, potentially making the bound loose.\n* L253 \"benfits\" --> \"benefits\"\n* L255 \"on D4RL\" --> \"on the D4RL\"\n* L256 \"are consisted of\" --> \"consist of\"\n* (many places) -- \"Imitation\" --> \"imitation\"\n* L267 -- L275 -- Great job making the results reproducible.\n* Fig 2 -- I was unsure how to interpret the right panel of these plots. It seems like the higher values are in the bottom/left, but I'm unsure how that relates to $g(s)$ and $s'$.\n* L308 \"this two approach as\" --> \"these two approaches as\"\n* L318 \"lable\" --> \"label\"\n* L320 \"up tp\" --> \"up to\"\n* L361 \"may be biased\" -- I didn't understand this.\n\n[1] https://arxiv.org/pdf/1912.12773.pdf\n\n[2] http://proceedings.mlr.press/v70/pathak17a/pathak17a.pdf 1. Since the guide policy is predicting the next state, it's output could be very high dimensional, right? Does this pose a problem?\n2. How does network capacity affect the performance of the *guide* policy?\n3. Eq. 4 -- How carefully does $\\alpha$ have to be tuned?\n4. For the experiments in Fig 3, I suspect that most of the benefit from the \"mixed\" approach is that learning the execute policy on the expert data effective amounts to behavioral cloning (e.g., see analysis in [3]). If so, this benefit can be injected into the TD3+BC and CQL methods, too. For example, for TD3+BC, we could learn the Q-function on the combined dataset and train the actor on just the expert data. *How would these \"mixed\" versions of TD3+BC and CQL perform?*\n4. Can the method be used to perform transfer across agents with different action spaces? E.g., learn a guide policy for one robot and an execute policy for another robot, and then mix and match them.\n\n\n[3] https://arxiv.org/pdf/2206.03378v1.pdf, Section 3.2 Yes, the limitations are well addressed.", " This paper proposes a totally new paradigm to achieve Offline RL, compared to the alternatives that stitch actions for constraining the target policy to stay close to the behavior policy. Instead of composing actions, the proposed $POR$ allows state compositionality through learning a guided policy $g(s)$ producing **target state to reach** and optimizing the execute policy $\\pi(a|s, s')$ conditioned on the goal state in an imitation learning manner. After that, the agent makes decisions according to $\\underset{a}{\\mathrm{argmax}}\\ \\pi(a|s, g(s))$ in the inference stage. \n\nThe decoupled two-stage learning process benefits from the Imitation-based method's stability and the RL-based method's out-of-distribution generalizability. Theoretical analysis shows the lower bound of the proposed method and how this bound will be influenced by the guided policy $g(s)$. The comprehensive experiments show that $POR$ achieves SOTA on *Mujoco* and *AntMaze* dataset and new applications are enabled by this new learning paradigm. Strength:\n1) It is an interesting idea to design a goal-conditioned policy for Offline RL tasks. The learned policy only encodes state reachability via supervised learning and thus can learn stably. In addition, the out-of-distribution generalization is completed through stitching states via a variant of *Bellman Operator* and yields $s'=g(s)$ for providing a high-value target goal $s'$. \n2) The paper is well.\n3) Authors do comprehensive experiments to evaluate the new method and discuss its potential applications in the real world.\n\nWeakness and typos:\n1) Action selection should follow **Eq.(6)** in Algorithm 1, line 16 :).\n2) The axes can be added to Figure. 1 showing the toy example, so readers can know if the start index is 0 or 1. It indeed takes some time for me to find (5,4) and (6,5)\n3) The results of t-NSE are not clear enough, especially in Fig. 2, left panel, ant-maze-large. It only shows that the guided policy $g(s)$ can select some out-of-distribution goal states. However, it is hard to observe that these out-of-distribution states are in higher value than the states contained in the dataset. Consider using circles in the figure to highlight which area shows the $g(s)$ manages to generate high-value OOD states to help understand this figure.\n\n Q1: As stated in the paper, $POR$ can pick logical out-of-distribution actions for reaching the state-to-go produced by $g(s)$. However, in my view, although the $g(s)$ can generate an out-of-distribution goal state $s'$ for $\\pi$, the lack of transition $(s, a, s')$ may prevent $\\pi$ from arriving $s'$. Let's consider the toy example. When the agent is at $s=(2, 0)$ and the $\\hat{s}=g(s)$ indicates that $\\hat{s}=(3, 1)$ has the highest value, the policy is supposed to select the upper right action according to $\\hat{a}=\\underset{a}{\\mathrm{argmax}}\\ \\pi(a|s, \\hat{s})$. However, there is no such a transition $(s, \\hat{a}, \\hat{s})$ contained in the dataset, and hence the training policy $\\pi$ can not know how to arrive $(3, 1)$. Would the policy $\\pi$ fails to reach the target state $\\hat{s}$ in this situation? I am wondering whether this method can still work well on discrete control tasks." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 7, 6, 8, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 3 ]

[ "Ll7aJdQz7oe", "9Wo4XGd4LA2", "6h8nVNvyfnG", "nFZ3685pCVu", "ELLD1V0c9mL", "j_HThPtGF1h", "6h8nVNvyfnG", "-hNZGQ4AAQh", "nips_2022_CKbqDtZnSc", "nips_2022_CKbqDtZnSc", "nips_2022_CKbqDtZnSc", "nips_2022_CKbqDtZnSc" ]

[ "pHmZc94-nr", "dV5VuRHmrv", "_pzH64ZNIkZ", "UG-vK2d9xZ2", "1yVJxhbtR1L", "hxT02hTE_u", "YdmltLDNir5F", "y2Q3ddAQ6H", "PKUhjol0X03", "iQ4mTUewKVI", "gPMHtWAwjWB" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for the detailed feedback. We will improve our manuscript further in the final version.", " Thank you for your detailed response. I also apologize for the late reply --- there were significant changes to the paper and a lot of details to carefully review. I'd also like to apologize that some of my criticisms came off as harsh. This was certainly not my intention.\n\nI appreciate the authors' various clarifications and the new additions to the paper regarding related work and new theoretical contributions. In particular, tackling learnable encoder variance and low-rank design matrices are valuable novel contributions. For brevity, I limit my response to only the most relevant issues.\n\nI did not review Appendix C in detail. Though, from my quick look-through, this appears to be a valuable contribution that pushes beyond existing prior work.\n\n> First of all, we point out that Eqs. (2)-(5) are correct. They are just different from those of Lucas et al..\n\nMy issue was both technical and philosophical. Technically, Equation (3) contains the expected value of $\\log(p(y∣z))$, by definition this term, corresponding to the log density of a Gaussian, includes a partition function. Equality is used in the further derivation of the objective but the partition function is dropped. The philosophical issues that I raised in my review will be discussed further below.\n\n### Appendix D\n\nI must admit that I had a hard time following along with Appendix D. The proof is long and detail-oriented, perhaps necessarily. Early on, you take the optimal form of the parameters given in Proposition 1 to form the objective $G(s)$ (Equation 44). But the objectives no longer exactly align when we allow $\\eta_{\\textrm{dec}}$ (now $s$) to be a learnable parameter (as you have removed the $1/s$ factor in front). Nonetheless, I believe that the derivation is correct with these issues falling away in the details.\n\nI agree that this analysis is interesting and am more convinced that the inclusion of $\\beta$ changes the optimal solution non-trivially. I would like to point out that the general finding that $\\beta=1$ produces posterior collapse in the case where the $d - k + 1$ minor eigenvalues are equal is already known; see Appendix A.4 in the pPCA paper. In this case, posterior collapse _is_ the maximum likelihood solution. Further, this case is generally regarded as uninteresting (as stated in the pPCA paper) and, I would assume, is never the setting for posterior collapse occurring in deep latent variable models practically.\n\nOverall, I would still push back on the idea that \"being able to tune $\\beta$ can still be very important\" for **linear VAEs**. However, speculatively, these results do perhaps shine some light on why tuning $\\beta$ remains important for deep VAEs.\n\n\n### Remaining comments\n\n\n> First of all, the suggestion that “there is no need for a beta parameter as all low-rank stationary points become saddle points” is incorrect.\n\nI now agree with the authors on this point.\n\n> if applying A (making decoder variance learnable) can remedy B (posterior collapse), then [not] A causes B.\n\nI am worried that I am missing your point here. At no point did I imply that fixed decoder variance is the cause of posterior collapse. My point was that if the problem is remedied, then $\\beta$ becomes unimportant. The new Appendix D investigates this issue.\n\nThe conclusion of Appendix D, as it pertains to this point, is that there _is_ a case where the linear VAE (and pPCA) have posterior collapse when $\\beta=1$. I would argue that this case is relatively uninteresting; in the sense that users of linear VAEs need not worry about it for any realistic data sets. However, the apparent difference when including $\\beta$ certainly makes it worthy of study and I appreciate the authors going through the effort of proving this in response to my claim.\n\nFor what it is worth, I would be more precise in the main paper. The following sentence in your rebuttal; \"The global minimum solution becomes low-rank when the smallest $k+1$ eigenvalues of $\\Lambda$ are identical\", is considerably more informative than the current sentence in the main paper: \"Our analysis shows that even if $\\eta_{\\textrm{dec}}$ is learnable, posterior collapse can happen for some datasets.\" I'd suggest replacing \"for some datasets\" with \"when the smallest $k+1$ eigenvalues of $\\Lambda$ are identical\" (and also cite Tipping & Bishop).\n\n### Summary\n\nThe paper has been significantly improved by the authors. The author's addressed all of my biggest concerns and I have decided to increase my score to reflect this. I still feel that the presentation of the paper could be improved; ensuring that all of the mathematical details are correct, providing some more detail in proofs, and .\nMinor comment:\n\n- The form of the data-dependent variance in Appendix C is non-standard in practice (more typical would be to write $\\sigma(x) = e^{Cx + f}$).\n- L538 in Appendix D (and elsewhere), the partition function is missing factors of pi.", " > Please state the trace inequality that you are using exactly (trace of matrix product upper bounded by sum of product of eigenvalues). It is also worth including the derivation of equation 45 --- the proof is difficult to follow without this. Similarly for equation 46 (how did you verify that only the larger solution is related to the minimum?).\n- We added a description of the von Neumann inequality and how this equality is applied in the proof of proposition 2\n\n> Proof of proposition 3. It is written that the gradient is an increasing function and so the minimum value is determined when the gradient is zero. You also need to add the condition that ℓ′(σ)<0 for some σ which is then given in closed-form.\n\n- We added closed-form $\\sigma_+$ and $\\sigma_-$ such that $l’(\\sigma_+) > 0$ and $l’(\\sigma_-) < 0$. Therefore $l’(sigma) = 0$ indicates the global minimum.\n\nMinor comments:\n\n> L23: in what sense is this more general? Due to x and y? Or due to the stochastic reparameterization trick used in VAEs? There is also no marginalization over y and it is unclear what x and y represent here. (This is corrected later, in Section 3).\n- We have now modified this related sentence and fixed the expression.\n\n> L34: \"in the deep learning context\" -> suggests you are doing this. But it is a stretch to claim this when studying linear models only.\n- We modified this sentence to avoid overclaiming.\n\n> L44-45: a strong claim given referenced work. May need further justification.\n- Our updated analysis of the case when $\\eta_{\\rm dec}$ is learnable suggests that the results of Lucas et al. are insufficient to identify the cause of the collapse, and this claim is, in fact, strengthened by the additional analysis.\n\n> L245: your posterior collapse condition also depends on the decoder variance. You also write above that the decoder variance can also be controlled to alleviate posterior collapse. And finally, you do not analyze learning the decoder variance but if you included the partition function in the objective I expect that the same analysis of Lucas et al. could be repeated in this setting to the same general effect.\n- See the newly added analysis of the case of a learnable $\\eta_{dec}$ in Appendix Section C. Our result suggests that being able to tune $\\beta$ can still be very important.\n\n> L284: Similar to L245, this is only true when excluding the partition function from the objective (and restricting what we mean by \"the effect\").\n- True. We have now updated this statement according to the newly added theoretical analyses.\n\n> L326-327: \"Moreover, can we design a Bayesian-principled method for avoiding posterior collapse that does not involve hand-tuning β or ηdec?\" This is exactly one of the contributions of Lucas et al., in the case of the linear VAE.\n- As we have argued above and in the newly added theoretical analysis, the suggestion of Lucas et al. is insufficient to fully remedy the problem of posterior collapse.\n", " > It is also not surprising that the choice of the prior variance scale has no effect on posterior collapse. In the models considered (and in deep VAEs), this variance can be trivially accounted for by scaling the encoder and decoder weights up and down respectively. This can be understood easily via appendix B of Lucas et al., where such a transformation is shown under which the likelihood term is invariant --- this (full-rank) transformation can be chosen to adjust for any choice of prior variance.\n- We feel that this is an overinterpretation of Appendix B of Lucas et al. Lucas et al. does not point out or discuss its relevance to collapses. \n\n> And finally, the point could be made that beta VAEs are a common method used in practice and certainly they are worthy of study in their own right. Though, note that Lucas et al. discuss beta VAEs in Chapter 5 and draw a clear connection between the role of beta and of the observation noise in the general ELBO objective with Gaussian likelihood. In particular, that when treating both as fixed hyperparameters the exact same gradient update can be computed in either case.\n- We now added the case when the decoder variance is learned and when beta is included. This makes the result of Lucas a strict subset of our results because their result is only applicable when (1) $\\beta=1$, (2) $y=x$, and (3) $d_1<d_2$, whereas our updated analysis removes all three constraints. As you argued, it is important to consider the case when $\\eta_{\\rm dec}$ is learned and $\\beta$ is a hyperparameter, and our results are thus more relevant and general than the previous works.\n\n> The remaining contribution of this work that is not supported by prior work is that the authors consider more general models than VAEs (with different output dimensions). However, I do not consider this contribution to be significant enough to overcome the negative points discussed elsewhere in my review.\n- With the updated results, we are confident that this criticism no longer applies.\n\n> Missing discussion of related work\n- Thanks for pointing out the relevant works. We have now added all five works to the reference and discussed them where appropriate.\n\n> I feel that the following is too strong a statement: \"Up to now, there has not been any precise identification of neither the nature nor the cause of the posterior collapse problem.\" See discussion above.\n- We softened this statement to “Up to now, the study of nature or the cause of the posterior collapse problem is limited.”\n\n> A is positive semi-definite but it is then assumed that A1/2 is invertible. This is equivalent to assuming that all eigenvalues of the data covariance matrix are strictly positive, and it is stated in footnote that it is straightforward to extend to the low-rank case. But this is not evident to me from the proofs. For such a claim, ideally, the proofs in the supplementary material would apply to the low-rank case. You could keep the assumption in the main paper if it heavily simplifies notation etc., but I do not quite see how.\n- We have now updated Proposition 1 and the related parts to include the case when $A$ is not full-rank.\n\n> Why does notation appear at the end of the problem setting section? There is some duplication here, as much of it has already been defined above.\n- The point is just to summarize the notation in case the readers need a quick reference.\n\n>There is some confusing notation in the statement of Proposition 1. It swaps between U and W with U∗ doubly defined as the optimum of both objectives implicitly. Notation is also swapped in the proof. Further, the proof of Proposition 1 claims that these minimization problems are identical. It is have shown that, L_VAE(U,W)=L(U,A1/2W), which is not quite the claim (particularly in the case where A is not full-rank, then each minimizer of the former may correspond to a manifold of solutions for the latter). The proposition statement compares the minimizers, but note that both objectives are non-convex and a unique minimizer has not yet been established. Perhaps a more accurate statement is that any stationary point has these dual forms (under a full-rank A).\n- We have updated Proposition 1 and its proof to make it applicable to the case when A is not full-rank.\n\n> Proof of proposition 2. The proof begins by stating conditions on the global minimum; but this is a non-convex optimization problem and so this condition guarantees only a stationary point. As written, this is not incorrect but is a little confusing. The conditions are established for a stationary point and then solved for the global minimum by finding the stationary parameters with the smallest loss.\n- We updated the writing in the proof of proposition 2\n\n> I encourage the authors to state the SVD of Z within the proof again (otherwise the definition of F can be a source of temporary confusion).\n- We added the supplement information about SVD of Z in the proof of proposition 2\n\n", " We would like to thank you for the detailed criticisms and constructive feedback you gave. We have significantly updated the manuscript to make the generality of our analysis extend beyond that of the previous works. In particular, the following three additions make our results more general (and also more practically relevant) than that of Lucas et al.: \n1. when the decoder variance is learnable as in Lucas et al. (2019) [Appendix Section D]\n2. when the data covariance $A$ is not invertible [Updated Proposition 1 and its proof]\n3. when the encoder variance is dependent on the input, which is common in practice [Appendix Section C]\n\nSee the detailed reply below. Please let us know if there is any remaining problem, and we are willing to make further updates in future versions. At the same time, we feel that some of your original criticism may have been overly harsh, and we also point this out along the way. \n\n\n> The objective presented in Equations (2)-(5) is incorrect and does not include the log partition function from the decoder observation model. There is an argument to be made that this matches practical implementations or perhaps that this term can be ignored when the decoder variance is not learned. But as I will discuss further, this is a problematic assumption that has been carefully studied for this setting in prior work.\n- First of all, we point out that Eqs. (2)-(5) are correct. They are just different from those of Lucas et al.. We consider the case then the decoder variance is not learned, and, as you already point out: this matches common practice in the field. \n- That being said, we now added the analysis of the case when the decoder variance is learned in Section D. The updated result is more general than that of Lucas et al. because (1) the effect of having the $\\beta$ term is included, and is shown to have a crucial impact on the nature of the problem; (2) our result also applies to the case when $d_2\\neq d_0$, when $d_1\\geq d_2$ and when $d_1\\geq d_0$.\n\n>A limitation of the analysis, relative to Lucas et al., is that only the form of the global optimum is analyzed under this objective and none of the other stationary points are characterized. \n- We didn't consider this case because we found global minima sufficient to explain the experimental results. While it is interesting and not difficult to explore the other stationary points, we feel that it is more a digression rather than an addition to our results. \n\n> Moreover, beta plays the role of controlling the rank of the global optimum but in the linear VAE with learned decoder variance there is no need for a beta parameter as all low-rank stationary points become saddle points.\n- We point out that this statement is (1) mathematically incorrect and (2) is insufficient to understand posterior collapse even if it is correct. First of all, the suggestion that “there is no need for a beta parameter as all low-rank stationary points become saddle points” is incorrect. See Eq. (7)-(8) of Lucas et al.. The global minimum solution becomes low-rank when the smallest k+1 eigenvalues of \\Lambda are identical. Therefore, even if the decoder variance is learnable, posterior collapse can still happen in principle: this implies that a learnable decoder variance is not sufficient to remedy or account for the cause of the posterior collapse. Even if the statement is true, it is insufficient to suggest that a decoder variance is related to the cause of the posterior collapse. In essence, this criticism is based on the following logic: if applying A (making decoder variance learnable) can remedy B (posterior collapse), then A causes B. This logic is not scientific. Consider the following example. Suppose we have a noisy radio. The fact that removing the battery can remove the noise does not mean that the battery is the cause of the noise.\n- Therefore, it is both reasonable and important to study the case then the decoder variance is not learned, contrary to the criticism that it is “incorrect” to do so.\n\n> Further to this point, the authors write that \"one alternative way to fix posterior collapse[s] that have not been suggested in the field is to use a sufficiently small [decoder variance]\". But this is exactly the suggestion of Lucas et al. (!) where the decoder variance is treated both as a learned or fixed parameter.\n- This is a misinterpretation of our result. We mentioned this method only in order to criticize it. For example, we suggested that it does not agree with the Bayesian principle. We have updated the statement to avoid claiming this as a contribution.\n\n\n", " \nThank you very much for appreciating our work. We have added a section in the appendix to study the effect of a data-dependent encoder variance, and we clarify here the questions you raised. \n\n> I really miss a greater discussion of the link to (P)PCA in the paper. If I understand correctly, it is these links that are examined in the prior work by Lucas et al., but given that a linear VAE is basically a variant of PCA, I found it rather confusing that these links are not discussed in the paper.\n- More discussions of pPCA are added in the paper now. See the updated related works section and updated discussion after some of the theorems.\n\n> In line 179, it is stated that one solution to the posterior collapse problem is to pick the variance of the likelihood to be small. First, this doesn't really work for non-Gaussian likelihoods (which are the most common), and second it seems like a poor solution to effectively have a delta-likelihood in a probabilistic model (then there is little point in being probabilistic in the first place).\n- We agree. We only suggested it as a possible “technical” solution but not as a “good” solution. We have made this point clear in the updated draft.\n\n> Line 217 (a): it is argued that a learnable variance does not change the posterior collapse. This is under the assumption that the learnable variance is data independent. Do the comments still hold true if the variance is data dependent (as is the common case) ?\n- Thanks for this suggestion. We have added the theoretical analysis of the case when the encoder variance is dependent on the input data in Section C, and it shows that in the case of a linear dependence on the input data, our results and messages remain unchanged. This also answers the first weakness raised above and the second limitation pointed out below. That being that, we still do not consider the case when the decoder variance is data-dependent, given that it is rare in practice and that we do not think that it would play a significant role in influencing the collapses. \n\n\n> Line 262-275: It is observed that an optimum may exist where the parameters are equal to zero. Is it correctly understood that this is due to the data being zero mean, i.e. that the mode is for the model to predict the data mean?\n- Let us clarify that the main result does not assume that the data is zero-mean (e.g., our result applies to the case when $\\mathbb{E}[x] \\neq 0$ and/or $\\mathbb{E}[y]\\neq 0$). Thus, the optimum being zero is not a consequence of the data being zero-mean.\n\n", " Thank you very much for pointing out the typos and unclear points. We have fixed the typos in the updated manuscript. The following are the answers to your specific questions.\n\n> To the understanding of the reviewer, he believes that there is a physical interpretation of the term $\\frac{\\beta\\sigma_i \\eta_{dec}}{\\eta_{enc}}$. Inspired by the author(s) to explain $\\zeta_i$ as the strength of the alignment between the input $x$ and the target $y$ (Line 152), the term could be explained as the relative variance of the alignment between the model prediction. Then the thresholding in Eq(8) is to encourage U and V to be low-ranking by discarding the modes that the model variance scale $\\frac{\\beta\\sigma_i \\eta_{dec}}{\\eta_{enc}}$ is higher than the data signal $\\zeta_i$. Is the understanding correct?\n- Yes. You are correct to interpret $\\frac{\\beta\\sigma_i \\eta_{dec}}{\\eta_{enc}}$ as the model variance scale. However, we would not call it “relative” because we have shown that $\\sigma_i$ roughly scales as $\\eta_{enc}$, and so the model is more like the “absolute model variance scale.”\n\n> In Line 169, \"we have a complete posterior collapse: both U and V are identically zero\". It seems suffice to have posterior collapse with V (henceforth W as in line 97) being zero. Is there any significance for U being identically zero?\n\n- It is true that $W=0$ is sufficient to cause the complete collapse. Here, we mention $U$ and $W$ together because they are always zero simultaneously. $U=0$ has the effect of reducing the reconstruction variance to zero and is thus encouraged when $W=0$.\n\n> In line 176, \"one alternative way to fix posterior collapses ... is to use a sufficiently small $\\eta_{dec}$.\" Does it mean a more deterministic decoder is less likely to have posterior collapse? If so, does it generalise to nonlinear models?\n- Thanks for asking this question. It is not correct to say that a deterministic decoder is less likely to collapse. For example, see https://arxiv.org/abs/1901.08168 for how a deterministic autoencoder could have a collapse-like behavior when $L_2$ regularization. Mathematically speaking, the case of a VAE is similar to that of an $L_2$-regularized autoencoder because the randomness in the model causes an effective $L_2$-regularization. Thus, collapses are not unique to stochastic models. ", " We thank all the reviewers for their careful and constructive suggestions. In the update, we made significant updates to (1) make our theoretical analysis more comprehensive, (2) remove overclaiming, and (3) improve the discussion of the previous works.\nContent-wise, we significantly extended the theoretical analyses in the appendix to include cases asked about by the reviewers, making our work as comprehensive as possible. The major additions are colored in orange. We have added the following analyses\n1. when the decoder variance is learnable as in Lucas et al. (2019) [Appendix Section D]\n2. when the data covariance $A$ is not invertible [Updated Proposition 1 and its proof]\n3. when the encoder variance is dependent on the input, which is common in practice [Appendix Section C]\n\nWith these updates, we are confident that our work presents a solid and significant theoretical contribution to the community. In our specific replies to the reviewers, we clarify the misunderstandings or the points that were unclear. Also, if the reviewers point out any remaining problems, we are willing to make revisions to the manuscript accordingly.\n", " The work identifies the cause and the precise condition of posterior collapse of a linear latent variable model, and proposed methods to alleviate the problem by making the latent variance learnable. * Originality: The theoretical analysis and the direct pinpointing of the cause of posterior collapse problem for linear latent variable models are novel and insightful.\n * Quality: The derivation and theoretical analysis are sound. \n * Clarity: The paper was written in a clear and concise way, with detailed derivation to prove the propositions/corollary/theorems in the appendix. Some minor fixes are required, for which the reviewer listed in the Questions section.\n * Significance: Better understanding of the posterior collapse is important not only for theoretical understanding of deep learning, but also for designing better principles to build models and training strategies to improve training stabilities. This work is important on this front.\nOverall, the paper is theoretically sound, well written and carefully explained. The reviewer enjoys the reading. \n Some minor problems with the writing and derivations, for which the reviewer hopes the author(s) could clarify or fix:\n\nTypos:\n1. Line 117, $\\Psi$ should be $\\Sigma_Z$.\n2. Line 140 and Eq (7), $U=F\\Lambda P$, but in Line 466 of appendix, $U=Q\\Lambda P$. Also F has been used by SVD of Z in Line 116 and in proofs. Please fix U's definition here to make things consistent. \n3. Line 151 and 152, $\\sigma_i$ should be $\\zeta_i$, as introduced in Line 118.\n4. Line 200, it should be $\\mathrm{min}(d_0, d_2)$ instead of $\\mathrm{min}(d_1, d_2)$\n\nIn Appendix:\n\n 5. Line 444, the mean should be $U z + b_d$.\n 7. Eq 24, should be $\\frac{\\partial L_{VAE}}{\\partial b_d}$.\n 6. Eq 36, should be $VU^TU - Z^TU + \\cdots, sign is wrong for the second term.\n 7. Line 469, $\\Sigma$ should be $\\Sigma_Z$. Line 470, $\\sigma_i$ should be $\\zeta_i$ as of the singular value $\\Sigma_Z$. \n 8. Eq 52, $\\zeta^2_i$ should be $\\zeta_i$.\n\nDerivations:\n\n 9. For proof of Corollary 1, Appendix Eq (49) is correct. But going from App. Eq(49) to Eq(11) is unclear to the reviewer.\n 10. The proof of Proposition 4, in appendix. To reach Eq (23), it already used $b^*_{d}=E_x[y]$ The correct proof should be put together two equations for $\\frac{\\partial L_{VAE}}{\\partial b_d}=0$ and $\\frac{\\partial L_{VAE}}{\\partial b_e}=0$, two equations together to reach the $b^*_{d,e}$ solutions.\n 11. For Eq (44), the author(s) should add the condition, when the equality holds for von Neumann's Trace Inequalities. (btw, it's \"von Neumann, \"v\" without capitalisation) \n\nSome of questions to help the reviewer understand better:\n\n1. To the understanding of the reviewer, he believes that there is a physical interpretation of the term $\\frac{\\sqrt{\\beta}\\sigma_i\\eta_{dec}}{\\eta_{enc}}$. Inspired by the author(s) to explain \"$\\zeta_i$ as the strength of the alignment between the input $x$ and the target $y$\" (Line 152), the term could be explained as the relative variance of the alignment between the model prediction. Then the thresholding in Eq(8) is to encourage U and V to be low-ranking by discarding the modes that the model variance scale $\\frac{\\sqrt{\\beta}\\sigma_i\\eta_{dec}}{\\eta_{enc}}$ is higher than the data signal $\\zeta_i$. Is the understanding correct? \n\n2. In Line 169, \"we have a complete posterior collapse: both U and V are identically zero\". It seems suffice to have posterior collapse with V (henceforth W as in line 97) being zero. Is there any significance for U being identically zero? \n\n3. In line 176, \"one alternative way to fix posterior collapses ... is to use a sufficiently small $\\eta_{dec}$\". Does it mean a more deterministic decoder is less likely to have posterior collapse? If so, does it generalise to nonlinear models? The author(s) discussed some limitations and future work plans in 6. Outlook.", " This paper analyzes the globally optimal solutions to linear latent variable models. The authors show that these solutions exhibit low-rank structure that is equivalent to so-called posterior collapse.\n\nThe paper introduces a \"(generalized) variational autoencoder\" objective where the input and target spaces need not match. They show (Proposition 1) that solutions of the VAE objective with a fixed approximate posterior variance are aligned with solutions of a related matrix factorization problem (up to an [assumed] full-rank matrix multiplication). The optimal solution of this matrix factorization problem is computed and the (possibly) low-rank structure is characterized.\n\nThe results are then generalized (Section 4.3) to the setting where the variance of the approximate posterior is learned (and is assumed to be data-independent, which is optimal in the linear VAE setting [Lucas et al. 2019]). The authors interpret their results in terms of the posterior collapse phenomena that occurs in deep VAEs and empirically investigate their findings on synthetic data and the MNIST dataset.\n\n**Post-rebuttal update:** The authors have made significant changes to their paper following the reviews. With these, they address the vast majority of the issues that I presented below. They also pointed out that my claims on $\\beta$ being unnecessary in the linear VAE setting are not technically correct. Following this, I have updated my score to recommend that the paper be accepted. I hope that the authors will continue to improve the presentation of the work. ## Strengths\n\nThe theoretical results are well-connected and the proofs are (mostly) well-written and easy to follow. This is also true of the main paper itself (bar a few minor notational issues).\n\nThe authors analyze (a variant of) the beta-VAE objective which is widely used in practice.\n\n## Weaknesses\n\nThe objective presented in Equations (2)-(5) is incorrect and does not include the log partition function from the decoder observation model. There is an argument to be made that this matches practical implementations or perhaps that this term can be ignored when the decoder variance is not learned. But as I will discuss further, this is a problematic assumption that has been carefully studied for this setting in prior work.\n\nA limitation of the analysis, relative to Lucas et al., is that only the form of the global optimum is analyzed under this objective and none of the other stationary points are characterized. Moreover, beta plays the role of controlling the rank of the global optimum but in the linear VAE with learned decoder variance there is no need for a beta parameter as all low-rank stationary points become saddle points. I suspect that all other stationary points here are also saddles, but many of the higher rank solutions have larger loss until beta is reduced. Further to this point, the authors write that \"one alternative way to fix posterior collapse[s] that have not been suggested in the field is to use a sufficiently small [decoder variance]\". But this is exactly the suggestion of Lucas et al. (!) where the decoder variance is treated both as a learned or fixed parameter.\n\nIt is also not surprising that the choice of the prior variance scale has no effect on posterior collapse. In the models considered (and in deep VAEs), this variance can be trivially accounted for by scaling the encoder and decoder weights up and down respectively. This can be understood easily via appendix B of Lucas et al., where such a transformation is shown under which the likelihood term is invariant --- this (full-rank) transformation can be chosen to adjust for any choice of prior variance.\n\nAnd finally, the point could be made that beta VAEs are a common method used in practice and certainly they are worthy of study in their own right. Though, note that Lucas et al. discuss beta VAEs in Chapter 5 and draw a clear connection between the role of beta and of the observation noise in the general ELBO objective with Gaussian likelihood. In particular, that when treating both as fixed hyperparameters the exact same gradient update can be computed in either case.\n\nThe remaining contribution of this work that is not supported by prior work is that the authors consider more general models than VAEs (with different output dimensions). However, I do not consider this contribution to be significant enough to overcome the negative points discussed elsewhere in my review.\n\nTo my knowledge, the authors have provided novel theoretical results. They generalize past results in the sense that they account for a KL-annealing term and a different output dimensionality. But they are weaker in the ways discussed above. Considered in balance, I feel that these contributions are not significant enough to warrant acceptance.\n\nFinally, the empirical results may not be a primary contribution of this work but they are markedly weaker than similar publications at previous venues. The authors train linear VAEs on MNIST and a synthetic dataset. And two-layer fully-connected encoder/decoder networks are also trained on MNIST. [Note that the variance is not global as in the theoretical analysis but is instead data-dependent, but I agree with the authors that this is a reasonable choice.] For comparison, Lucas et al. 2019 train fully-connected VAEs on MNIST, and convolutioanl VAEs on CelebA. Their empirical evaluation included different objectives, varying encoder architectures, KL annealing schedules, fixed/learned decoder variance, and more. Dai et al. 2020 train on MNIST, Fashion-MNIST, SVHN, CIFAR10, CIFAR100, and CelebA. They used fully-connected, convolutional, and residual architectures and evaluated different objectives and model capacity. Shekhovtsov et al. 2022 (see below) have a similarly thorough empirical evaluation. In summary, while I see no significant issue with the empirical evaluation in this paper I also am unable to recommend it as a strength of the work relative to other papers investigating the same issue.\n\n### Missing discussion of related work\n\nThe connection between linear VAEs and matrix factorization are already well-known [1,2,3]. In these references, non-amortized variational inference is used but many of the findings overlap with that of this paper. A suitable discussion and comparison must be included.\n\nSome other work investigating posterior collapse has also been missed in discussion [4,5].\n\n[1] S. Nakajima and M. Sugiyama. Implicit regularization in variational bayesian matrix factorization. ICML, 2010.\n\n[2] S. Nakajima, M. Sugiyama, S. D. Babacan, and R. Tomioka. Global analytic solution of fully observed variational bayesian matrix factorization. Journal of Machine Learning Research, 2013.\n\n[3] S. Nakajima, R. Tomioka, M. Sugiyama, and S. D. Babacan. Condition for perfect dimensionality recovery by variational bayesian PCA. Journal of Machine Learning Research, 2015. \n\n[4] A. Shekhovtsov, D. Schlesinger, and B. Flach. VAE approximation error: ELBO and exponential families. ICLR, 2022.\n\n[5] J.Lücke, D. Forster, and Z. Dai. The evidence lower bound of variational autoencoder converges to a sum of three entropies. ICLR, 2022. I feel that the following is too strong a statement: \"Up to now, there has not been any precise identification of neither the nature nor the cause of the posterior collapse problem.\" See discussion above.\n\n$A$ is positive semi-definite but it is then assumed that $A^{1/2}$ is invertible. This is equivalent to assuming that all eigenvalues of the data covariance matrix are strictly positive, and it is stated in footnote that it is straightforward to extend to the low-rank case. But this is not evident to me from the proofs. For such a claim, ideally, the proofs in the supplementary material would apply to the low-rank case. You could keep the assumption in the main paper if it heavily simplifies notation etc., but I do not quite see how.\n\nWhy does notation appear at the end of the problem setting section? There is some duplication here, as much of it has already been defined above.\n\nThere is some confusing notation in the statement of Proposition 1. It swaps between $U$ and $W$ with $U^*$ doubly defined as the optimum of both objectives implicitly. Notation is also swapped in the proof. Further, the proof of Proposition 1 claims that these minimization problems are identical. It is have shown that,\n$L_{\\mathrm{VAE}}(U,W) = L(U, A^{1/2}W)$, which is not quite the claim (particularly in the case where $A$ is not full-rank, then each minimizer of the former may correspond to a manifold of solutions for the latter). The proposition statement compares *the* minimizers, but note that both objectives are non-convex and a unique minimizer has not yet been established. Perhaps a more accurate statement is that any stationary point has these dual forms (under a full-rank $A$).\n\n#### Proof of proposition 2\n\nThe proof begins by stating conditions on the global minimum; but this is a non-convex optimization problem and so this condition guarantees only a stationary point. As written, this is not incorrect but is a little confusing. The conditions are established for a stationary point and then solved for the global minimum by finding the stationary parameters with the smallest loss.\n\nI encourage the authors to state the SVD of Z within the proof again (otherwise the definition of F can be a source of temporary confusion).\n\nPlease state the trace inequality that you are using exactly (trace of matrix product upper bounded by sum of product of eigenvalues). It is also worth including the derivation of equation 45 --- the proof is difficult to follow without this. Similarly for equation 46 (how did you verify that only the larger solution is related to the minimum?).\n\n#### Proof of proposition 3\n\nIt is written that the gradient is an increasing function and so the minimum value is determined when the gradient is zero. You also need to add the condition that $\\ell'(\\sigma) < 0$ for some $\\sigma$ which is then given in closed-form.\n\n\nMinor comments:\n\nL23: in what sense is this more general? Due to `x` and `y`? Or due to the stochastic reparameterization trick used in VAEs? There is also no marginalization over `y` and it is unclear what `x` and `y` represent here. (This is corrected later, in Section 3).\n\nL34: \"in the deep learning context\" -> suggests you are doing this. But it is a stretch to claim this when studying linear models only.\n\nL44-45: a strong claim given referenced work. May need further justification.\n\nL245: your posterior collapse condition also depends on the decoder variance. You also write above that the decoder variance can also be controlled to alleviate posterior collapse. And finally, you do not analyze learning the decoder variance but if you included the partition function in the objective I expect that the same analysis of Lucas et al. could be repeated in this setting to the same general effect.\n\nL284: Similar to L245, this is only true when excluding the partition function from the objective (and restricting what we mean by \"the effect\").\n\nL324: \"to [what] extent the result carries\"\n\nL326-327: \"Moreover, can we design a Bayesian-principled method for avoiding posterior collapse that does not involve hand-tuning β or ηdec?\" This is exactly one of the contributions of Lucas et al., in the case of the linear VAE. Limitations are discussed adequately within the paper. However, it is my feeling that the framing of the paper relative to the related work is inaccurate and the discussion of limitations should be updated therein.", " The paper provides a theoretical analysis of (a simplified) linear VAE in order to improve our understanding of the posterior collapse often observed with similar nonlinear Bayesian models. The main finding is that these models naturally perform a thresholding of singular values, which is at the root of the issue. This can then be linked to the prior on the mean. ### Strengths\n* The paper is fairly easy to read, and the authors do a nice job of summarizing their findings along the way to keep the reader engaged.\n* The main findings are interesting, and inspirational.\n* The empirical results on nonlinear models, while not the focus of the paper, provides evidence in support of the findings from linear models may generalize.\n\n### Weakness\n* The paper treats both encoder and decoder as data independent, which is quite far from the usual VAE setting. I understand that using linear models to predict uncertainties would be rather useless, but I still think it would be good if the paper acknowledged the limitation.\n* I really miss a greater discussion of the link to (P)PCA in the paper. If I understand correctly, it is these links that are examined in the prior work by Lucas et al., but given that a linear VAE is basically a variant of PCA, I found it rather confusing that these links are not discussed in the paper.\n* In line 179, it is stated that one solution to the posterior collapse problem is to pick the variance of the likelihood to be small. First, this doesn't really work for non-Gaussian likelihoods (which are the most common), and second it seems like a poor solution to effectively have a delta-likelihood in a probabilistic model (then there is little point in being probabilistic in the first place).\n\n### Minor comments\n* Line 105 says that A is full rank, while in 111 it is semidefinite. That's confusing.\n* In line 136, it is stated that Sigma is learnable, yet earlier it was not learnable. Again, confusing.\n* In lines 299-300 it would be good to use the proper notation $10^{-3}$ rather than 1e-3.\n* Late in the paper it is stated that the introduction of beta (as in the beta-VAE) makes little sense from a probabilistic perspective. I think this should be stated when beta is initially introduced. * Line 217 (a): it is argued that a learnable variance does not change the posterior collapse. This is under the assumption that the learnable variance is data independent. Do the comments still hold true if the variance is data dependent (as is the common case) ?\n* Line 262-275: It is observed that an optimum may exist where the parameters are equal to zero. Is it correctly understood that this is due to the data being zero mean, i.e. that the mode is for the model to predict the data mean? The most fundamental limitation of the paper is that it studies a linear model in the hope that this may tell us something about nonlinear models. Here we can only hope. The paper is quite clear on this limitation.\n\nA second limitation is that all noise variances are assumed to be data independent, which is quite far from common practice (esp. for the encoder) and is at odds with some of the driving ideas of VAEs. I think the paper could be more clear about this limitation." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 8, 7, 8 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 3, 4, 3 ]

[ "dV5VuRHmrv", "_pzH64ZNIkZ", "iQ4mTUewKVI", "iQ4mTUewKVI", "iQ4mTUewKVI", "gPMHtWAwjWB", "PKUhjol0X03", "nips_2022_zAc2a6_0aHb", "nips_2022_zAc2a6_0aHb", "nips_2022_zAc2a6_0aHb", "nips_2022_zAc2a6_0aHb" ]

[ "lPkjXkeA_f", "0HbMW58Nip4", "No5WLH60hoG", "J0Xz25xwSZN", "qG_os2P3fv8", "cSbSqvBRFKW", "bipFrzVe_MC", "UTvh-8B78ju", "ICg9kou8vnd", "14MMqUee_n", "iR3f1_e5LHu", "ngmn3CYxeoH", "WvWCwrCG9J2", "k50T6lBAj_X", "Xbh7KWQrIov" ]

[ "author", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " **We are afraid to say that both convergence proofs have severe logical flaws, which are unacceptable for us in any case.** Again, the convergence claim *on the null set* is vacuously true. *The reviewer *fhr7* must show a counter-example that does NOT converge to the true model in a finite-data regime.* Otherwise, there's nothing to prove.\n\nWe reject all of the follow-up requests. It's *our courtesy* to include the CoreMSE result in our Appendix as a response to the request in the rebuttal. The convergence proof is nothing to do with our main results. **We firmly emphasize that it's not our standard to include inconsistent results in our main article.** \n\n", " Thank you for the response to the review comments.\n\n1. Regarding the comparison against ELR schemes, while I agree with certain points argued by the authors, it would be beneficial to include at least a brief discussion between the proposed BalEntAcq with other acquisition functions used in the ELR strategy.\nIf the authors wish to do so, they may choose a few representative ELR schemes of their choice, and discuss the pros/cons/limitations of these schemes in comparison with BalEntAcq.\n\n2. The \"small-data\" setting occurs frequently in various scientific domains, including life sciences and materials science, where the labeling cost might be formidable due to the time/cost/labor that would be needed for performing experiments to label data points.\nIt appears that the authors mainly have \"computational cost\" in mind - which may be why they mention that \"the cost of active learning is typically higher than the cost of getting all label information\" - but this is not necessarily true in various science domains.\n\n3. It appears that the authors unfortunately misunderstood the \"convergence\" results in the two papers mentioned.\nThe main issue is whether the acquisition of the labels for the data points selected based on a given acquisition function will make the model learned thereupon converge to the \"true\" model.\nIn the case of classification, this \"model\" will be an (unknown) feature-label distribution, which needs to be inferred from the data.\nGiven the posterior of the parameters defining a feature-label distribution, the optimal classifier for this uncertain feature-label distribution will be the OBC (optimal Bayes classifier).\nAnd the mentioned papers show that their classifier converges to this OBC.\n\nIf the authors believe that the convergence guarantees of these recent Bayesian active learning schemes are meaningful *only* in restrictive settings, it would be beneficial to include a brief discussion in the manuscript on this aspect for future readers.\nAlso provide insights into the convergence of the model learned via the data points labeled using the proposed acquisition function.\n", " Thank you very much again for taking the time. We tried our best to address most of the concerns as much as we could. We hope that our rebuttal mitigates your concerns accordingly.", " We included more experiments in the revision. Please check both the main draft and supplementary materials. Here's the summary.\n* **Single acquisition BADGE in MNIST** - See Figure 3 and Table 1 in the main article\n - We added a single acquisition BADGE result in MNIST. **We observe that the performance of BADGE is very similar to the entropy. So it's worse than our BalEntAcq.** This is reasonable because BADGE focuses on maximizing the loss gradient similar to Entropy, as explained in Section 3.3.\n * **Another BNN experiment with Variational dropouts** - See Appendix A.18\n - We added Bayesian neural network experimental results with $3\\times$CIFAR-10 when variational dropouts [1] have been applied in Appendix A.18. Again, we observe a consistent outperformance compared to other linearly-scalable methods. Also, our BalEntAcq eventually merges with the performance of BADGE.\n - This additional BNN result should be very important because it implies our method's extendability to any other BNN frameworks.\n - Therefore, we hope this addition mitigates your concerns about the extendability to other BNNs.\n\n* **Comparison with other baselines** - no addition\n - Thank you for suggesting to add more baselines. *We see that this is an additional request after the initial review.* Of course, it's helpful to include many other baselines. However, **given the limited time and computation resources, comparing our method with many other existing methods is beyond our scope.** We do not have a computational infrastructure to train a large batch with a large image dataset of active learning like cluster-margin. We recognize that TypiClust is a recent work, but focusing on a better initial selection is beyond our scope. From our point of view, it's NOT a fair comparison with other selection methods like Figure 4 [2], i.e., we should match the same initial selections for all methods. That being said, we can share our performance expectations of SIMILAR.\n - SIMILAR is a generalized framework with submodular functions. But **figuring out the best combination of the embedding and the target submodular function is still open to the user.** Naive choice of submodular function should not perform better.\n - For example, if we focus on the feature embedding and the Euclidean distance similarity with *LogDet/MI*, the performance should be similar to CoreSet, as we already presented in Appendix A.15. LogDet/MI is equivalent to the selection of k-DPP (determinantal point process) method. Still, it only focuses on the diversification of feature space with Euclidean distance. As the authors of [3] suggested, it is important to accommodate both the decision boundary and the diversification with the k-DPP method. So the performance improvement in active learning with feature embedding and the euclidean distance similarity should be limited because it does not consider any information about the decision boundary (or loss function).\n - If we focus on the submodular joint mutual information, it should be the same as BatchBALD as we presented in Appendix A.15.\n - If we focus on the gradient embedding, it would be similar to BADGE. So we don't see any good reason to compare it further.\n - As Figure 6 of the SIMILAR paper [4] suggested, the performance of LogDet is worse than BADGE in CIFAR-10.\n\nWe hope that this helps you mitigate your further concerns. Thanks again for taking the time for our paper.\n\n[1] Kingma, Durk P., Tim Salimans, and Max Welling. \"Variational dropout and the local reparameterization trick.\" Advances in neural information processing systems 28 (2015).\n\n[2] Hacohen, Guy, Avihu Dekel, and Daphna Weinshall. \"Active learning on a budget: Opposite strategies suit high and low budgets.\", ICML 2022.\n\n[3] Bıyık, Erdem, et al. \"Batch active learning using determinantal point processes.\" arXiv preprint arXiv:1906.07975 (2019).\n\n[4] Kothawade, Suraj, et al. \"Similar: Submodular information measures based active learning in realistic scenarios.\" Advances in Neural Information Processing Systems 34 (2021): 18685-18697.", " 1) Thank you for adding the non-Bayesian AL model, BADGE, to the experiments and explaining why you do not compare with it in the first place. I agree that BADGE is not ``linearly scalable standalone measure'' and computational complexity is high. CoreSet and BADGE are strong baselines. It is better to include them in the experiment to show the performance gap even though they have high computational complexity. Recent AL algorithms, e.g., Cluster-Margin (large batch size), SIMILAR (imbalance and rare classes), and TypiClust (low budget regime), consider a diverse set of datasets.\n2) The authors added another dataset SVHN to the main experiment. \n3,4) The authors added discussion and complexity analysis. \n\nSome concerns about the baselines are solved. The rating is raised accordingly.", " Thank you very much for reviewing our paper. After receiving all reviews, we realized that our work has been highly under-valued in the following aspects:\n - Most reviewers didn't validate our mathematical contributions properly. Our paper leverages a unique mathematical/or information-theoretic tool, a.k.a. **point process entropy**, to quantify the marginalized joint information between the model and the output.\n - **Point process entropy is neither Shannon entropy nor differential entropy. It is a new type of entropy in AI/ML community.** \n - We should NOT expect that the point process entropy is always similar to Shannon entropy or differential entropy. The behavior of the point process entropy is sometimes completely different from Shannon entropy (for discrete domain) and differential entropy (for continuous domain). \n - Our understanding of the point process entropy is still limited. For example, as shown in the form of *MJEnt[x]*, the derived form involves both the differential entropy and Shannon entropy. There has been no clear interpretation of the quantity which contains both differential entropy and Shannon entropy in the literature. **Our Theorem 4.1 connects two different entropies and provides a deep insight into the differential entropy and Shannon entropy simultaneously.**\n - Nevertheless, Beta approximation combined with point process entropy facilitates the theoretical study of Bayesian neural networks. That's how we could develop our own active learning method.\n - Again, **Theorem 4.1 is our main theorem** to justify the BalEntAcq[x] form as a ratio between MJEnt[x] and Shifted entropy. **We emphasize that this theorem is highly non-trivial.** We spent a significant amount of time developing Theorem 4.1 and ensuring the proof's correctness.\n\n- To illustrate a better insight into our proposed method, we added **Appendix A.13**. Our proposed method BalEntAcq[x] is strongly aligned with active learning with abstention [1,2], which **guarantees to save labels exponentially for binary classification problems.** It has been well-known that active learning cannot perform better than passive learning (random selection) in general [3]. However, we can still achieve exponential savings on the labels by leveraging active learning with abstention. Therefore, these lines of work theoretically validate the benefits of active learning algorithms in practice. Our proposed method is well aligned with this theoretically guaranteed active learning algorithm (in terms of exponential savings).\n\nSo we revised and uploaded our main article and the supplementary material by addressing the majority of raised issues. We used the *red* color wherever we revised. *In the supplementary material, we also included our active learning source code under \"active_learning_src\".* \n**We hope this rebuttal session helps you understand our core contributions properly, and we would be very grateful if you could re-evaluate our works. Thank you very much.**\n\n[1] Zhu, Yinglun, and Robert Nowak. \"Efficient Active Learning with Abstention.\" arXiv preprint arXiv:2204.00043 (2022).\n\n[2] Puchkin, Nikita, and Nikita Zhivotovskiy. \"Exponential savings in agnostic active learning through abstention.\" Conference on Learning Theory. PMLR, 2021.\n\n[3] Castro, Rui M., and Robert D. Nowak. \"Minimax bounds for active learning.\" IEEE Transactions on Information Theory 54.5 (2008): 2339-2353.", " Thank you very much for validating our work. We would be happy to answer any further details if you have any questions or concerns to increase your confidence.\n\n- Benefits of Beta approximation\n - For empirical validation of Beta approximation, we already added an extensive numerical validation in Appendix A.8. It would be helpful to check this.\n - We may understand the Beta approximation **as a calibration step of the predictive output.**\n - By doing so, we have a much more detailed output distribution resolution (=density function) **with very few parameters**. So we can derive more tangible insights about uncertainties.\n - For example, given $\\text{Beta}(\\alpha,\\beta)$, the epistemic uncertainty is maximized as $\\alpha,\\beta\\to 0$. Instead, the aleatoric uncertainty is maximized as $\\alpha,\\beta\\to +\\infty$.\n - If we take a non-parametric approach such as ELR (please refer to the comments to the reviewer *fhr7*), it could give more flexibility. But typically, we end up with high computational cost problems. \n - Instead, our Beta approximation facilitates a closed-form formula such as MJEnt[x]. So we were able to design a linearly-scalable acquisition measure.\n\n- Lack of Limitation\n - We added the Limitation section that our experiments had been limited to dropout-based BNNs.\n\nThank you very much again.", " Thank you for raising many issues. We want to clarify and explain the details.\n\n- Regarding the conflict with \"BABA: Beta Approximation for Bayesian Active Learning,\" here's our response.\n - To the best of our knowledge, BABA has never been officially published. The reviewer might need to consider many other possibilities without any prejudice.\n - We sent our private comment to Senior AC about addressing this issue.\n - We also note that Theorem 3.1 provides more insight than the DirichletBALD[x] result of \"Analytic Mutual Information in Bayesian Neural Networks.\" i.e., BetaMarginalBALD[x] tells us that BALD[x] is a function of marginals. Thinking about the dependency in Dirichlet distribution between marginals, it is not trivial to conclude this insight - BALD[x] is a function of marginals. This implies that the core information is embedded in the marginal distribution. Therefore the choice of MJEnt[x] (*marginalized* joint entropy) could be the key term in BalEntAcq[x]. \n\n- Beta Approximation\n - **We already explained the justification of the Beta approximation in Section 3.1.** Here's the short outline of the approximation. We are happy to answer more details if you are not convinced.\n - We consider BNN as a proxy of the Gaussian process [1].\n - Taking softmax would produce Dirichlet distribution [2].\n - Each marginal of Dirichlet follows the Beta distribution.\n\n - Therefore, our Beta approximation is well-supported by the theory. **One can always criticize that any parametric family might not fit perfectly.** For example, people may criticize the linear regression model because data distribution is not linear. However, linear model tells us how those variables are linearly related. This is important because we can *understand* how different variables are linearly correlated. It's also crucial when we analyze the noisy dataset through linear models. Similarly, the Beta distribution family $\\text{Beta}(\\alpha,\\beta)$ is one of the most richest and flexible parametric families to generate random values on $[0,1]$. This parametric modeling helps humans to explain/understand the behavior of the BNN. This way, we can derive and understand important insights explained in Section 3.4 and Appendix A.7-A.10 through closed forms.\n\n- Decomposition in MJEnt[x]\n - After applying Jensen's inequality, **MJEnt[x] term is a valid decomposition by leveraging point process entropy on each marginal.** Please check the equation (8) in Appendix A.1. There's nothing wrong with our statement. *Decomposition does not require independency between terms.*\n - MJEnt[x] involves both differential entropy (in Posterior Uncertainty) and Shannon entropy (in Epistemic+Aleatoric Uncertainties). With the current textbook information theory [3], there's no proper way to interpret the MJEnt[x] term involving differential entropy and Shannon entropy. Nevertheless, we have successfully proved Theorem 4.1. Theorem 4.1 provides the most profound insight into understanding the MJEnt[x] term. **Theorem 4.1 is a highly non-trivial statement.**\n\n- Section 3.3\n - We understand similar observations with specified papers. However, **the nuances of \"over-confident\" and \"over-fitting\" are entirely different.** For example, there is a paper \"Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem\" [4]. We can't say, \"Why ReLU networks yield **over-fitted** predictions far away from the training data and how to mitigate the problem.\" In other words, \"over-confident\" is meant for the test data at the inference stage. And \"over-fitting\" is meant for the specific training data point at the training stage.", " \n- No justification of ratio term in BalEnt[x]\n - **The reviewer's perception is wrong.** As the reviewer *Swnb* agreed, Theorem 4.1 justifies the ratio term of BalEnt[x].\n\n- Relationship with BABA\n - BABA[x] is a rescaled term of BalEntAcq[x]. i.e., $\\frac{\\text{BALD}[x]}{H(Y)+\\log 2}\\text{BalEntAcq}[x]=\\text{BABA}[x]$ when $\\text{MJEnt}[x]\\geq 0$. The criticism of BABA[x] has been a lack of motivation in the ratio. However, BalEntAcq[x] is supported by Theorem 4.1.\n\n- $P4 = \\text{BalEnt}[x]^{-1}$.\n - We added P4 in Appendix A.16. P2 and P4 show almost the same performance because negative BalEnt[x] points have not been acquired in our experiments. However, it does not make sense once P4 reaches the negative sign. As P1 result suggests, adding a high magnitude negative BalEnt[x] point (which will be prioritized when P4 reaches the negative sign) should deteriorate the performance of active learning. So it's not a consistent way to prioritize points.\n\n\n[1] Gal, Yarin, and Zoubin Ghahramani. \"Dropout as a bayesian approximation: Representing model uncertainty in deep learning.\" international conference on machine learning. PMLR, 2016.\n\n[2] MacKay, David JC. \"Choice of basis for Laplace approximation.\" Machine learning 33.1 (1998): 77-86.\n\n[3] Cover, T.M. and Thomas, J.A., 2006. Elements of information theory 2nd edition.\n\n[4] Hein, Matthias, Maksym Andriushchenko, and Julian Bitterwolf. \"Why relu networks yield high-confidence predictions far away from the training data and how to mitigate the problem.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2019.", " Thank you for reviewing our paper. We see that the reviewer *xmoA* didn't validate any of our theoretical development. **We request to focus on our theoretical contribution.** \n\nFirst of all, there's a huge misunderstanding about our intention to set baselines.\n- We didn't make any statement like \"we can not apply non-Baysian AL algorithms to BNNs\" in our paper. **It's the reviewer's wrong perception.** The second question is not a valid request.\n- We have chosen BALD, Entropy, MeanSD, and PowerBALD because they are linearly scalable standalone measures. So it's a **FAIR** comparison.\n- As a response, we added BADGE in our main experiments to better understand our BalEntAcq performance. We also added SVHN in our main experiments. Please check our updated paper in Section 5.\n - In Appendix A.15, we added $3\\times$MNIST and $3\\times$CIFAR-10 datasets with **a smaller acquisition size**. In these experiments, we added Variational Ratios, BADGE, BatchBALD, and CoreSet. **We don't see any performance drops of our BalEntAcq in other acquisition sizes.**\n\nSecond, we have tested various datasets with MNIST, CIFAR-100, $3\\times$CIFAR-100, and TinyImageNet. **We cannot understand why they are limited choices of datasets.**\n- Regarding the weakness of data formats, **it's not a valid point, again.** Please check Appendix A.12.5 to get an idea of the input data format.\n - For example, our fixed feature experiments such as CIFAR-100 or $3\\times$CIFAR-100 are equivalent to tabular datasets. \n - ResNet-50 with SimCLR [1] generates 2048 dimensional tensor from each image. So the entire training dataset is $50000\\times 2048$ sized tabular data.\n - MNIST is a single-channel gray image dataset. $1\\times28\\times 28$ size.\n - TinyImageNet is a three-channel realistic RGB image dataset. $3\\times64\\times 64$ size.\n - With the above datasets, we tested the performance of our BalEntAcq with different dropout-based BNN architectures.\n\nThird, regarding the experiments with other Bayesian neural networks, **we clearly stated that we would focus on Dropout-based BNNs in Introduction.**\n - L37-39. \"we focus on developing an active learning framework in the Bayesian deep neural network model by leveraging the Monte-Carlo (MC) dropout method as a proxy of the Gaussian process [26], which may facilitate further analysis.\"\n - Nevertheless, in response, we stated in the Limitation section that our experiments had been limited to dropout-based BNNs.\n - But, our theoretical development does not require special architectural assumptions if we can apply Beta approximation. So one can apply our proposed method to any Bayesian classification network with Beta approximation.\n\nLastly, we added a time complexity analysis in Appendix A.14.\n - For BADGE, we tested it with k-means++ instead of k-DPP. In either case, BADGE requires a more expensive computational cost. \n - Instead, our proposed method BalEntAcq is a linearly-scalable solution. Performance is comparable with BADGE. **In SVHN, TinyImageNet, our BalEntAcq performs better.**\n\n[1] Chen, Ting, et al. \"A simple framework for contrastive learning of visual representations.\" International conference on machine learning. PMLR, 2020.", " Thank you for reviewing our paper. Here's our overview of the contributions of the suggested two papers. \n\n**We conclude that [1] showed contrived convergence results.** So insights from [1] and its descendent [2] are entirely misleading. Mathematically, Theorem 1 in [1] has no contribution at all. It assumes the finite size of the data and finite parameter space. So there's no room to play with infinite limits. Under the finite setting, we can always guarantee convergence because at some finite time $T$, **any active learning algorithm will acquire all data points.** This implies that any algorithm can achieve the optimal classifier in a finite time. \n\nMoreover, even if we follow the proof, **we cannot guarantee uniform convergence under a countably (or uncountably) infinite data space $X$**, which is the key component of the proof of Theorem 1 in [1]. Therefore all the notions of \"almost sure\" and \"infinitely often\" are misleading. Under the finite domain, those infinitely often sets are measure-zero and empty sets. So logically, Lemma 5 in [1] is just *vacuously true*.\n\n[2] also relies on the finite size domain assumption, so all proofs were built on top of the finite space borrowing the idea from [1]. Therefore, the convergence proof in [2] does not mean anything. Unlike the claim in [2], there's no surprise that authors' notion of BALD in [2] converges.\n\nConsequently, **we have serious concerns about the contributions of those papers [1] and [2].**\n\nHere're more comments:\n- Small-data regime: What's the point of active learning in the small-data regime? If the dataset size is small (let's say <1000), the cost of active learning is typically higher than the cost of getting all label information. And if the model has sufficient expressiveness, it will eventually acquire the entire cross-entropy loss. So applying entropy acquisition should be enough under a single acquisition scenario. \n\n- In [2], the authors misinterpreted the definition of BALD under the Bregman divergence framework. BALD is the mutual information between the model and the output for *a single data point*, NOT the weighted average of the mutual information over the entire domain. Therefore the explained BALD in [2] is neither the BALD nor BatchBALD (joint mutual information).\n\n- Nevertheless, since the acquisition idea is still valid, we tested the CoreMSE method [2], seemingly the best under this category, with MNIST under a single acquisition scenario. It showed a better performance than BALD but worse than our BalEntAcq. See **Appendix A.17** in our updated supplementary material.\n - With a large dataset size, the computational costs of ELR, CoreLog, and CoreMSE are very expensive. They require a vast memory size unless we apply size reductions on the data space $X'$ and MC samples as the authors of [2] did - https://github.com/davidtw999/BEMPS. When the number of classes is large, it is impossible to run the code. Therefore **the naive application of the ELR-based algorithm is not scalable.**\n\nAs a final remark, we clarified the term \"bias\" to \"redundant\" in our revision. Thank you very much for this suggestion.\n\n[1] Zhao, Guang, et al. \"Uncertainty-aware active learning for optimal Bayesian classifier.\" International Conference on Learning Representations (ICLR 2021). 2021.\n\n[2] Tan, Wei, Lan Du, and Wray Buntine. \"Diversity Enhanced Active Learning with Strictly Proper Scoring Rules.\" Advances in Neural Information Processing Systems 34 (2021): 10906-10918.", " By assuming a beta distribution on the softmax probabilities of a Bayesian classification network, the authors derive the marginalized joint entropy of a datapoint x and use it in a new acquisition function (balanced entropy learning acquisition) for active learning. **Strength**\n- The paper is well organized. The authors explained their assumptions carefully and also the method.\n- Theorem 4.1 motivates the reciprocal of BalEnt well. Note that I haven't checked the proof in detail.\n\n**Weakness and Question**\n- I wonder how the assumption about the beta distribution of the softmax probabilities holds in practice. It would be beneficial to test this, for the dropout network, and for other types of Bayesian variational approximation methods.\n\n- The authors didn't seem to discuss the limitations of the work clearly. Please see above The authors didn't seem to discuss the limitations of the work although they claimed to have done that in the checklist (my apologies if I missed it somewhere).", " The context is Bayesian active learning, using MC dropout-based models. The paper places Beta distributions over the class marginals (ie one for each $p(y=i|x, w)$). The paper states that BALD as it is usually computed cannot be computed as such and instead proposes a different formulation, which it upper-bounds using what the paper calls a *marginalized joint entropy (MJEnt)* based on the entropy of the Beta distribution approximations. It then introduces a balanced entropy as the ratio between the MJEnt and the regular prediction entropy. Finally, it uses either this value or the reciprocal as the acquisition score (depending on the sign). The paper tries to motivate all this as principled and reports encouraging experimental results.\n The paper presents a few interesting perspectives on BALD. The experiments show good performance on CIFAR-100 and superior performance on CIFAR-100x3 and TinyImageNet.\n\nI was aware of the papers \"BABA: Beta Approximation for Bayesian Active Learning\" and \"Analytic Mutual Information in Bayesian Neural\nNetworks\" (Anonymous, 2021 &2022), but not the authors. Comparing the text of these papers, there might seem to be a case of self-plagiarism. While the former only exists as a preprint, the latter is to be published in ISIT 2022 (as also noted in this paper). I'm flagging this for the AC to decide and take a look at. The portions in question are not restricted to the Background section of this paper.\n\nIn regards to the content of the paper:\n\n1. It is not clear why the Beta approximation makes sense. Indeed, only the marginals $p(y=i | x)$ could be motivated to follow a Beta distribution, similar to the central limit theorem, as these are marginalized over $w$. The $p(y=i|x, w)$ as r.v. of $w$ however, need not follow such a distribution. This is a well-known criticism of e.g. prior networks (Malinin et al, 2018), which fit Dirichlet distributions.\n\n2. The paper states in (4) and (5) that the common formulation of BALD is equal to the more complex formulation using $\\Phi$. It then finds an upper bound to this formulation (MJEnt). This is similar to how the predictive entropy (Ent) upper-bounds normal BALD. In (10), the paper states that MJEnt = Ent + some additional term (\"Posterior Uncertainty\") = Epistemic Uncertainty + Aleatoric Uncertainty + Posterior Uncertainty, and that it thus decomposes three different uncertainties. This is wrong: it actually confounds these three terms (as it takes a sum/is a function of them)! \n\n The citation right before (4) and (5) is actually wrong. Gal et al, 2017, do not motivate the statement that follows.\n\n3. Section 3.3 is not novel and only restates what is known from Houlsby et al, 2011, Gal et al, 2017, and Kirsch et al, 2019: entropy acquisition is over-confident compared to BALD because it adds in aleatoric (irreducible) uncertainty (Ent = Epistemic Uncertainty (BALD) + Aleatoric Uncertainty), which will not be learnt away.\n\n4. BalEnt falls out of nowhere as a ratio and is not actually motivated. 1. How does BalEntAcq compare to BABA?\n\n2. Appendix A.12.2 contains ablations. Could you provide an ablation for P4 = BalEnt[x]^-1.\n\nIt would seem that BalEntAcq's second case (for negative scores) does not matter as long as there are sufficient positive scorers. This raises the question: it is needed at all even for the experiments provided in the main paper? --", " This paper proposes a new uncertainty measure, called BalEntAcq (Balanced Entropy Acquisition), that aims to correct the potential \"bias\" of existing active learning schemes based on information-theoretic uncertainty measures, such as the popular BALD (Bayesian active learning by disagreement).\nThe paper shows that the proposed BalEntAcq captures the \"information balance\" between the uncertainty of the underlying softmax probability and the label, thereby outperforming other active learning schemes based on similar entropy-based principles.\nBased on popular benchmarks, the authors demonstrate the potential advantages of active learning based on BalEntAcq compared to other alternatives.\n\n STRENGTHS\n\n1. The proposed uncertainty measure \"BalEntAcq\", which aims to effectively capture information balance between the uncertainty of the underlying softmax probability and the label variable, has been shown to result in well-diversified data point selection near the decision boundary, consistently outperforming other information-theoretic uncertainty measures often utilized for active learning.\n\n2. The closed-form expression of the proposed BalEntAcq leads to a computationally efficient active learning scheme, which nevertheless may improve the learning outcomes compared to other existing alternatives.\n\n\nWEAKNESSES\n\n1. The overall presentation - both literary and technical - requires improvement. For example, the authors do not clearly explain nor define what type of \"bias\" this study is focusing on, although this is crucial for understanding the main motivation of the proposed scheme as well as the major contributions in this work. Furthermore, many acronyms should be clearly defined before using them.\n\n2. Literature review on existing relevant schemes is too short and shallow. For example, although the authors present a brief summary of existing active learning schemes in Sec. 2.3, the treatment and review of other schemes is not comprehensive and fairly sketchy to be informative for the readers.\n\n3. While BalEntAcq has been shown to result in improved performance over some alternatives, a more comprehensive evaluation is needed to clearly demonstrate the advantage of the proposed scheme. For example, how does it compare to various active learning schemes based on ELR (expected loss reduction) strategy, which focuses on maximally reducing the expected error, and thereby focus on acquiring data points that can maximize the uncertainty directly impacting the predictive performance?\n\n4. Current results show that the proposed BalEntAcq may have potential benefits over other alternatives in terms of efficiency (through closed-form expression of the acquisition function) and performance gain (as reflected in Figure 3 and Table 1). However, the uncertainty measure BalEntAcq is defined in a somewhat heuristic manner, and it is unclear whether it would provide meaningful advantages over recently proposed Bayesian active learning schemes - in terms of performance, robustness, and convergence properties.\n\nFor example, the following papers propose Bayesian active learning schemes based on ELR strategies, which have shown to effectively reduce model uncertainty that directly affect the predictive performance of the learned model. \n\nZhao et al. \"Uncertainty-aware Active Learning for Optimal Bayesian Classifier\", ICLR 2021.\n\nTan et al. \"Diversity Enhanced Active Learning with Strictly Proper Scoring Rules\", NeurIPS 2021.\n\nBoth papers provide theoretical convergence guarantees to the optimal model as well as consistent performance improvements compared to other existing schemes, including BALD, the main method to which BalEntAcq is compared in this study. It would be helpful if the authors could compare their scheme to the above methods or other recent Bayesian active learning schemes and discuss what would be the main benefits of the proposed scheme.\n\n5. Based on Figure 3, it is unclear whether BalEntAcq would provide meaningful advantages over other alternatives in the small-data regime, which would be of special interest when studying active learning schemes.\n\n\n 1. How does the performance of BalEntAcq compare to the popular ELR strategy, which directly focuses on reducing model uncertainty via active learning so as to improve the predictive performance?\n\n2. How does the proposed active learning scheme perform, in comparison with other existing schemes, in a small-data regime, where the role of active learning would be most important?\n\n3. Does BalEntAcq provide any convergence guarantee - either theoretically or empirically? What would be its main advantages over recently proposed Bayesian active learning schemes?\n The authors do not explicitly discuss the limitations of the proposed work. The authors note there are no specific \"negative societal impacts\" relevant to the proposed method.\n", " This paper proposes a new acquisition function BalEntAcq for Al in BNN. It captures the information balance between the uncertainty of underlying softmax probability and the label variable. It facilitates parallelization over all classes (by estimating distribution parameters in marginal distribution). It is a purely standalone measure that could reduce relational computation like BatchBALD, CoreSet, and BADGE. Nevertheless, the paper shows that BalEntAcq captures a well-diversified selection near the decision boundary. The authors also demonstrate the new principle can outperforms other well-known Bayesian active learning algorithms. Strengths:\n1) The new acquisition function is novel. It facilitates the parallelization both over classes and batch selection (there is no relational computation within data points inside a batch). It captures both informativeness (uncertainty) and diversity.\n\nWeaknesses:\n1) Baselines are limited. (a) The paper mentioned BatchBALD. The computational cost for selecting a batch is proportional to the batch size. It is still tolerable. As shown in the paper, it is superior to BALD in many settings. This paper can compare its method with BatchBALD with a small batch size, e.g., batch size <= 40. (2) Variation-Ratio [1] is also a potential baseline that have shown competitive performance. (3) Non-Bayesian AL algorithms can be applied to BNN. For example, in order to apply CoreSet to BNN, we can take the average last-layer representations with N MC dropouts or simply one representation with MC dropout, which is also the case for any DNN with dropout layers. Similarly, we can also apply BADGE to BNN. For all the examples, we can still maintain the expressiveness of the BNNs.\n2) The authors only tried their method on MC dropout. There are many other BNNs, e.g., [2] and [3], that need to be considered since the paper focus on AL in BNNs.\n3) Datasets are limited. The datasets considered in the paper should cover different aspects of AL, e.g., batch size, data format, and dataset size. The authors can compare their method with BatchBALD and [4] on MNIST and Repeated-MNIST with small batch size, i.e., <= 10. The author can also consider some small UCI datasets and some larger batch sizes for datasets like CIFAR10 and SVHN. If the new method does not work well in these settings, the authors should discuss it in the limitation or conclusion section.\n\nReferences:\n[1] Kirsch, Andreas, Joost Van Amersfoort, and Yarin Gal. \"Batchbald: Efficient and diverse batch acquisition for deep Bayesian active learning.\" Advances in neural information processing systems 32 (2019).\n[2] Lakshminarayanan, Balaji, Alexander Pritzel, and Charles Blundell. \"Simple and scalable predictive uncertainty estimation using deep ensembles.\" Advances in neural information processing systems 30 (2017).\n[3] Kingma, Durk P., Tim Salimans, and Max Welling. \"Variational dropout and the local reparameterization trick.\" Advances in neural information processing systems 28 (2015).\n[4] Kirsch, Andreas, Tom Rainforth, and Yarin Gal. \"Test Distribution-Aware Active Learning: A Principled Approach Against Distribution Shift and Outliers.\" arXiv preprint arXiv:2106.11719 (2021). 1) Discuss computational complexity and compare it with other AL algorithms.\n2) Can the authors explain why we can not apply non-Baysian AL algorithms to BNNs? See 3 weaknesses." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 3, 3, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 3, 4, 3 ]

[ "0HbMW58Nip4", "iR3f1_e5LHu", "cSbSqvBRFKW", "qG_os2P3fv8", "14MMqUee_n", "nips_2022_pk1C2qQ3nEQ", "ngmn3CYxeoH", "WvWCwrCG9J2", "WvWCwrCG9J2", "Xbh7KWQrIov", "k50T6lBAj_X", "nips_2022_pk1C2qQ3nEQ", "nips_2022_pk1C2qQ3nEQ", "nips_2022_pk1C2qQ3nEQ", "nips_2022_pk1C2qQ3nEQ" ]

[ "AsoTAOvzHTe", "QuTH3-YBRLI", "B0GelQznc6O", "oNhISEgcBEq", "R9isFYPWowS", "5so-KWzecbO", "C7RXbXrsx0y", "kB0MuSd-I_2", "K4jHTdXyBu-", "YUkZK8OjEs1", "-9SVisgBpl7", "uYFVvAgRPle", "r1T_4wE1wwF", "RcOOWiEW-ZH", "9ScPfZgeMM-", "FmDeuaql3h0", "-xXAtkiw_Id", "06N1mDn3HYJ", "k9MT2sk0mSE", "mOZQ5CJSazh", "O93fOlHIqhc" ]

[ "author", "official_reviewer", "author", "author", "author", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your valuable comments!", " Thanks for answering the questions and the additional analysis. I am increasing my rating to 8.", " Thanks for your valuable reviews. We’re pleased that our response addresses your concerns and the Reviewer is happy to increase the rating to accept. \n\nAs the rebuttal phase is coming to the end in 10 hours, please don’t hesitate to let us know if there are any additional clarifications or experiments that we can offer. We are really looking forward to your updated review and rating. Thanks!", " Thank you for the followup and for reconsidering your score! We’re pleased that our response addresses your concerns.\n\nAs for the Semantic MapNet variant that takes a UNet as a decoder, our MGMap is still different from this variant in the following two aspects. 1) Our MGMap explicitly incorporates a predicted global semantic map, which contains higher-level information compared with implicit features. Also, it allows agents to hallucinate the environment out of view range. Experimental results in Table 3 of the paper and in Q5 (ablation on hallucination) of the original response have proved its effectiveness. 2) The decoder of Semantic MapNet attempts to learn implicit multi-granularity features in map space (i.e., input and output of the decoder are both in map space). In contrast, we extract a fine-grained map directly from original RGB images, which may contain more detailed information. We are not clear about the exact effect brought by this difference yet and it would be interesting to conduct further study in further works.\n\nOverall, we believe that introducing MGMap for VLN and exploring weakly-supervised signals for localizing instruction objects in the map is a promising and intriguing direction.", " Thanks again for your insightful suggestions and comments. As the deadline for discussion is approaching, we are glad to provide any additional clarifications that you may need.\n\nIn our previous response, we have added evaluation results on RxR-Habitat dataset and carefully revised the paper to complement your suggestions. We summarize our responses with regard to the following aspects:\n\n* We have added evaluation results on RxR-Habitat dataset. Our method achieves state-of-the-art performance under non-panoramic settings, which further demonstrates the merit of our method (Q1).\n* We have carefully revised the paper to make it more clear. The revisions include the following points. 1) We have mentioned and cited VLN-CE in Introduction (Q2). 2) We have weakened the statement of human behavior in the Introduction (Q3). 3) We have changed \"self-supervised\" to \"weakly-supervised\" throughout the paper, which is also recognized by Reviewer kB3d in the latest response (Q4). All the revisions are highlighted in red in the revised submission. \n\nWe hope that the provided new experiments and revisions could convince you of the merits of our work. Please do not hesitate to contact us if there are other clarifications or experiments we can offer.\n\nThank you for your time again!\n\nBest, Authors", " Yes, this is the exact experiment I'm looking for. Thanks for presenting the results. I'm inclined to agree with the authors' reasoning that the lack of a UNet for Semantic MapNet model limits it from having fine-grained features. It's largely comparable to the semantic map row from table 3. This addresses my final concern. I'm happy to increase my rating to accept. Please stay tuned for my updated review + score in the next 1-2 days. \n\nI have one question that's more of a curiosity than a concern (so it won't affect my rating or review negatively). Depending on time constraints, the authors can feel free to not respond in detail to this. Will using a UNet encoder-decoder instead of 5-layer decoder for Semantic MapNet achieve something similar to MGMap? That is, if we train a Semantic MapNet model with a UNet encoder-decoder for map prediction, and use the final layer features there. ", " Thank you for the followup and comments! We're pleased that our response addresses the majority of your concerns, and hope to address the remainder now.\n\n> **Q1, Q2 - Whether the multi-granularity map achieves something different from what prior work does?**\n\nWe conduct an experiment to replace the multi-granularity map with the last layer features of the decoder in Semantic MapNet. We keep all settings the same except for replacing the map. The results below show that using Semantic MapNet features significantly underperforms our method on val-unseen data split. \n\n| Map Features | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|------------------------------|-----------|----------|----------|----------|----------|\n| Semantic MapNet Features | 10.27 | 6.72 | 42.1 | 33.1 | 29.0 |\n| Multi-granularity Map (Ours) | **10.00** | **6.28** | **47.6** | **38.9** | **34.3** |\n\nWe speculate the reason is that **the Semantic MapNet features contain little object low-level features** while **our map contains both low-level and high-level features**. The detailed analysis is as follows.\n\n\n1. For the Semantic MapNet, its decoder, which consists of five convolutional layers, can be considered as a segmentation model, performing top-down semantic segmentation. Existing network interpretability works [a, b] indicate that low-level features (e.g., color and texture) dominate at lower layers while high-level features dominate higher layers. In this sense, **the last layer of this decoder, as its highest layer, naturally contains few low-level features.**\n2. By comparison, we project the last layer features of a pretrained U-Net to build our fine-grained map. **Because of the skip-connection mechanism of the U-Net, its last layer features are the combination of features from lower layers and higher layers. These naturally contain both low-level and high-level features.** We concatenate this fine-grained map with a predicted semantic map to further incorporate higher-level information to build our multi-granularity map.\n\n\nBased on the above results and analysis, our multi-granularity map 1) provides richer information in different granularity for VLN, and 2) achieves significantly better performance compared with the existing works.\n\n\n\n> **Q3-Q11: At a high-level, the authors have addressed the majority of my concerns.**\n\nWe're pleased that our response addresses the majority of your concerns. We have updated the response contents in the revised paper. The revisions are listed as follows:\n* We have added ablation studies on the hallucination module and DAgger training in Sections D and E, respectively in the supplemental material. [Q5, Q10]\n* We have added quantitative results about object ambiguity in Section 1. Also, we have visualized some ambiguity cases in Section G. [Q7]\n* We have clarified some implementation details in the revised paper. [Q6, Q8, Q9]\n* We have changed SS-MGMap to WS-MGMap.\n\nPlease don’t hesitate to let us know if there are any additional clarifications or experiments that we can offer. We appreciate your suggestions. Thanks!\n\n\n\n**Reference:**\n\n[a] Shape or Texture: Understanding Discriminative Features in CNNs. ICLR 2021.\n\n[b] Interpreting Deep Visual Representations via Network Dissection. TPAMI 2018.", " Thank you for the followup and comments! We're pleased that our response addresses the majority of your concerns. We will update the response contents in the revised paper and upload the revision later. \n\nAs for Q1 and Q2, let us make sure we understand your comment correctly. \n* Do the \"Semantic MapNet features\", which the Reviewer suggest us replace our multi-granularity map with, refer to the last layer features of the decoder in Semantic MapNet? If yes, we are running such an experiment and will **update and discuss the results once the experiment finishes**.\n\n\nPlease don’t hesitate to let us know if there are any additional clarifications or experiments that we can offer, as we would love to convince you of the merits of the paper. We appreciate your suggestions. ", " I thank the authors for their responses and efforts to address reviewer concerns. At a high-level, the authors have addressed majority of my concerns. One particular point remains unaddressed (see below). I will be happy to raise my rating to 6+ if this is also addressed. Please see detailed comments below.\n\nQ1, Q2 - I agree that the goals are different, and the proposed method aims for something different. My question is whether it achieves something different from what prior work does. What I'm looking for:\n* Replace multi-granularity features with Semantic MapNet features (keeping rest of the pipeline fixed). Note that this is different from fine-grained features used in the method. Semantic MapNet trains the map features end-to-end for semantic reconstruction. The proposed method uses pre-trained image segmentation feature and projects them without any learning.\n* Why do this? Semantic MapNet may be implicitly learning the coarse and fine-grained features by performing top-down semantic segmentation. This is akin to how the image segmentation learns fine-grained features through segmentation training.\n\nQ3, Q4 - Thanks for the comparison with [e] as well as object localization performance. The denseness of the trajectory provides better supervision than sparse waypoints and helps identify instruction-relevant objects. This addresses my concern.\n\nQ5 - Agreed that it is reasonable to expect hallucination to be useful. Having this comparison is convincing.\n\nQ7 - Great. Please hint at these statistics in the paper to emphasize the importance of addressing this ambiguity. \n\nQ6, Q8, Q9, Q10 - Yes, these make sense. Please clarify the points in the paper.\n\nQ11 - Interesting. The logits might be a better option for mapping then. \n\nI also appreciate the change from self-supervised to weakly-supervised. The paper reads more naturally with this change. A minor nit: The method can be named WS-MGMap instead is SS-MGMap to reflect the change to weakly-supervised.", " \n> **Q7) In addition to discussing limitations due to object and environmental supervision, it would also improve the paper to discuss more possible directions that could improve the language-to-object grounding.**\n\nThanks for your suggestions. One possible direction to improve the language-to-object grounding is exploiting commonsense (e.g. ConceptNet) to find relevant objects of the instruction-mention objects. In this way, the agent can localize instruction-mention objects by finding relevant objects. We will add more discussions about possible future directions in the revised paper.\n\n**Reference:**\n\n[a] Cross-modal Map Learning for Vision and Language Navigation. CVPR 2022.\n\n[b] Beyond the Nav-Graph: Vision-and-Language Navigation in Continuous Environments. ECCV 2020.\n\n[c] Mapping Navigation Instructions to Continuous Actions with Position-Visitation Prediction. CoRL 2018.\n\n[d] MaAST: Map Attention with Semantic Transformersfor Efficient Visual Navigation. ICRA 2021.\n\n[e] Language-Aligned Waypoint (LAW) Supervision for Vision-and-Language Navigation in Continuous Environments. EMNLP 2021.", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n> **Q1) One weakness of the approach is that the full version depends on ground-truth 3D semantic information from the Matterport3D simulator in training.**\n\nThanks for your comment. Our full version uses ground-truth 3D semantic information from the simulator for training but not for inference. We want to point out that some existing works (e.g., CM2 [a], MaAST[d]) also use this ground-truth information in training. During inference, we strictly follow the standard evaluation settings [b] for a fair comparison.\n\nWe agree that not all datasets contain 3D semantic annotations. We will clarify this point in the limitation part.\n\n> **Q2) If I understand Table 3 correctly, without ground-truth semantic maps in training (just using the fine-grained map with segmentation features), the approach underperforms most of the other non-panoramic approaches (CMA, LAW, CM2).**\n\nWe agree with the Reviewer that only using the fine-grained map performs slightly worse than some approaches, as shown in Tab. 3. We speculate this is due to the lack of high-level semantic information about the environment. However, we want to argue that we could easily obtain this semantic information even if the ground-truth semantic map annotations are not available for training. \n\nSpecifically, we use a frozen pretrained segmentation model (e.g., Faster-RCNN) to segment the RGB images. Then we project the predicted segmentation results on a top-down map to build a semantic map. We use this map to replace the global semantic map in our method. In this sense, no semantic annotations are needed for training. \n\nAlthough the prediction from the pretrained segmentation model is imperfect, it provides complementary high-level information for our fine-grained map. We concatenate them to build a multi-granularity map. We conducted experiments on this variant, keeping all other settings the same except for the way of constructing a semantic map. The results on val-unseen data split are as below:\n\n| Method | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:---|:---:|:---:|:---:|:---:|:---:|\n| CMA [b] | 8.64 | 7.37 | 40.0 | 32.0 | 30.0 |\n| LAW [e] | 8.89 | 6.83 | 44.0 | 35.0 | 31.0 |\n| CM2 [a] | 11.54 | 7.02 | 41.5 | 34.3 | 27.6 |\n| Ours w/o semantic annotations | 11.0 | 6.45 | 44.6 | 36.7 | 32.1 |\n| Ours w/ semantic annotations | 10.00 | **6.28** | **47.6** | **38.9** | **34.3** |\n\nFrom the results, the variant without semantic annotations for training outperforms current non-panoramic approaches. This demonstrates the flexibility of our method to be adapted to the dataset without semantic annotations. For the datasets with semantic annotations (e.g., R2R, RxR), our method can exploit these annotations to further improve the performance.\n\n> **Q3) The approach is quite similar to the approach of Blukis et al, \"Mapping Navigation Instructions to Continuous Actions with Position-Visitation Prediction\", CoRL 2018. It would strengthen this paper to contrast with that approach in the related work.**\n\nThanks for advising. Instead of only projecting a feature map generated from ResNet to construct the map as done in [c], we combine both fine-grained map and semantic map to generate a multi-granularity map. These two types of maps provide complementary object information to perceive a more complex photo-realistic environment. We will discuss that approach in the related work.\n\n> **Q4) Could the authors clarify what sources of ground-truth semantic information from the Matterport3D simulator are used, and when they are used?**\n\nWe only use the semantic annotation from the simulator during training. In testing, we only need to obtain RGB and depth observation, which is a standard setting for evaluation [a,b]. Consequently, our evaluation is fair with the existing works.\n\n> **Q5) What parts of the model are updated during each of the two stages of training: teacher-forcing, and DAgger training?**\n\nThe RGB and depth encoders, segmentation pre-trained model (a U-Net), and DD-PPO local policy are fixed during both two stages. All the other networks (namely semantic hallucination module, map decoder, Bi-LSTM, object localization module, progress predictor, and waypoint predictor) will be updated during both two stages. We will clarify these details in the revised paper.\n\n> **Q6) What are the off-the-shelf RGB and depth encoders?**\n\nFollowing existing paper VLN-CE [b], the off-the-shelf RGB and depth encoders are instantiated by a ResNet50 pretrained on ImageNet and a ResNet-50 trained to perform point-goal navigation, respectively. We will add these details in the revised paper.\n", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n> **Q1) No evaluation on RxR-Habitat. Evaluation of this dataset would be very helpful in evaluating the method.**\n\nWe agree that RxR-Habitat is very helpful for evaluating our method. In the rebuttal period, due to the time limit and large scale of this dataset, we are hard to retrain models in three languages of RxR-Habitat dataset. In this sense, we leverage the model trained on R2R-Habitat and transfer it to test on RxR-Habitat English data split. The results are shown in the table below. We compare our methods with LAW [a], which is a competitive baseline in the VLN task. We report the results below:\n\n* Table A: Results on RxR-Habitat val-seen data split.\n\n| Method | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:---|:---:|:---:|:---:|:---:|:---:|\n| LAW pano [a] | 6.27 | 12.07 | 17.0 | 9.0 | 9.0 |\n| LAW step [a] | 7.92 | 11.94 | 20.0 | 7.0 | 6.0 |\n| Ours | 10.37 | **10.19** | **27.7** | **14.0** | **12.3** |\n\n* Table B: Results on RxR-Habitat val-unseen data split.\n\n| Method | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:---|:---:|:---:|:---:|:---:|:---:|\n| LAW pano [a] | 4.62 | 11.04 | 16.0 | 10.0 | 9.0 |\n| LAW step [a] | 4.01 | 10.87 | 21.0 | 8.0 | 8.0 |\n| Ours | 10.80 | **9.83** | **29.8** | **15.0** | **12.1** |\n\nFrom the results, our method outperforms different variants of LAW on both val-seen and val-unseen data splits. It is worth noting that our model is directly transferred from R2R-Habitat to RxR-Habitat without finetuning. These results demonstrate the effectiveness and robustness of our method. We believe the performance could be further improved when the model is trained and tested on the RxR-Habitat. We will train and evaluate the complete dataset in the future.\n\n> **Q2) The intro to the task should cite + mention VLN-CE since that's the variant of the task being studied. I recommend referring to the task as VLN-CE to avoid confusion.**\n\nThanks for your suggestions. We will update the manuscript to make it more clear.\n\n> **Q3) L28-29: We don't know why humans build cognitive maps. Neither Tolman nor O'Keefe claims to know why cognitive maps were learned to be built. I recommend weakening this statement.**\n\nThanks for your reminding. We agree with the Reviewer that why and how humans build map-like representations are still unknown. We will weaken this statement in the revised paper.\n\nAlthough the mechanism of human mapping is unclear yet, in robotics, there exist many methods of building map (e.g., occupancy map [b], semantic map [c], topological map [d]) for navigation task. These methods achieve gratifying results. Inspired by these works, we consider to construct a similar map-like representation to perceive the environment. Meanwhile, to make the map better represent the instruction-relevant objects for VLN task, we propose a multi-granularity map and an instruction-relevant object localization auxiliary task to improve the VLN performance.\n\nWe will carefully revise the paper to make our motivation more accurate and clear.\n\n> **Q4) Self-supervised map representation learning via object location task is not a correct name. The weakly-supervised part is probably fine.**\n\nThanks for your valuable suggestions. We agree with the Reviewers that the term \"weakly supervised\" is more accurate. We will replace the \"self-supervised\" description with \"weakly supervised\" carefully in the revised paper to make it more clear and accurate.\n\n**Reference:**\n\n[a] Language-Aligned Waypoint (LAW) Supervision for Vision-and-Language Navigation in Continuous Environments. EMNLP 2021.\n\n[b] Learning to Explore using Active Neural SLAM. ICLR 2020.\n\n[c] Object Goal Navigation using Goal-oriented Semantic Exploration. NeurIPS 2020.\n\n[d] Topological Planning with Transformers for Vision-and-Language Navigation. CVPR 2021.", " > **Q8) Does P remain the same for all time-steps of the trajectory?**\n\nNo, P is rotated at each time step to guarantee that the agent is facing upward. Consequently, it is impossible for the model to predict P just from instruction because the instruction does not contain agent heading information. \n\n> **Q9) In Tab. 3 ablation study - do all rows benefit from the auxiliary task? For example, the result without the auxiliary task in Tab. 4 is close to the semantic map (row 3 in Tab. 3). If the semantic map does not use the auxiliary task, then the gain from multi-granular representations itself is limited.**\n\nAll rows in Tab. 3 have used the auxiliary task (except for the \"No Map\" row because it is hard to localize objects without a map). With the same experimental settings, just replacing the multi-granularity map with the semantic map (row 3 in Tab. 3) or fine-grained map (row 2 in Tab. 3) significantly drow the performance. This demonstrates the importance of the proposed multi-granularity map.\n\n> **Q10) L231 - how is the DAgger training performed without a human in the loop?**\n\nWe use the same DAgger training technique as the compared baselines [g,h,i]. In the table below, removing schedule sampling (i.e., using ground-truth trajectories at all time) drops the performance. We will add and discuss these results in the supplementary.\n\n| Training Method | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:---|:---:|:---:|:---:|:---:|:---:|\n| Teacher Forcing | 7.90 | 7.61 | 30.0 | 24.6 | 22.5 |\n| Dagger Training | 10.00 | **6.28** | **47.6** | **38.9** | **34.3** |\n\n> **Q11) In Tab. 5, classification layer logits are better than semantic map from Tab. 3.**\n\nThanks for your comment. In the classification layer variant, the projected features are the logits on 27 categories (i.e., softmax of the predicted scores for each class). In the semantic map variant, the projected features are the image segmentation results (i.e., one-hot encoded the argmax of the scores). We speculate that the logits in the classification layer variant could provide with soft labels to ease the imprecise segmentation results problem caused by the off-the-shelf segmentation model.\n\n**Reference:**\n\n[a] MapNet: An Allocentric Spatial Memory for Mapping Environments. CVPR 2018.\n\n[b] Semantic MapNet: Building Allocentric Semantic Maps and Representations from Egocentric Views. AAAI 2021.\n\n[c] Cognitive Mapping and Planning for Visual Navigation. CVPR 2017.\n\n[d] Geometry-Aware Recurrent Neural Networks for Active Visual Recognition. NeurIPS 2018.\n\n[e] Cross-modal Map Learning for Vision and Language Navigation. CVPR 2022.\n\n[f] Occupancy Anticipation for Efficient Exploration and Navigation. ECCV 2020.\n\n[g] Beyond the Nav-Graph: Vision-and-Language Navigation in Continuous Environments. ECCV 2020.\n\n[h] Language-Aligned Waypoint (LAW) Supervision for Vision-and-Language Navigation in Continuous Environments. EMNLP 2021.\n\n[i] Bridging the Gap Between Learning in Discrete and Continuous Environments for Vision-and-Language Navigation. CVPR 2022.", " \n> **Q3) Comparisons with waypoint prediction (like [e]).**\n\nOur auxiliary task is fundamentally different from waypoint prediction in the aspect of supervision signal. \n\nSpecifically, the waypoint prediction task only requires predicting one or several discrete points on the ground-truth path. Taking CM2 [e] as an example, it aims to predict 10 waypoints, each of which is represented as a Gaussian distribution. Combining these 10 Gaussian distributions obtains a **waypoint heatmap** $P_w$ as the prediction target. However, this heatmap cannot represent the potential location of instruction-relevant objects. Because these objects are very likely to appear in the area between two adjacent waypoints, but the waypoint heatmap [e] has a low value in these areas. In contrast, we build an **object heatmap** $P_o$, which follows the principle that the regions closer to the path have a higher probability of containing these objects. Our heatmap provides more precise supervision for object localization.\n\nWe have conducted an experiment that replaces our proposed object heatmap $P_o$ with waypoint heatmap $P_w$ [e]. From the table below, the waypoint heatmap performs worse than ours. Its instruction-relevant object localization accuracy is also worse than ours (see **Q4** for experimental details and localization IoU). These results demonstrate the effectiveness of our proposed auxiliary task.\n\n| Heatmap Type | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:--|:--:|:--:|:--:|:--:|:--:|\n| Waypoint Heatmap [e] | 11.80 | 6.53 | 45.4 | 34.4 | 29.3 |\n| Object Heatmap (Ours) | **10.00** | **6.28** | **47.6** | **38.9** | **34.3** |\n\n> **Q4) Is the supervision of the auxiliary task learn to localize instruction-relevant objects? What about the heatmap from [e]?**\n\nTo evaluate the localization performance, we manually annotate the accurate position of instruction-relevant objects in 1/5 trajectories (total 360 trajectories) in the val-unseen split. Specifically, we localize the instruction-relevant objects in the RGB images, and then project them to the top-down map. We consider the 20% area with the highest score on the prediction map as the predicted location. From the table below, our method achieves 0.33 IoU, outperforming the variant that uses waypoint heatmap [e] as supervision and the variant without an auxiliary task.\n\n| Auxiliary Task | Heatmap Type | IoU ↑ |\n|:---:|:---:|:---:|\n| X | None | 0.0654 |\n| Y | Waypoint Heatmap [e] | 0.2241 |\n| Y | Object Heatmap (Ours) | **0.3314** |\n\n> **Q5) Is hallucination of maps beyond the field of view helpful quantitatively?**\n\nThe hallucination helps agents explore the environment more effectively, which is proved by existing works [e,f]. To evaluate its effectiveness, we implement a variant that only predicts the semantic map within the field of view (i.e., w/o hallucination). From the table below, this variant underperforms our agent.\n\n| Method | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:---|:---:|:---:|:---:|:---:|:---:|\n| w/o hallucination | 10.05 | 6.51 | 44.9 | 37.3 | 33.2 |\n| w hallucination (Ours) | **10.00** | **6.28** | **47.6** | **38.9** | **34.3** |\n\n> **Q6) Eqn 1 - is it a pixelwise loss?**\n\nYes, exactly. We will update the paper to make it more clear. \n\n> **Q7) How often does instruction-object ambiguity occur?**\n\nThese ambiguous cases actually occur quite often. Quantitively, 1) there are **51%** instructions containing objects described by specific attributed words (e.g., wooden table). 2) **33%** trajectories of these instructions occur instruction-object ambiguity. We obtain these numbers by manual annotations in the AMT crowdsourcing platform.", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n> **Q1) Comparisons with prior works [a,b,c,d].**\n\nWe have cited and discussed the four suggested papers in the revised version. We use mapping in high-dimensional feature spaces (named fine-grained map) for a fundamentally different goal compared with these works. Directly exploiting the maps in [b] for VLN performs significantly worse than our method. We in fact have already provided these comparison results in Tables 3 and 4. The detailed comparisons are shown as follows.\n\n**1. The goals of using fine-grained map are fundamentally different**. In VLN task, there exist diverse objects with different attributes (typically hundreds of object categories) in the instruction and environment. Being aware of these object locations is critical for agents to find the navigation path. We aim to use the fine-grained map for providing detailed object information (e.g., color and material) to represent diverse instruction-relevant objects. In contrast, existing works use this map for localizing robot [a], predicting semantic map with limited object category [b], navigating to a few target objects [c,e], and 3D reconstructing objects [d]. **None of these works have investigated how to build a map for representing diverse objects with different attributes.**\n\n**2. To achieve our goal of representing diverse objects in a map, we propose the following two innovations upon existing works.**\n\n**2.1 Constructing a multi-granularity map.** Instead of only using a fine-grained map as done in [a,b,c,d] or only using a semantic map, we are the first to combine them to generate a multi-granularity map for the VLN task. These two types of maps provide complementary object information, i.e., a fine-grained map provides detailed object information and attributes while a semantic map provides commonly seen object category information. From the table below, only exploiting a fine-grained map built in [b] or semantic map significantly drops the performance. These results have been already provided in Tab. 3 in the paper.\n\n| Map Type | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:---|:---:|:---:|:---:|:---:|:---:|\n| Fine-grained Map [b] | 10.11 | 7.11 | 41.1 | 31.6 | 28.2 |\n| Semantic Map | 10.89 | 6.80 | 42.2 | 33.3 | 28.2 |\n| Fine-grained Map + Semantic Map (Ours) | **10.00** | **6.28** | **47.6** | **38.9** | **34.3** |\n\n\n\n**2.2 Constructing an auxiliary task for localizing diverse objects.**\nTo provide supervision for learning such a multi-granularity map to represent diverse objects, we propose an instruction-relevant object localization auxiliary task. As a comparison, [b] uses a semantic map with limited categories as supervision, while [c] uses final navigation actions as supervision for learning map representation. These supervisions can not explicitly teach models to represent diver objects. We have also tried a variant that only uses these two types of supervision (i.e., using semantic loss in Eq. (1) and navigation loss in Eq. (5)). From the table below, this variant performs worse, while our proposed auxiliary task improves the performance significantly. These results have been already provided in Tab. 4 in the paper.\n\n| Supervision Signal | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:---|:---:|:---:|:---:|:---:|:---:|\n| Semantic Loss [b] + Navigation Loss [c] | 10.24 | 6.68 | 41.7 | 33.1 | 29.0 |\n| Ours | **10.00** | **6.28** | **47.6** | **38.9** | **34.3** |\n\n\n\n\n> **Q2) The multi-grained map may be obtained implicitly in prior works [a,b,c,d].**\n\nDirectly using these implicit multi-grained maps achieves inferior performance. This is because they cannot represent diverse objects in VLN due to **the lack of high-level semantic information and appropriate supervision**. Upon these maps, we further 1) propose to explicitly build a multi-grained map and 2) propose an auxiliary task for learning diverse object representation. Experimental results show these two techniques bring significant improvement (please refer to the two tables in Q1).\n\nWe will include and discuss these works in Sec. 2.2 in the revised paper.", " We sincerely appreciate all reviewers’ time and efforts in reviewing our paper and for the constructive feedback. In addition to the response to specific reviewers, here we would like to 1) thank reviewers for their acknowledgment of our work, 2) summarize our contributions 3) highlight the new results added during the rebuttal and 4) higilight the revision in the revised paper:\n\n**1) We are glad that the reviewers appreciate and recognize our contributions.**\n\n- The paper presents of novel application of map-based navigation techniques [2vTe]\n- The proposed method is well motivated [kB3d,eYGK,RkNa]\n- The experimental results show good improvements over comparable methods [kB3d,eYGK,RkNa]\n- The paper performed a thorough set of experiments [2vTe,kB3d,eYGK,RkNa]\n- The paper writing is good and it was easy to read [kB3d]\n\n\n\n**2) We summarize our contributions as follows.**\n\nWe emphasize that we do not claim our main contribution is how to build a fine-grained map or a semantic map. As discussed in the related works and pointed out by Reviewer RkNa, there are existing works focusing on building a fine-grained map from RGB features or a semantic map from semantic segmentation prediction. \n\nHowever, as shown in Tab. 3 and 4 in the paper, directly using one of these maps achieves inferior performance. The underlying reason is that individually using these maps without specific supervision can not represent diverse objects with different attributes in the VLN instruction and environment. How to learn a map representation, which is representative for diverse objects, for VLN has never been investigated or solved in previous works. Our work aims to answer the questions that how to provide sufficient information and supervision for learning such a map representation for VLN task.\n\nTo summarize, our contributions are summarized as followed.\n\n- We are the **first** to **introduce multi-granularity knowledge**, which contains both fine-grained details and semantic information of objects, in a map format to build a multi-granularity map for VLN task.\n- We propose a weakly-supervised object localization auxiliary task to provide supervision for the agent to **learn to represent diverse instruction-relevant objects** in the map representation.\n- Experimental results on VLN-CE benchmark show our method achieves state-of-the-art results, improving navigation success rate by 4.0% and 4.6% in seen and unseen environments, respectively.\n\n**3) In this rebuttal, we have added more supporting results following the reviewers’ suggestions.**\n\n- Performance of our method under panoramic setting [2vTe]\n- Comparison of sample efficiency between WPN and our method on training samples [2vTe]\n- Ablation results of different heatmap types for the auxiliary task [kB3d]\n- Ablation results of hallucinating maps beyond the field of view [kB3d]\n- Evaluation on RxR-Habitat [eYGK]\n- Performance of our method without semantic annotation [RkNa]\n\n**4) We make the following modifications in our revision to address reviewers' questions. (highlighted in magenta).**\n\n\n- We add discussion of prior works that build a map in high-dimensional spaces in the related work section [kB3d, RkNa]\n- We remove the motivation of human behavior in the introduction section [eYGK]\n- We add more implementation details. [2vTe, kB3d ,RkNa]\n- We add more discussion about limitations and future work [RkNa]\n- We replace the \"self-supervised\" description with \"weakly-supervised\" [eYGK]", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n> **Q1) There is a published method (CWP-CMA) that performs better than the proposed approach on the public VLN-CE benchmark. The benefit of the proposed approach is that it doesn't require the agent to turn-around to get a panorama between waypoints. However, it is unclear which approach would be better given access to a panoramic camera.**\n\nIn this paper, we strictly follow the standard setting of VLN-CE [a] to use a camera with limited field of view. \n\nTo evaluate the performance of our method under a panoramic setting, we encode 12 views in panoramic RGB images using the same visual encoder and project their features to a top-down map. We report the experimental results on val-unseen data split as below:\n\n| Method | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ |\n|:---|:---:|:---:|:---:|:---:|:---:|\n| CWP-CMA [b] (concurrent) | 10.90 | 6.20 | 52.0 | 41.0 | 36.0 |\n| Ours w/ pano | **10.58** | **6.19** | 50.2 | **41.9** | **37.4** |\n\nFrom the experimental results, our method performs competitively with the concurrent work CWP-CMA [b]. We believe our performance could be further improved if we carefully design how to use panoramic images. Also, exploiting rich environment information encoded by our multi-granularity map to enhance the candidate waypoint predictor proposed in CWP-CMA is an interesting research direction. We leave this for future works.\n\n> **Q2) It seems a bit misleading to me because the granularity of the map for both objects and properties is the same. What parts of the map have multiple granularities?**\n\nSorry for the confusion. The term \"multi-granularity\" in our paper means that our map contains different types of features instead of different map resolutions. Specifically, our multi-granularity map consists of a fine-grained map and a semantic map. The fine-grained map represents low-level detail information, such as texture, and color. The predicted semantic map reveals the categories information of common seen objects. This term is also used in some existing works [d, e] to represent the similar meaning. We will make it more clear in the revised paper.\n\n> **Q3) A potential benefit of a modular map-based approach which is trained offline vs end-to-end RL approaches is the sample efficiency. Did you observe such benefits for the proposed approach as compared to the baselines?**\n\nYes, we have also observed that our method is much more sample efficient than end-to-end RL approaches. Specifically, a common end-to-end RL approach WPN [c] is trained using around 200M samples (note: we consider one step as one training sample). By comparison, our model is trained using only 13M training samples and achieves better performance on val-unseen data split as shown below:\n\n| Method | TL ↓ | NE ↓ | OS ↑ | SR ↑ | SPL ↑ | # Training Samples↓ |\n|:---|:---:|:---:|:---:|:---:|:---:|:---:|\n| WPN [c] | 7.62 | 6.31 | 40.0 | 36.0 | 34.0 | 200M |\n| Ours | 10.89 | **6.2** | **47.6** | **38.9** | **34.3** | **13M** |\n\nWe speculate that end-to-end RL approaches require large amounts of data to learn all navigation components like mapping, planning, and control in a single network. \n\n**Reference:**\n\n[a] Beyond the Nav-Graph: Vision-and-Language Navigation in Continuous Environments. ECCV 2020.\n\n[b] Bridging the Gap Between Learning in Discrete and Continuous Environments for Vision-and-Language Navigation. CVPR 2022.\n\n[c] Waypoint Models for Instruction-guided Navigation in Continuous Environments. ICCV 2021.\n\n[d] Multiple Granularity Descriptors for Fine-Grained Categorization. ICCV 2015.\n\n[e] Multi-granularity for knowledge distillation. Image and Vision Computing 2022.\n", " This paper presents a map-based method for Vision-and-Language Navigation (VLN). The approach builds a semantic map which includes object categories and properties such as color, texture and shape. The semantic map is used to localize the objects and their properties mentioned in the instruction. The localization, map and instruction is used to predict waypoints for a local policy. Experiments onVision-and-Language Navigation in Continuous Environments (VLN-CE) benchmark show competitive results. Strengths:\n- The paper presents of novel application of map-based navigation techniques to VLN-CE. The use of maps encoding both object categories and properties for navigation is also novel to the best of my knowledge.\n- The use of ground truth trajectories for language-to-map grounding is innovative. It allows the authors to have a localization objective without requiring map annotations.\n- The ablation experiments show the importance of both kinds of map.\n\nWeaknesses:\n- There is a published method (CWP-CMA) which performs better than the proposed approach on the public VLN-CE benchmark. The benefit of the proposed approach is that it doesn't require the agent to turn-around to get a panorama between waypoints. However, it is unclear which approach would be better given access to a panoramic camera. - I do not understand why the authors use the term \"Multi-granularity\" for describing maps representing objects and their properties. It seems a bit misleading to me because the granularity of the map for both object and properties is the same (denoted by m L143 and L154). What parts of the map have multiple granularities?\n- A potential benefit of a modular map-based approach which is trained offline vs end-to-end RL approaches is the sample efficiency as shown in https://arxiv.org/abs/2201.10029. Did you observe such benefits for the proposed approach as compared to the baselines? Yes.", " This paper tackles the Visual & Language Navigation task. The paper proposes a new \"multi-granular\" map representation for encoding coarse-grained (semantic) and fine-grained (textures, colors, etc) details about the 3D space. It also proposes a self-supervised loss to localize \"instruction-relevant\" objects on the map. Experiments are performed on the VLN-CE benchmark on MP3D dataset. The work demonstrate strong improvement over prior methods for VLN-CE while using limited field-of-view sensing (as opposed to panoramic sensing). # ----------------------- Post-rebuttal update --------------------\nThe author's responses during the rebuttal were very convincing and addressed my concerns. The main weaknesses pre-rebuttal were the novelty of the multi-grain map representation and the auxiliary loss. In response, the authors compared and contrasted with the cited works, and even showed quantitative benefits in relation to them. I've raised my rating to 7 (accept).\n\n# ----------------------- Pre-rebuttal review --------------------\n# Strengths\n\n- The paper is well motivated in building multi-granular maps for wholistic object representations and grounding instructions to relevant objects on the map. \n- The paper writing is good and it was easy to read and understand the ideas and contributions.\n- Experiments are well designed. A lot of relevant and appropriate baselines have been compared with. The experimental results show good improvements over comparable methods. Ablation studies confirm the value of the contributions. Following traditions from prior work on this task, the authors also present results on an online leaderboard, which verifies the claims made under standardized settings. \n\n# Weaknesses\n## Novelty of multi-granular maps for embodied AI\n- The proposed multi-granular maps does the following: (1) use image segmentation features to capture fine-grained details, (2) project the features to get a top-down 2.5D fine-grained map, (3) obtain coarse-grained segmentation maps with potential expansion beyond observed cells, and (4) jointly merging fine-grained and coarse-grained to obtain final representations. This particular pipeline itself appears novel (particularly in VLN).\n- However, prior work [1, 2, 3, 4] has extensively studied mapping in high-dimensional feature spaces (as opposed to occupancy / semantic maps). These have not been discussed in Sec. 2.2.\n- More importantly, they might be doing exactly what the proposed method intends to do. The general idea is to get visual feature maps of the egocentric inputs, and project them in a geometric / learned fashion to top-down maps / voxel grids. That is, the multi-grained map may be obtained implicitly here as opposed to explicitly as done in the Fig. 2. \n- For example, Semantic MapNet [2] builds such maps from visual inputs in the encoder, and decodes them to obtain semantic maps. In L145-146, the authors suggest that the last layers of an image segmentation model (Unet) contain a good mix of textural and semantic features. It is reasonable to expect the same to hold true for the last layers of Semantic MapNet to encode something similar, but in the top-down map space. \n\n\n## Novelty of auxiliary task\n- L174-176: \"The principle for generating coarse ground-truth is that the regions closer to the path have a higher probability of containing instruction-relevant objects.\" --- It is unclear to me whether this supervision is resulting in localizing \"instruction-relevant\" objects. \n- This objective could also plausibly be viewed as a form of imitation learning for waypoint prediction (like [5]). For example, in Figure 3, the model could be learning to predict the locations of future waypoints to follow instead of referring to the carpet (i.e., the carpet being along the waypoints could just be a coincidence). \n- If the model were to just predict future waypoints, then the method will no longer be self-supervised. The self-supervised component only refers to how \"instruction-relevant\" objects are localized without explicit supervision.\n\n\n## Need clarifications in approach and experiments\n- L152-156 - is hallucination of maps beyond the field of view helpful quantitatively?\n- Eqn 1 - is it a pixelwise loss?\n- L173 \"Because we do not know the exact locations of these instruction objects\" --- how often does this type of instruction-object ambiguity occur? For example, the instruction object being a long-bench and there are multiple benches nearby. I can imagine that in quite a few cases, the objects might be unique and can be localized accurately. \n- L177-184 - does P remain the same for all time-steps of the trajectory? If so, is it possible for the model to just ignore visual inputs and map the fixed language instruction to the fixed P (regardless of the agent states)?\n- In Tab. 3 ablation study - do all rows benefit from the auxiliary task? For example, the result without auxiliary task in Tab. 4 is close to semantic map (row 3 in Tab. 3). If semantic map does not use auxiliary task, then the gain from multi-granular representations itself is limited.\n- **[Minor point, not weakness]** L231 - how is the DAgger training performed without a human in the loop? Might be useful to add a section in the supplementary to explain this.\n- **[Minor point, not weakness]** In Tab. 5 ablation study - classification layer logits are better than semantic map from Tab. 3. Could the authors comment on this?\n\n\n# Typos and grammatical errors\nL11 - \"Moreover, we propose\" -> \"We further propose\" \nL64 - followings -> follows \nL87 - \"disables the agent to ground … well\" -> \"prevents the agent from effectively grounding …\" \nL114 - \"access to predefined\" -> \"access the predefined\" \nL122 - \"larger number\" -> \"large amount\" \nL164 - procuding -> producing \nL168 - \"reason precise semantics\" -> \"reason precisely about semantic\" \nL231 - \"teaching force\" -> \"teacher forcing\" \nL322 - \"carper\" -> \"carpet\" \n\n\n\t\n[1] **MapNet:** Henriques, Joao F., and Andrea Vedaldi. \"Mapnet: An allocentric spatial memory for mapping environments.\" proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2018. \n[2] **Semantic MapNet:** Cartillier, Vincent, et al. \"Semantic mapnet: Building allocentric semantic maps and representations from egocentric views.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 2. 2021. \n[3] **Cognitive Mapping and Planning**: Gupta, Saurabh, et al. \"Cognitive mapping and planning for visual navigation.\" Proceedings of the IEEE conference on computer vision and pattern recognition. 2017. \n[4] **Geometry-Aware RNNs**: Cheng, Ricson, Ziyan Wang, and Katerina Fragkiadaki. \"Geometry-aware recurrent neural networks for active visual recognition.\" Advances in Neural Information Processing Systems 31 (2018). \n[5] **Cross-Modal Map Learning**: Georgakis, Georgios, et al. \"Cross-modal Map Learning for Vision and Language Navigation.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022. # Novelty of multi-granular maps\n\n- Is the proposed mapping method achieving something different compared to prior work [1, 2, 3, 4]? \n- If so, can the authors quantitatively compare against map representations from [2] (and maybe even [1, 3, 4]) and verify it is indeed better? That is, replace the proposed multi-granular maps while keeping the auxiliary task and waypoint navigation as it is.\n\n# Novelty of auxiliary task\n\nThe method from [5] picks waypoints along the demonstration trajectory, and places gaussians at each waypoint to obtain the target heatmap for prediction. \n- Is the heatmap P in L177-182 different from the heatmap in [5]? \n- If they are indeed different (i.e., P focuses more on instruction-relevant objects rather than waypoints), could the authors replace the heatmap P with the heatmap from [5] and verify that the proposed method is indeed better? (note: the multi-granular maps and waypoint navigation pipeline remain the same)\n- Is the auxiliary task really self-supervised? That is, is it learning to localize instruction-relevant objects? Is the heatmap from [5] not resulting in localizing instruction-relevant objects in that case?\n\n# Other clarifications in approach and experiments\n- Could the authors clarify the questions raised in the weaknesses?\n\n[1] **MapNet:** Henriques, Joao F., and Andrea Vedaldi. \"Mapnet: An allocentric spatial memory for mapping environments.\" proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2018. \n[2] **Semantic MapNet:** Cartillier, Vincent, et al. \"Semantic mapnet: Building allocentric semantic maps and representations from egocentric views.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 2. 2021. \n[3] **Cognitive Mapping and Planning**: Gupta, Saurabh, et al. \"Cognitive mapping and planning for visual navigation.\" Proceedings of the IEEE conference on computer vision and pattern recognition. 2017. \n[4] **Geometry-Aware RNNs**: Cheng, Ricson, Ziyan Wang, and Katerina Fragkiadaki. \"Geometry-aware recurrent neural networks for active visual recognition.\" Advances in Neural Information Processing Systems 31 (2018). \n[5] **Cross-Modal Map Learning**: Georgakis, Georgios, et al. \"Cross-modal Map Learning for Vision and Language Navigation.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022. Yes. They have been sufficiently addressed.", " ## Post Rebuttal\n\nI thank the authors for their response. My main concern was addressed and the zero-shot evaluation on RxR is helpful. I encourage the authors to include a full evaluation on RxR. I have increased my rating.\n\n## Pre-rebuttal\nThis paper presents a method for building an environment map towards the end of performing natural language instruction following in continuous environments (VLN-CE). In the proposed method, the map has multiple granularities of information. A coarse granularity with features projected from UNet, and a global semantic map created by hallucinating semantic labels for the entire environment based on the coarse granularity map.\n\nThe encourage the map contain features relevant to instruction following, the authors also propose an additional objective that predicts the location of the ground-truth path on the environment map. This predicted path location is then used to attend to the map.\n\nThe method is evaluated on the VLN-CE dataset and outperforms all existing single camera methods. It is also competitive with panoramic methods. ### Strengths\n\nThe proposed method is well motivated. It makes sense to have multiple levels of information in a semantic map and to augment what is given to the agent based on the instruction.\n\nThe method works well. VLN-CE is a challenging task and a +4.5% SR increase is meaningful.\n\nThe ablation studies are well-done and provide useful insight.\n\n### Weaknesses\n\nNo evaluation on RxR-Habitat (https://ai.google.com/research/rxr/habitat). This uses the more recent RxR dataset that fixed some of the issues with the original VLN dataset and thus evaluation on this dataset would be very helpful in evaluated the method.\n\nThe intro to the task should cite + mention VLN-CE since that's the variant of the task being studied (and the less common one). I recommend referring to the task as VLN-CE to avoid confusion.\n\nL28-29: We don't know why humans (or any animal for that matter) build cognitive maps. Neither Tolman nor O'Keefe claim to know why cognitive maps were learned to be built (other than that they are useful for survival). They are an explanation of observed behavior, seen, but we don't know why that mechanism exists other than it's useful for survival (and thus is something that was learned implicitly). I recommend weakening this statement.\n\nSelf-supervised map representation learning via object location task is not a correct name. The objective is not self-supervised. Self-supervised implies that the learning objective is valid regardless of the dataset source (i.e. training data or data we'd see at evaluation). Ground-truth paths are certainly not part of the data we'd see at evaluation so this method doesn't fit. The task is possibly object localization with pseudo-labels (so weakly supervised), but those pseudo-labels are soft labels for predicting the ground-truth path. Since the motivation comes from object localization, that part of the name is probably fine, but the self-supervised part isn't.\n\nOverall, I think this paper presents a meaningful contribution and am happy to increase my rating if these concerns are addressed. See weaknesses Yes", " This paper presents an approach for vision-and-language navigation in continuous environments, centered around a semantic map which both aggregates and is used to predict object-centric information from the agent's observations. The approach uses fine-grained features extracted from a U-Net segmentation model applied to the agent's visual observations, as well as features for unseen parts of the environment predicted by a network supervised with ground-truth 3D info from the Matterport environment. This \"multi-granularity\" map is supervised using the ground-truth path of the agent through the environment, and used together with a recurrent, instruction-conditioned attention mechanism to predict waypoints for an off-the-shelf point-nav model to navigate to. The approach obtains the highest performance, by a substantial margin, among published VLN-CE leaderboard approaches that do not use panoramic image representations. Ablations show that each component of the approach helps pretty substantially. *Strengths*\n\nS1) The object representation and semantic map approach is well-motivated and well-executed, and the performance on the benchmark seems very strong.\n\nS2) The paper performed a thorough set of experiments that helped me convince me all the decisions made in the approach (both levels of granularity in the semantic map; the localization task) were useful. \n\n*Weaknesses*\n\nW1) One weakness of the approach is that the full version depends on \nground-truth 3D semantic information from the Matterport3D simulator in training (although not in inference, I believe). If I understand Table 3 correctly, without this info (just using the fine-grained map with segmentation features) the approach performs underperforms most of the other non-panoramic approaches (CMA, LAW, CM2). Since this info is only used in training, I don't think it's a crucial weakness, but I feel the paper could be clearer about this limitation, in particular perhaps rephrasing or removing the motivating claim in the intro that contrasts its approach with \"a naive solution that annotated a dataset ... with object classes and attributes for a segmentation model\". (lines 40-41). \n\n_Edit after response_: The response presented some compelling experiments showing that the proposed approach also improves when the semantic information is predicted by a pre-trained Faster R-CNN model, so I now feel like this is even less of a weakness. \n\nW2) The approach, as I understand it, is quite similar to the approach of Blukis et al, \"Mapping Navigation Instructions to Continuous Actions with Position-Visitation Prediction\", CoRL 2018, which also uses object-centric semantic maps and waypoint prediction, to do language-conditioned navigation in a continuous environment. However, I don't think this is a crucial weakness as that approach was applied in a different environment with what seem to be much simpler visual observations (involving a discrete set of objects). It would strengthen this paper to contrast with that approach in the related work.\n\n_Edit after response_: As the authors pointed out in their response, Blukis et al. does not use the multi-granular information that the proposed approach does. \n\nW3) The writing could be clearer, see suggestions below.\n Q1) Could the authors clarify what sources of ground-truth semantic information from the Matterport3D simulator (beyond RGB and depth imagery) are used, and when they are used -- in training, inference, or both?\n\nQ2) What parts of the model are updated during each of the two stages of training: teacher-forcing, and DAgger training? (e.g. is DD-PPO model held fixed during both of these, and the map prediction and object localization modules fine-tuned)?\n\nQ3) What are the off-the-shelf FGB and depth encoders (line 197)?\n I found the discussion of limitations in the paper somewhat lacking, although it should be easy to address given more space. In addition to discussing limitations due to object and environmental supervision (see above), it would also improve the paper to discuss more about possible directions that could improve the language-to-object grounding.\n\n*Suggestions*\n- Figure 1: the \"bed\" and \"door\" layers were unclear.\n- The motivation in the intro confused me a bit about what type of object supervision is used.\n- The object supervision in coarse localization was confusing to me. The localizer doesn't really seem to get any explicit object supervision, just closeness to the path -- and there doesn't seem to be flexibility for the model to choose how to focus the region attention using e.g. some sort of weakly-supervised or MIL loss. I think it might help to present this in a different way, e.g. as learning general info about the path (which may or may not be object-relevant). \n\n*Minor suggestions*\n- 112: \"continued\" -> \"continuous\"\n- 149: \"camera is with a\" -> \"the camera has a\"\n- 168: \"reason over precise semantic information\"\n- 322: \"carper\" -> \"carpet\"\n" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 7, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 3 ]

[ "QuTH3-YBRLI", "-xXAtkiw_Id", "5so-KWzecbO", "5so-KWzecbO", "uYFVvAgRPle", "C7RXbXrsx0y", "kB0MuSd-I_2", "K4jHTdXyBu-", "r1T_4wE1wwF", "-9SVisgBpl7", "O93fOlHIqhc", "mOZQ5CJSazh", "RcOOWiEW-ZH", "9ScPfZgeMM-", "k9MT2sk0mSE", "nips_2022_gyZMZBiI9Cw", "06N1mDn3HYJ", "nips_2022_gyZMZBiI9Cw", "nips_2022_gyZMZBiI9Cw", "nips_2022_gyZMZBiI9Cw", "nips_2022_gyZMZBiI9Cw" ]

[ "eA56QAsGp3A", "M6dzKx5KdqS", "gzqcQ5y9JNv", "tumZj8JG5m5", "5BniBY6R2cy", "0NfpjVWoO2l", "kEv5Kx33_8i", "uVgfCR1IBJdD", "eYUlHPwePCG", "b_9P96pwI7E", "51rhZtcqOP_", "WjuQq9gfoHM", "RQba-I2AUB4", "BIqCjZUEBoq", "bgkTbZHXX8m" ]

[ "author", "author", "author", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " As suggested by the Reviewer, applying noise at train time has the potential to improve robustness in a noisy evaluation environment. We totally agree with this idea. To evaluate its effectiveness, we conduct an experiment where we train and evaluate the agents in an environment with actuation noise and pose sensor noise. The evaluation results in a noisy environment for a MultiON-based active-camera agent are shown in the table below. \n\n\n| Train w/ Noise | SPL | PPL | Success | Progress |\n|----------------|------|------|---------|----------|\n| No | 17.1 | 25.2 | 35.4 | 56.9 |\n| Yes | 31.0 | 39.3 | 48.8 | 66.0 |\n\nFrom the results, simply applying noise at train time significantly increases the performance. This provides a simple but effective method for us to mitigate the effect of actuation and sensor noise. We believe applying other more complex noise estimation techniques could further improve the robustness.", " Thank you for your valuable reviews! We agree that these clarifications will make the paper better and will add them to the revised paper. Also thanks for your suggestion on multi-camera agents. We will consider it in a larger-scale experiment.", " Thank you for your valuable reviews. We agree that these clarifications will make the paper better. We will add them to the revised paper.", " Thank you authors for taking time to providing further analysis and clarifications.\n\nQ 1) 3) 5) -- I think this information is good to fit in the main paper.\n\nQ 2) I am also surprised by the results of multi-fixed camera being this bad compared to active camera or even single camera policy. I see your analysis in response to reviewer pNpw. It would be nice to have a large scale experiment in the final version. One idea also could be to add position of the cameras (front, right, left, rear) and concatenate that with the image features for multi-camera policy.\n\nQ 4) Thanks for providing further experiment with different mapper input-size. ", " Thank you for taking the time to respond to my comments.\n\nI appreciate that you explicitly quantified the deviation of the learned policy from the heuristic, I believe this defines the merit of the proposed approach more clearly. In particular, it seems like the heuristic on its own is very strong in SLAM contexts already, and navigation based on end-to-end learning is primarily where the proposed learned active policy has an edge.\n\nIn terms of state estimation and a POMDP treatment, I understand that the paper's main contribution is orthogonal to devising state estimators. Currently the method assumes perfect poses are available for end-to-end learning for MultiON, or it assumes the state estimates from SLAM are perfect. I agree that this is pragmatic from a research standpoint, allowing you to focus on the active data acquisition alone. It might be a good idea to highlight this aspect in the final version.\n\nThe motivation for my original comments was that imperfect state estimation will inevitably arise on real hardware (which you mentioned is out of scope for now), and then the effect of future observations might have to be accounted for by the policy. E.g. the active camera policy & the navigation policy might need to learn to avoid regions that can throw off the state estimator. State estimation uncertainty would also matter in that case.", " Thank you for the followup and comments! We're pleased that our response addresses some of your concerns, and hope to address the remainder now.\n\n> **Concerns on multi-camera results.** \n \nWe totally agree with the Reviewer that positional encoding is important for the e2e baseline. Actually, in our experiments, we have concatenated each RGBD feature with its corresponding heading embedding. We also have carefully checked our code and believe the code runs as expected. \n\n**We speculate the worse performance is mainly caused by non-convergence.** As shown in the tables below, when we continue to train the models, the performance of the multi-camera agent continuously increases （Table A） while the performance of front-facing single-camera agent does not change a lot (Table B). We speculate the multi-camera agent may need more training samples for learning how to map the relatively large amount of information from different directions to correct actions. Due to the time limitation of rebuttal, we will conduct a larger scale experiment after rebuttal and update the results in the revised paper.\n\n* Table A: Results of e2e-based multi-fixed-camera agents (the absolution performance difference from 30M are shown In parentheses).\n\n| Camera Type | # Training Samples | SPL | PPL | Success | Progress |\n|:--------------------:|:--------------------:|:---:|:---:|:-------:|:--------:|\n| Multi-Fixed-Camera | 30M | 14.4 | 29.1 | 17.9 | 38.7 |\n| Multi-Fixed-Camera | 33M | 15.8 (+1.4) | 31.5 (+2.4) | 19.0 (+1.1) | 40.0 (+1.3) |\n| Multi-Fixed-Camera | 36M | 17.3 (+2.9) | 32.8 (+3.7) | 20.2 (+2.3) | 41.1 (+2.4) |\n\n\n* Table B: Results of e2e-based single-fixed-camera agents (the absolution performance difference from 30M are shown In parentheses\n\n| Camera Type | # Training Samples | SPL | PPL | Success | Progress |\n|:--------------------:|:--------------------:|:---:|:---:|:-------:|:--------:|\n| Single-Fixed-Camera | 30M | 33.0 | 43.8 | 44.1 | 60.5 |\n| Single-Fixed-Camera | 33M | 33.1 (+0.1) | 44.6 (+0.8) | 43.2 (-0.9) | 60.4 (-0.1) |\n| Single-Fixed-Camera | 36M | 33.7 (+0.7) | 44.2 (+0.4) | 43.8 (-0.3) | 60.8 (+0.3) |\n\n\n**We also have conducted multi-camera experiments on the SLAM-based method.** The information captured by multiple cameras helps agents build a map efficiently. This map provides more information for path-planning. The results are shown below (Table C). The multi-camera agent outperforms our active camera agent. Because the SLAM-based multi-camera agent does not need to learn a neural network to map RBGD observation to navigation actions, it will not suffer from the slow convergence problem as in e2e-based agents. It is worth noting that although using a single camera, our active camera policy helps the agent achieve comparative performance compared with an agent with four fixed cameras.\n\n* Table C: Comparisons of SLAM-based agents with different camera types.\n\n| Camera Type | SPL | PPL | Success | Progress |\n|:---:|:---:|:---:|:---:|:---:|\n| Multi-Fixed-Camera | 68.3 | 72.2 | 79.4 | 85.3 |\n| Single-Active-Camera | 57.9 | 62.1 | 75.6 | 82.6 |\n\n> **Actuation Noise.**\n\nWe totally agree with the Reviewer that applying noise at train time has the potential to improve robustness. We will add the actuation noise experimental results in the revised paper and leave the noise mitigation study for future work.\n\nPlease don’t hesitate to let us know if there are any additional clarifications or experiments that we can offer. We appreciate your suggestions. Thanks!", " * **Multi-camera**: Thank you for the experiments. I am a bit puzzled regarding the poor performance of the multi-camera setup. It seems to perform very poorly, much worse than a front-facing camera, which does not make sense. Could it be a bug in the code, or do you think it's just due to the policy not having converged yet? It would be interesting to see a larger-scale experiment, especially based on a SLAM method, and see if the trend continues. For e2e policies some positional encoding may be necessary in the inputs in order to allow the robot to properly map view directions to actions.\n* **Clarity**: Thank you for addressing the clarity question. The diagram should help improve the paper's clarity.\n* **Actuation noise**: Thanks for including this experiment as well. It's worth adding it to the full paper. It seems that also applying noise at train time has potential to improve robustness!", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n> **Q1) Would it be possible to add a diagram, showing the specific information flow used when the end-to-end paradigm is used in navigation?**\n\nThanks for your valuable suggestion. We will make it more clear by adding an information flow diagram for the end-to-end paradigm in the supplementary.\n\n> **Q2) Multi-Camera Baseline: A multi-pinhole-camera robot could make for an interesting comparison. That being said, I still think it makes sense for the active camera setting to exist, as coordinating between motion and active sensing is generally an important problem in robotics, which hasn't received as much attention as it should have.**\n\nThank you for your recognition of our active camera. \n\nTo compare our single active camera with the multi-fixed-camera agent, we equip an agent with four fixed pinhole cameras facing different directions (front, left, right, and back). Specifically, we concatenate the features of these four images and feed them to an end-to-end navigation baseline (i.e., OccAnt). We train this baseline for 30 million frames, which is the same as our active camera agent. The results are shown below:\n\n| Camera Type | SPL | PPL | Success | Progress |\n|:---|:---:|:---:|:---:|:---:|\n| Multi-Fixed-Camera | 14.4 | 29.1 | 17.9 | 38.7 |\n| Single-Active-Camera (Ours) | **38.7** | **49.5** | **51.1** | **67.3** |\n\nFrom the results, our single-active-camera agent performs better than the baseline with four fixed cameras. We also observe that the multi-fixed-camera agent has not converged within 30 million frames. We speculate this is because the large amount of information from different directions increases the learning difficulty. More specific designs for using multi-fixed-camera are needed for further study.\n\n> **Q3) What is the actuation noise in the environment? If the policy always expects turning itself or its camera in exact 30° increments, suddenly rolling out in an environment with noisy actuation may cause serious problems.**\n\nThanks for your valuable comment. In this paper, we follow the existing works [b, c] to simplify the problem by training and testing without considering noise. However, we agree that actuation and sensor noises are unavoidable in the real world.\n\nTo respond to the Reviewer's concerns, we also evaluate our agents, which are trained in a noise-free environment, on a noisy environment. Specifically, we leverage the noise simulator in ANS [d] to simulate actuation noise and sensor noise for both body and camera movements. The results based on the MultiON baseline are as below (the absolution improvement are shown in the bracketed):\n\n* Evaluation without Noise:\n\n| Method | SPL | PPL | Success | Progress |\n|:---|:---|:---|:---|:---|\n| MultiON | 33.0 | 43.8 | 44.1 | 60.5 |\n| MultiON + Active Camera (Ours) | **38.7 (+5.7)** | **49.5 (+5.7)** | **51.1 (+7.0)** | **67.3 (+6.8)** |\n\n* Evaluation with Noise:\n\n| Method | SPL | PPL | Success | Progress |\n|:---|:---|:---|:---|:---|\n| MultiON | 3.1 | 9.4 | 6.7 | 22.5 |\n| MultiON + Active Camera (Ours) | **17.1 (+14.0)** | **25.2 (+15.8)** | **35.4 (+28.7)** | **56.9 (+34.4)** |\n\nFrom the results, the noise drops the performance of both our active camera agent and baseline agent. However, even under the noise evaluation setting, our active camera agent performs better than the baseline. We also observe that the agent with an active camera performs more robust under the noise condition.\n\nIn this work, we focus on proposing a camera policy that helps to actively move the camera. To mitigate the effect of noise, there are many existing techniques, including training a neural pose estimator [d] and designing specific rewards for the RL process [a]. These techniques are proven to be effective for navigation tasks. Incorporating these noise mitigation techniques with our camera policy is an interesting research direction. We will leave it for future work. \n\n\n**Reference:**\n\n[a] Occupancy Anticipation for Efficient Exploration and Navigation. In ECCV\n\n[b] MultiON: Benchmarking Semantic Map Memory using Multi-Object Navigation. In NeurIPS\n\n[c] Cross-modal Map Learning for Vision and Language Navigation. In CVPR\n\n[d] Learning to Explore using Active Neural SLAM. In ICLR", " > **Q6) Have you considered quantifying the exact way in which the trained camera policy deviates from the heuristic?**\n\nThank you for your valuable suggestion. Quantitatively, we summarize the frequency that the trained camera policy deviates from the heuristic: 6.8% for SLAM-based baseline (i.e., OccAnt), 52.9% for end-to-end baseline (i.e., MultiON). These deviations bring 1.6% and 23.5% improvement in terms of success rate (as shown in Tab. 3 in the paper), respectively. \n\nFrom these results, we notice that the deviation occurs more frequently for end-to-end baseline, and brings more significant improvement. We speculate this is because the observation obtained by heuristic camera actions cannot provide desired information for end-to-end learned navigation policy for deciding navigation actions. In this sense, the deviation occurs frequently. By contrast, the SLAM-based navigation policy decides actions by performing a path-planning algorithm on a progressively built map. This eases the demand for controlling camera action to get specific observations (as discussed in the second point in Q2). \n\n> **Q7) The solution is very specific in scope, tailored to the problem of actively controlling a camera for exploration, but on the other hand spatial exploration is an important topic and spatial agents are ubiquitous.**\n\nThanks for your comment. The main purpose of our paper is to propose an active camera policy that can cooperate with most existing navigation policies (i.e., SLAM-based and end-to-end policies). Experimental results show consistent improvements in these two types of mainstream navigation policies. Exploring a specific navigation policy that can better cooperate with our proposed camera policy for spatial exploration is a good research direction but out of scope in this paper.\n\n**Reference:**\n\n[a] Deep Recurrent Q-Learning for Partially Observable MDPs. In AAAI.\n\n[b] Memory-based Control with Recurrent Neural Networks. In NeurIPS\n\n[c] MultiON: Benchmarking Semantic Map Memory using Multi-Object Navigation. In NeurIPS\n\n[d] Occupancy Anticipation for Efficient Exploration and Navigation. In ECCV.\n\n[e] Learning to Explore using Active Neural SLAM. In ICLR", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n> **Q1) Are the agent states actually observed? The ideal decision problem would technically be a POMDP.**\n\nThank you very much for pointing it out. We totally agree with you that the agent's observations cannot fully specify the state of the environment in navigation tasks. In this sense, formulating the multi-goal navigation as a POMDP is more accurate. We will revise and discuss the formulation carefully in the revised paper.\n\n\n> **Q2) For the SLAM-based controllers, I am not convinced conditioning on the movement controls is enough. What is the reason to keep the controllers separated in the SLAM case?**\n\nWe agree that optimizing two policies as a joint control task enables coordination between two policies. We also want to point out that, in the SLAM case, the two policies are not totally separated for the following reasons. \n\n1) The **camera policy** decides camera actions conditioning on the output of the navigation policy so that it is not separated from the navigation policy. \n2) The **navigation policy** decides navigation action conditioning on a progressively built map, which is built from historical camera policy output. In this sense, the navigation policy is not separated from the camera policy. It is worth noticing that the SLAM-based navigation policy works well (i.e., planning the shortest path) without the need of knowing current camera actions. This is because the path planning destination always appears within the explored area of the map built in the last time step. In this sense, the images perceived in the future do not change the planned navigation actions.\n\nTo further alleviate the concerns of the Reviewer, we have conducted experiments using a joint action space in the SLAM case. In the table below, this variant performs slightly worse than ours. We speculate this is because the larger joint action space increases the learning difficulty. We will add these discussions in the revised paper.\n\n\n| | SPL | PPL | Success | Progress |\n|:---:|:---:|:---:|:---:|:---:|\n| SLAM-based Joint Actions | 52.0 | 56.5 | 71.4 | 79.0 |\n| SLAM-based (Ours) | **57.9** | **62.1** | **75.6** | **82.6** |\n\n\n\n> **Q3) In a POMDP the uncertainty of the state estimates normally plays a role, and I believe the agent states used to update the occupancy map are deterministic.**\n\nWe agree that the uncertainty of the state estimates is important in a POMDP problem. In our paper, although we have not estimated the state uncertainty explicitly, we exploit a recurrent neural network to summarize the historical partial observations to better estimate the underlying system state. The recurrent neural network is proven to be effective to solve POMDP problems [a, b]. In addition, existing navigation works also demonstrate their effectiveness in solving partially observed navigation problems [c, d]. \n\nEven so, we still believe the performance of our active camera agent can be further improved if we design a specific mechanism for estimating state uncertainty. We leave it for future work.\n\n> **Q4) The method is evaluated in only two environments in simulation, a real-world experiments have remained out of scope.**\n\nFollowing standard settings in visual navigation[c, d], we have evaluated our method in two benchmark simulated environments. Besides, we have evaluated the transferability ability of our method, i.e., training in one environment and testing in another environment. We agree that adapting the active camera policy to a real-world robot is an interesting research direction and we leave it for future work.\n\n> **Q5) Where do the camera poses come from in the end-to-end learned RL experiments (for the SLAM-based navigation task I assume the SLAM estimates are used)?**\n\nWe follow standard settings in MultiON [c] that equip agents with a perfect camera pose sensor to simplify the problem. There exist many works for estimating pose [d, e] and achieving good performance on navigation. Our main focus is to propose a camera policy that helps to move the camera actively during the navigation process. Exploring pose estimation methods is out of scope in this paper. ", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n\n> **Q1) Since the method is primarily trying to increase the scan horizon while moving, the authors should provide some details on the camera's field of view.**\n\nThanks for your suggestion. We follow the standard settings of the multi-object navigation task [a] and set the HFoV to 79°. We will add more crucial implementation details to the revised paper.\n\n> **Q2) While an active camera is a great idea to scan an unexplored environment map while moving, the same can be achieved by fitting multiple cameras and ensuring we have a large field of view.**\n\nThank you for your recognition of our active camera. \n\nTo compare our single active camera with a multi-fixed-camera agent, we equip an agent with four fixed pinhole cameras facing different directions (front, left, right, and back). Specifically, we concatenate the features of these four images and feed them to an end-to-end navigation baseline (i.e., OccAnt). We train this baseline for 30 million frames, which is the same as our active camera agent. The results are shown below:\n\n| Camera Type | SPL | PPL | Success | Progress |\n|:---|:---|:---|:---|:---|\n| Multi-Fixed-Camera | 14.4 | 29.1 | 17.9 | 38.7 |\n| Single-Active-Camera (Ours) | **38.7** | **49.5** | **51.1** | **67.3** |\n\nFrom the results, our single-active-camera agent performs better than the baseline with four fixed cameras. We also observe that the multi-fixed-camera agent has not converged within 30 million frames. We speculate this is because the large amount of information from different directions increases the learning difficulty. More specific designs for using multi-fixed-camera are needed for further study.\n\n> **Q3) I encourage authors to mention more limitations of the method. For example, different types of robots, especially the high DOF robots, are needed to be evaluated with active cameras.**\n\nThanks for your valuable suggestion. Although we have evaluated the transferability of camera policy among different datasets (transferring from MatterPort3D to Gibson) in our paper, evaluating its robustness among different robot types and different embodied tasks is a valuable research direction. We will discuss these limitations and future work directions in the revised paper.\n\n> **Q4) What is the egocentric map size and how did you choose it? How does the policy performance change with increasing / decreasing this map size?**\n\nThe egocentric map size is set to 125x125. We choose it by considering whether the map provides enough information for deciding actions. Specifically, we first set the map resolution as 0.08m, so that the map is fine-grained enough for path planning. Then, we have tried different map sizes, including 50x50, 75x75, 100x100, 125x125 and 150x150. The map with different map size cover different area of the environment. The results of our active camera agent based on OccAnt are as follows.\n\n| Map Size | SPL | PPL | Success | Progress |\n|:---|:---|:---|:---|:---|\n| 75x75 | 56.3 | 60.4 | 73.8 | 81.0 |\n| 100x100 | 56.5 | 61.1 | 73.4 | 80.8 |\n| 125x125 (Ours) | **57.9** | **62.1** | **75.6** | **82.6** |\n| 150x150 | 56.7 | 61.0 | 73.2 | 80.8 |\n\nFrom the results, an agent with a 125x125 map (which represents 10m x 10m around the agents) performs best. We observe that the map with a too small size cannot provide enough information for deciding navigation and camera actions. If the map is too large, it contains too much envrionment information far away from the agent, which may also deteriorate the performance. \n\n> **Q5) For the experiment with an imperfect mapper, can the authors please also add what was the accuracy of such a trained mapper?**\n\nWe use the pre-trained Mapper from existing work [b], whose accuracy for local map prediction is 75.2%. More analysis and visualization results of this mapper can be seen in the original paper [b]. We will add these details in the revised paper.\n\n**Reference:**\n\n[a] MultiON: Benchmarking Semantic Map Memory using Multi-Object Navigation. In NeurIPS\n\n[b] Occupancy Anticipation for Efficient Exploration and Navigation. In ECCV\n", " We sincerely appreciate all reviewers’ time and efforts in reviewing our paper and for the constructive feedback. In addition to the response to specific reviewers, here we would like to thank reviewers for their acknowledgment of our work and highlight the new results added during the rebuttal:\n\n**We are glad that the reviewers appreciate and recognize our contributions:**\n\n* The proposed solution has value [iN1f]\n* Coordinating between motion and active sensing is an important problem in robotics [pNpw]\n* An active camera is a great idea [uqJh]\n* The paper is well written and easy to follow [iN1f, uqJh]\n* Trained active camera policy generalizes to the other datasets well on both SLAM-based and learning-based settings [iN1f, pNpw, uqJh]\n\n**In this rebuttal, we have added more supporting results following the reviewers’ suggestions.**\n\n* Evaluate the SLAM-based method under joint action space [iN1f]\n* Summarize the frequency that the trained camera policy deviates from the heuristic camera policy [iN1f]\n* Compare our single active camera with the multi-fixed-camera agent [pNpw, uqJh]\n* Evaluate our agents, which are trained in a noise-free environment, on a noisy environment [pNpw]\n* Conduct ablation study on different map sizes [uqJh]\n\n\n**We also address the reviewers’ questions by adding the following revision to the revised paper.**\n\n* We reformulate the problem as POMDP in Section 3.1 [iN1f]\n* Detailed analysis of how two policies coordinate in the SLAM case is added in Section 3.4 [iN1f]\n* An information flow diagram for the end-to-end paradigm is added in the revised supplementary material [pNpw]\n* Some crucial implementation details, including the camera FoV, are added in the revised supplementary material [uqJh]\n* More limitations and future works are discussed in Section 5 [uqJh]", " This paper enables efficient multi-goal navigation through active perception.\nThe camera of the agent, which determines its limited field of view, is actively controlled to turn towards scene regions that are still unexplored.\nCamera rotation is decoupled from agent movement, i.e. the agent can still move in directions other than the facing direction.\nThe camera control problem is framed as an MDP with rewards proportional to spatial exploration of the environment (measured in uncovered area, based on a maintained 2D occupancy map).\nCamera actions are produced by a parametric policy optimized through PPO for the aforementioned MDP (with an explicit critic that approximates state values).\nThe policy is informed through a very strong heuristic for how the camera should turn, in the form of an extra objective term, but also seems to improve upon it (due to the refinement through the exploration objective from the described MDP).\nIt is demonstrated that actively controlling the camera leads to improved efficiency and success rate for the multi-goal navigation task on the MatterPort3D and Gibson data sets.\nBoth SLAM-based and end-to-end RL navigation baselines are augmented with the active camera policy in the experiments.\nGeneralization from MatterPort3D (used for training) to Gibson is demonstrated.\n\n**Technical details**\nThe proposed scheme is used to augment existing navigation methods that are already tailored to the multi-goal navigation task.\nThe camera policy is recurrent and is conditioned on features from a top-down 2D map. \nIt also takes in the hand-crafted heuristic camera control and the action produced by the movement policy as input (the latter is necesary only when a SLAM model is used, as camera and movement controllers are decoupled).\nWhen an end-to-end RL model is considered, the camera and movement policy are modelled by the same recurrent neural network, jointly optimizing an MDP with rewards for both navigation and exploration. **Strengths**\n- The approach appears straightforward & functional. The design choices are pragmatic.\n- The motivation is easy to understand and follow.\n- The fact that camera and motion control needs to be considered jointly has been accounted for, albeit only for the end-to-end learned systems.\n- Ablations of the method are appreciated, they indicate that the different modelling choices were necessary.\n- It is nice to see the policy generalizes from one data set to the other.\n\n**Weaknesses**\n- The authors discuss the camera policy in the context of an MDP, but are the agent states actually observed? My impression was that the multi-goal navigation task is a partially-observed problem, where the observations are only RGB-D images. In that case the ideal decision problem would technically be a POMDP, and this should be discussed in the manuscript. \n- Optimizing the camera policy in isolation of the overarching movement control problem can be problematic, as the authors have also noted in the experimental section. This has been accounted for in the end-to-end learned experiments, where a joint control task is formulated. But for the SLAM-based controllers, I am not convinced conditioning on the movement controls is enough. Particularly if you consider the ideal POMDP formulation, the movement controller should be aware of the images that will be perceived in the future (due to camera control), as this will affect the quality of state estimation (which both policies should account for). What is the reason to keep the controllers separated in the SLAM case?\n- In a POMDP the uncertainty of the state estimates normally plays a role, and I believe the agent states used to update the occupancy map are deterministic.\n- The method is evaluated in only two environments in simulation, real-world experiments have remained out of scope.\n\nOverall, I find that the proposed solution has value, the proposed idea is straightforward and seems to work as intended.\nThe solution is very specific in scope, tailored to the problem of actively controlling a camera for exploration, but on the other hand spatial exploration is an important topic and spatial agents are ubiquitous.\nThe other reservations I have are related to the missing discussion of how the method fits into the POMDP paradigm; I do not necessarily expect the method to change, but being explicit about its limitations would be appreciated.\n **Questions**\n- The proposed method maintains a 2D occupancy map of the environment, which is necessary to compute the exploration heuristic. Where do the camera poses come from in the end-to-end learned RL experiments (for the SLAM-based navigation task I assume the SLAM estimates are used)? These poses are needed to update the occupancy map with the RGB-D observations.\n- Have you considered quantifying the exact way in which the trained camera policy deviates from the heuristic?\n I don't see any major negative societal impact. There is a short section on limitations right before the conclusion that mentions the lack of real-world experiments. It could be extended based on the remarks above.", " The paper tackles the challenge of SLAM-based multi-object navigation for indoor\nrobots. This task is typically approached with an algorithmic or RL method which\ndrives a robot equipped with an RGB-D sensor through an unknown finite\nenvironment. The robot's goal is to find a series of predefined objects under a\nlimited step budget. \n\nThe paper makes the observation that prior approaches, such as Active Neural\nSLAM, assume a fixed camera robot configuration with a limited forward-facing\nFoV. The paper then proposes decoupling the robot motion from the camera yaw.\nThe robot can thus choose to, e.g., move in a direction while looking to the\nside if it decides this provides more information. Two policies are learned,\none for navigation, one for looking around, with the navigation decision\nfeeding into the camera policy. The navigation policy is also responsible for\ndetecting the goal.\n\nThe paper focuses on the camera policy, which is designed to work both on top\nof SLAM-based, as well as end-to-end navigation policies.\n\nThe method is trained on-policy using the photorealistic 3D environment\nMatterport3D. The camera policy can generalize to the Gibson environment without\nfine-tuning. In general, allowing the robot to move its camera independent of\nits movement direction improves over baselines like not moving the camera,\nmoving it randomly, or moving it according to predefined patterns. This\nimprovement is consistent when evaluated on top of multiple navigation methods.\nThe paper also includes ablation studies for some of the key design decisions. \n ## Strengths\n- [S1] The paper demonstrates cross-domain generalization by training on\n Matterport3D and successfully transferring the policies to the Gibson Env\n without any fine-tuning. \n- [S2] The proposed method is also shown to help improve both a SLAM-based, as\n well as a learning-based baseline.\n- [S3] The paper defines an interesting new direction in active sensing.\n\n## Weaknesses\n- [W1] Clarity: It took me a while to realize that the method is actually fully\n compatible with both SLAM-based and end-to-end navigation systems. Would it be\n possible to add a diagram, maybe in the supmat if the main paper can't fit it,\n showing the specific information flow used when the end-to-end paradigm is\n used in navigation?\n - Either way, it would be nice to clarify this earlier in the paper, as it\n makes it easier to understand how the camera policy fits into the existing\n navigation pipeline.\n- [W2] Multi-Camera Baseline: While I do understand the point brought up in\n Appendix A, I am not fully convinced by the argument.\n - A multi-pinhole-camera robot could make for an interesting comparison, in\n spite of the increased costs. A complex panoramic camera (with the\n associated geometric and hardware complexity) is not strictly required. \n - An additional advantage of multiple fixed camera is eliminating the need for\n the moving parts of the revolute joint and its associated servo. \n - Second, I wouldn't call the computational overhead of, say, four cameras\n \"huge\", since naive baselines like concatenating the images before feeding\n them to an end-to-end navigation policy would probably work pretty well\n already.\n - Multi-camera systems, albeit not depth-based, are already ubiquitous in mobile\n phones, drones, and (even non-autonomous) vehicles.\n - That being said, I still think it makes sense for this problem setting to\n exist, as coordinating between motion and active sensing is generally an\n important problem in robotics, which hasn't received as much attention as it\n should have. \n\n\n## Suggestions\n- L194: \"module SLAM-based\" -> \"modular, SLAM-based\"?\n - [Q1] What is the actuation noise in the environment? If the policy always expects\n turning itself or its camera in exact 30° increments, suddenly rolling out in an\n environment with noisy actuation may cause serious problems.\n Please see \"Weaknesses\".", " In this paper, the authors propose to learn the active camera policy for multi-object robot navigation. Specifically, they show how to use camera rotations effectively to increase the information while in motion, and how to integrate the active camera policy with the navigation policy. Authors train active camera policy using Reinforcement Learning (RL) and carefully design a reward function that encourages robots to explore more areas. Through multiple baseline methods composed of SLAM-based, and end-to-end learning-based, the authors show that integrating active camera policy with the base navigation policy improves object navigation accuracy and efficiency on multiple metrics. Strengths:\n1. Paper is well written. The authors show clear motivation for the need for active cameras to aid exploration while navigating. They formulate the problem, propose a reinforcement-learning-based solution, and show the effectiveness of active cameras through extensive experiments.\n2. Trained Active Camera Policy (EXPO) generalizes to other datasets than the one it’s been trained on (MatterPort3d → Gibson)\n3. Authors show ablation study to show the usefulness of Active Camera Policy design components\n4. Authors show improvements on 4 different baselines applied to 2 datasets. Baseline methods consist of SLAM-based, end-to-end learning-based methods, and hybrid methods.\n\nWeakness:\n1. Since the method is primarily trying to increase the scan horizon while moving, the authors should provide some details on the camera field of view. While I understand this is standard for the datasets like Mattterport3D, and Gibson, to be comprehensive it is necessary to include the field of view in the paper.\n2. While an active camera is a great idea to scan an unexplored environment map while moving, the same can be achieved by fitting multiple cameras and ensuring we have a large field of view. Ideally, having multiple cameras covering a larger field of view will serve as an upper bound of what can be achieved.\n3. I encourage authors to add more limitations of the method as described in the limitations review section\n 1. What is the egocentric map size and how did you choose it? How does the policy performance change with increasing / decreasing this map size? I believe increasing cropped egocentric map would increase % of an unexplored area of the input map, and it would be good to see how it affects the policy. \n2. For the experiment with an imperfect mapper, can the authors please also add what was the accuracy of such a trained mapper? \n The authors have mentioned very generic limitations. Few assumptions of the paper should be part of the limitations as well.\n1. Along with testing the effectiveness of such a method in the real-world environment, it is also useful to mention the limitation that different types of robots might also have to experiment with environment representations. \n2. This active camera policy limits the use of a learning-based locomotion policy for high DoF robots such as Spot, and ANYMAL. Since the camera is not facing the robots' traversal path continuously. \n\n" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 4 ]

[ "0NfpjVWoO2l", "tumZj8JG5m5", "5BniBY6R2cy", "51rhZtcqOP_", "eYUlHPwePCG", "kEv5Kx33_8i", "uVgfCR1IBJdD", "BIqCjZUEBoq", "b_9P96pwI7E", "RQba-I2AUB4", "bgkTbZHXX8m", "nips_2022_iH4eyI5A7o", "nips_2022_iH4eyI5A7o", "nips_2022_iH4eyI5A7o", "nips_2022_iH4eyI5A7o" ]

[ "2JTMG58rKME", "dXVK3fe_f7", "5Y3WB-jp_KM", "i0WJNiz_YkH", "9rJtPH00wzh", "ygOOybgIAI", "EiDChq7MSTZ", "dftRrH0uYG", "k4DW-Z1-_g9", "xq2V7ox9q0A", "DSRtoXRN8c7", "l2d_WfsRZXS", "XEA1Ai6fY4", "vrtUbXesFLr", "CdXcHBzQ9ji", "SueoUOqUiX", "U8JK7cxakOSS", "D1cBAthyIX", "u78amX2Rj2M", "OO2Ae8kiNR", "uwUSi65ySgF", "_z7F07wK6zw", "A3BPjTcVr7J", "M6iD6n_FP-M", "B3bzwgmnmI" ]

[ "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I appreciate the responses from the authors. I'm increasing my score to 5 at this point, while I look forward to discussing more with the other reviewers in the next phase.", " We appreciate the reviewer's positive comments. We have updated Fig. 4 which visualizes comparisons against other image denoising methods. We also updated Fig. 8 which shows the application of our model in complex geometry processing. Hope these could strengthen the practical significance of our paper and help this paper turn more positive in your mind.", " We appreciate the reviewer's positive comments. We've made changes in our revised draft as suggested by the reviewer.", " We thank the reviewer for their positive comments. We've updated our results in Fig. 8, which demonstrates the capability of our INSP-Net in processing complex geometries encoded by INRs.\n", " We thank the reviewer for their insightful comments. Our responses to the concerns are listed as follows.\n\n**Q1. The quality of the solutions is not very satisfying. As a result, the advantages of working in the INR domain are not very appealing.**\n\nWe appreciate the reviewer’s comments on Fig. 4 and Tab. 2. Though the result of DnCNN has a better visual looking, the result of our INSP-Net has a smaller pixel-wise error against the reference image. The reason why the quantitative performance of DnCNN/MPRNet is lower is that they obtain a blur result. We’ve updated Fig. 4 with Gaussian noise examples and removed the original Tab. 2 from the pdf as suggested by the reviewer.\n\nWe would also like to re-emphasize the advantages of INRs as well as our signal processing framework.\n\n1. INR has demonstrated great success in image and video compression [1,2]. These exciting advances advocate INR to potentially become the next universal data compression and representation format for the future.\n\n There already exist various attempts to process image [4] and video [3] compressed representation directly, alleviating the unnecessary cost of decoding the representations first. Thus, a corresponding continuous processing method for INRs without the need of decoding is in great demand.\n\n2. INRs have now become irreplaceable in many computer vision tasks, such as reconstructing SDF. As shown by [5], only adopting INR can effectively solve the Eikonal boundary value problem to recover fine details in 3D geometries. In this scenario, any attempt of discretization will cause information loss. Our method directly edits SDF on the network weights and structures, which preserves all the information in the continuous space. We updated our results in Fig. 8, which demonstrates the capability of our INSP-Net in processing complex geometries encoded by INRs.\n\nOur work on continuous signal processing is forward-looking. We do not expect to outperform existing endeavors for decades in processing the discretized instances. However, our novel setting is highly worth investigating given its above-mentioned advantages.\n\n\n[1] Zhang et al. Implicit Neural Video Compression\n\n[2] Dupont et al. COIN: COmpression with Implicit Neural representations\n\n[3] Wu et al. Compressed Video Action Recognition\n\n[4] Xu et al. Learning in the Frequency Domain\n\n[5] Sitzmann et al. Implicit Neural Representations with Periodic Activation Functions\n\n**Q7. Given by $\\Pi = \\Phi(x)$, $\\Pi$ will not be shift-invariant (unless $\\Phi$ represents a constant image...).**\n\nFirst of all, we would like to remind the reviewer of our notation. $\\mathcal{A}$ is the operator (e.g., a convolution) that maps a function (INR) to another function (INR), while $\\Pi$ as a part of $\\mathcal{A}$ is just a multivariate function. Operator $\\mathcal{A}$ maps a function by composing $\\Pi$ on top of its derivatives. An operator is shift-invariance if it is commutative with coordinate transformation (cf. Definition 1 & 2). **Our Theorem 1 discusses the invariance of $\\mathcal{A}$ instead of $\\Pi$.** $\\mathcal{A}$ is shift-invariant regardless of whether $\\Pi$ is shift-invariant because $\\Pi$ is a pointwise function with respect only to derivatives (which are known to be shift-invariant).\n\nWe do not think $\\Pi = \\Phi(x)$ is generally allowed since their input spaces are different (The input space of $\\Pi$ is $M$-dimension while $\\Phi$ is $m$-dimension). So we guess the reviewer means $\\mathcal{A}\\Phi(x) = \\Phi(x)$, i.e., $\\mathcal{A}$ is an identity mapping. Clearly, the identity operator is shift-invariant since $ \\mathcal{A}[\\Phi \\circ T] (x) = \\Phi \\circ T (x) = \\mathcal{A}[\\Phi] \\circ T (x)$. We have to admit that rigorously speaking, we need to change “invariance” to “equivariance”. However, since “invariance” is a common “misnomer” used over decades in computer vision [1], we do not see there is a risk of causing confusion in this community.\n\n[1] Lecun et al., Gradient Based Learning Applied to Document Recognition, 1998\n", " Thanks for providing detailed feedback. All my concerns have been well addressed. I would like to keep my initial rating and make a final rating after discussion with other reviewers.", " Thank you to all the reviewers for the great effort in reviewing the paper and the authors for the responses.\n\nAs the author-reviewer discussion period is almost over, I want to ensure that reviewers have read the authors' responses and engage with the authors if needed.\n\nIf you haven't done this, could you please take a moment to read through the authors' responses, update the reviews to indicate that you have read the authors' responses, or communicate with the authors if needed? You can also share in private conversations with the reviewing team.\n\nPlease continue to share your thoughts. Thank you!", " Thank you for the detailed response. I appreciate the additional information regarding geometry and audio processing, which was originally missing from the paper. I would be open to increase the rating, after further discussions and confirmations with other reviewers.", " Thank you - I am happy with the changes you made. Minor comments:\n\n1. I think the section should be called \"Limitations.\" instead of \"Limitation\".\n2. I think in the Limitations section, you should clarify that you aren't addressing how to reconstruct / infer INRs, and that the present paper does not give any hint of how that might be achieved in a scalable manner. \n\nAll in all, I remain positive about this paper, and will champion it the discussion with the other reviewers.", " I thank the authors for their thorough responses to my questions and comments. Some follow ups:\n\nQ1. I completely understand that comparing is hard, given the discrete vs continuous nature of the different algorithms. Yet, the authors study image processing tasks, and images and signals are (for most practical purposes) discrete objects, so this is inevitable. I still believe the denoising performance (as well as in other tasks) if far behind conventional methods. Once again, I don't understand how a difference of 2dB (w.r.t DnCNN) is possible in the example on Fig. 4, given that the results of INSP-Net is so much more noisy. \n\nI certainly appreciate the inclusion of the Tables and the comparison with other 2 methods for image denoising, and they indeed improve and clarity the contribution of this paper. One small comment: The authors can include Table 2 (denoising on noise that is not Gaussian) but this does not mean much: it is clear that these off-the-shelf denoising models were trained on a specific data distribution (in this case, natural images + Gaussian noise). These methods performing bad under different distributions has nothing to do with overfitting (which implies fitting to a finite sample *from the same distribution as the testing data*), but rather with how robust these are to shifts in the data distribution. I presume the authors did not make any claims on robustness to distribution shifts, and as a result the comparison seems unfair. The authors may choose to keep this table if they wish - but I would remove it if this were my paper :)\n\nQ2. Thanks\n\nQ3. Thanks for the clarification: indeed, I don't think this is a very standard definition of \"closed form\".\n\nQ4. Thanks.\n\nQ5. Thanks\n\nQ6. Thanks. As a remark: wavelet bases and an (orthogonal) basis are very different things. One can indeed have wavelet frames that are not orthogonal.\n\nQ7. Thanks for the clarification. Yet, this pointed to a new question on the same topic: Theorem 1 states that \"$\\mathcal A$ can be shift invariant *for every* $\\Pi$\". I agree with the claim that \"every shift invariant operator can be represented by *some* $\\mathcal A$\", but this is not what the statement of the theorem says. My concern comes from the following observation: Consider the operator $\\Pi$ given by $\\Pi=\\Phi(x)$, which is certainly allowed by the definition in Eq. (3). Now, in this case, $\\Pi$ will not be shift invariant (unless $\\Phi(x)$ represents a constant image...), which contradicts the original statement. What am I missing?\n\nQ8. Thanks.\n\nQ9. Thanks.\n\n\n", " Dear Reviewer qGk1,\n\nWe want to thank you again for your reviewing time and positive assessment. We would like to kindly remind you that the discussion period is ending soon. We hope to use this open response period to discuss the paper to solve the concerns and improve the quality of our paper. Have you gotten a chance to read our responses above, which attempt to address all of your concerns? We would be more than happy to provide more information or clarification. \n\nWe have re-stated the significance of our work and demonstrated more experiments on geometry processing (Fig. 8) and audio denoising (Fig. 14). Given all results, for the first time, we demonstrate the possibility of editing INR on the weight and network structure space.\n\nIf our response could resolve your concerns, could you please kindly consider raising the rating of our work? We sincerely wish to bring our theoretical grounded solution for direct signal processing on INR into the neural field community.\n\nBest,\n\nAuthors of paper 988", " Dear Reviewer 1Ys6:\n\nWe would like to thank you again for the favorable assessment of our work. We have put our two cents in your insightful open questions, and hope they are helpful. As a follow-up on our responses, we would like to kindly ask if you want to have further discussion as the author-reviewer interaction session is ending soon. We would be more than happy to provide more information or clarification.\n\nAny suggestions to improve the quality of this paper would be greatly appreciated. We sincerely wish to bring our theoretical grounded solution for direct signal processing on INR into the neural field community.\n\nBest,\n\nAuthors of paper 988", " Dear Reviewer edqT,\n\nWe want to thank you for the constructive comments in your review. As a follow-up on our responses, we would like to kindly remind you that the discussion period is ending soon. We hope to use this open response period to discuss the paper to solve the concerns and improve the quality of our paper. Have you gotten a chance to read our responses above, which attempt to address all of your concerns?\n\nWe have fixed all the writing flaws and provided more experiments on geometry processing (Fig. 8) and audio denoising (Fig. 14). Given all preliminary results, for the first time, we demonstrate the possibility of editing INR on the weight and network structure space.\n\nWe sincerely hope to have further discussions with you to see if our response solves the concerns. We would be more than happy to provide more information or clarification, should it be necessary. We hope our paper could receive a positive and fair assessment. We sincerely wish to bring our theoretical grounded solution for direct signal processing on INR into the neural field community.\n\nBest,\n\nAuthors of paper 988", " Dear Reviewer Uh51,\n\nWe appreciate it if you could please review our response to your comments since the reviewer-author discussion session has started several days. We have provided more results on geometry smoothing (Fig. 8) and audio denoising (Fig. 14). We are willing to reply to your further questions in this time window if you have any feedback.\n\nIf our response could resolve your concerns, could you please kindly consider raising the rating of our work? We sincerely wish to bring our theoretical grounded solution for direct signal processing on INR into the neural field community. Thank you very much for your efforts and time.\n\nBest,\n\nPaper 988 Authors\n", " \nWe thank all reviewers for their time and detailed comments. We are glad that all the reviewers acknowledged our strong motivation and novelty. We also noticed some of the reviewers are more or less concerned about our experimental results. Hereby, we would like to re-state the significance of our work.\n\nINR has achieved ubiquitous success in signal compression [2], 3D reconstruction [1,3,4], and even scientific computing [1,5,6]. Representing signals with a coordinate-based neural network enjoys promising properties, such as continuous representation and unlimited resolution [1]. These advocate INR potentially becoming the next universal data format for the future. However, being represented by implicit neural network weights, such signals cannot be manipulated or processed easily unless decoding INR into grid-based representations. The proposed framework is the **first** generic framework that achieves INR editing directly on the weight space and network structures, with a **theoretical guarantee**.\n\nThe goal of this paper is not to beat the state-of-the-art baselines on low-level vision or image classification tasks. Instead, our experiments are designed to demonstrate the effectiveness of leveraging differential operators to analytically process INRs. Although the experimental results do not demonstrate superiority in every aspect, they are still encouraging considering this is the first time that implicit fields can be processed and even learned on the weight space. To further demonstrate the practical significance, we also added experiments on geometry and audio processing.\n\nAccording to reviewers’ suggestions, we have made these several changes (highlighted in blue) to our PDF, summarized as below :\n\n1. We have added experiments in geometric processing (Sec. 5.3) and audio denoising (Fig. 14). This extends the application range of our work so that we can safely claim our method is for general-purpose signal processing.\n2. We have added quantitative comparisons on a large dataset in Tab. 2 & Tab. 3.\n3. We have added a limitation paragraph (Sec. 6) to clarify the existing downsides of our methods, which are left for future works.\n4. We have carefully revised our manuscript correcting detail errors and adding missing references.\n5. Due to page limit, we deferred the detailed introduction to INSP-ConvNet to the Appendix C, and added pseudocode for clarity.\n\nWe would appreciate it if all reviewers could please take a look and finalize their assessments of our work, hopefully more positively. We trust the reviewer and AC discussion would eventually lead to an informed and fair decision, and we thank everyone again for the valued efforts!\n\nBest,\n\nPaper 988 Authors\n\n[1] Sitzmann et al. Implicit Neural Representations with Periodic Activation Functions\n\n[2] Dupont et al. COIN: COmpression with Implicit Neural representations\n\n[3] Park et al. DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation\n\n[4] Mildenhall et al. NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis\n\n[5] Li et al. Fourier Neural Operator for Parametric Partial Differential Equations\n\n[6] Zhong et al. CryoDRGN: reconstruction of heterogeneous cryo-EM structures using neural networks\n\n", " We thank reviewer qGk1 for the favorable assessments and constructive suggestions. Typos have been fixed in our revision.\n\n**Q1. From experiments, it seems that INSP-Net operating on INRs cannot exhibit superiority against convolution operating on pixels.**\n\nOur experiments are not aimed at achieving state-of-the-art performance on the low-level vision tasks, but to verify the correctness of our theory and the feasibility of our method of directly processing continuous implicit fields on the weight space. Moreover, designing a fair comparison setting can be tricky. As far as we know, a general signal processing framework for implicit fields remains an open question. All the compared baselines are “discrete” methods, and they are served only for reference. We admit the experimental results indicate there is still a gap compared to our final goal, but we believe it is more important to show the value of constructing closed-form operators to edit INR on the weight space, which can potentially lead to a promising direction in the neural implicit field community.\n\n**Q2. For image classification, why is Depthwise CNN used as a baseline rather than typical CNN?**\n\nNo existing techniques can classify INR directly using its network weights. Comparing with discrete CNN is for feasibility demonstration and expressive power justification. We use depth-wise CNN because our INSP-ConvNet has the same architecture to trade off the efficiency. As our theory shows, our INSP-ConvNet should have at least the same expressiveness as the compared depth-wise CNN. \n ", " **Q2. Notation confusion.**\n\nIn Eq. 1, indeed we meant $\\arg\\min$ instead of $\\arg\\max$. We have fixed this typo in our revision. To avoid confusion, we have also replaced the notation of number of measurements in Eq. 2 to $N$. We used $m$ to denote the dimension of input coordinate, $M$ to denote the input dimension of $\\Pi$. Hence, we still believe in line 117, it should be $x \\in R^m$ instead of $R^M$.\n\n\n**Q3. Gradients can be obtained \"in closed form\", but operators defined only as parametric functions learned from data operators cannot.**\n\nBy saying \"in closed form\", we mean the forward pass of processed INR is a mathematical expression with a finite number of standard operations and can be computed analytically without any discretization and approximation, instead of meaning computed the parameterization is a closed form solution to some objectives. AutoInt [1] used similar terminology. We added a footnote to clarify this definition.\n\n[1] Lindell et al. AutoInt: Automatic Integration for Fast Neural Volume Rendering \n\n\n**Q4. How to handle nonlinear activations and normalizations?**\n\nSince nonlinear activation and normalization are usually element-wise operations, we can directly compose such operations to the output of INSP-Net (Eq. 3). To illustrate how convolutional layers and nonlinearity cooperate with each other, we include an algorithm paradigm in Algorithm 1.\n\n**Q5. The novelty of Theorem 1 is very limited.**\n\nWe are aware that group invariance has been well investigated in partial differential equations (line 148-152), and we also cite a series of those papers. Even though Theorem 1 is not our main result, we still feel it is necessary to formalize it as a theorem in our paper, which highlights some desirable properties of our framework to the readers.\n\n**Q6. It is unclear why the authors mention that the differential operators form a wavelet basis.**\n\nDifferential operators are not strictly orthogonal to each other, however, they form an independent basis. We have removed the word \"wavelet\" in the revision to avoid confusion.\n\n**Q7. In line 204, the authors comment that their operators can simulate exact convolutions. This seems incorrect to me, as the exact equivalence holds for an infinite sequence, and thus only a finite approximation is possible in this framework.**\n\nWe respectfully disagree with the reviewer's opinion on our Eq. 5 is not an exact convolution. Let's recall that convolution is defined as the linear and shift-invariant operator. As we revealed in Thm. 1, Eq. 5 is both linear and shift-invariant, thus simulating an exact convolution. It is safe to state $A$ is approximating any convolution inside the linear and shift-invariant family when fixing $\\Pi$ to be a linear transformation (cf. line 207-208).\n\n**Q8. There are many errors that make reading quite difficult. It's unclear what the authors mean by \"semantic labels y_i\" in line 235.**\n\nThanks for pointing out writing errors. We have fixed all the mentioned typos and proofread the main text.\n\n**Q9. What are \"agnostic\" parameters? (line 4) What do the authors mean by \"parameter stored\" in line 33?**\n\n\"Agnostic parameters\" means the INR's parameters in the weight space have no intuitive meaning, being agnostic to people. We replace this terminology with \"unintuitive parameter\" in our revision. \"Parameter stored\" means all the parameters of a model which store all the information for the represented signal.\n", " We thank reviewer edqT for the reviewing time and detailed comments. Typos have been fixed in our revision. However, we are not able to agree with the reviewer's over-concerning about our practical significance due to our experiment results. Our responses to your concerns are listed as follows.\n\n**Q1. The quality of the solutions is not very satisfying. As a result, the advantages of working in the INR domain are not very appealing.**\n\n\nWe respectfully disagree that the experimental results will damage the value of this work. INR has achieved undebatable success in signal compression [2], 3D reconstruction [1,3,4], and even scientific computing [1,5,6]. It enjoys continuous and compact representation, unlimited resolution, and closed-form derivative computation [1]. The ubiquitous application of INR has given us a tantalizing hope of utilizing INR as a universal data format in the future.\n\nThe proposed framework is the first generic framework that processes INRs without breaking down their implicit and continuous nature by leveraging closed-form differential operators. Although the experimental results are not demonstrated to show superiority in every aspect (e.g., it is comparably slow compared to traditional filters), they are still encouraging, considering that the progress of INR still lies in an emerging stage (In [7], authors revealed the imperfectness of existing INRs). Moreover, frankly speaking, finding comparable baselines is tricky since all the existing image processing methods are established for vectorized signals. That being said, all the baselines are processing totally different input data from our method. Thus they are not fairly compared. Even so, we have successfully demonstrated the promise of adopting continuous convolution on INR, which largely outperforms discrete convolution-based methods. \n\nThe performance of our method is close to the state-of-the-art \"discrete\" models. Even though it indicates there is still a gap compared to our final goal, we believe it is more important that this work will potentially motivate following future works and shed light on how to directly process INR without decoding it. As admitted by Reviewer 1Ys6, our work makes the first step towards analytically processing implicit fields, and can \"inspire work that will push this idea further, maybe eventually to the point where we will be able to compute functions of neural fields directly in the weight space\".\n\nAs per reviewer's request, we also list the average numerical results on the full test set in Tab. 2 and Tab. 3. Additionally, we create two baselines on image classification on MNIST dataset: directly applying 1) MLP and 2) PCA + SVM on the INR weights. Their inferior performances (9.8% for MLP and 11.3% for PCA + SVM) further support the significance of our algorithm.\n\n\nTable 2: Quantitative result of image denoising on 100 testing images from DIV-2k dataset, where the synthetic noise is gray gaussian noise clipped to be positive. MPRNet and MAXIM overfit to the SIDD dataset they were trained on, and don't generalize well on the synthetic Gaussian noise we are using here.\n\n| | PSNR | SSIM | LPIPS |\n|:------------------------:|:---------:|:--------:|:--------:|\n| Input (decoded from INR) | 23.23 | 0.64 | 0.33 |\n| MPRNet | 21.70 | 0.73 | 0.32 |\n| MAXIM | 24.32 | 0.80 | 0.26 |\n| INSP-Net | **27.95** | **0.82** | **0.23** |\n\nTable 3: Quantitative result of image denoising on 100 testing images from DIV-2k dataset, where the synthetic noise is rgb gaussian noise. The noise is similar to the ones seen during the training of MPRNet and MAXIM, so they obtain better performance with the help of a much wider training set.\n\n| | PSNR | SSIM | LPIPS |\n|:------------------------:|:-----:|:----:|:-----:|\n| Input (decoded from INR) | 20.51 | 0.47 | 0.40 |\n| MPRNet | 23.95 | 0.72 | 0.36 |\n| MAXIM | 24.64 | 0.74 | 0.33 |\n| Mean Filter | 22.57 | 0.60 | 0.43 |\n| INSP-Net | 23.86 | 0.65 | 0.38 |\n\n[1] Sitzmann et al. Implicit Neural Representations with Periodic Activation Functions\n\n[2] Dupont et al. COIN: COmpression with Implicit Neural representations\n\n[3] Park et al. DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation\n\n[4] Mildenhall et al. NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis\n\n[5] Li et al. Fourier Neural Operator for Parametric Partial Differential Equations\n\n[6] Zhong et al. CryoDRGN: reconstruction of heterogeneous cryo-EM structures using neural networks\n\n[7] Yuce et al. A Structured Dictionary Perspective on Implicit Neural Representations\n", " \n**Q5. Across all experiments, it is not clear what number k, or how many high-order derivatives, should one use.**\n\nFor image processing, we set k=5. For geometric processing, we set k=4. For audio denoising, we set k=3. The k values are empirically set to fit in the GPU memory and shared across all corresponding experiments, without any bell-and-whistle tuning per case.\n\n**Q6. Some related papers are not correctly interpreted or not included.**\n\nThanks for pointing out the incorrect interpretation of existing works for INR editing. We have revised this section according to the reviewer’s suggestions. For FFM [30], to our best understanding, the Gaussian mapping mentioned in their paper is just another variant of Fourier feature mapping. It simply samples the frequency weights from a Gaussian distribution, which does not contradict our description “Fourier Feature Mapping (FFM) places a sinusoidal transformation before the MLP”. We still insist Sec. 4.2 is necessary, because it shows the demand and promise of editing implicit fields. As we added a demonstration for 3D object editing, discussing them is no more out-of-scope. We also added the missing citations mentioned by the reviewer.\n\n**Q7. Isn’t the INSP-Net with the “A” kernel just a fully connected MLP (Line 119)? Why would stacking multiple INSP-Net be called INSP-ConvNet?**\n\nThe INSP-Net is not only a fully-connected MLP, but also includes all the computation steps of derivatives. By simplifying the MLP $\\Pi$ to a linear layer (Eq. 5), INSP-Net can precisely simulate a convolution operator (i.e., a conv layer). By interleaving Eq. 5 with non-linearity, we form a multi-layer structure, and we call it INSP-ConvNet because it simulates “continuous” CNN on INRs.\n\n**Q8. What does “modify an INR without explicit decoding” mean?**\n\n“Modification without explicit decoding” means we do not need to query the INR at every grid point and extract it to a pixel array before processing it. Recall our formulation Eq. 3, to compute the value at point $x$, INSP-Net only does pointwise computation for $x$ by feeding different order derivatives at $x$ into the MLP $\\Pi$ instead of the derivatives at every location $x$. Eq. 3 as a whole is a computational graph that can output the value at arbitrary coordinates without explicitly decoding other points, which therefore can be regarded as the network representing the processed INR. We decode Eq. 3 to image grids only when visualizing or evaluating its visual quality.\n\n**Q9. Why not show the inference speed / network run-time? How much slower would it be due to computing the high-order derivatives?**\n\nTaking the audio denoising task as an example, the original unprocessed INR takes on average 0.01s to inference a 3.5s audio, while ours takes 0.12s (12x). We have added a limitation paragraph in our revision to clarify the efficiency problem. We leave more efficient processing operator representation for future works. We recall that even a plain INR is much slower than “explicit” methods. Likewise, processing continuous representation should presumably be much heavier than processing on regular grids. Even so, directly operating INR on the weight space is always a desirable feature since it does not involve discretization or approximation, which may cause information loss.\n", " We thank reviewer Uh51 for the time and actionable suggestions on providing more demonstration beyond the image domain. However, especially for your concerns on our experimental soundness, we would emphasize that our experiments are not aimed at showing the state-of-the-art performance on the low-level vision tasks, but to verify the feasibility of directly processing continuous implicit fields without explicit decoding. Actually, designing a fair comparison setting can be tricky. All the compared baselines are “discrete” methods. To our best knowledge, there is no prior method that can edit INR in the continuous regime. That being said, the input data of our methods and compared baselines are totally different. For other questions, we also provide detailed responses as below.\n\n**Q1. The paper is actually only about image processing. And more experiments on geometric processing and time-series signal processing.**\n\nThanks for proposing to apply our method to other representative data domains. Our method is a generic framework for processing all multimedia signals. We proved that our framework is expressive enough to represent continuous convolution. Therefore, we can safely believe the application range of INSP-Net is at least as wide as the convolution based signal processing techniques. Our method should be independent of the data modality and can be easily extended to other data. To support our argument, we have provided the additional results in geometry smoothing and audio denoising in our revision. Please refer to Fig. 8 and Fig. 14. Our new results demonstrate the feasibility of our INSP-Net in 3D and audio domains.\n\n**Q2. The paper should provide average results across a large dataset to avoid cherry-picking.** \n\nThe numbers listed in the paper are only given to quantitatively demonstrate our method’s feasibility. And the originally shown examples are non-curated. As per reviewer’s request, we have included a table of average scores evaluated on a large dataset in our revision. Please refer to Tab. 2 and Tab. 3. \n\n\nTable 2: Quantitative result of image denoising on 100 testing images from DIV-2k dataset, where the synthetic noise is gray gaussian noise clipped to be positive. MPRNet and MAXIM overfit to the SIDD dataset they were trained on, and don’t generalize well on the synthetic Gaussian noise we are using here.\n\n| | PSNR | SSIM | LPIPS |\n|:------------------------:|:---------:|:--------:|:--------:|\n| Input (decoded from INR) | 23.23 | 0.64 | 0.33 |\n| MPRNet | 21.70 | 0.73 | 0.32 |\n| MAXIM | 24.32 | 0.80 | 0.26 |\n| INSP-Net | **27.95** | **0.82** | **0.23** |\n\nTable 3: Quantitative result of image denoising on 100 testing images from DIV-2k dataset, where the synthetic noise is rgb gaussian noise. The noise is similar to the ones seen during the training of MPRNet and MAXIM, so they obtain better performance with the help of a much wider training set.\n\n| | PSNR | SSIM | LPIPS |\n|:------------------------:|:-----:|:----:|:-----:|\n| Input (decoded from INR) | 20.51 | 0.47 | 0.40 |\n| MPRNet | 23.95 | 0.72 | 0.36 |\n| MAXIM | 24.64 | 0.74 | 0.33 |\n| INSP-Net | 23.86 | 0.65 | 0.38 |\n\n\n**Q3. It is not clear how much the proposed training actually improves from the INR simply fitted against the corrupted input image. Why not show the initial decoded images after fitting the INR on the corrupted images?**\n\nWe observe that INR is not naturally against all corruptions. The unprocessed input images shown in the original draft are already the decoded images from the original INR. We’ve updated the wording to avoid confusion.\n\n**Q4. How only training a 2-layer depthwise CNN is a “fair comparison”. Why does it not consider training a small MLP?**\n\nWe only intend to verify the learning expressiveness of our framework by showing comparable results with CNNs on image classification. We choose the two-layer depthwise CNN because we believe our two-layer INSP-ConvNet is mathematically as powerful as this two-layer depthwise CNN. The purpose of comparing the number of parameters remains unknown and thus, its conclusions may be less meaningful. CNN and INSP-ConvNet are processing different data. Our INSP-ConvNet is learning on continuous and implicit signals (or namely, a set of MLP networks), which presumably requires a larger parameter budget.\nWe provide additional baselines on MNIST dataset that process the weight of the INR directly: 1) We train an MLP classifier with the same number of parameters as our INSP-ConvNet that takes the MLP weights as input, its classification accuracy is 9.8%; 2) We use PCA + SVM to classify the weight of the INRs, its classification accuracy is 11.3%.\n", " We tremendously appreciate reviewer 1Ys6’s positive assessment and highlighting our contribution to the neural field community. In regards to your questions, see our responses below:\n\n**Q1. Could the authors comment on the effective (not theoretical) receptive field of the operators that can be parameterized by the proposed approach?**\n\nWe appreciate this good question. Our insight is that even SIREN is a highly local INR, its derivatives can encode neighbor information. We can characterize the receptive field by looking back at the “equivalent” kernels in the discrete domain, where higher order differential operators are usually implemented by larger kernels. For example, first-order differential operators are often represented by a 3x3 kernel (e.g., sobel), while second-order differential operators can be approximated by 5x5 kernels. Likewise, in the continuous domain, we can simply consider that higher order of adopted differential operators in INSP-Net induces a larger receptive field. Considering the effective receptive field defined in [1], we admit it remains an open question to directly compute the measure of impact between every pair of points because the computation of two points seems independent of each other in our INSP-Net.\n\n[1] Luo et al. Understanding the Effective Receptive Field in Deep Convolutional Neural Networks\n\n\n**Q2. How to lift the limitation that their approach requires a-priori fitting of all the neural fields?**\n\nFitting an INR and processing an INR are two independent tasks. Our paper focuses on how to process an INR after acquiring it through a standard reconstruction pipeline. Avoiding a-priori fitting is beyond the scope of our discussion. Nevertheless, there indeed exists several effective solutions, such as latent code [1] and sparse coding [2], which acquire the representation in one-shot inference. Our INSP-Net is independent of the INR’s network architecture and is thus also generalizable to all those aforementioned methods.\n\n[1] Park et al. DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation.\n\n[2] Wang et al. Neural Implicit Dictionary Learning via Mixture-of-Expert Training.\n\n**Q3. Suggestions on typos and a limitation section.**\n\nThanks for these constructive comments. We have fixed all the grammar errors and added a limitation section in our revision which clarifies all the limitations mentioned by the reviewer.\n", " The paper proposes a method to perform signal processing of a signal represented via a neural field directly, without the need to first sample the underlying MLP. To this end, the authors propose to express operators on top of the neural field as functions of the first- and higher-order derivatives of the MLP. Though the output is *not* a new, monolithic MLP parameterizing the output of the operator, but instead a linear combination of derivative MLPs, the output nevertheless retains the \"resolution-invariant\" property of the underlying neural field representation. \n # Originality\nThe paper is original and the proposed approach novel. To the best of my knowledge, no prior work on directly computing convolutional operators on top of neural fields without sampling exists. The treatment of how to approximate any shift-equivariant and certain group-invariant kernels as the linear combination of first- and higher-order gradients of a neural field is similarly novel. The authors propose and demonstrate a set of applications, ranging from image processing to a simple convolutional neural network, that have also not been tackled in this way before. All in all, this paper is highly original and was joyful to read.\n\n# Quality\nThe paper is of high quality. Figures are informative to a degree that a single pass through the paper already provides high-level understanding of the method. A detailed read-through yields cool insights, such as the derivation of universal approximation of any convolutional filter, though that is, as the authors remark, not a new result. The quality of the experiments is similarly high, with relevant experiments that show-case the use-case of the proposed method - in particular, I enjoyed the low-level image processing tasks and image inpainting.\n\n# Clarity\nThe paper is very clear, especially the figures serve to lay out the key contributions of the paper.\n\n# Significance\nThe practical significance of the proposed approach seems to be limited for now: First, it requires one to already have access to a set of neural fields fit to the signal at hand. Second, the cost of evaluating the resulting network can be rather prohibitive, as it requires evaluating the stack of all derivative networks to decode a single pixel.\n\nHowever, I am not overly concerned with the practical significance of the approach. In my opinion, the key significance of this paper lies in educating the neural field community about the fact that operators on neural fields can be expressed as functions of the derivative networks. Further, I am convinced that this paper will inspire work that will push this idea further, maybe eventually to the point where we will be able to compute functions of neural fields directly in the weight space.\n Could the authors comment on the effective (not theoretical) receptive field of the operators that can be parameterized by the proposed approach? In particular, SIREN is known to be a highly local INR: the directions in weight space to change the colors of pixels even a small distance apart are basically orthogonal (increasingly so with higher frequencies). It would seem that this \"local support\" also somehow impacts the receptive field of a convolutional operator expressed via the gradients of the SIREN?\n\nDo the authors have a way in mind in which they might lift the limitation that their approach requires a-priori fitting of all the neural fields? Note that I do not expect this to be the case, any insight is simply appreciated!\n\nMinor comments:\n- line 49: \"are loaded from the INR being processing...\" - this sentence does not make sense to me. Maybe being -> during?\n- line 51: \"even though we are not able to (perform) surgery\"\n The processing remains expensive, in that the output of the proposes INSP-Net is not a single neural field, but rather, a linear combination of derivative operators, each of which is expensive to query. \n\nThe present effort still requires recovering all neural fields of all the signals upfront. \n\nThe authors certainly discuss these limitations, but I would have expected a \"limitations\" section where these issues are made explicit.\n\n", " Motivated by recent advances in implicit neural representation (INR) for images, this paper seeks to develop an approach to modify learned INR *\"without decoding”*. Specifically, the paper proposes training an additional network which operates on the high-order spatial derivatives of the original INR previously fitted for some image. This extra neural network takes in the original INR prediction, as well as its high-order derivatives w.r.t. the input coordinates (hence the spatial derivative); the objective of this network depends on the specific task, and the paper discusses tasks such as denoising, deblurring, inpainting, and classification. Strengths:\n\n**Clear and reasonable motivations.**\nINR has achieved great success in accurately fitting images, and it is therefore well-motivated to explore possibly modifying the learned INR for further downstream tasks. It is also admirable that the paper points out the potential benefits of improving INR based on ideas from the field of digital signal processing\n\n**Variety of tasks.**\nThis paper presents a wide range of applications, such as edge detection, blurring, deblurring, denoising, inpainting, and classification. It is helpful for the community to be aware of the huge potential of INR of images.\n\nWeaknesses:\n\n**Experimental design.**\n\n* The title suggests a general framework of signal processing, and the teaser figure (Fig. 1) shows a 3D mesh and explicitly states “geometric processing”, but the paper is actually only about image processing. \n\n* The paper has no experiment on geometric processing on signed distance fields, despite the fact that DeepSDF [10] is one of the most prominent examples of successful INR applications. \n\n* The paper has no experiment on signal processing of time series signals (e.g. audio or speech), which is arguably the most representative data domain for the entire field of digital signal processing. The SIREN paper [27] that this paper is based on has covered audio signals, so it is not a foreign type of data for INR.\n\n* It is completely fine if a paper only focuses on images, but the title and its first figure should at least appropriately reflect the content and scope.\n\n**Validation rigor.**\n* The paper does indeed cover a lot of image processing applications, but it lacks sufficient rigor in validating the proposed approach.\nThe paper presents quantitative metrics (PSNR/SSIM) for five selected images only (Figures 4 to 7). Those provided in the supplement do not contain any quantitative metric, and even if they do, the paper should still provide average results across a large dataset to avoid cherry picking.\n* In the denoising/deblurring/inpainting experiments, the INR is first fitted against the noisy/blurry/masked image before then processed by the task-specific network. The results seem to suggest that this task-specific network can successfully denoise/deblur/inpaint from the corrupted input image. However, the paper does not show the decoded image from the original INR. It is well-known that INR itself can at least do denoising [30], so it is not clear how much the proposed training actually improves from the INR simply fitted against the corrupted input image.\n* In the classification experiment, it is not clear how only training a 2-layer depthwise CNN is a “fair comparison”. The paper does not provide the number of network parameters, nor does it explain why it does not consider training a small MLP.\n* Across all experiments, it is not clear what number k, or how many high-order derivatives, should one use. The paper presents no analysis on the impact of having more high-order derivatives. It is not even clear if one really needs high-order derivatives.\n\n**Literature review.** \\\n*Some related papers are not correctly interpreted.*\n* While discussing “existing approaches\" for “editing on INRs”, the paper mentions (Line 36 to 37) that “another main direction” and only references three works, [27], [28], and [29]. However, [28] and [29] are both from 2017, well before the recent introduction of INR, whose main characteristic is the “coordinate-to-value mapping” (Line 25). In fact, [28] makes no use of neural networks, and does not even mention the phrase “neural network” at all; [29] is about using GAN to generate 3D voxels, hardly related to INR either.\n* While introducing FFM (Line 89 to 98) and Eq. (2), the notation seems to suggest that “positional encoding” is merely a sine function (Line 97 to 98), and ignores the fact that FFM [30] introduces the Gaussian mapping and uses it by default.\n* Section 4.2 discusses the supposedly related works on “editing the reconstructed 3D scenes”. This paper only focuses on image processing, so the relevance of this subsection is really weak.\n\n*Some highly related papers are not included.*\n* Using the derivatives of INR has been explored by [a] (with similar computational graph discussion) in the context of faster INR-based rendering. \n* Using INR for downstream applications (e.g. classification) has been explored by [b].\n* Using INR for image and video compression has been also explored by [c] (with a PDE-based positional encoding) in the context of light fields.\n* [d] introduces a technique that significantly accelerates the fitting of INR on 2D images.\n* [e] introduces a technique for improving the representation efficiency of INR of images via reducing the parameter count.\n\n* These works contain far higher relevance to this paper, compared to the 7 referenced papers on 3D shapes (there’s no 3D shape in this paper) and the other 7 referenced papers about 3D GANs\n\n[a] Autoint: Automatic integration for fast neural volume rendering. Lindell et al. CVPR 2021. \\\n[b] From data to functa. Dupoint et al. ICML 2022. \\\n[c] Signet: Efficient Neural Representation for Light Fields. Feng et al. ICCV 2021. \\\n[d] Learned Initializations for Optimizing Coordinate-Based Neural Representations. Tancik et al. CVPR 2021. \\\n[e] Meta-learning Sparse Implicit Neural Representations\" Lee et al. NeurIPS 2021. \n\n * Why is the title about general signal processing but the paper only deals with images? \n* What happened to the geometric processing and the 3D shape shown in Fig. 1?\n* For Fig. 4 to 7, why not show the initial decoded images after fitting the INR on the corrupted images? How much does the extra network actually help?\n* Isn’t the INSP-Net with the “A” kernel just a fully connected MLP (Line 119)? Why would stacking multiple INSP-Net be called INSP-ConvNet? Is it because MLP is equivalent to 1D Convolution? By this logic, isn’t the original INR also a “ConvNet”?\n* What does “modify an INR without explicit decoding” mean? Doesn’t the proposed method need to decode the INR (Eq. 3) by evaluating the “acquired INR” on every single pixel “x”? Isn’t that decoding already?\n* If we need to evaluate every pixel “x” with the INR, before feeding it to the extra network, what benefit does it bring over simply using the decoded image?\n* Why not show the inference speed / network run-time? How much slower would it be due to computing the high-order derivatives?\n\nIn particular, it would be critical to elaborate the \"without decoding\" claim, clarify why the proposed method is not also decoding from the INR, and how the proposed INSP-ConvNet really is **convolutional** instead of just **multiple MLPs**. These would determine the validity of the main claims and conceptual contributions of this paper, no matter how good or bad the experimental results are. The authors have not really addressed them. Discussion about at least the limitation of a potentially slower run-time should be expected in the revision.", " This paper studies implicit (and continuous) neural representations (INRs) of data defined on discrete lattices. In particular, the authors present a way of performing different operations on these INRs directly without the need for \"decoding\" them by parametrizing these operators with learnable operators on these representations. The authors demonstrate these ideas on Image denoising, deblurring (and blurring), inpainting and classification. + This reviewer likes the general idea of this paper. While INR are becoming increasingly popular, it's not obvious how one can perform operations on these continuous elements that are similar to the discrete operations defined over lattices. This paper proposes the first solution to do this (to the best of my knowledge).\n+ The method is intuitive and demonstrated on a series of image processing tasks, from low to higher level.\n\n- While the general idea is intuitive, the text is not very clear. There are several typos and general English usage issues that are cumbersome while reading (see below).\n- While this demonstrates that these operations can be *approximated* on INRs, the quality of the solutions is not very satisfying. As a result, the advantages of working on the INR domain are not very appealing. - In Eq. (1), did the authors mean \\arg\\min instead of \\arg\\max?\n- Notation is confusing, as the authors use m and M to denote several things: m is the dimension of the discrete input lattice; e.g. m=2 for images, and M denotes the number of discrete measurements of the continuous function. However, line 117 denotes $x\\in R^m$ - shouldn't it be $x\\in R^M$? At the same time, Eq. (3) then makes use of $M$ to define the dimension of the domain of the operator $\\mathcal A$, which is independent of $m$ and $M$ and depends on the order of the computed derivatives.\n- One of the main theses of this paper is that common signal processing operations can be instead defined on INRs, which the authors attempt to demonstrate. However, all of these operators (with the exception of edge detection\") are defined only as parametric functions learned from data in a supervised way - as opposed to the original way of defining these operators, \"from scratch\". This should be clarified, because while gradients can be obtained \"in closed form\", these operators cannot.\n- This reviewer believes that while the idea proposed in this work is nice, the results are far from satisfying: \n\ni) the denoising performance seems quite poor, and the 2 db difference with DnCNN looks very strange given the (inverse) difference in SSIM. Indeed, the INSP-Net image looks considerably more noisy. Moreover, while it's fine comparing with DnCNN, this method is by now 5 years old, and much better algorithm exist (see the methods used for comparison in [1] for a good subset of them). Generally speaking, the denoising performance does not look good and appears far below normal current methods (even below previous methods based on non-local means, dictionary learning, and more).\n\nii) Likewise, the deblurring performance is also not very satisfying: note the considerable noise introduced in the sky area shown on Fig. 5. The same holds for inpainting (very high levels of noise are introduced in the sky).\n\niii) Importantly, image processing results are just demonstrations and numbers are presented for only those individual examples - no numbers are reported over the entire dataset. \n\niv) I also appreciate the comparison on MNIST and CIFAR-10, but such low numbers are concerning. Recall that simple linear models (e.g. PCA +SVM) can better than 87%. \n\n- In line 230, the authors mention that \"nonlinear activations and normalizations are naturally element-wise functions\", but the authors never state what these are. What are they?\n- Throughout the paper, a supervised learning setting is never presented, and so labels are never defined. Thus, it's unclear what the authors mean by \"semantic labels y_i\" in line 235. Only later in the experimental section one understands what labels the authors are referring to.\n- I appreciate the result in Theorem 1, although it's novelty is very limited: indeed, differential operators are shift invariant, and any function defined on norms of vectors is rotation invariant. \n- It is unclear why the authors mention that the differential operators form a *wavelet* basis - do these operators satisfy the properties that wavelet must satisfy?\n- In line 204, the authors comment that their operators can simulate *exact* convolutions. This seems incorrect to me, as the exact equivalence holds for an infinite sequence, and thus only a finite approximation is possible in this framework.\n- Lastly, there are many errors that make reading quite difficult. A non exhaustive list (just the first page) includes:\n - \"Implicit Neural Representations (INR) encoding continuous multi-media data...\" -> encodes?\n - what are \"agnostic\" parameters? (line 4)\n - \".. can be computed analytically and invariant to translation\" -> invariant to translation, line 11.\n - \"presented\" -> represented (line 23)\n - \"study to encoder\" -> study how to encode?\n - what do the authors mean by \"parameter stored\" in line 33?\n\n\n\n[1] Tu, Zhengzhong, et al. \"Maxim: Multi-axis mlp for image processing.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022. The authors did not address negative societal impacts nor the limitations of their contribution.", " The paper introduces a novel signal processing framework named INSP-Net that directly operates on INRs without explicit decoding. The INSP-Net can process INRs by combining high-order differential operators. The authors prove any continuous convolution filter can be uniformly approximated by a linear combination of high-order differential operators and empirically validate the effectiveness of the proposed method across both low- and high-level vision tasks. Strength: \n\n1. The idea is novel. The proposed method attempts to directly process INRs by utilizing high-order differential operators. Theoretically, the authors prove continuous convolution filter can be uniformly approximated by a linear combination of high-order differential operators. Besides, extensive experiments are conducted to validate the effectiveness across various vision tasks.\n2. The paper is well organized and easy to be understood.\n\nWeakness:\n\n1. From experiments, it seems that INSP-Net operating on INRs cannot exhibit superiority against convolution operating on pixels. For example, edge detection results of other filters seems contain more detailed textures than that of INSP-Net. In Figures 4 and 5, although the PSNR score is higher, the processed images still contain obvious noise or other artifacts. As for image classification, why is Depthwise CNN used as baseline rather typical CNN? \n\n2. There are some typos in the paper, e.g. Line 77 “sought to to”\n See weakness. The authors points out some future works without adequately discussing limitations and negative societal impact." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 6, 5, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 4, 4 ]

[ "9rJtPH00wzh", "ygOOybgIAI", "k4DW-Z1-_g9", "dftRrH0uYG", "xq2V7ox9q0A", "DSRtoXRN8c7", "nips_2022_qqIrESv4f_L", "vrtUbXesFLr", "l2d_WfsRZXS", "U8JK7cxakOSS", "B3bzwgmnmI", "_z7F07wK6zw", "M6iD6n_FP-M", "A3BPjTcVr7J", "nips_2022_qqIrESv4f_L", "B3bzwgmnmI", "D1cBAthyIX", "M6iD6n_FP-M", "OO2Ae8kiNR", "A3BPjTcVr7J", "_z7F07wK6zw", "nips_2022_qqIrESv4f_L", "nips_2022_qqIrESv4f_L", "nips_2022_qqIrESv4f_L", "nips_2022_qqIrESv4f_L" ]

[ "INjPip1OWD", "5PZt6MjdA12", "DvJ901IXT65", "_PgC_gtF85W", "0XjrPMg0oVP", "qEmuWStn581", "_Z-RvLfCSbc", "AH2tsiIdC-a", "hEUk35pS2SH", "-irANMddrbJ", "1UBikxWW91a", "Jp_0ZPwekbH", "zGZt3VlWZ3_", "US2ILHA-SIU", "_R9GtChfZpl", "lie0Cgor6n6", "HuClDt4VCTO" ]

[ "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your patient reply. After reading the feedback from the authors, I understand how the method work.\n\n1. The problem is interesting. But, as shown in Table. 2, the computational cost is extremely heavy (more than x10). While the proposed method costs less memory compared with the sliding window methods, it is not a good tradeoff between computational and memory costs, especially when we use the Cuda implementation.\n\n2. Due to the limited time, the generalization of the method on other transformer-based backbones is still unclear.\n\nAs a result, I am leaning towards rejecting this paper.", " **Q3:** Layer Expectation Propagation\n\n**A3:** 3-1 LEP requires the nearly same memory as the fixed window partition. For the sliding window strategy, the context for each token is different so that it requires more memory compared with the fixed window strategy. Please refer to Fig. 1 in the SM for intuitive illustration and Algorithm 2 in the SM for implementation details (The implementation derives from [5][(code)](https://github.com/MartinGer/Stand-Alone-Self-Attention-in-Vision-Models)). Besides, the sliding window strategy is the scientific approach [2,6,7] and we also compare with the fixed window strategy in our paper. We comprehensively analyze the superiority of our method, including performance improvements compared with fixed window strategy and efficiency improvements compared with the sliding window strategy. The comment ``Actually, the proposed method requires multiple inferences and requires the memory to store the intermediate features`` is not correct, since we only need to maintain the averaged feature and intermediate features are directly discarded. We have measured the actual memory usage in the A3 to Reviewer S7Qf. We copy it below for your convenience.\n\nThe meaning of each symbol: $B$: batch size, $(H, W, C)$: feature size, $s$: local window size, $h$: number of heads. We also report FLOPs and memory cost on a single attention layer, in which $B=1, h=1, s=8, H=W=256, C=128.$ We use GTX 1080Ti GPU as the computing device. OOM means out of memory(>11G).\n\nTable 1: The complexity for training. \n|Strategy|Time Complexity|Space Complexity|FLOPs (G)|Memory(G)|Trans. Inva.|\n|:----|:----:|:---:|:---:|:---:|:---:|\n|Fix. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|5.4|1.3|False| \n|Slid. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWCs^2+BHWhs^2)$|5.4|OOM|True| \n|Sto. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|5.4|1.3|True| \n\nTable 2: The complexity for testing.\n|Strategy|Time Complexity|Space Complexity|FLOPs (G)|Memory(G)|Trans. Inva.|\n|:----|:----:|:---:|:---:|:---:|:---:|\n|Fix. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|5.4|1.2|False| \n|Slid. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWCs^2+BHWhs^2)$|5.4|OOM|True| \n|Sto. Win.|$\\Theta(BHWCs^4+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|72.3|1.2|True| \n\n3-2 Our strategy contains two parts, stochastic window for training and LEP for testing. The proposed ``Performance gains from extra computation is not surprising`` demonstrates stochastic window for training is effective and provides a strong baseline, which is also our contribution. The LEP can even consistently outperform the strong baseline with more computations.\n\n**Q4:** Figure 4\n\n**A4:** Please refer to Sec. 4.2 where we provide explanations and details.\n\n\n[1] Swin transformer: Hierarchical vision transformer using shifted windows. ICCV, 2021.\n\n[2] Swin transformer v2: Scaling up capacity and resolution. CVPR, 2022.\n\n[3] Hrformer: High-resolution vision transformer for dense predict. NeurIPS, 2021.\n\n[4] Twins: Revisiting the design of spatial attention in vision transformers. NeurIPS, 2021.\n\n[5] Stand-alone self-attention in vision models. NeurIPS, 2019.\n\n[6] Local relation networks for image recognition. ICCV, 2019.\n\n[7] Uformer: A general u-shaped transformer for image restoration. CVPR, 2022.\n\n[8] Swinir: Image restoration using swin transformer. ICCV Workshops, 2021.\n\n[9] Bishop C M, Nasrabadi N M. Pattern recognition and machine learning[M]. 2006.", " Thank the reviewer for the response. Here are our responses.\n\n**Q1:** Translation invariance vs translation equivariance.\n\n**A1:** We can comprehend the difference between invariance and equivariance. We must re-clarify that the terminology translation invariance is accurate since it reflects the invariance to shifts of the interested degradation. The reviewer's understanding of invariance and equivariance is not general enough. The reviewer believes that translation must be conducted on the whole noisy image, which is not true. The reviewer admits translation invariance is needed for image classfication. In classification, translation can be focused on interested object and the recognized label should be invariant to the shifts of the object. Therefore, translation invariance is needed in classfication. Consider the case where we want to recognize two independent digits in a image. If translation was limited on the whole image, it means that translation invariance could only be ensured by joint shifts of the digits. Obviously, it is not reasonable because translation invariance should allow to return the same results regradless of *independent shifts* of the digits within the image. Consequentlty, translation should be allowed conducted on particular objects. Moreover, as the given material says (Page 95), ``A network that is insensitive to shifts of the object of interest in an image is called shift invariant.`` We can also provide another evidence in the classic book [9] that supports our argument: ``a particular object should be assigned the same classification irrespective of its position within the image (translation invariance)`` in Chapter 5.5.3 Invariances. If the reviewer can understand this, the concern can be readily solved. Here, the so-called interested object is dagradation, which is the target of image restoration algorithm. **Consequently, translation invariance is the proper terminology.** The commemt ``If an image restoration algorithm is translation invariant, it means that it will always return the same output regardless of the input, making the algorithm useless`` is apparently wrong. Because we only allow invariance to the shifts of degradation. If the image background is changed, the output is changed accrodingly. \n \n1-2 Besides, we fix up the broken translation invariance of transformers for image restoration tasks. We do not mean other desired properties are not necessary. **We believe the reviewer should focus on image restoration but also transformer.** Translation invariance can be approximately accomplished by the sliding window adopted in CNN, while the sliding window strategy is too expensive in local window based transformers [5,6]. Hence, existing transformers adopt the fixed window strategy, which leads to the broken translation invariance and local information loss. Equipped with our stochastic window strategy, transformer can possess the desired translation invariance and intact locality, which is more suitable for image restoration. We have conducted extensive experiments to demonstrate that the stochastic window transformer outperforms existing fixed window strategy, i.e., shifted window transformer, for image restoration tasks.\n\nWe have to remind the reviewer that equipped with the stochastic window strategy, transformer can be translation invariant and exploit intact local information for image restoration. These properties are desirable for image restoration tasks (other tasks, e.g., image classification, may also be suitable). Our strategy aims to eliminate the limitations of existing fixed window strategy of transformers for image restoration.\n\n**Q2:** Locality\n\n**A2:** Existing works that implement local window based attention include the sliding window strategy [5,6] and fixed window strategy [1,2,3,4,7,8]. The fixed window strategy (e.g., shiftded window strategy) is the mainstream for local attention based transformer since it is more efficient compared with the sliding window strategy. There is no ``overlapping patches and crop out the boundaries`` strategy for local attention in existing literatures because it is purely meaningless. The sliding/fixed window strategy have their own merits, i.e., the sliding window can maintain translation invariance and intact locality while the fixed window strategy is more efficient. As for ``overlapping patches and crop out the boundaries``, it is neither efficient nor keeping desired property. We remind the reviewer that the parition of feature prepares for the calculation of local attention not for procossing high-resolution images. ", " I thank the authors for their rebuttal and detailed explanations.\nHere are post-rebuttal responses.\n\n1. Translation invariance vs translation equivariance.\n\nI am pretty much confident that translation invariance is what we don't usually want in image restoration literature. \nTranslation invariance refers to the property where the output of a model does not change by the translation of input.\nTranslation equivariance refers to the property where the output of a model changes by the same amount of translation as the input.\nIf an image restoration algorithm is translation invariant, it means that it will always return the same output regardless of the input, making the algorithm useless.\nI highly recommend the authors check the definition of basic concepts. I can easily find many materials explaining the differences between invariance and equivariance from a quick search on the web.\nex) https://www.doc.ic.ac.uk/~bkainz/teaching/DL/notes/equivariance.pdf\n\nNote: I don't mean translation equivariance is what we always want. I'm trying to explain translation invariance is not usually a desired property.\n\nI am concerned that the authors are abusing the term invariance by referring to the degradation instead of the input.\n(I initially thought it was a grammar/clarity issue, but from the author response, it seems not.)\nHowever, translation in- / equi-variance are terms describing the behavior of model to its input, not to another function applied to input (here, degradation).\nIf my understanding is correct, the authors should claim they want to build a degradation position-agnostic image restoration algorithm instead of misleading terms.\nOne additional concern is that the authors are mixing up the two concepts (the claimed invariance to degradation position and typical translation equivariance) throughout the paper and the above response.\nThe proposed approach is building on the translation equivariance but not on the idea of handling degradation position variation.\n\nBesides the terminology, the authors' claim is not very precise. No practical image restoration methods produce the same output from an image with different degradation positions. (except trivial solutions such as global averaging)\nSoTA methods do not achieve the authors' desired property is not because they adopt transformer architectures but simply because it is an extremely difficult problem (if not impossible). (L2-3, 7-9)\n\nFurthermore, to be precise, we expect that an ideal image restoration method to recover the image regardless of the degradation types, strength, direction, etc., not just limited to the position of degradation artifacts.\nIf the authors would claim the degradation position-agnostic recovery is important, they should justify it first.\n\n2. locality\nIt is hard to agree that the proposed method handles the locality issue better than overlapping patches.\nIn principle, the proposed Layer Expectation Propagation is computing the features multiple times by shifting the window.\nI don't see essential differences.\n\n3. Layer Expectation Propagation algorithm\n\n3-1. I don't understand how LEP reduces memory consumption. By referring to L54-56, are the authors comparing their method with sliding-window style inference?\nThat is not a fair baseline. \nThe authors aim to improve the baseline transformer architecture and the comparison should be made with the baseline model's single inference.\nComparing the proposed method with an imaginary bad method is not a scientific approach.\nActually, the proposed method requires multiple inferences and requires the memory to store the intermediate features.\nLEP potentially increases peak memory consumption, not reduces it.\nDid the authors measure the actual memory usage?\n\n3-2. Performance gains from extra computation is not surprising.\n\n4. Figure 4\n\nI understand what the authors' intention is. Will the authors add the missing explanations and details to the manuscript?\n\n5. Figure 5\n\nOk. \n", " Thank you for taking the time to review our work. We would be glad to provide more details if you have any question.", " We appreciate for your comments. We hope that this response can address your concerns. We are delighted to provide more details if needed.", " Thank you for the careful evaluation of our paper. We hope that this answer your question, and we would be happy to provide additional details if needed.", " Thank you sincerely for your positive comments and suggestions.", " I appreciate your responses. All of my concerns have been addressed by the response. \n\nIn my opinion, this work is interesting since it analyzes the drawbacks of transformer, including broken translation invariance and local information loss, and proposes the novel stochastic window strategy to effectively solve this problem. \n\nMoreover, I like the toy examples in Figure 4, which visualizes the restored translation invariance of the stochastic window strategy. \n\nOther reviewers mention the issue of complexity and the authors provide sufficient comparisons with other strategies in rebuttal. I believe this work is novel enough and pushes the development of transformers. After seeing the rebuttal and other review comments, I still insist on my score or consider arising the score.", " **Q1:** Explanations about why the implied posterior distribution is uniform.\n\n**A1:** In this work, we discard infinite favoritism towards the certain partition and propose to exploit all the local windows fairly. In order to achieve this goal, we assume the posterior distribution is uniform and stochastic shifts are sampled from uniform distribution independently and identically.\n\n**Q2:** Adding a concrete explanation about the reason of taking expectations.\n\n**A2:** The reason we take expectation of the stochastic shifts can be two-fold. First, taking expectation is proven to consistently improve the model performance in the SM (L48-53). Hence, taking expectation is favorable. Second, we need to maintain the translation invariance and intact locality during testing. Taking expectation means all the local windows are treated fairly so that the translation invariance and intact locality can be ensured. However, as we analyze in the paper, naive implementation will incur unacceptable computational burden. To this issue, we propose to take layer-wise expectation to replace original expectation, in which computational complexity reduces from $\\Theta(s^{2N})$ to $\\Theta(Ns^2)$. Besides, the layer expectation propagation still maintains the desired translation invariance and locality.\n\n**Q3:** It is suggested to release the code to encourage further research about transformers on low-level vision.\n\n**A3:** We will release the code to encourage reproducibility.", " **Q1:** Complexity of new stochastic window is not practically analyzed.\n\n**A1:** We provide a detailed time/space complexity analysis for a single attention layer. Specifically, we compare our strategy with the fixed and sliding window strategy for training and testing, respectively. We adopt notations: $B$: batch size, $(H, W, C)$: feature size, $h$: number of heads, $s$: local window size.\n\nTable 1: Time and space complexity for training. \n|Strategy|Time Complexity|Space Complexity|Trans. Inva.|Locality|\n|:---- |:----:|:---:|:---:|:---:| \n|Fix. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|False|False| \n|Slid. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWCs^2+BHWhs^2)$|True|True|\n|Sto. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|True|True|\n\nFor training, our strategy is as efficient as the fixed window for both speed and memory cost, as shown in Tab. 1. But the fixed window loses the translation invariance and locality. The sliding window can fulfill the translation invariance and locality while suffer from huge memory burden, which often incurs OOM in practice. In contrast, the stochastic window enjoys efficient training while maintains translation invariance and locality.\n\nTable 2: Time and space complexity for testing. \n|Strategy|Time Complexity|Space Complexity|Trans. Inva.|Locality|\n|:----|:----:|:---:|:---:|:---:| \n|Fix. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|False|False|\n|Slid. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWCs^2+BHWhs^2)$|True|True|\n|Sto. Win.|$\\Theta(BHWCs^4+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|True|True|\n\nFor testing, it requires to exploit all the local windows for a single forward pass so that extra cost is required. As shown in Tab. 2, the fixed window can inference efficiently but suffer from the broken translation invariance and locality loss. Compared with the sliding window, our stochastic window strategy requires more computations but less memory cost. We have added the complexity analysis to the SM (L54-63).\n\n**Q2:** Improvement on visual quality is not very obvious.\n\n**A2:** Indeed, visual improvement can be more obvious within regions with more textures. We have added markers in Blurry of to assist to locate some of these regions. Please refer to the revision (Page 7) and visual improvement can be easier to be captured. \n\n**Q3:** Can this technique be extended to other CV tasks?\n\n**A3:** Local attention based transformers, e.g., Swin Transformer [1], have achieved remarkable success on several CV tasks, including image classification, dense prediction, and semantic segmentation. However, they also compute attention based on specific local windows and cannot treat all the local windows fairly. The consequences are that unexpectable information loss occurs during feature processing and the translation invariance is also absent. Our proposed stochastic window strategy can provide an effective mechanism towards this problem. Therefore, it is very promising to extend the strategy to other tasks where local attention based transformers have exhibited competitive performance. Indeed, except for other restoration tasks mentioned in Limitation and Future Work, we are also considering extending this strategy to other CV tasks, such as image classification, dense prediction and semantic segmentation.\n\n**Q4:** Failure cases can be presented.\n\n**A4:** In this paper, we propose the stochastic window strategy to recover the broken translation invariance and locality loss. Extensive experiments and analyses have demonstrated the strategy can accomplish this goal and improve performance across multiple tasks. We cannot observe and forecast failure cases from the sense of violating the translation invariance and intact locality. But for restoring clean images, there are some cases where the degenerations are so heavy that our strategy cannot remove thoroughly. Please refer to the SM (L95-96 and Fig. 10) for failure cases.\n\n[1] Swin transformer: Hierarchical vision transformer using shifted windows. ICCV, 2021.", " **Q1:** The authors should use translation equivariance rather than translation invariance.\n\n**A1:** First, we would like to re-emphasize the translation invariance is actually what we delve into. As we have clearly stated in the submisison, the ideal image restoration method should be invariant to the translation of degradation. In other words, the algorithm should be immune to the position of degeneration (e.g., rain streaks, noise). Degeneration concerned in image restoration is analogy with the number whose position can be shifted in image classification, and the restored image corresponds to the recognized label. *Therefore, there is no doubt that in this paper, the use of translation invariance to describe the problem of our study is correct.* **L29** is not unique. We have modified it as one of the desiderata to avoid confusion. Translation invariance is also required for image distortion and vignetting, since ideally the same clean image is returned. **L39-40.** We are discussing about translation invariance not equivariance. Due to weight sharing, translation invariance among paritioned windows happens [1,2].\n\n**Q2:** Overlapping patch can solve the problem locality.\n\n**A2:** Fig. 1b intuitively illustrates the loss of local relationships brought by the fixed window partition. The non-overlapping partition of feature is conducted for *calculating local attention*. Note that partition here serves for *calculating local attention rather than processing high-resolution images.* Overlapping partition cannot solve the locality problem unless the overlapping configuration is as compact as the sliding window, which is demanding for computational resources [5,6]. Most local attention based transformers [1,2,3,4] adopt non-overlapping rather than overlapping partition for the issue of efficiency. Besides, CNNs have efficient implementation based on the sliding window so that partition (overlapping or non-overlapping) for feature processing is unnecessary. Consequently, locality loss that comes with the fixed window partition is a non-trivial issue. Our strategy can solve the locality problem elegantly. \n\n**Q3:** Layer expectation propagation (LEP) algorithm.\n\n**A3:** Eq. (5) requires inference over $\\xi$ to calculate the expectation per attention block, which incurs extra computations. However, the extra computations can bring: 1) lower memory cost. LEP is proposed to approximately take expectation of the introduced stochastic factors. Hence, LEP requires to process all the local windows for a single forward pass. Compared with the sliding window, which also achieves the function, LEP requires more computations but less memory (please refer to L54-63 of the SM). 2) consistent performance gains. Despite being relatively smaller, the performance gains can be consistently obtained. 3) translation invariance and locality. For training, we propose to implement the translation invariance and locality using stochastically shifted window. For testing, we resort to LEP to maintain the above two functions.\n\n**Q4:** What is shown in Fig. 4?\n\n**A4:** In Fig. 4, we use the toy experiment to validate that our stochastic window strategy can achieve the translation invariance. As shown in Fig. 4 (a), when we shift the added Gaussian noise patch with offset $(\\xi_h, \\xi_w)$, the model with translation invariance should produce the same recovered result so the PSNR distribution w.r.t. offset should be as flat as possible. PSNR is normalized to [0, 1] because we aim to visualize variations of PSNR w.r.t. offset. Extensive experiments are conducted in Sec. 4.3-4.5 to demonstrate the superior performance of our strategy. In Fig. 4, we visualize the broken translation invariance of fixed window based transformer and our strategy can yield relatively uniform outputs like CNNs-based VDN.\n\n**Q5:** Visual improvement is not very obvious in Fig. 5.\n\n**A5:** Indeed, visual improvement can be observed within regions with more textures. We have added markers in Blurry of Fig. 5 to assist to locate some of these regions. Please refer to Fig. 5 of the revised vision and visual improvement can be easier to be captured.\n\n**Q6:** References & Typos & Grammar.\n\n**A6:** We have carefully polished the whole manuscript in the revision.\n\n[1] Swin transformer: Hierarchical vision transformer using shifted windows. ICCV, 2021.\n\n[2] Swin transformer v2: Scaling up capacity and resolution. CVPR, 2022.\n\n[3] Hrformer: High-resolution vision transformer for dense predict. NeurIPS, 2021.\n\n[4] Twins: Revisiting the design of spatial attention in vision transformers. NeurIPS, 2021.\n\n[5] Stand-alone self-attention in vision models. NeurIPS, 2019.\n\n[6] Local relation networks for image recognition. ICCV, 2019.", " **Q1:** How does the testing step avoid the original expensive operations?\n\n**A1:** For testing, we design the layer expectation propagation (LEP) to approximate the expectation of the stochastic factors. The exact inference procedure is Eq. 4. Since the $(\\xi^0_h, \\xi^0_w,\\ldots,\\xi^{N-1}_h, \\xi^{N-1}_w)$ has exponential combinations ($s^{2N}$, where $s$ is the window size), the exact calculation involves summation over items whose number grows exponentially with $N$ $(\\Theta(s^{2N}))$. Earlier researches [1, 2] also introduced the stochastic factors into the models to solve their own chanllenges and proposed to approximate the exact expectation by layer-wise expectation. Inspired by these works, we further propose the LEP to approximate the exact inference. Apparently, it involves $s^2$ items per layer. Hence, the complexity grows linearly with $N$ $(\\Theta(Ns^2))$.\n\n**Q2:** Do the testing FLOPs increase compared with the training?\n\n**A2:** Due to the layer-wise expectation, the testing FLOPs are higher than those of training. The higher FLOPs derive from that all local windows are taken into account for a single forward propagation. But the increase in FLOPs is deserved because it brings: 1) consistent performance gains, 2) lower memory cost compared with the sliding window (please refer to A3), 3) translation invariance and locality. Moreover, we also found that LEP can offer more flexibility to the FLOPs-performance trade-off, as described in Sec. 4.6.\n\n**Q3:** The detailed comparison (FLOPs and memory cost) with the fixed and sliding window.\n\n**A3:** We provide a detailed analysis about time and space complexity of the stochastic window strategy. We compare our strategy with the fixed and sliding window for training and testing, respectively. The meaning of each symbol: $B$: batch size, $(H, W, C)$: feature size, $s$: local window size, $h$: number of heads. We also report FLOPs and memory cost on a single attention layer, in which $B=1, h=1, s=8, H=W=256, C=128.$ We use GTX 1080Ti GPU as the computing device. OOM means out of memory(>11G).\n\nTable 1: The complexity for training. \n|Strategy|Time Complexity|Space Complexity|FLOPs (G)|Memory(G)|Trans. Inva.|\n|:----|:----:|:---:|:---:|:---:|:---:|\n|Fix. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|5.4|1.3|False| \n|Slid. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWCs^2+BHWhs^2)$|5.4|OOM|True| \n|Sto. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|5.4|1.3|True| \n\nFor training, our strategy is as efficient as the fixed window for both speed and memory cost, as shown in Tab. 1. But the fixed window loses the translation invariance and locality. Note that the space complexity of the sliding window is significantly higher than others, which causes OOM and prevents the network training. \n\nTable 2: The complexity for testing.\n|Strategy|Time Complexity|Space Complexity|FLOPs (G)|Memory(G)|Trans. Inva.|\n|:----|:----:|:---:|:---:|:---:|:---:|\n|Fix. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|5.4|1.2|False| \n|Slid. Win.|$\\Theta(BHWCs^2+BHWC^2)$|$\\Theta(BHWCs^2+BHWhs^2)$|5.4|OOM|True| \n|Sto. Win.|$\\Theta(BHWCs^4+BHWC^2)$|$\\Theta(BHWC+BHWhs^2)$|72.3|1.2|True| \n\nFor testing, since it requires to exploit all the local windows for a single forward pass, the extra cost is required. As shown in Tab. 2, the sliding window spends more memory ($\\times s^2$) while our strategy spends more computations $(\\times s^2)$. We have added the complexity analysis to the SM (L54-63).\n\n**Q4:** Integrating with existing transformers (e.g., Uformer, swinIR).\n\n**A4:** To validate the effectiveness of our method, we adopt the proposed strategy on one of the most popular U-shaped network architecture in this work. In fact, Uformer also adopts the same architecture except its specific modulator design. We discard the modulator because it is not general enough and unnecessary to verify our strategy. We are conducting experiments to intergrate our strategy with more architectures, including SwinIR. However, due to the time issue, we have to defer related content to future version. \n\n**Q5:** why does the model performs well without LEP?\n\n**A5:** During training, the stochastic window can exploit all the local windows fairly while the fixed window relies attention on the specific local windows. This means that the fixed window suffers from the loss of local information and translation invariance, while the stochastic window can leverage both to achieve a better generalization ability. Without LEP, the testing procedure is equivalent to the fixed window. In this setting, the using of the stochastic window for training can optimize the network better, resulting in improved performance.\n\n**Q6:** The dot and matrix production are mixed in SM.\n\n**A6:** We have fixed this error and carefully polished the whole manuscript in the revision.\n\n[1] Dropout: a simple way to prevent neural networks from overfitting. JMLR, 2014.\n\n[2] Deep networks with stochastic depth. ECCV, 2016.", " This paper proposes a stochastic window strategy for training transformers and elaborates layer expectation propagation algorithm during the testing. This strategy consistently improves the performance of several image restoration tasks. Strengths:\n1. The idea is interesting. With the stochastic window strategy, attention modules can avoid the broken translation invariance.\n2. The experiments show the improvements of each step clearly.\n\nWeaknesses:\n1. The training step is easy to understand. But, I do not fully understand the testing step. How to implement it to avoid the original expensive operations? Does the testing flops increase compared with the training? How about the detailed comparisons (flops and memory cost) of your method with the fixed(shift) window and sliding window during the training and testing?\n\n2. I encourage the author to adopt this strategy to existing transformer-based methods (e.g., Uformer[1], swinIR[2]) to evaluate the generalization on different backbones.\n\n3. L245. Without the layer expectation propagation algorithm, why does the model performs well? The window during the testing is the same as the shift windonw and the local information has been broken as in previous works.\n\n4. L21-L47 in the Supplemental Material. Two algorithms mixed the dot production and matrix production.\n\n[1] Uformer: A general u-shaped transformer for image restoration\n\n[2] Swinir: Image restoration using swin transformer.\n See the Strengths And Weaknesses. See the Strengths And Weaknesses.", " This paper raises an issue regarding the loss of translation equivariance in image restoration problems due to the transformer-based architectures. Often, attention or MLP layers operate on a predetermined window locations and the authors argue this could cause undesired artifacts or performance drops.\nThe authors proposes Stochastic Window Transformer by 1) allocating random window positions at training time and 2) averaging the results from multiple window positions.\nThe experiments were done in image deraining, denoising, and deblurring. - translation equivariance\n\ntranslation invariance -> translation equivariance\nAs translation equivariance is the key property this paper is addressing, the authors should use a proper terminology. \nAn example task where translation invariance is needed is image classification, recognizing a number correctly whether it is shifted or not.\nGiven a translation function T, \nTranslation invariance: f(T(x)) = f(x)\nTranslation equivariance: f(T(x)) = T(f(x))\n\nL29 is the desiderata -> is one of the desiderata\nI would omit ‘any’ to be safe. There could be cases the position is important, ex) recovering from image distortion, vignetting, etc.\n\nL39-40 As attention layers are involved, I don’t expect the method to be translation equivariant in any ways.\n\n- locality\n\nL36, Figure 1b. If non-overlapping patches cause problems in locality, we could always use overlapping patches and crop out the boundaries at the cost of additional computation. It could be less efficient but solves the problem. Such strategy is commonly used to process high-resolution images even for translation-equivariant methods (CNNs).\n\n- layer expectation propagation algorithm\n\nHow does equation (5) work? Does it require inference over xi to compute expectation per attention block?\nThis introduces s^2 times more inference computations. Is the result worth the computation?\nWhile Figure 7 claims reducing the number of inference brings efficiency, however, x8 inference is still a very large burden.\nAlso, in the supplementary material, the PSNR differences between the inference results with and without the layer expectation propagation are minor.\n\n\n- Figure 4\n\nWhat is shown in Figure 4?\nWhat does the z-axis mean?\nL211 Is the PSNR normalization factor the same across 4b, 4c, and 4d?\nTranslation equivariance is one of the desired property but achieving high PSNR is also important.\nWhich approach achieved the best average PSNR?\n\nWhy want translation equivariance in transformers? People use transformers by sacrificing equivariance to achieve better results. Does bringing approximate translation equivariance lead to higher accuracy?\n\n- Figure 5\n\nWhile the PSNR gains in the Stoformer++ is big, the visual result doesn’t look that much different from other results.\nI don’t find this example to be appealing.\n\n- References\n\n[30] It is ICCV Workshop paper, not ICCV\n\n- Typos and Grammar\n\nL17 constantly -> consistently\nL32 What does ‘concluded’ mean? Is it ‘considered’?\nL167 By contrast -> In contrast\n I would suggest the authors check the definition of translation-equivariance and translation-invariance.\nAlso, the proposed method does not guarantee translation-equivariance.\n\nPlease refer to the weaknesses. Limitations were addressed by the authors.", " This paper is interesting. Spatial attention is essential in windowed transformer. By stochastic varying the window sizes and shapes, image restoration benefits from signficantly in various testsets compared with SOTAs. Strengths:\n1. First work of Stochastic Window transformer for image restoration \n2. New SOTAs for image restoration\nWeaknesses:\n1. Complexity of new stochastic window is not practically analyzed. \n2. Improvement on visual quality is not very obvious. 1. Can this technique be extended to other CV tasks ? 1. Failure cases can be presented. ", " The paper points out the deficiencies, i.e., loss of locality and broken translation invariance, of existing transformers for image restoration tasks. To address these problems, the authors introduce the stochastically shifted window to replace the original fixed window with transformers and elaborate the layer expectation algorithm to take the average of corresponding stochastic factors. The paper also provides sufficient experimental evidence to support the effectiveness of the proposed method. Strength:\n1. The paper provides significant insights about applying transformers to image restoration tasks. For low-level vision, researchers often directly apply high-level design keys of transformers into low-level vision without careful considerations. This paper exhibits consequent loss of locality and broken translation invariance of transformers. Given the potentially general impact of transformers on computer vision, analyzing the impropriety of transformers on specific tasks is of great meaning. \n2. The proposed method is quite novel and effective. To address the problem of the broken translation invariance and locality loss, the authors adopt the idea of sampling to uniformly sample one shift configuration (ξ_h, ξ_w) and design the efficient yet effective layer expectation propagation algorithm to take the expectation of the introduced stochastic factors. The authors also conduct extensive experiments to support the proposed method.\n3. The paper is well organized and easy to be understood.\n\nWeakness:\n1. Line 144-145 says that “stochastic shifts should be averaged according to their posterior distribution” and Eq. 4 implies that these random variables are averaged according to a uniform distribution. So, there should be some explanations about why the implied posterior distribution is uniform.\n2. The stochastic window transformer contains the layer expectation propagation algorithm to approximate the exact average (expectation) of stochastic shifts. It is suggested to add a concrete explanation about the reason of taking expectations. \n 1. See weaknesses.\n2. It is suggested to release the code to encourage further research about transformers on low-level vision.\n In Limitation and Future Work (Sec. 4 of S.M.), the authors point out that they will validate the proposed stochastic window strategy on more architectures and image restoration tasks. In this paper, extensive experiments across multiple degradations (image deraining, denoising, deblurring) to demonstrate that the stochastic window strategy can bring consistent improvements. Moreover, the paper also provides clear and reasonable interpretations of the improvements. Hence, it can be anticipated that the stochastic window strategy can bring improvements to other image restoration tasks and architectures. As for the potential negative societal impacts, the authors also provide several solutions to mitigate them." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 6, 8 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 3, 5 ]

[ "_Z-RvLfCSbc", "DvJ901IXT65", "_PgC_gtF85W", "0XjrPMg0oVP", "Jp_0ZPwekbH", "1UBikxWW91a", "zGZt3VlWZ3_", "hEUk35pS2SH", "-irANMddrbJ", "HuClDt4VCTO", "lie0Cgor6n6", "_R9GtChfZpl", "US2ILHA-SIU", "nips_2022_0ucMtEKCihU", "nips_2022_0ucMtEKCihU", "nips_2022_0ucMtEKCihU", "nips_2022_0ucMtEKCihU" ]

[ "5ve0CHEmbL5", "GB9uktcFyOk", "k3cmX6TRy6L", "e4B_8WmgnNY", "_wJz9mH2wYB", "RrqTESF49n", "F4bZORMR-Ik", "c5Q-Vh6OWIj", "TbfsqMY0U5wO", "aj-rfx2XwWYH", "aWaRz0U8fq", "_P1b8gj3N19", "apAuRsuANRa", "dMLNMf7I2_F", "solBD3SzCwQ", "iSsosWT0upi6", "V3tY56-7OOj", "eaqMF7TtCXW", "-r-qr-Zdxj", "5NwnmMi0xI6D", "Ozh8b9tcYuP", "U_6Vl5DNUxp", "M7VFpbXrhdz", "KxpLb2eG3IT", "T5q3SoJ-Nr", "kpSa_0r_VLJ", "ij4wkUqhGXB", "hIDsJpsHTqL" ]

[ "author", "author", "author", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear Reviewer s3YA,\n\nAs stated in the discussion with Reviewer beE6, regarding your concern that we did not show the superiority of MED, we have added more evidence to demonstrate its superiority. In the revised draft, we added **Appendix I**, which contains both experimental and theoretical analysis to show that in some cases, all other metrics fail to give meaningful and fair results but MED is robust to all situations.\n\nYou could refer to the discussion with Reviewer beE6 and **Appendix I** in the revised draft for details. Here, we provide a brief description to send the major messages.\n\n**1. Experimental Observations:**\n\n| | BetaVAE score | FactorVAE score | DCI | MED |\n|-----------------------------------|---------------|-----------------|------|------|\n| 10-d trained model (DIP-VAE-II) | 81.5 | 58.6 | 12.3 | **14.7** |\n| 1000-d randomly initialized model | **82.7** | **61.4** | **19.8** | 3.8 |\n\n| | MIG | SAP | MED |\n|---------------------------------|-----|-----|-----|\n| 10-d randomly initialized model | **6.7** | **3.0** | 2.9 |\n| 1000-d trained model (BYOL) | 5.2 | 2.8 | **6.0** |\n\n\nFor the disentangled representation learning, if a metric is robust and valid, it is expected not to score high to randomly initialized encoder weights. However, as shown in the two Tables above, because of the bias of existing metrics towards models of different dimensions, **a randomly initialized 1000-d model can achieve higher score than a well-trained 10-d disentangled representation learning method in terms of BetaVAE score / FactorVAE score and DCI. On the other hand, a randomly initialized 10-d model can get higher score than a 1000-d well-trained model in terms of SAP and MIG metrics.** Such an experimental observation obviously counters our expectation and high-level intuition about a robust disentanglement metric. On the contrary, it both cases, MED maintains reasonable scoring to the models.\n\n**2. Theoretical Analysis:**\n\nIn **Appendix I**, we prove case by case to show that existing metrics can fail in many obvious situations but MED is robust in all cases to output meaningful and consistent disentanglement evaluation.\n\n1. **MIG and SAP** biasedly prefer models of low dimensions: MIG and SAP desire not just **disentanglement** but also **completeness** that one factor should relate to only one dimension. With such an intrinsic bias, MIG/SAP prefers models whose dimension is close to the number of factor. We show an example in **Appendix I** where a model's every dimension is perfectly disentangled to a factor but the model dimension is higher than the number of factor. We will get **MIG=SAP=0**, indicating \"fully entangled\". But in fact, every dimension of the model is perfectly responsive and disentangled to only one factor.\n\n2. **DCI** suffers from the curse of dimensionality: by increasing the dimension of a model, we can encourage DCI to falsely go higher. For example, given a model of $D$ dimensions, of which the first two dimensions are disentangled and all following dimensions are fully entangled to factors, DCI score goes higher with increasing $D$ and finally approaches 100, indicating \"perfectly disentangled\". This is obviously false and against our expectation.\n\n3. **BetaVAE and FactorVAE score** also prefer models of high dimensions. We provide two situations as example in Appendix I. \n\n- In the first situation, all dimensions of the model are entangled to more than one factors. However, we show that, once there is a dimension that has lower response to one dimension than all other dimensions, BetaVAE and FactorVAE score can go as high as 100, indicating \"perfectly disentangled\". This is obviously a failure of the metrics as in fact every single dimension is correlated to all factors. Biased to such a \"lucky\" dimension, the two metrics tend to score high to high-dimensional models. \n\n- In the second situation (same as the example for DCI), only the first two dimensions are disentangled to the factors while all other dimensions are fully entangled to all factors. BetaVAE and FactorVAE scores would still output 100 to suggest the model is \"perfectly disentangled\". This counters our expectation to a reasonable disentanglement metric again.\n\nGiven all the situations above where existing metrics fail to give meaningful and fair scoring, MED is robust to make consistent disentanglement evaluation. The score by MED is well aligned with the human sense and high-level intuition about representation disentanglement. \n\nPlease refer to the details in **Appendix I** for more complete experiment analysis and mathematical demosntrations.\n", " Dear Reviewer d961,\n\nIt is close to the end of the author-reviewer discussion period. We would like to ask if our responses have addressed your concerns and answered your questions adequately. If not, we are happy for any further discussions.\n\nRegards,\n\nThe authors.", " Dear Reviewer s3YA,\n\nAs it is close to the end of the author-reviewer discussion stage, we would like to ask if our responses and the follow-up discussions have addressed your concerns and questions adequately. We would be more than happy to discuss further if you still have concerns to any part.\n\nRegards,\n\nThe authors.", " Your response clarified my question. I confirm my mark of acceptance.", " Thanks for recognizing the value of MED and raising the rating. We will make more detailed, complete, and formal analysis towards comparing MED and other metrics, both empirically and theoretically in the next version.", " Thanks for the question! \n\n**According to our experimental results, the answer is: No, we don't need that many dimensions for 50 factors, where the bottleneck is not the dimension**. \n\nWe study the relationship between dimension and disentanglement of BYOL in **Figure 5** on dSprites with has only 5 factors. BYOL's performance is better as we increase the latent dimension, until 512-d. Its performance plateaus near 512 dim (see **Section 5.4**). Beyond that, there is no further benefit by increasing the dimensions. On the CelebA dataset with nearly 10 times more factors (40 factors), this observation keeps almost the same. The following table shows MED and top-3 MED scores of BYOL with variant dimensions on CelebA. We can observe that BYOL's disentanglement performance plateaus at 1024-d. Further increasing dimensions does not obtain advantages. Our experimental results on CelebA throughout the paper are all obtained with 1000-d latent space, and it achieves SoTA disentanglement performance. CelebA is such a challenging real-world dataset that the disentanglement performance on it is overall very low. A higher latent dimension will make no difference.\n\n| | 128-d | 256-d | 512-d | 1024-d | 2048-d | 4096-d|\n|-----------|-------|-------|-------|---------|---------|-------|\n| MED | 3.5 (2.1) | 4.7 (0.2) | 4.6 (0.2) | 4.8 (0.4) | 4.5 (0.2) | 4.4 (0.3) |\n| Top-3 MED | 3.9 (2.3) | 5.3 (0.1) | 5.6 (0.1) | 6.8 (0.7) | 6.1 (0.5) | 6.5 (0.5) |\n\n**The high dimension required by CL is more likely because of its intrinsic design and architecture, such as the redundancy required by the InfoMax principle[1]**. When dimension is lower than a threshold (e.g., around 256-d for BYOL), CL is difficult to have smooth training loss descent and suffers from bad downstream performance. Such an observation happens on datasets of different complexities. As long as the latent dimension is higher than the factor number and enough for the intrinsic requirement of CL, higher dimensions show no difference. We didn't observe the sensitivity of the dimension with respect to the factor number of datasets.\n\nReferences:\n\n[1] \"On Mutual Information Maximization for Representation\", ICLR'2020", " I appreciate the authors' responses, particularly in Table 7, Table 8, Figure 17, and Section I.2. Now, I am convinced that MED is a good metric for disentanglement. Although Section I.2. is simple, I can get an insight into the drawback of other metrics, e.g., DCI having a curse of dimensionality. Thus, I raise my score to borderline accept. If the paper was accepted, I would like to see a more complete Table 7, Table 8, and Section I.2 in the main body. ", " I have a hypothesis about the poor performance of CSL in low dimensions, that is, VAEs naturally encourage compactness of latents. In contrast, the learned representations by CSL have redundant information, causing the model entangled. Maybe each factor need more dimensions to be represented. So, a problem emerges if that is true. If we need 512-d for 5 factors, do we need 5120-d for 50 factors?", " Thank you for the follow-up discussions. For your questions:\n\n1.**Additional third party to verify MED is aligned with disentanglement**: In Table 1, we provide the comparison between CL methods and existing methods by the proposed new metrics. In Table 4, we want to show that, with the participation of high-dimensional methods, existing metrics can not agree with each other anymore. And your suggestion is good, so we add additional visualization as third party to verify MED is aligned with the human sense of disentanglement and the shared definition: to which degree a dimension is related to only one factor.\n \n*<The following content is duplicated with that to Reviewer s3YA>*\n\nWe update the draft and add a new section **Appendix H**. In this part, we do latent traversing of low-dimensional (10-d) models on Shapes3D for visualization (**Figure 17**). We select 6 model weights whose MED scores are divergent. We make a subfigure for each model. Each subfigure has 10 columns, at each of which we change the value of a single latent dimension. In such a manner, we could observe if a latent dimension is correlated to a factor or not. \n\nBy manual inspection, we observe which factors each latent dimension is correlated to. We use a red arrow to indicate a latent dimension if we find it is entangled to express multiple factors. We use a green arrow to indicate a latent dimension if it is disentangled to correlate to only one factor. And we comment on the indices of factors the latent dimensions are correlated to.\n\nSuch a latent traversing visualization follows the practice in DisLib. Through the visualization, we could find that if a model has a higher MED score, it is obvious that it has more dimensions disentangled to represent only one factor, while fewer dimensions entangled to multiple factors. I think this can serve as a convening third party to show the consistency between MED score and the intuition of dimension-factor disentanglement by human sense.", " | | BetaVAE score | FactorVAE score | DCI | MED |\n|-----------------------------------|---------------|-----------------|------|------|\n| 10-d trained model (DIP-VAE-II) | 81.5 | 58.6 | 12.3 | **14.7** |\n| 1000-d randomly initialized model | **82.7** | **61.4** | **19.8** | 3.8 |\n\n| | MIG | SAP | MED |\n|---------------------------------|-----|-----|-----|\n| 10-d randomly initialized model | **6.7** | **3.0** | 2.9 |\n| 1000-d trained model (BYOL) | 5.2 | 2.8 | **6.0** |\n\nYour suggestions are great. We add more evidence to show that generally or in some cases, MED is better than other metrics by keeping a consistent evaluation of method disentanglement. We add **Appendix I** for this part from both an experimental perspective and a theoretical perspective.\n\n2.1 **Experimental Evidence**: By intuition and qualitative understanding of representation disentanglement, randomly initialized weights should not show high disentanglement score with a meaningful metric. But we extend the observation in L136 (**\"a randomly initialized 1000-d model could reach a FactorVAE score of 61.4 on dSprites, close to many well-trained 10-d VAE-based models’ scores\"**.) in Appendix I.1 with more detailed and comprehensive experimental observations. Results are shown in the two Tables above. \n\nThe results that, on dSprites, the BetaVAE score/FactorVAE score/DCI tend to overestimate the disentanglement property of the model of higher dimensions as we analyzed from their definition in Section 3.2 and Appendix A. To be precise, a randomly initialized 1000-d model can achieve a higher score by these metrics than a well-trained 10-d model. This is obviously not aligned with our expectation to a metric robust to the dimension variance in disentanglement measurement.\n\nOn the other hand, in the second Table on Shapes3D, we see that MIG/SAP tend to underestimate the disentanglement of the model of higher dimensions. Even a randomly initialized 10-d model can get a higher disentanglement score by MIG and SAP than a trained 1000-d trained model. The reason is that SAP and MIG use only two dimensions to calculate the score and they desire additional completeness other than disentanglement. So they tend to overestimate methods' disentanglement if their dimension number is close to the factor number.", " 2.2 **Theoretical Analysis**: Following your suggestions, we add additional theoretical analysis to compare MED and existing metrics in our constructed synthetic linear cases. For the discussions, we assume there are two factors $v_0, v_1 \\in {0,1}$. And their value is determined by uniform chances, i.e. $p(v_j=1) = p(v_j=1)=0.5, j=0,1$. The latent representation $c$ is of $D$ dimensions. The details are in **Appendix I**. \n\n*Note:* By the definition, MED is a percentage number (its maximum value is 1 = 100%), which is the same as other metrics. For the analysis below, we don't write % to simplify the expression and align that with the convention in paper.\n\n(1) **MED vs MIG/SAP**: In the linear case we construct where each dimension of the model is perfectly disentangled to a factor: $c_i = v_{i mode 2}$. Through the human sense of disentanglement, we could expect a reasonable metric to output a high score in this situation. But in fact, we will get MIG(c) = SAP(c) =0, indicating \"totally entangled\"! On the other hand, MED(c)=1, indicating a good disentanglement as we expect and derive from intuition.\n\n(2) **MED vs DCI**: In the linear case we construct, we see that DCI: We construct a linear situation as \n\\begin{equation}\nc_i = \\\\begin{cases}v_0 &,i=0\\\\\\\\\nv_1 &,i=1\\\\\\\\\n0.5(v_0+v_1) &,i>1\\\\\\\\\n\\end{cases}\n\\end{equation}\n\nAnd we simplify the case to assume that the regressor, such as GBT, in DCI uses the absolute of first-derivative as the importance of a dimension with respect to a factor. Under the sparsity limit of GBT, we could see that the expectation of DCI score is \n$$1-\\frac{log2}{D-2},$$\n and MED score is \n$$1-\\frac{D-2}{D}log2.$$\nWe plot their value change with the variance of the dimension $D$ in **Figure 18**. We see that even if only the first two dimensions are disentangled and all following dimensions are fully entangled, DCI score increases along with increasing $D$ by adding more entangled dimensions. We have $DCI(c)=69.9$ for $D=3$ and $DCI(c)=99.9$ for $D=1000$. This is significantly not aligned with our high-level expectation to a good disentanglement metric. On the other hand, we have $MED(c)=76.9$ for $D=3$ and $MED(c)=30.8$ for $D=1000$, which is more reasonable: with the increase of total dimension, the overall disentanglement degree decreases.\n\n(3) **MED vs BetaVAE/FactorVAE**: We construct two situations to show how MED is better than BetaVAE/FactorVAE scores.\n\n**Situation 1:** We construct a situation as \n\n\\begin{equation}\nc_i = \\begin{cases} \\frac{1}{3}v_0 + \\frac{2}{3}v_1 &, i=0\\\\\\\\\n\\frac{1}{3}v_1 + \\frac{2}{3}v_0 &, i=1\\\\\\\\\n\\frac{1}{2}(v_0+v_1) &,i>1\\end{cases}\n\\end{equation}\n\nThis is a very entangled situation in which every dimension is correlated to all factors. But by the calculation of BetaVAE and FactorVAE scores, they can achieve 100 for this case, falsely indicating \"perfectly disentangled\". This is obviously not aligned with the human sense and intuition. On the other hand, we have $MED(c)=1 - log2 = 30.7$, indicating a relatively low degree of disentanglement. We would regard the score from MEDa as still valid while BetaVAE/FactorVAE scores fail significantly.\n\n**Situation 2:** For the situation same as we construct in the comparison with DCI where the first two dimensions are perfectly disentangled to the two factors respectively while all following dimensions are full entangled, BetaVAE and FactorVAE scores would still give 100 scores, indicating \"perfectly disentangled\". While for the case of MED, we have $MED(c)=30.8$, which can better reflect the high-level justification that only limited dimensions are disentangled and most dimensions are highly entangled. Moreover, in this situation, by selecting the suitable subset, we can achieve a high Top-k MED score. This shows the meaning of the Top-k MED score especially when the model dimension is higher than the number of underlying factors.\n\nWith all the situations constructed and analyzed above, we could notice the failure of existing metrics to achieve evaluation results (1) meaningful, (2) fair, and (3) aligned with the human sense to disentanglement in some scenarios. On the other hand, our proposed MED always keeps the evaluation and comparison reasonable and aligned with the expectation from the human high-level institution.", " Thanks for the reply and suggestions.\n\nWe update the draft and add a new section **Appendix H**. In this part, we do latent traversing of low-dimensional (10-d) models on Shapes3D for visualization in **Figure 17**. We select 6 model weights whose MED scores are divergent. We make a subfigure for each model. Each subfigure has 10 columns, at each of which we change the value of a single latent dimension. In such a manner, we could observe if a latent dimension is correlated to a factor or not. \n\nBy manual inspection, we observe which factors each latent dimension is correlated to. We use a red arrow to indicate a latent dimension if we find it is entangled to express multiple factors. We use a green arrow to indicate a latent dimension if it is disentangled to correlate to only one factor. And we comment on the indices of factors the latent dimensions are correlated to.\n\nSuch a latent traversing visualization follows the practice in DisLib. Through the visualization, we could find that if a model has a higher MED score, it is obvious that it has more dimensions disentangled to represent only one factor, while fewer dimensions entangled to multiple factors. I think this can serve as a convening third party to show the consistency between MED score and the intuition of dimension-factor disentanglement by human sense.", " I appreciate the authors' thorough revision and detailed response. I agree that the previous metric has some problems. However, I cannot draw the conclusion that MED is a good metric for disentanglement. For example, from Table 1 and Table 4, how can we say MED is a good metric? I cannot see a clear relationship here. I agree with Reviewer s3YA. We need a third party to verify the metric is aligned with disentanglement. \n\nFor the F1-score and accuracy case, we can build different synthetic scenarios and theoretically analyze them. Then we can draw a conclusion that \"accuracy fails to capture the quality of a classifier in an imbalanced classification problem but F1 score can capture it\". I would like to see a similar conclusion for MED, e.g., the MED is better than other metrics in some properties under some conditions or scenarios.", " I am not doubting the advantages of the proposed metric. Of course, MED measures a property, but there is a gap in proving that such a property is disentanglement. You need a justified third party. For example, you can use latent traversals to visualize latent variables in low-dimension cases. A trustable third party is required to show superiority.", " **Q7: The superiority of MED**\n\n**A7 <The response is partially duplicated from that to Q2 of Reviewer beE6>:** As we discussed in **Section 3.2** and the newly added **Appendix F.2**, the positive results from traditional metrics such as BetaVAE, FactorVAE, and DCI can NOT prove that the BYOL method has overall better disentanglement because those metrics are not applicable to high dimensional cases. \n1. The BetaVAE and FactorVAE scores develop classifiers to identify a dimension that correlates most to the intervening factor. Higher dimensional representations with redundant information make it easy to overfit the classifiers, leading to higher final scores. For example, in **L137, \"a randomly initialized 1000-d model could reach a FactorVAE score of 61.4 on dSprites, close to many well-trained 10-d VAE-based models’ scores\"**.\n2. MIG and SAP require an extra property, i.e., a factor should be responded to by only a single dimension, termed **completeness**. Moreover, the significant difference between representation dimensions and the number of factors (1000 v.s. 10) enlarges the disagreement between **disentanglement** and **completeness**.\n3. The reason for the traditional DCI metric's failure is that it uses a classifier, such as GBT, that gives an unfair advantage to high-dimensional representations. GBT encourages sparsity (see **Figure 6**), leading to underestimating some responses between factors and latent dimensions. With a dimension correlating with fewer factors, it scores high-dimensional dimensions **falsely high**. Or at least, we can not use the score to compare with other methods of different dimensions.\n4. Our metric MED is a fix based on the traditional DCI metric. Instead of GBT, we use MI per dimension, which won't give extra advantages to the high dimensional representation. MED only focuses on disentanglement measured by the entropy of importance matrix rows, decoupled from completeness (which should be the entropy of columns). In addition, our empirical justification of the MED metric show MED is a plausible metric for the high-dimensional case. Please refer to **Appendix F.2** for a detailed discussion.\n5. The newly added **Appendix G** also provide a lot of evidence. For example, **Figure 16** shows that the traditional metrics are usually consistent when ranking a low-dimensional model. But for BYOL, MIG and SAP score it as the worst, but betaVAE, factorVAE, and DCI score it as the best. The MED score, on the other hand, is designed to be able to handle the high dimensional latent space. ", " **Q6: Why negative-free contrastive learning (CL) is important.**\n\n**A6:** Negative-free CL (also termed as \"Non-contrastive Self-supervised Learning\") is important for multiple reasons, especially in the comparison with CL with negative samples:\n1. First, **why self-supervised learning (SSL) is important**: self-supervised learning proposes a path to training large-scale pre-trained models without expensive labeling. The success of a line of this work, such as MoCo, SimCLR, and BYOL, has made the performance on downstream tasks close to or even superior to supervised-pre-trained models.\n2. Second, **why negative-free contrastive SSL:**\n* Contrastive SSL often suffers from model collapse that the representation becomes trivial constant vectors. By removing negatives, previous works observed the relief of this problem. This may be the main reason why researchers such as Yann Lecun (https://twitter.com/ylecun/st suffers from model collapse that the representation becomes trivial constant vectors. By removing negatives, previous works observed the relief of this problem. This may be the main reason why researchers such as Yann Lecun (https://twitter.com/ylecun/status/1508253087789637643) puts more attention to negative-free contrastive learning. Many recent works have discussed this, such as \n 1. https://arxiv.org/pdf/2105.00470.pdf (ICCV'2021 oral)\n 2. https://openreview.net/forum?id=r4xe3nMQ3AY (ICML 2021 Outstanding Paper Honorable Mention)\n 3. https://openreview.net/forum?id=YevsQ05DEN7 (ICLR'2022) \n* The success of SSL relies on heavy empirical observations and heuristic practice, such as stop-gradient, the set of projector and predictor, moving average update, etc. Thus researchers are always seeking more theoretical understanding of it. Though the original study of SSL uses negative pairs as a necessary component, later research found it is at the core of SSL's good performance. So, by removing negative pairs from SSL, many works make good progress in understanding the internal mechanism of SSL. Related works include:\n 1. https://arxiv.org/pdf/2206.02574.pdf\n 2. https://arxiv.org/pdf/2205.11508.pdf\n 3. https://openreview.net/forum?id=CR1XOQ0UTh- (ICLR'2021)\n 4. https://ieeexplore.ieee.org/document/9706613 (WACV'2022)\n* Contrastive SSL with negative samples requires heavy computation of data augmentation, and it also introduces additional heuristic choices. This proposes a risk of generalizability on different datasets or tasks. For the details of this aspect, related works include:\n 1. https://arxiv.org/pdf/2002.05709.pdf (ICML'2020)\n 2. https://arxiv.org/abs/2109.05941 (EMNLP'2021)\n 3. https://arxiv.org/pdf/2007.13916.pdf (NeurIPS'2020)\n\nGiven all the discussion above, considering (1) the performance of pretraining by negative-free contrastive learning can already be comparable to traditional contrastive learning, (2) helping to understand SSL, (3) avoiding model collapse, or (4) more generalizable pretraining, it is important to study for more understanding of negative-free contrastive learning. And disentanglement property is one of the core characteristics to understand it.", " Dear reviewer,\n\nThank you so much for your review and suggestions. Below are our responses to your questions.\n\n**Q1: Grammar issues:** We have fixed the issue in the revised version.\n\n**Q2: Suggestions for re-draw Figure 4:** We provide a new version of Figure 4 in the revised draft (**Figure 15**) where the value of multiple metrics is included in a single subfigure. However, we note that including multiple metrics in a single subfigure may cause confusion because the value of different metrics can't be compared directly and they are usually at different scales, so this figure can't well explain the disagreement between these metrics. So instead, we visualize the ranking of the corresponding methods on SmallNORB with different metrics in **Figure 16**. We believe this can clearly show the disagreement of existing methods when the representation dimension varies. Also, we highly encourage to refer to **Table 4**, which shows complete results on different methods and metrics, more convincingly suggesting the disagreement of existing metrics.\n\n**Q3: Include orientation in results on dSprites:** For all the evaluation results, the orientation factor was already included without selection. We excluded it just in the visualization to avoid misleading or confusing. But yes, a full presentation helps deliver a more complete picture. We make a new visualization with orientation factor in **Figure 7(c)** and **Figure 8(d)**.\n\n**Q4: Clarification of factor manipulation.** For questions related here, we answer them by points:\n\n**Q4.1: How the traverse is done?**\n\n**A4.1:** Unlike generative methods, contrastive learning methods do not model the generating process from factors to images. So manipulating factors here means we sample a batch of images from the dataset with only one factor varies. This is possible since we have access to the ground truth factors for synthetic datasets like dSprites. Then we extract representations from the corresponding batch of images for each factor.\n\n**Q4.2. Could you color the latent index with the factor you picked?**\n\n**A4.2:** We have included a new visualization of the top-k process in **Figure 13**, where the selected dimensions are highlighted in yellow. Please refer to **Appendix F.3**. \n\n**Q4.3: I cannot see the existence of a well-disentangled subset for orientation.**\n\n**Q4.3:** Yes that is true. In **Figure 3**, we show orientation as a failure case. As explained in Section 4.1 and **Appendix B.2** and **B.3**, it is due to the orientation factor being ill-defined. \n\n**Q5: I find some relevant papers, e.g., Contrastive Disentanglement in Generative Adversarial Networks [P1]. Could the authors discuss the differences?**\n\n**A5:** Contrastive learning and method in [P1] are very different from multiple perspectives:\n1. As we discussed in the introduction (**L21**), contrastive learning is a class of discriminative methods while previously studied disentangled representation learning methods are generative models. And the method proposed in [P1] is still a generative method (GAN) instead of a contrastive learning method. \n2. Second, In [P1], the term \"contrastive\" is misleading. The “contrastive loss” they use is actually a **\"classification\"** instead of a **\"contrastive\"** loss. In the common definition of contrastive learning, \"contrast\" comes from the feature distance of positive and negative pairs. And the positive pairs come from the same raw data sample. However, in the mentioned paper, the positive/negative pairs are defined as samples from the same/different categories, which is in fact classification instead of feature contrast.\n3. Finally, the metrics in [P1] are all for classification/clustering performance (ACC/NMI/NRI) or generation performance (IS/FID). They do not show any evaluation on the feature disentanglement metrics.", " **Q5. how to get ground truth factor on a real-world dataset.**\n\n**A5:** To have confident analysis of disentanglement evaluation, the factors definition should be conclusive that images with the same value of all factors should be exactly the same. Or deep models can capture other undefined signals to learn discriminative features. Hence, it is extremely difficult to define ground truth factors on real-world datasets. This is a main obstacle preventing disentangled representation learning from extending to real-world datasets. And CelebA is the only real-world dataset we find that has well-controlled factor definitions. Other datasets, such as COCO or Imagenet, only have limited high-level attribution labels, such as object categories, which is far away from the requirement of a factor-controlled disentanglement study.\n\n**Q6. How to calculate Mutual Infomation for two scalars.**\n\n**A6:** As explained at the end of **Appendix A.2**, we follow the implementation and preset paramaters of the Dislib paper [L1] to calculate the Mutual Information (MI). Firstly we sample a large batch (size=10000) of images and their factor labels. Then we feed these images to the models and receive 10000 samples of $(\\boldsymbol{c}, \\boldsymbol{v})$ pairs, where $\\boldsymbol{c}$ is the representation vector, and $\\boldsymbol{v}$ is the ground truth factors. To calculate $I(\\boldsymbol{c}_i, \\boldsymbol{v}_j)$ in Eq. 1, we first discretize $\\boldsymbol{c}_i$ by 20 bins. Since the factor $\\boldsymbol{v}_j$ is naturally discrete, we use the MI formula for discrete random variables as in https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mutual_info_score.html . \n\n**Q7. How to select k in partial disentanglement estimation.**\n\n**A7:** The parameter $k$ is an evaluation choice for the top-k MED. In the main text, we choose $k$ to match the dimension of VAE methods in Dislib[L1]. To show the influence of $k$, we have proposed an ablation study on $k$ in **Appendix F.3**. The conclusion is that the ranks of top-k MED are consistent with a wide range of k (see **Figure 14**). \n\n**References:**\n - [E1] Eastwood, Cian, et al. \"A Framework for the Quantitative\nEvaluation of Disentangled Representation\".\n - [L1] Locatello, Francesco, et al. \"Challenging common assumptions in the unsupervised learning of disentangled representations.\"\n - [K1] Kornblith, Simon, et al. \"Similarity of neural network representations revisited.\"\n - [H1] He, Kaiming, et al. \"Momentum contrast for unsupervised visual representation learning.\" \n - [W1] T. Wang and P. Isola. \"Understanding contrastive representation learning through alignment and uniformity on the hypersphere\"\n - [Z1] R. S. Zimmermann, Y. Sharma, S. Schneider, M. Bethge, and W. Brendel. \"Contrastive learning inverts the data generating process\"\n - [C1] Chen, Ting and Kornblith, Simon and Norouzi, Mohammad and Hinton, Geoffrey, \"A Simple Framework for Contrastive Learning of Visual Representations\"\n - [G1] Jean-Bastien Grill et al, \"Bootstrap Your Own Latent: A New Approach to Self-Supervised Learning\"\n - [C2] Xinlei Chen and Kaiming He, \"Exploring Simple Siamese Representation Learning\"\n - [T1] Tian, Yuandong, Xinlei Chen, and Surya Ganguli. \"Understanding self-supervised learning dynamics without contrastive pairs.\" International Conference on Machine Learning. PMLR, 2021.", " **Q3. Further discussion:** in the area of self-supervised learning, most advances are made by empirical observations, such as the setup of moving average update[H1], projector[C1] and predictor[G1], stop-gradient[C2], etc. People have been studying the mechanism of SSL without negative samples, but the progress on this topic is still at an early stage. For example, until recently, the work [T1] analyzes why SSL without negative on linear networks won't collapse to the identity function. We emphasize that our contribution is mainly finding this new phenomenon empirically. In the following, we give some initial hypotheses to why this happens. \n\n**Q3.1: Why the model can learn a well-disentangled subset of representation without negative samples?**\n\n**A3.1:** Here is our hypothesis. In contrastive learning, the training algorithm pulls the embedding of two augmentations of the single image close to each other and pushes embeddings of different images further apart. Since the embedding space we use in contrastive learning is usually very high dimensional (typically at least 1000-dim), and we need to pull close the two augmentations of the same image, it is intuitively better for the augmentation to only affect a few dimensions of the embedding, instead of all dimensions of the embedding. Because the former would lead to a smaller distance between the two augmented embedding vectors. Thus, this is the intuition why it would encourage disentanglement.\n\n**Q3.2: Disentanglement difference from CL with and without negative samples**\n\n**A3.2:** First of all, the disentanglement property of CL with negatives is also barely explored. In [Z1], researchers find negative samples can encourage identifiability of representation from CL, which is related to disentanglement but not the same as discussed in related works. The finding is based on the assumption of [W1] where (approximately) negative samples should be available in CL. However, negative-free contrastive learning does not satisfy the assumption. Moreover, to the best of our knowledge, we are also the first to benchmark CL methods (not just negative-free ones) on standard datasets (**Table 1** and **Table 4**) for which the proposed MED metric is the necessary tool. So to conclude, before this work, people[W1, Z1] found that negative samples can encourage CL to learn representation with some extent of disentanglement, but no standard evaluation was provided. In this work, we find that CL can learn disentangled representation even without any negative samples and in a novel pattern. We also benchmark them with the other methods on standard datasets. \n\n**Q4: why not provide results on ImageNet?**\n\n**A4:** To evaluate disentanglement on a dataset, we need to know the multiple attributes of an image. For example, in CelebA, we know the person's eye color, nose size, facial color etc. It is not suffice to only know an object label for each image as in ImageNet. Since there is no way to tell whether a representation dimension is entangled on unlabeled factors such as background color, etc, which will serve as noise when studying disentanglement. With the too high-level and limited labels on ImageNet, we can't do factor-controlled evaluation on as its label (category) can not represent all the variance between samples. For example, two images of the same label, e.g., dog, can have totally different background, surroundings etc. CelebA is the only real-world dataset we find that has well-defined and complete factor labels.", " **Q2: Theoretical analysis and soundness of MED.**\n\n**A2:** \n* It is tempting to have theoretical guarantees to show some metrics are better than the others. However, while it is possible to provide a theory for some method under a specific metric, it is usually very hard to have a theory for comparing two metrics. This is because we are designing the metrics itself, thus we don't have anything quantitative to measure the metric. Take metrics in classification problems as an example. We can define accuracy as metric A, and F1-score as metric B. It is hard to theoretically prove that metric B is better than metric A. What people do is to show some cases where accuracy fails to capture the quality of a classifier in an imbalanced classification problem. In the meantime, people also show that F1-score can distinguish the quality of two classifiers.\n* MED is meaningful because MI and Entropy are widely recognized tools to measure variable correlations. What we did for the disentanglement metric is similar to the classification metric above: we show that in the cases we are interested in, the traditional metrics fail (**Section 3.2, Appendix F.2, and Appendix G**). We analyzed the reasons for the failure. \n * The BetaVAE and FactorVAE scores develop classifiers to identify a dimension that correlates most to the intervening factor. Higher dimensional representations with redundant information make it easy to overfit the classifiers, leading to higher final scores. For example, in **L137, \"a randomly initialized 1000-d model could reach a FactorVAE score of 61.4 on dSprites, close to many well-trained 10-d VAE-based models’ scores\"**.\n * MIG and SAP require an extra property, i.e., a factor should be responded to by only a single dimension, termed as **completeness**. Moreover, the significant difference between representation dimensions and the number of factors (1000 v.s. 10) enlarges the disagreement between **disentanglement** and **completeness**.\n * The reason for the traditional DCI metric's failure is that it uses a GBT classifier and that gives an unfair advantage to high-dimensional representations. GBT encourages sparsity (see **Figure 6**), leading to underestimating some responses between factors and latent dimensions. With a dimension correlates with fewer factors, it scores high-dimensional dimensions falsely high.\n * Our metric MED is a fix based on the traditional DCI metric. Instead of GBT, we use MI per dimension, which won't give extra advantages to the high dimensional representation. MED only focuses on disentanglement measured by the entropy of importance matrix rows, decoupled from completeness (which should be the entropy of columns). In addition, our empirical justification of the MED metric show MED is a plausible metric for the high-dimensional case. Please refer to **Appendix F.2** for a detailed discussion.", " Dear reviewer,\n\nThank you so much for your review and suggestions. Below are our responses to your questions.\n\n**Q1: The intuition and process details of MED.**\n\n**A1:** Thank you for pointing out the concerns about the intuition and soundness of MED. Besides the discussion in **Section 3.2** about why we need MED and how it makes evaluation, we also provide a more detailed discussion of MED in **Appendix F**. Here we will summarize our response by points.\n1. **High-level intuition of MED:** We note there is no uniform definition of disentanglement in this community yet which is the reason why many different metrics are designed. But they follow a shared basic understanding of disentanglement: **the degree to which a representation dimension only responds to a single factor**. However, how to measure the \"response\" or \"importance\" remains unclear. Some metrics (MIG) use statistical measurement such as mutual information while some others (DCI, BetaVAE, FactorVAE, SAP) use estimates from learnable modules. The foundation that researchers can use them at the same time is DisLib (L1) proves their agreement with each other with large-scale empirical studies. However, per the discussion in **Section 3.2** and the experiment results shown in **Section 5.2** and **Appendix C, G**, they can not agree with each other anymore when the dimension of models varies. More importantly, the scores from those metrics can not be thought fair and meaningful anymore. So, we design MED to avoid their internal bias triggered by the high dimension. Based on the fact that mutual information is a widely recognized tool to estimate factor correlation, we design MED to gain fair and meaningful disentanglement even with varying representation dimensions as explained in **Section 3.2**. And different from MIG, MED evaluates in a global view of all dimensions. This makes MED more meaningful given different model dimensions.\n2. **Details of MED:** The process of MED is a variant of DCI Disentanglement score in [E1]. It consists of 3 steps:\n * The first step is to calculate the importance matrix $R$. Its element $R_{ij}$ describes the amount of information of factor $v_j\n$ captured by the $i$-th dimension of learned representation $c_i$, which is defined by their mutual information normalized by the column $R_j$ (see Eq 1). The normalization ensures the summation of $R_{\\cdot j}$ equals 1 to eliminate the effects of difference in the entropy of factors. **Figure 1** is the visualization of the transpose of the importance matrix. \n * Then we assign a score $S_i$ for each latent dimension to indicate their disentanglement property. Intuitively, if $c_i$ is disentangled, the row $R_i$ will have one element much larger than the others, corresponding to a column with a single bright entry in **Figure 1**. Here we treat each row $R_{i\\cdot}$ as a distribution $P_{i\\cdot}$ and employ entropy to quantify the intuition above (see Eq 2). To verify the equation, for example, a perfectly disentangled latent dimension, $c_i$, corresponds to a distribution that $P_{ik}=1, P_{i,j\\neq k}=0$, yielding that $S_i = 1$. On the contrary, a totally entangled latent dimension, $c_{i'}$, corresponds to a uniform distribution $P_{i' \\cdot}$, yielding that $S_{i'}=1-\\log K$, where K is the number of factors.\n * Finally, Eq 3 is a weighted sum of $S_i$s summarizing the overall disentangle property. The weight $\\rho_i$ indicates the relative importance of each latent dimension. Note that in **Figure 1** there are some columns with no bright entries and they will be down-weighted by $\\rho_i$. **Combining $\\rho_i$ and $R_{ij}$ in Eq 3 is to account for those dead or irrelevant dimensions that encode no or very little information**. ", " Dear reviewer,\n\nThank you so much for your review and suggestions. Below are our responses to your questions.\n\n**Q1. Missing comparison with other metrics from related works.**\n\n**A1:** Thanks for the references! For the three papers you mention:\n1. The first paper (https://openreview.net/pdf?id=HJgK0h4Yw) proposes 4 new metrics, namely, WSEPIN, WINDIN, RMIG, and JEMMIG. Unfortunately, for contrastive learning (CL) methods, we can not implement these metrics since the output of the CL encoders is a point estimate. They do not output the distribution $q(z_i | x)$ as in VAEs. Here we denote the output of CL methods as $o$ with other notations same as the original paper. In our paper, to calculate MIG for CL methods, VAE methods estimate posterior mean $\\mathbb{E} = \\mathbb{E}_{q(z_i | x)}[z_i]$ but we only have $o_i$ in CL methods. An adoption of those metrics to CL methods won't provide new information because:\n 1. For WSEPIN and WINDIN, since we can not assume the independence between $o_i$ for CL methods, Eq. (9) in this paper does not follow. Moreover, even given that $o_i = \\mathbb{E}$, it is still impossible to estimate $I(z_i, z_{\\neq i})$ by quantization since $z_{\\neq i}$ is a too high-dimensional vector. \n 2. For RMIG and JEMMIG, their key contribution is the probabilistic assumption. However, CL methods do not take probabilistic assumptions for $o_i$. So the decomposition of $p(z_i, y_k, x^{(n)})$ is not meaningful for representations learned by CLs. If we ignore their probabilistic background and replace $\\mathbb{E}_{q(z_i | x)}[z_i]$ with $o_i$, RMIG degrades to MIG.\n2. We noticed the SlowVAE paper (https://openreview.net/pdf?id=EbIDjBynYJ8) and included it in our comparison (**Figure 4** and more results in **Table 4 in the appendix**). They use metrics in DisLib protocol and MCC from the ICA evaluation. As we explained in the second part of Related Works, MCC evaluates identifiability, which is different from \"disentanglement\". On the other hand, Modularity used in SlowVAE is proven not aligned with other metrics in DisLib, so we don't include these two metrics in our evaluation. Moreover, on the method side, we can hardly include SlowVAE in all experiments because it requires temporal information to work. This is why this paper does not include standard image disentanglement datasets but uses video-based datasets such as KITTI-Masks. And to implement SlowVAE on standard image datasets, the SlowVAE paper samples the input pairs to satisfy their assumption on temporal factor transition. This sampling process requires access to ground truth factors, thus it is supervised instead of unsupervised as VAE/GAN/CL.\n3. In the paper of Lie Group VAE (https://arxiv.org/abs/2106.03375), four disentanglement metrics are used: FVM (FactorVAE metric), SAP, MIG, and DCI Disentanglement score. We had included these four metrics in our experiments (see **Table 4 in the appendix**). \n\n**Q2. Evaluation with traditional metrics on the subspace:**\n\n**A2:** Thanks for your suggestions. We include traditional metrics on the top-k subspaces in **Table 4**. Our observations are as follows. \n1. For BetaVAE and FactorVAE scores, the subspaces have better or compatible scores compared with unsupervised methods with low latent dimensions. (Note that Ada-GVAE, Ada-ML-VAE, SlowVAE, and EBM are supervised methods.)\n2. Regarding MIG and SAP scores, the performance of the top-k subspace is inferior. It is not surprising because MIG and SAP require a large gap between the two most relative dimensions of each factor. However, we pick k most relative dimensions out of 1000. Thus, the gap should be small.\n3. Except for dSprites and CelebA, the top-k subspaces have lower DCI scores. The key reason behind this is the significant drop in the amount of information in the top-k process (We cut down the dimension from 1000 to 10), which drastically destroys the original encoding pattern. Consequently, the GBT trained during the DCI process tends to \"borrow\" information from latent dimensions emphasizing other relevant factors to predict some complicated factors. Then the dimensions \"lending\" information become less disentangled. For example, to classify 183 types of cars in Cars3D from only 9 dimensions with only 3 emphasizing *object type* (note that k=3), GBT has to use information from *elevation* since these two attributes are correlated (see **Appendix B.3.**) However, for other low-dimensional methods, we keep all they have learned from training. Therefore, they are not affected by the information loss issue.\n4. To summarize, the top-k subspaces are better than or on par with other unsupervised methods with low latent dimensions regarding FactorVAE and BetaVAE scores. Yet, for the other traditional metrics, the top-k subspaces have less impressive performance due to the mechanism of these metrics.\n", " Dear reviewer,\n\nThank you so much for your review and suggestions. Below are our responses to your questions.\n\n**Q1: the paper does not directly show results in lower-dimensional spaces (no additional PCA required, just set the projection dimension), such as 100 or 200**\n\n**A1:** The results of MED scores for methods with variant dimensions are shown in the following tables. In the revised version, we plot the MED scores in **Appendix C.2** for methods with variant dimensions. Please see **Figure 12** for the details. The MED scores of BYOL increase as the representation dimension increases due to the inferior performance of contrastive methods with low latent dimensions. In contrast, VAEs' failure to scale to higher latent dimensions leads to a negative correlation between MED scores and latent dimensions. The conclusion for the effect of dimension on MED score is similar to that of top-k MED.\n\n| Metrics | Models | 8-d | 16-d | 128-d | 512-d | 1024-d |\n|-----------|-----------|------------|-----------|-----------|-----------|-----------|\n| MED | BYOL | 5.7 (2.3) | 15.0 (4.8) | 26.9 (1.3) | 31.8 (0.8) | 31.3 (0.4) |\n| Top-k MED | BYOL | 5.7 (2.3) | 15.0 (5.9) | 47.8 (2.4) | 52.8 (0.9) | 53.7 (0.7) |\n\n| Metrics | Models | 10-d | 100-d | 500-d | 1000-d |\n|-----------|-----------|-------------|-----------|-----------|-----------|\n| MED | BetaVAE | 32.6 (10.0) | 3.7 (0.3) | 2.8 (0.3) | 2.0 (0.2) |\n| MED | FactorVAE | 32.5 (10.1) | 1.3 (1.2) | 1.4 (1.8) | 0.3 (0.3) |\n| MED | DIP-VAE-I | 18.8 (5.6) | 1.2 (0.5) | 1.4 (1.2) | 0.1 (0.1) |\n| top-k MED | BetaVAE | 32.6 (10.0) | 11.7 (1.6) | 12.6 (4.7) | 16.6 (6.2) |\n| top-k MED | FactorVAE | 32.5 (10.1) | 2.4 (1.5) | 4.7 (0.2) | 3.0 (4.0) |\n| top-k MED | DIP-VAE-I | 18.8 (5.6) | 6.2 (2.5) | 5.6 (3.3) | 7.0 (1.3) |\n\n**Q2: It is not yet known how the subspace performs on downstream tasks, such as classification tasks.**\n\n**A2:** In the revised version, we report the accuracy of predicting factor values from the whole and top-k representations by Logistic Regression. Please refer to **Appendix F.3** and **Table 6**. We find that on 3 out of 5 datasets (dSprites, Shapes3D, and CelebA), the subspaces of contrastive learning methods have better or comparable performance compared with VAEs' full spaces. The factor predictor trained upon full space is usually better than that upon subspace, showing the advantage of high-dimensional representation again. An exception is CelebA where their performance is close, suggesting complex real-world dataset can be more robust to overfitting.", " We sincerely thank the suggestions and comments from all reviewers. Here we emphasize the motivation, contribution, and limitations of this work to clarify some related confusion. In the original submission, due to the page limit, we included many details and extended discussion in the appendix (supplementary). \n\n**Motivation and contribution of this work**: Current self-supervised learning is mainly advanced by empirical observations. And we noticed two topics remain unexplored: the disentangled property of negative-free contrastive learning and representation disentanglement evaluation in a high-dimensional space. These two are related because contrastive self-supervised learning requires a high dimension of representation for training. Therefore, we analyzed the existing disentanglement metrics and found their limitations when evaluating methods of different dimensions. We thus propose MED as a new metric for **fair and meaningful** disentanglement evaluation for models of different dimensions. With the tool, we can evaluate the disentanglement of negative-free contrastive learning methods for the first time. And we can benchmark contrastive learning (not just negative-free contrastive learning) with popular disentangled representation learning methods together for the first time.\n\n**Limitations of this work**: We found two huge obstacles to measuring the disentanglement property of contrastive learning. First, there is no widely accepted definition of \"disentanglement\" yet, so we have to face diverse existing metrics with different designs to define and measure \"disentanglement\". Second, the area of contrastive learning is still advanced by empirical observations without fundamental theoretical understanding. For example, the reason why self-supervised learning can learn meaningful representation with nonlinear neural networks instead collapse even without negative samples remains a mystery. Limited by these practical constraints, this work aims to extend the disentangled representation learning study to high-dimensional space and get more understanding of representation from CL. But we can only mainly make the discussion and provide the evidence in an empirical fashion. We believe the empirical study is useful to both communities. And as said at the end of the paper draft, we hope our work can reveal some clues to motivate future theoretical justifications.\n\nWe submitted a new version of the draft, including the appendix. To clearly show the modification of this version and fit the page limit, we added the most revised content in the appendix and wrote it in **blue**.\n\n*Changelog of the revised draft and supplementary*\n1. In **Section 1** and **Section 2**, we add more illustrations of the motivations and contributions of this work.\n2. We improve the writing of **Section 3.2** to make the high-level intuition of MED clearer. \n3. We provide more qualitative results: \n 1. The importance matrix heatmap **(Figure 7(c))** and co-occurrence **(Figure 8(d))** matrix of dSprites including all the factors. \n 2. We correct the typos in **Figure 8(a) and (c)**.\n4. We add more results for quantitative evaluation.\n 1. We include the existing disentanglement metrics scores on the top-k subspace in **Table 4**, with analysis in **Appendix C.1**.\n 2. We plot the MED scores for different representation dimensions in **Figure 12**, covering the results for BYOL with lower latent dimensions and VAEs with higher latent dimensions. \n5. We add more details for MED and top-k MED in **Appendix F**. \n 1. In **Appendix F.1** we provide more explanation of the intuition and rationale of MED.\n 2. In **Appendix F.2**, we discuss the limitations of previous metrics in detail and show how MED can resolve them.\n 3. In **Appendix F.3**, we study more properties of top-k MED, covering the visualization of the top-k process **(Figure 13)**, ablation study on k **(Figure 14)**, and downstream factor prediction performance **(Table 6)**. \n6. We add more discussion about the disagreement of existing metrics in **Appendix G**. We redraw Figure 4 as **Figure 15** as suggested by Reviewer s3YA. But putting multiple metrics of different scales with a shared y-axis can lead to confusion. So to better explain the disagreement among existing metrics, we visualize the ranking of methods on SmallNORB with different metrics in **Figure 16**.\n7. We include the source code of MED implementation in the **supplementary**. We removed sensitive information in the submitted source code to keep anonymity.\n8. We add visualization of traversing latent code in **Appendix H** on Shapes3D. The results show that MED score can be well aligned with the human sense and high-level expectation to \"disentanglement\".\n9. We add more analysis to show the superiority of MED compared to other metrics in **Appendix I**. It includes both more comprehensive experimental support and theoretical analysis in constructed linear scenarios.", " This paper takes the negative-free contrastive learning methods as an example to explore the disentanglement property of the self-supervised methods experimentally. To address the limitations of existing disentangled metrics in high-dimensional representation models, the author proposes a new decoupling metric-MED based on mutual information. Experiments on real-world datasets and high-dimensional representation space demonstrate this metric's superiority and applicability. Strengths:\n1. Existing work on Disentangled Representation Learning is limited to the generative model. This paper empirically studies the disentanglement property of negative-free contrastive learning, which is an exploratory work.\n2. This paper proposes a new metric, MED/top-K MED, which extends the decoupling metric to high-dimensional space.\n3. The paper is well organized, so the reader can get the gist of the article. The authors clearly describe the proposed method. In addition, the experimental results show the effectiveness of the proposed method.\n\nWeaknesses:\n1. The author designed a version of MED/top-k MED, to evaluate the disentanglement. Section 5.4 analyzes the effect of dimension on Top-2 MED. However, the effect of dimension on MED is unclear. In the upper part of Table 1, the authors provide results in 1000-dimensional representation space. However, the paper does not directly show results in lower-dimensional spaces (no additional PCA required, just set the projection dimension), such as 100 or 200.\n2. The author found that contrastive learning without negatives learned a well-disentangled subspace of latent representation from experiments. It is not yet known how this subspace and the subspace learned by disentangled representation learning perform on downstream tasks, such as classification tasks. Refer to Weaknesses The authors have not addressed the limitations and potential negative societal impact of their work", " This paper provides experiments on disentanglement for negative-free contrastive learning. The results indicate that current metrics have limitations on this setup. As a result, the authors present a novel metric for evaluating disentanglement in the proposed scenario.\t\n Strengths. \n- Investigating and expanding current metrics for quantifying disentanglement can address an important issue in deep learning. \n- The assessment of current issues on disentangled metrics is done properly \n- They assess disentanglement on real-datasets rather than synthetic\n- Validation of the new metric with qualitative results on generative factors\n\nWeaknesses. \nMissing comparison with other recently proposed metrics. \n- https://openreview.net/pdf?id=HJgK0h4Ywr\n- https://openreview.net/pdf?id=EbIDjBynYJ8\n- https://arxiv.org/abs/2106.03375\n In section 4 the authors show how the MED metric finds sub-sample of disentangled factors, however a correspondent analysis for traditional metrics could also be performed for comparison? The work validates the proposed metric empirically, however would be also interesting to investigate the theoretical justification of this method.", " The paper tries to empirically study the disentanglement of negative sample free contrastive learning methods, e.g. BYOL, SimSiam. The authors find that the existing disentanglement metric does not fit with the disentanglement of high-dimension feature representation space. Thus, the authors propose a new running time-efficient metric named “Mutual information based Entroy Disentanglement” and MED for short. The authors evaluate the new metric on some popular synthetic datasets and a real-world dataset CelebA and argue that negative sample free contrastive learning methods can learn a well-disentangled subset of representation. Strength: \n1. The paper points out previous methods’ drawback and propose a time-efficient metric that is designed for high-dimension space. \n2. The author report various ablation studies to show the properties and effectiveness of the new metric, i.e. uniqueness of factor-representation correspondence, and influence from manipulating factors.\n\nWeakness:\n1. The main weakness is that the authors do not theoretically prove the new metric is sound. The major message of this paper is that the previous disentanglement metrics are not good enough and the proposed new metric can fix these problems. However, the paper only showed the drawback of previous metrics and for the new metric, the authors only empirically show it may work e.g. Figure 4. Why should we believe the new metric is better than other methods? Why the value of MED can be regarded as a measure of disentanglement property? From my perspective, the best way to prove a proposed metric work is theoretical analysis, i.e. [1], and the paper misses that part. I recommend the authors consider a high-dimension linear case and prove that MED can beat some other metrics or prove some property of MED. \n2. Also, in Section 3.2, the high-level intuition of MDE is not clear. The metric has three parts, Equation (1) (2) (3) and it is quite complicated. I did not get a clear insight, i.e., $R_{ij}$ used in $\\rho_i$ and $S_i$. Why should we combine them in the way in Equation (3)? The last paragraph of Section 3.2 should be longer and provide more explanation. \n3. The authors argue that contrastive learning can learn a well-disentangled subset of representation without negative samples. The conclusion here is weak. There are many further important questions that the paper does not give answers to. Why the model can learn a well-disentangled subset of representation without negative samples? What is the disentanglement difference between methods with and without negative samples? Is there any high-level intuition or further suggestion about this conclusion? More discussion is needed here. \n\n[1] Kornblith, Simon, et al. \"Similarity of neural network representations revisited.\" International Conference on Machine Learning. PMLR, 2019. 1. The paper only reports performance on CelebA. Why does not evaluate MED on ImageNet?\n2. In line 155, it is easy to get ground truth factors for synthetic datasets. How to get ground truth factors for real datasets?\n3. In Equation (1), how to calculate Mutual Infomation for two scalars, or do they represent a distribution over the whole dataset?\n4. For Partial Disentanglement Evaluation Metric, how to know which k should be used? Binary search?\n5. In line 324, how to get k=3 and how to know the latent space dimension of a real dataset? \n Limitations are the theoretical analysis mentioned above. ", " This paper empirically studied the disentanglement property of self-supervised methods, such as MoCo, BarlowTwins, and BYOL. Besides, the authors validated the disagreement of current disentanglement metrics for the models with high-dimensional latent space. The authors proposed a new metric based on mutual information to measure high-dimensional representations. Massive experiments conducted on synthetic datasets and a real-world dataset showed that negative-free contrastive methods can learn a disentangled subset of representation. \n\nContribution:\n1. This work studied the disentanglement properties of negative-free contrastive models for the first time.\n2. This work proposed a new metric for high-dimensional models and a selection strategy to pick a disentangled subset of representation. Strength:\n1. The experiments were comprehensive and massive to cover popular conventional disentanglement methods and negative-free contrastive models.\n2. This paper aims to address the disentanglement measurement of high-dimensional representations and bring negative-free contrastive learning into disentanglement learning.\n\nWeakness:\n1. line 34: “latent representation, This” → “latent representation. This”\n2. Comparing metrics for a model in a subfigure may better show the disagreement or agreement of metrics in Figure 4.\n3. We know Orientation is hard to be disentangled, but the authors still need to show ALL experimental results without selection.\n4. What is manipulating a factor in section 4.3? Getting a set of images by traversing one factor? Could you color the latent index with the factor you picked? I cannot see the existence of a well-disentangled subset for orientation. The authors claim that disentanglement property remains unexplored in negative-free contrastive learning, but I find some relevant papers, e.g., Contrastive Disentanglement in Generative Adversarial Networks. Could the authors discuss the differences? Why negative-free contrastive learning is important?\n\nHow to prove the superiority of your proposed metric? Beta VAE, Factor VAE score, and DCI disentanglement show positive results for BYOL. \n\n\n The authors did not show the superiority of the proposed metric. They need to find some cases where all metrics fail to measure the disentanglement except the proposed metric. \n\n" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 6, 5, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 3, 4 ]

[ "solBD3SzCwQ", "T5q3SoJ-Nr", "hIDsJpsHTqL", "U_6Vl5DNUxp", "F4bZORMR-Ik", "c5Q-Vh6OWIj", "ij4wkUqhGXB", "solBD3SzCwQ", "apAuRsuANRa", "apAuRsuANRa", "apAuRsuANRa", "dMLNMf7I2_F", "5NwnmMi0xI6D", "solBD3SzCwQ", "hIDsJpsHTqL", "hIDsJpsHTqL", "hIDsJpsHTqL", "ij4wkUqhGXB", "ij4wkUqhGXB", "ij4wkUqhGXB", "ij4wkUqhGXB", "kpSa_0r_VLJ", "T5q3SoJ-Nr", "nips_2022_fJguu0okUY1", "nips_2022_fJguu0okUY1", "nips_2022_fJguu0okUY1", "nips_2022_fJguu0okUY1", "nips_2022_fJguu0okUY1" ]

[ "Ogq71NPljpu", "pwtQO-OYonk", "t0Q0gO_DqvF", "9uCidmised6", "FLIezUj0wYf", "dkyahZIHfAO", "1VgxA8lzrnB", "_SgSaqbnCIX", "rtbVifDy4naX", "QD_N6rj0xyf", "TVcnXf27GiE", "s0e6VhbLAbx", "fQbFQraV-R3", "OzP2iE7rn_", "Dovw34AVwKV", "TXDes3J-aih", "e5Bc5UmMfg2", "Uc3VcYyfQv", "6KTFD95uEN" ]

[ "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " The major concerns I've raised have been sucessfully adressed by the authors, thus I am updating my score accordingly.", " We are pleased to have successfully addressed most of the reviewer's concerns. Please kindly find additional clarifications below.\n\n**Yes, my initial comment was misguided, I did not phrase correctly, I'll try to explain myself better now. My \"reproducibility\" concern is more of a problem with the fact that tuning any \"new\" explainer with this setup is problematic, since everytime I want to change a hyper-parameter I would have to re-run the entire human experiment so it is very hard to adapt an explainer to maximize the proposed metric in the benchmark. However, I do understand this is an intrinsic limitation of this kind of setup. This is why I proposed to rebrand the paper as a study of attribution methods.**\n\n>We want to make it clear that we are indeed not proposing a metric to optimize every hyper-parameter of the explainer, but rather what we see as the first robust human-centered method to evaluate how good explainability methods are at explaining how models behave. With that said, since the reviewer’s main concern seems to have to do with “branding” can we suggest a new title as a compromise? What I Cannot Predict, I Do Not Understand: A Human-Centered Approach to Evaluate Explainability Methods and an Application to SOTA Attributions Methods.\n\n**My concern here is that, the main conclusion of the paper is something we already know which is that attribution methods have severe limitations, because they lack the \"what\" component as mentioned in [1] \"Heatmaps are useful to understand things like which objects in an image contributed to a classification. However, they cannot visualize/explain well attributes that are not spatially localized, like size, color, etc. In addition, they can show which areas of the image may be changed in order to affect the classification, but not how they should be changed.\"**\n\n>Two points: We want to emphasize that while we agree that the possible limitations of attribution methods might have been discussed before in the literature, 1) there are still dozens of attribution methods that are being developed every year, and 2) our study is the first to demonstrate these limitations scientifically by identifying positive and negative test scenarios (in addition to laying the groundwork for a potential image-computable metric to identify those scenarios).\n\n**Yes that is precisely my point, the fact that the meta-predictor is a human, really limits the amount of classes with which the benchmark will work. Consider scenario 3 where all the classes being evaluated are really similar, even in a one vs all setting I seriously doubt a human would perform well in that circumstance given a high amount of classes (10, 100).**\n\n>Again we believe this is a misunderstanding of our approach.\nIf the concern of the reviewer has to do with going beyond binary datasets, the problem can be trivially reformulated as a Target class vs Other binary classification problem. As the human only has to learn the rules the model uses for the Target class, he should be able to perform well regardless of the number of classes in the dataset.\nIf the concern of the reviewer has to do with human cognitive limitation, we believe the reviewer’s concern is unwarranted. What we propose is a human-derived metric, therefore, we do not understand why accurately reflecting human cognitive limitation is a “limit” of the proposed evaluation method. If a participant does not perform well in a setting, it should be an accurate reflection of the performance of end-users in such setting.", " **Since for scenario 2 you only provide correctly classified samples, I assume that for scenario 3 you only provide incorrectly classified samples (otherwise there would be an overlap with scenario 2) is this assumption correct? Further, this should be clarified in the paper because right now since the authors mention a balance ratio of correctly and incorrectly classified samples when describing scenario 1 (\"In this situation where prior knowledge of subjects can affect their Meta-predictor score, we balance data correctness (50% of correct/incorrect examples shown\") but make no such clarification for scenario 2 and 3.**\n\n>To be clear: for scenario 3, while providing only incorrectly classified samples makes perfect sense, we provide 50% of correct/incorrect examples because we have to control for participants' prior knowledge which would otherwise confound the results. But this does not mean that scenarios 2 and 3 overlap because we define “Identifying an expert strategy” as a case where participants do not already come equipped with the right strategy to classify, and they must learn the one successfully used by the model. In case 3, the participants already come equipped with the right strategy, therefore, this assumption does not hold. We mention the balance ratio, or what we call “controlling for prior knowledge”, L.223 for scenario 1, L.235 for scenario 2, and L.245 for scenario 3, and we give more explanations about it in section B.1 of the SI. We will further clarify that in the paper.", " We thank the reviewer for taking into consideration our comments and raising his score.", " We thank the reviewer for reading our review. Please kindly find further clarifications below.\n\n**effective explanation definition: the paper's methods defines an effective explanation as one that enables people to “predict the predictor”. Other potential definitions would involve the user being able to accurately explain how the algorithm works, not just the predictions it will make.**\n\n>We believe that while the potential definition given by the reviewer is sound, in theory, it is not actionable in practice. To evaluate if users “accurately explain how the algorithm works” we would need a ground truth explanation about how the algorithm works, which we do not have for deep neural networks. Our definition is narrower but it is quantifiable using our framework.", " Thank you for the answers. I am slightly improving my score, however, the argument that a couple of other papers (one of which is a short paper -- hence acceptable to have fewer datasets) are using 2 datasets is not a convincing one. Moreover, while you have 3 datasets in total, each scenario has only one, which is also very trivial in some cases, e.g., Huskey vs Wolf. Would this method help with more complex datasets? (this is also the concern of Reviewer LEiC). More (and more complex) datasets per scenario are needed to prove that the work would be helpful in practice. ", " Thank you to the authors for their response to my review. Overall I am maintaining my score of weak accept.\n\n* effective explanation definition: the paper's methods defines an effective explanation as one that enables people to “predict the predictor”. Other potential definitions would involve the user being able to accurately explain how the algorithm works, not just the predictions it will make.\n\n* psychophysics experiments: I agree this falls under the broadest definition of a psychophysics task, but typically when a researcher explicitly defines their experiment as a psychophysics experiment, it is good practice to place their experiment within the psychophysics literature (e.g. does it build off a classical psychophysical method?)", " __We agree that the problem of overlap and distinction between use cases of XAI in general is not always clear, but important, and we will add a discussion about it in the paper. Here specifically, we agree that there exists some overlap between the scenario 1 and 3, as bias detection is a special case of a failure case (we use scenario 1 because it was already used in the literature before and it allows us to validate that our framework works). Regarding scenario 2, we only provide correctly classified samples as pointed out by the reviewer (and model accuracy on those classes is 90.2%), hence we think it is reasonable to say that this is a scenario of identifying an expert strategy.__\n\n>Since for scenario 2 you only provide correctly classified samples, I assume that for scenario 3 you only provide incorrectly classified samples (otherwise there would be an overlap with scenario 2) is this assumption correct? Further, this should be clarified in the paper because right now the authors mention a balance ratio of correctly and incorrectly classified samples when describing scenario 1 (\"_In this situation where prior knowledge of subjects can affect their Meta-predictor score, we balance data correctness (50% of correct/incorrect examples shown\"_) but make no such clarification for scenario 2 and 3. \n\n__This is a very good question! The most interesting case is Saliency,..__ \n\n>Thanks for such a detailed answer!", " In general most of my concerns/questions have been addressed and I have modified my score accordingly, however that are still a couple left, that I think are important\n\n__This comment is misguided. A reproducibility concern would arise if the methods were not described in sufficient detail to allow someone else to run the same exact set of experiments. This is not the case here since we will provide the code and all necessary details. Filtering participants for online experiments is standard and necessary to remove participants that are not properly engaged or following explanations [1,2]. We agree that the use of human participants creates a burden on the researcher over automated scores but given that our results suggest that current scores are sometimes misleading we do not see any alternatives at the moment. We would like to highlight that this framework is one of the very few human studies [3] that can be scaled, as all code will be made available and all types of explainability methods can be tested.__\n\n>Yes, my initial comment was misguided, I did not phrase correctly, I'll try to explain myself better now. My \"reproducibility\" concern is more of a problem with the fact that tuning any \"new\" explainer with this setup is problematic, since everytime I want to change a hyper-parameter I would have to re-run the entire human experiment so it is very hard to adapt an explainer to maximize the proposed metric in the benchmark. However, _I do understand this is an intrinsic limitation of this kind of setup_. This is why I proposed to rebrand the paper as a study of attribution methods. \n\n__We are also interested in evaluating counterfactuals on the use case where attribution methods are not useful. But this would constitute future work because our main focus is to show that attribution methods do not help because they lack the “what” component, which is independent of whether or not current counterfactual explainers address this concern.__\n\n>My concern here is that, the main conclusion of the paper is something we already know which is that attribution methods have severe limitations, because they lack the \"what\" component as mentioned in [1] _\"Heatmaps are useful to understand things like which objects in an image contributed to a classification. However, they cannot visualize/explain well attributes that are not spatially localized, like size, color, etc. In addition, they can show which areas of the image may be changed in order to affect the classification, but not how they should be changed.\"_\n\n__Having to classify more than 2 classes would increase the participants’s cognitive load and bring unnecessary difficulty to the task. This is not necessary because classification problems with more than 2 classes can always be reformulated as one vs. all / binary classification problems without lack of generality. Our task could be trivially reformulated as predicting Target class vs Other, instead of Class 1 vs Class 2 as we did in the paper...__\n\n>Yes that is precisely my point, the fact that the meta-predictor is a human, really limits the amount of classes with which the benchmark will work. Consider scenario 3 where all the classes being evaluated are really similar, even in a one vs all setting I seriously doubt a human would perform well in that circumstance given a high amount of classes (10, 100).\n\n\n[1] Lang, O., Gandelsman, Y., Yarom, M., Wald, Y., Elidan, G., Hassidim, A., ... & Mosseri, I. (2021). Explaining in style: Training a gan to explain a classifier in stylespace. In Proceedings of the IEEE/CVF International Conference on Computer Vision (pp. 693-702).", " **I think it would be useful to incorporate the meta-predictor response time into the metric since an explanation that is correctly predicted instantly is probably better than one that gets correctly predicted after some time. Conversely an explanation that is incorrectly predicted instantly could be considered more \"misleading\" than one that gets incorrectly predicted after some time.**\n\n>We agree with the reviewer that response time can be an interesting complement to the main metric to decide between 2 equally informative methods. We will add a discussion about the response time in the SI for the final version of the manuscript.\n\n**The limitations of the work should be discussed beyond the cost of human evaluation, since the framework itself has some limitations (mentioned above) such as scalability and reproducibility.**\n\n>We have incorporated a section about limitations and societal impact in SI.\n\n* [1] Oppenheimer, Daniel M., Tom Meyvis, and Nicolas Davidenko. \"Instructional manipulation checks: Detecting satisficing to increase statistical power.\" Journal of experimental social psychology 45.4 (2009): 867-872.\n* [2] Berinsky, Adam J., Michele F. Margolis, and Michael W. Sances. \"Separating the shirkers from the workers? Making sure respondents pay attention on self‐administered surveys.\" American Journal of Political Science 58.3 (2014): 739-753.\n* [3] Kim, S. S., Meister, N., Ramaswamy, V. V., Fong, R., & Russakovsky, O. “HIVE: Evaluating the Human Interpretability of Visual Explanations”. In: European Conference of Computer Vision (ECCV). 2022.\n* [4] Smilkov, D., Thorat, N., Kim, B., Viégas, F., & Wattenberg, M. (2017). Smoothgrad: removing noise by adding noise. Arxiv 2017\n", " **In the section describing the understandability-completeness trade-off it would useful to mention/show examples of how an entirely faithful and more understandable explanations look like.**\n\n>Thank you for your suggestion, we will add examples of those explanations in the final version of the manuscript!\n\n**It seems to me that there is a potential overlap within the 3 scenarios used for evaluation (Bias detection, Identifying an expert strategy, Understanding failure cases). For example: In scenario 2 (Identifying an expert strategy) whenever a meta-predictor is provided with an image that the model has failed to predict, then the task is no longer: to understand the strategy that was discovered by the AI system, but instead it becomes either bias detection (scenario 1) or Understanding failure cases (scenario 3). Conversely, in scenario 3 (if the classes are really similar) whenever the meta-predictor is provided with an image that the model has successfully predicted then the task becomes Identifying an expert strategy (scenario 2). An easy fix would be to provide only correctly and incorrectly classified samples for scenarios 2 and 3 respectively, however as stated by the authors this would significantly affect the meta-predictor score if the meta-predictor has some prior knowlege about the domain (dataset) the scenario is being evaluated on. If this overlap does in fact exists, I think it should be discussed in the paper.**\n\n>We agree that the problem of overlap and distinction between use cases of XAI in general is not always clear, but important, and we will add a discussion about it in the paper. Here specifically, we agree that there exists some overlap between the scenario 1 and 3, as bias detection is a special case of a failure case (we use scenario 1 because it was already used in the literature before and it allows us to validate that our framework works). Regarding scenario 2, we only provide correctly classified samples as pointed out by the reviewer (and model accuracy on those classes is 90.2%), hence we think it is reasonable to say that this is a scenario of identifying an expert strategy.\n\n**Do the authors have any hypothesis as to why the best method for Bias detection and Identifying an expert strategy differ? I feel like the paper would be more complete with a small section explaining this phenomenon, not unlike the section: Why do attribution methods fail?. In which the authors investigate why all methods underperform on the 3rd setting.**\n\n>This is a very good question! The most interesting case is Saliency, which is the worst method on the bias dataset but the best on the “leaves” dataset. On the bias dataset, the model seems to focus on the background (i.e., a coarse feature), and on the “leaves'' dataset the model seems to focus either on the margin or on the vein of the leaf (i.e., very fine features). We hypothesize that different methods suit different granularity of features (coarse vs fine). [4] make the hypothesis that “the saliency maps are faithful descriptions of what the network is doing” but because “the derivative of the score function with respect to the input [is] not [...] continuously differentiable”, the saliency map can appear noisy. Because of this local discontinuity of the gradient, a large patch of important pixels is often portrayed in the saliency map as a collection of smaller patches of important pixels (i.e., a coarse feature vs multiple individual fine features) which can make it hard to identify if the strategy is the coarse feature or a more complex interaction of the smaller features. In the bias dataset, because the model relies on the background, the Saliency maps appear very noisy and the explanation ends-up not being useful. We note that SmoothGrad, which proposes to fix that discontinuity, is useful. On the other hand, on the leaves dataset, the model uses very fine features, therefore the Saliency maps suffer less from the discontinuity, it does not appear noisy, Saliency is useful. We also note that in this case, SmoothGrad is not better than Saliency, which can arguably be attributed to the fact that we do not need to fix the discontinuity of the gradient. Conversely, because the granularity of both Grad-CAM (the feature map is much smaller than image size) and Occlusion (the patch size is much bigger than a pixel) is too high, the heatmaps they offer on the “leaves” dataset are too coarse to specifically highlight the fine features and it seems to take more time for the subjects to pick-up on them. But on the biased dataset, Grad-CAM and Occlusion are the best performing methods. We will add this discussion to the final version of the manuscript.", " Thank you for your thorough review, thoughtful comments and helpful suggestions! Please kindly find our replies below.\n\n**The proposed framework poses some reproducitiblity concerns since in order to evaluate any explainability one would have to undergo the entire process described in the paper of hiring and filtering the meta-predictors. This also makes it hard to scale.**\n\n>This comment is misguided. A reproducibility concern would arise if the methods were not described in sufficient detail to allow someone else to run the same exact set of experiments. This is not the case here since we will provide the code and all necessary details. Filtering participants for online experiments is standard and necessary to remove participants that are not properly engaged or following explanations [1,2]. We agree that the use of human participants creates a burden on the researcher over automated scores but given that our results suggest that current scores are sometimes misleading we do not see any alternatives at the moment. We would like to highlight that this framework is one of the very few human studies [3] that can be scaled, as all code will be made available and all types of explainability methods can be tested.\n\n**I worry about the effectiveness of the meta-predictor whenever evaluating a dataset with more than 2 classes.**\n**Provide some experiments with a varying number of classes or at least a small section discussing how the effectiveness of the meta-predictor approach varies when increasing the number of classes**\n\n>Having to classify more than 2 classes would increase the participants’s cognitive load and bring unnecessary difficulty to the task. This is not necessary because classification problems with more than 2 classes can always be reformulated as one vs. all / binary classification problems without lack of generality. Our task could be trivially reformulated as predicting Target class vs Other, instead of Class 1 vs Class 2 as we did in the paper. We will integrate a discussion about this in the final version of the manuscript.\n\n**The authors state that the framework can be applied to other explainability methods and while this in principle makes sense, there are no experimental results supporting this claim.**\n\n>While it is true that the paper focuses on attribution methods because they are the main method used in the field and deserve a proper study, we give a formal definition of the framework L.131 which explains why this framework can, and will, be used in future works for other explainability methods.\n\n**In general I recommend rebranding the paper as a study of attribution methods instead of a framework, since the results are hard to scale, hard to reproduce and it is cumbersome to \"integrate\" a new explainer into this framework.**\n\n>We thank the reviewer for offering valuable suggestions to improve the paper, but regarding this specific suggestion, we respectfully disagree. We will empathize this point in the final version, but the paper is both about a framework as well as an instantiation of this framework to study the pitfalls of attribution methods. \nWe hope to have addressed the reviewer’ concerns about scaling and reproducibility. Regarding the last concern, we argue that the benefit for the community to have common human-centered evaluations outweighs the challenge associated with running human experiments.\n\n**The main reason the authors provide for the failure of attribution methods is an intrinsic limitation of said methods, since they can only show what regions in an image should be changed but not how. This is precisely one of the limitiations counterfactual explainers solve, and since the authors claim that the framework can be applied to any explainer it would be useful to explore if counterfactual explainers fail in the same way, whilst substantiating said claim.**\n\n>We are also interested in evaluating counterfactuals on the use case where attribution methods are not useful. But this would constitute future work because our main focus is to show that attribution methods do not help because they lack the “what” component, which is independent of whether or not current counterfactual explainers address this concern. \n\n**In the General study design section it is mentioned that each training session has 5 training samples, but the plots showcasing the results show 5, 10 and 15, this should be clarified.**\n\n>The plot showcases the total number of training samples seen at that point of the testing phase. During the 1rst testing phase, they’ve seen 5 samples from the 1rst training phase, during the 2nd testing phase, they’ve seen in total, 5 from 1rst training phase + 5 from 2nd training phase = 10 samples, etc ... We will clarify that in the legend of the figure.\n", " Thank you for your positive feedback and interesting questions! Please kindly find our replies below.\n\n**The methods the authors propose, assuming one buys their narrow definition of an effective explanation, seems reasonable and defensible.**\n\n>We argue that our definition is anything but narrow. We define explainability methods broadly as methods that are designed to help users better understand their model. Our evaluation method, which we call “usefulness” measures exactly this, how much they help. Furthermore, we emphasize L.47 that this definition of an effective explanation is backed-up by a body of literature on the psychology of explanations. We would gladly add a paragraph in the discussion if the reviewer could please expand on what would be broader definitions of effective explanations?\n\n**The concept of a meta-predictor seems to limit the author's approach to problems in which a model's goal is simply to replicate a human's intelligence, rather than to augment it or enhance it in ways the human could not do on its own**\n\n>We think the reviewer may have misunderstood our approach. By “meta-predictor”, we mean being able to understand a model sufficiently well to be able to predict how it will classify an image. There is absolutely no requirement for the underlying strategy to match that of a human observer as long as it is comprehensible to a human. In fact, our “leaves” dataset corresponds to a use case for which humans do not come equipped with any a priori strategy [1].\n\n**The authors claim they conducted psychophysics experiments. In what ways does their study design engage with psychophysics? The authors should explicitly say what they are borrowing from the psychophysics literature and why. (From my understanding of psychophysics, the connections seem tenuous and superficial at best).**\n\n>We conducted human behavioral experiments where we quantitatively measured the response of participants to the presentation of visual stimuli. These experiments required approval from an Institutional Review Board (IRB) and can be unambiguously labeled as psychophysics. \n\n**Might this approach apply for other definitions of an effective explanation?**\n\n>This is related to an earlier point made by the reviewer. We are having trouble imagining alternative definitions. Could the reviewer please be more specific about what they have in mind for an alternative definition?\n\n**The authors should deeply engage with the limitations around how creating a benchmark for their narrowly defined idea of an effective explanation might cause harm by shifting focus away from other ones.**\n\n>Again this is related to the above points. We would need more details about alternative definitions of effective explanations to answer this point. \n\n* [1] Edward J Spagnuolo, Peter Wilf, and Thomas Serre. “Decoding family-level features for modern and 506 fossil leaves from computer-vision heat maps”. In: American journal of botany (2022)", " Thank you for your positive feedback and valuable comments. Please kindly find our replies below.\n\n**I think the impact of the results is limited because the experiment is conducted only on limited scenarios, such as classification on Husky vs Wolf and classification on Kit Fox and Red Fox. Due to the limitation, the scores shown in Figures 4-6 are distributed in narrow areas. Therefore, if more scores are obtained by conducting experiments on more scenarios, the results may change.**\n\n>We would like to point out that the number of scenarios considered in our paper (=3 is greater than for any of the prior related work (respectively 1 scenario [1] and 2 scenarios [2,3,4]). The scenarios we chose are representative of different use cases: Husky vs Wolf is a classic example of bias detection [5]; Kit Fox vs Red Fox is a reasonable example of failure cases on a fine-grained dataset and the “leaves” dataset is a non-trivial use case for which humans do not come equipped with any a priori strategy and where they can potentially benefit from explanation methods to understand the underlying strategy used by a model [6]. We would also like to emphasize that all our experiments were conducted on a sufficiently large number of participants for the results to be statistically reliable. Adding more experiments or scenarios would not change the main contributions of the paper. That is, (i) a novel human-derived metric to evaluate the usefulness of explanations, (ii) a corresponding large study of attribution methods, and (iii) evidence that the widely used faithfulness metrics are unable to predict failure cases of attribution methods but that perceptual similarity scores derived from the explanations can do a better job at it.\n\n**There is a possibility that the predictive performance of the recognition model affects the utility score. When the recognition model has a poor predictive performance, the explanation methods depending on the predictions by the recognition model may also produce incorrect and uncertain explanations. The three scenarios in this study are settings that are difficult for the recognition model to accurately classify images. Therefore, I have a concern that whether the experiment can evaluate explanation methods only, excluding the impact of the recognition model.**\n\n>This is indeed a very important concern, that we think was carefully taken into consideration in our methodology. The proposed evaluation method measures how well people understand the strategy of the model, whether the model uses a good/correct strategy or not. Because participants predict a model’s decision and not the true label, it does not matter whether the model is good at recognition or not, the only thing that impacts the results is how easy the strategy of the model is for participants to comprehend -- which is independent of any performance metric –, and how well the explanation method captures that strategy and translates it in a manner which is interpretable by users –which is what we want to evaluate–.\n\n* [1] Hua Shen and Ting-Hao Huang. “How Useful Are the Machine-Generated Interpretations to General Users? A Human Evaluation on Guessing the Incorrectly Predicted Labels”. In: Proceedings of the AAAI Conference on Human Computation and Crowdsourcing. Vol. 8. 1. 2020, pp. 168–172.\n* [2] Peter Hase and Mohit Bansal. “Evaluating Explainable AI: Which Algorithmic Explanations Help Users Predict Model Behavior?” In: Proceedings of the Annual Meeting of the Association for Computational Linguistics (ACL Short Papers). 2020.\n* [3] Giang Nguyen, Daeyoung Kim, and Anh Nguyen. “The effectiveness of feature attribution methods and 468 its correlation with automatic evaluation scores”. In: Advances in Neural Information Processing Systems (NeurIPS), 2021.\n* [4] Kim, S. S., Meister, N., Ramaswamy, V. V., Fong, R., & Russakovsky, O. “HIVE: Evaluating the Human Interpretability of Visual Explanations”. In: European Conference of Computer Vision (ECCV). 2022.\n* [5] Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. “\"Why Should I Trust You?\": Explaining the Predictions of Any Classifier”. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. 2016.\n* [6] Edward J Spagnuolo, Peter Wilf, and Thomas Serre. “Decoding family-level features for modern and 506 fossil leaves from computer-vision heat maps”. In: American journal of botany (2022)\n\n", " Thank you for the positive comments about the value of our results and the insightful questions! Please kindly find our replies below.\n\n\n\n**There isn't much novelty in the evaluation method proposed, just minor improvements over previous studies, although it is still worth having these improvements.**\n\n>We respectfully disagree. Prior work either has serious methodological issues and/or was applied to a very different domain (tabular data vs. images). To the best of our knowledge, our study is the first to describe a properly designed human psychophysics experiment to evaluate the usefulness of explanation methods. This is not a trivial contribution!\n\n**For each of the 3 scenarios, only 1 dataset was used.**\n\n>We find the reviewer’s comment unfair as we use a total of 3 datasets which is more than any of the prior related work (1 dataset [1] and 2 datasets [2,3,4]).\n\n**Only attribution methods were tested. I think it is already quite clear for the community that attribution methods have lots of problems (and clearly they cannot provide the \"what\" that the authors mention) therefore it would have been more interesting to also test other types of explanatory methods.**\n\n>We focused on attribution methods because they are currently the most popular ones. Yes it is known that they have problems but we are not aware of any prior work systematically studying their limitations. To the best of our knowledge, our study is the first to rigorously study their pitfalls. We even propose a novel metric that can help identify cases where attribution methods will most likely not be useful. Our approach is general and should in principle be applicable to other explainability methods.\n\n**But even among attribution methods, popular ones such as SHAP and LIME were not tested.**\n\n>We agree that SHAP and LIME used to be popular methods, but they are no longer considered competitive on natural images, and are no longer used in recent studies (e.g., see refs [3, 5] both NeurIPS 2021). We used Occlusion, Grad-CAM, Saliency, SmoothGrad, Integrated Gradient and Input Gradient, which are commonly used as benchmarks in recent papers [5,6,7].\n\n**How do you think the evaluation method can help the community to design better explainability methods in the first place? Assume that one develops a novel explainer but evaluating it on your method shows that it is less useful than e.g., SmoothGrad. Would your evaluation provide any further insight as to how the novel explainability method could be improved to become more useful?**\n\n>It is true that our evaluation method only allows for a comparison with other methods but in all fairness there is currently no method that can be used for this purpose. Automated measures suffer from the same limitations, and on top of it, we show in this work that greater faithfulness does not necessarily mean greater human interpretability. We have added this point in the limitations. \n\n**I did not see a direct mention of potential limitations or negative societal impact, which I suggest the authors incorporate in their paper.**\n\n>We have incorporated a section about limitations and societal impact in SI.\n\n* [1] Hua Shen and Ting-Hao Huang. “How Useful Are the Machine-Generated Interpretations to General Users? A Human Evaluation on Guessing the Incorrectly Predicted Labels”. In: Proceedings of the AAAI Conference on Human Computation and Crowdsourcing. Vol. 8. 1. 2020, pp. 168–172.\n* [2] Peter Hase and Mohit Bansal. “Evaluating Explainable AI: Which Algorithmic Explanations Help Users Predict Model Behavior?” In: Proceedings of the Annual Meeting of the Association for Computational Linguistics (ACL Short Papers). 2020.\n* [3] Giang Nguyen, Daeyoung Kim, and Anh Nguyen. “The effectiveness of feature attribution methods and 468 its correlation with automatic evaluation scores”. In: Advances in Neural Information Processing Systems (NeurIPS), 2021.\n* [4] Sunnie SY Kim et al. “HIVE: Evaluating the Human Interpretability of Visual Explanations”. In: European Conference of Computer Vision (ECCV). 2022.\n* [5] Fel Thomas et al. “Look at the Variance! Efficient Black-box Explanations with Sobol-based Sensitivity Analysis”. In: Advances in Neural Information Processing Systems (NeurIPS). 2021.\n* [6] Adebayo, J., Gilmer, J., Muelly, M., Goodfellow, I., Hardt, M., & Kim, B. (2018). Sanity checks for saliency maps. Advances in neural information processing systems, 31.\n* [7] Fel, T., Ducoffe, M., Vigouroux, D., Cadène, R., Capelle, M., Nicodème, C., & Serre, T. (2022). Don't Lie to Me! Robust and Efficient Explainability with Verified Perturbation Analysis. In ICML: Workshop on Formal Verification of Machine Learning (2022)", " The paper introduces an evaluation framework for explanatory methods that uses human ability to predict a model's predictions as a measure of the utility of the explanations. The paper considers 3 scenarios for usefulness: bias identification, understanding how to solve too difficult tasks for non-experts, and understanding of failure cases. The paper looks at 6 attribution methods over 1 dataset per scenario. Strengths\nThe paper addresses a very important topic: the evaluation of explainability methods.\nIt is clearly written and has a good research methodology. \nTheir evaluation method is applicable to any explainability method. While the principal behind it is not novel (as the authors also point out), the evaluation is done in a more thorough manner than in the previous studies.\nSome of the results provide new and unexpected insight, which could potentially have a good impact on shaping the explainability field.\n\n\nWeaknesses\nThere isn't much novelty in the evaluation method proposed, just minor improvements over previous studies, although it is still worth having these improvements. \n\nFor each of the 3 scenarios, only 1 dataset was used.\n\nOnly attribution methods were tested. I think it is already quite clear for the community that attribution methods have lots of problems (and clearly they cannot provide the \"what\" that the authors mention) and therefore it would have been more interesting to also test other types of explanatory methods. But even among attribution methods, popular ones such as SHAP and LIME were not tested. \n\nSome of the conclusions have already been established before and/or are to be expected, as the authors also point out. However, it is still useful to have this paper show them again in a proper manner (e.g., eliminating potential confounds).\n\n\nMinor typos:\nUse \\citet when appropriate\nL74 \"score drop in score\"\nL81 remove . before citation\nL85 citet [5]\nL103 This removeS\nL107 measure reflectS\nL107 and L109, 112 explanationS\nL178: Meta-predictorS\nL191: space missing \".T\"\nL220 \"ref. [5]\" delete ref and citet\nL229: if --> is\nL320 citation missing\nL328: capital for section\nL367: vs. remove larger space\nL394 one needS\nL394: is -> are How do you think the evaluation method can help the community to design better explainability methods in the first place? Assume that one develops a novel explainer but evaluating it on your method shows that it is less useful than e.g., SmoothGrad. Would your evaluation provide any further insight as to how the novel explainability method could be improved to become more useful? I did not see a direct mention of potential limitations or negative societal impact, which I suggest the authors incorporate in their paper. ", " This paper addresses evaluating explanation methods for image classification based on human experiments. To evaluate them, this study proposes an evaluation metric that quantifies how well humans are able to understand the output of the system after looking at the explanation provided by each explanation method. Then, this study analyzes the explanation methods by considering three scenarios to do bias detection, identification of new strategies, and understanding of failure cases. ## Strengths\n- The experiment is well designed, the hypotheses tested are appropriate, and the experiment is done with enough participants. Therefore, the results obtained look convincing, except for the points in the weaknesses below.\n- Some results are valuable for XAI community. For example, the result of the third scenario can strengthen the statement in previous works, e.g., [57].\n\n## Weaknesses\n- I think the impact of the results is limited because the experiment is conducted only on limited scenarios, such as classification on Husky vs Wolf and classification on Kit Fox and Red Fox. Due to the limitation, the scores shown in Figures 4-6 are distributed in narrow areas. Therefore, if more scores are obtained by conducting experiments on more scenarios, the results may change.\n- There is a possibility that the predictive performance of the recognition model affects the utility score. When the recognition model has a poor predictive performance, the explanation methods depending on the predictions by the recognition model may also produce incorrect and uncertain explanations. The three scenarios in this study are settings that are difficult for the recognition model to accurately classify images. Therefore, I have a concern that whether the experiment can evaluate explanation methods only, excluding the impact of the recognition model.\n NA NA", " The authors propose a quantitative measurement to evaluate explainability methods by relying on how well the methods allows a human to predict what prediction a classifier will make. The authors conduct an experiment using their approach for a variety of image classification explainability tools. Strengths:\nSome sort of statistical approximation around the effectiveness of human-facing explanations is a worthwhile, if challenging goal.\nThe methods the authors propose, assuming one buys their narrow definition of an effective explanation, seems reasonable and defensible.\nThe initial experiments produce interesting and potentially useful results.\nThe paper is reasonably easy to follow, though would benefit from making fewer assumptions about reader's background knowledge in the introduction.\n\nWeaknesses:\nThe concept of a meta-predictor seems to limit the author's approach to problems in which a model's goal is simply to replicate a human's intelligence, rather than to augment it or enhance it in ways the human could not do on its own.\nThe authors claim they conducted psychophysics experiments. In what ways does their study design engage with psychophysics? The authors should explicitly say what they are borrowing from the psychophysics literature and why. (From my understanding of psychophysics, the connections seem tenuous and superficial at best). 1. Might this approach apply for other definitions of an effective explanation?\n2. Is this actually a psychophysics experiment? The authors should deeply engage with the limitations around how creating a benchmark for their narrowly defined idea of an effective explanation might cause harm by shifting focus away from other ones.", " The authors present a human-centered framework to evaluate the usefulness of attribution explainability methods. They evaluate 6 different attribution methods across 3 setttings. They show that generally, perceptual scores derived from attribution maps can be more useful at predicting failure cases of explainability methods better than fidelity metrics. Strengths:\n- The explainability evaluation framework the authors propose: \n - is human-centered, which is, ideally, how the usefulness of explanations should be evaluated.\n - includes a control group, which was lacking in previous work\n\n- The paper is easy to understand and generally well written.\n- The proposed metric is original and sound to the best of my knowledge.\n\nWeaknesses:\n- The proposed framework poses some reproducitiblity concerns since in order to evaluate any explainability one would have to undergo the entire process described in the paper of hiring and filtering the meta-predictors. This also makes it hard to scale.\n\n- I worry about the effectiveness of the meta-predictor whenever evaluating a dataset with more than 2 classes.\n\n- The authors state that the framework can be applied to other explainability methods and while this in principle makes sense, there are no experimental results supporting this claim. \n In general I recommend rebranding the paper as a study of attribution methods instead of a framework, since the results are hard to scale, hard to reproduce and it is cumbersome to \"integrate\" a new explainer into this framework. However, the manuscript as is could be improved in the following ways:\n\n#### Critical changes:\n - Provide some experiments with a varying number of classes or at least a small section discussing how the effectiveness of the meta-predictor approach varies when increasing the number of classes.\n\n- The main reason the authors provide for the failure of attribution methods is an intrinsic limitation of said methods, since they can only show what regions in an image should be changed but not how. This is precisely one of the limitiations counterfactual explainers solve, and since the authors claim that the framework can be applied to any explainer it would be useful to explore if counterfactual explainers fail in the same way, whilst substantiating said claim.\n- It seems to me that there is a potential overlap within the 3 scenarios used for evaluation (Bias detection, Identifying an expert strategy, Understanding failure cases). For example: In scenario 2 (Identifying an expert strategy) whenever a meta-predictor is provided with an image that the model has failed to predict, then the task is no longer: _to understand the strategy that was discovered by the AI system_, but instead it becomes either bias detection (scenario 1) or Understanding failure cases (scenario 3). Conversely, in scenario 3 (if the classes are really similar) whenever the meta-predictor is provided with an image that the model has successfully predicted then the task becomes Identifying an expert strategy (scenario 2). An easy fix would be to provide only correctly and incorrectly classified samples for scenarios 2 and 3 respectively, however as stated by the authors this would significantly affect the meta-predictor score if the meta-predictor has some prior knowlege about the domain (dataset) the scenario is being evaluated on. If this overlap does in fact exists, I think it should be discussed in the paper.\n\n#### Minor changes:\n\n- Figure 1 is not referenced anywhere, also there is a missing reference on line 320\n- In the section describing the understandability-completeness trade-off it would useful to mention/show examples of how an _entirely faithful_ and _more understandable_ explanations look like.\n- In the General study design section it is mentioned that each training session has 5 training samples, but the plots showcasing the results show 5, 10 and 15, this should be clarified. \n- I think it would be useful to incorporate the meta-predictor response time into the metric since an explanation that is correctly predicted instantly is probably better than one that gets correctly predicted after some time. Conversely an explanation that is incorrectly predicted instantly could be considered more \"misleading\" than one that gets incorrectly predicted after some time.\n\n#### Questions:\n- Do the authors have any hypothesis as to why the best method for Bias detection and Identifying an expert strategy differ? I feel like the paper would be more complete with a small section explaining this phenomenon, not unlike the section: __Why do attribution methods fail?__. In which the authors investigate why all methods underperform on the 3rd setting. The limitations of the work should be discussed beyond the cost of human evaluation, since the framework itself has some limitations (mentioned above) such as scalability and reproducibility. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 6, 6, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 3, 4 ]

[ "pwtQO-OYonk", "rtbVifDy4naX", "_SgSaqbnCIX", "dkyahZIHfAO", "1VgxA8lzrnB", "Dovw34AVwKV", "fQbFQraV-R3", "TVcnXf27GiE", "s0e6VhbLAbx", "TVcnXf27GiE", "s0e6VhbLAbx", "6KTFD95uEN", "Uc3VcYyfQv", "e5Bc5UmMfg2", "TXDes3J-aih", "nips_2022_59pMU2xFxG", "nips_2022_59pMU2xFxG", "nips_2022_59pMU2xFxG", "nips_2022_59pMU2xFxG" ]

[ "SSMrTU744Oi", "noBoymSGu6-", "yp9p2Cih7xo", "pFJIRP4d7fM", "QHCL1WOEYtn", "hf5NeA1B9_l", "piQcOLT4Vkv", "3JQPwPGiLCn" ]

[ "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank the reviewer for their feedback. We are pleased to see that the reviewer thinks that with this library researchers “can more easily design differentiable programming systems while spending less time...”; this is one of our main goals! We are also glad the reviewer recognized some of the engineering challenges we tackled: “Cuda solver is usually closed-source. Making a differentiable version of it takes effort.”\n\nThe reviewer points out that the novelty of this paper is unclear, to which we respectfully disagree. The last three paragraphs of the introduction in the paper state our novel contributions in detail. Theseus is essentially **the first library** that offers a “full-stack” solution for differentiable NLS including sparse solvers, Lie-algebra support, a wide range of out-of-the-box cost functions for robotics and computer vision, support for differentiable robot kinematics, support for custom cost functions and an easy to use API. As other reviewers have already pointed out, there is value for the community in having such a library, which did not exist before Theseus. \n\nWe agree with the reviewer that there will be overhead compared with forward code written in C++, but we must stress that our purpose is to offer a flexible library for research in *differentiable* optimization, most of which is written in Python, and a significant portion of it in PyTorch. As such, directly comparing computation against libraries that don’t support differentiation would be unfair. In the paper, we have included a benchmark against Ceres to both validate the correctness of our implementation, and to show that we have put a lot of emphasis in performance. We think the fact that Theseus can outperform Ceres in the batched setting for medium-to-large problems shows that performance is a major consideration. But if the user only needs to do non-differentiable forward optimization, this is not the problem that Theseus was designed for. \n\nWe also refer the reviewer to Sec 6 in the paper where we discuss limitations in detail which is also acknowledged by the other reviews as “properly discussed” and “clearly addressed”.\n", " We thank the reviewer for their thoughtful feedback. We are glad that the reviewer highlights the task-agnostic nature of our library and that its “motivation is well supported... and has value to the community” .\n\nRegarding comparing with application specific implementations, in this paper we put a lot of effort in evaluating and demonstrating the correctness of our differentiable optimizer, by comparing our results with an established stand-alone optimizer (Ceres), performing thorough unit testing of all gradient computations, and adding diverse illustrative examples of how to do learning through a TheseusLayer. We hope that this offers enough evidence that our features are sound and useful. We thus argue that comparing with application specific implementations is outside the scope of the paper, considering that a lot of their performance depends on the neural architecture used, which can be quite complicated and might require extensive hyperparameter tuning. We have opted for focusing our efforts on evaluating features that are direct responsibility of our library. \n\nRegarding the impact of hyperparameters for differentiable NLS optimization, this is likely to be problem dependent, and in many cases it can have a significant impact. We have thus added a lot of flexibility for users to easily change hyperparameters for the inner optimization when experimenting in their own research applications. This includes, number of iterations, choice of optimizer, choice of backward method, tolerance, turn on/off Lie-group gradient projection, among others. We hope that researchers find this useful in the future, and plan to adapt these options with evolving needs of the library’s users. \n", " We thank the reviewer for their comprehensive feedback. We are pleased to see that the reviewer found our library flexible, mentioning features such as sparse solvers and SO(3) support, that they see novelty in our adjoint differentiation methods in this context, and that they found our examples helpful in demonstrating the flexibility of the library. \n\nThe reviewer has pointed out that Figure 2 is somewhat hard to interpret and to derive a strong conclusion from. We agree that the explanatory text can be improved and plan to do so in the final revision. The main takeaway is that both solvers are comparable in terms of running time, with perhaps a slight advantage of LUCuda solver for smaller problems; moreover, if not many CPU-threads are available for CHOLMOD, any advantage of cudaLU is likely to increase. Thus, for most cases, starting with cudaLU is a good rule of thumb. On the other hand, as mentioned in Appendix D.2, for very large problems and GPU-memory constraints the CHOLMOD-based solver might be a better choice, as the solver for the most part runs on CPU and is thus less memory constrained. \n\nWe agree with the reviewer that it would be convenient to see the advantage of structured end-to-end learning with DNLS. However, we argue that this is outside the scope of the paper given that such advantages have already been illustrated in many previous work in this area (many of which we cite, as the reviewer pointed out), and it thus would distract from the focus of the paper, which is describing our flexibility- and efficiency-based design, and benchmarking our different features.\n\nSimilarly, we agree with the reviewer that exploring different backward modes across many applications would be very interesting, and it’s indeed one of the reasons why we have created the library: so that researchers can do this more easily in the future. Doing a comprehensive analysis of this across many applications is nevertheless outside the scope of this paper. \n\nRegarding the minor questions, thanks for pointing these out, we will fix them in the final version of the paper. The sets in line 74 do not have to be disjoint. Regarding the smaller speed up with larger batch size (Fig. 1), note that in this experiment we only run a single batch and that GPU computation generally slows down with increasing batch size. Since vectorization has a multiplicative effect on the batch size, at some point the cost of having a very large batch starts outweighing the savings resulting from parallel processing. We will also clarify that the Hessian computed in NLS is approximate ($J^TJ$) unlike second order Newton‘s method. \n", " We thank the reviewer for their thoughtful feedback. We are glad that they found our library “very exciting” and with potential to be adopted by a wide variety of the community. We are also pleased that the reviewer sees value in our supported features like sparse solvers, projection operators for Lie-algebra, and implicit differentiation. Moreover, it was exciting to see that the reviewer tried out the code for their own problem and found it helpful, even if not significantly faster for their problem. \n\nThe reviewer pointed out that Theseus doesn’t currently support learnable data-driven $\\lambda$ for LM solver, which is correct. We agree with the reviewer that this feature should be relatively easy to support, and it’s indeed on our stack of coming features. For our dense solvers, adding this is straightforward, by simply allowing $\\lambda$ to be a PyTorch tensor; however, adding this is a bit tricker with our custom sparse solvers, and would require some non-trivial amount of work. Thus, the main reason for its current omission has been limited time during which we have prioritized other features. \n", " The paper introduces a flexible, efficient, and task-agnostic open source library for nonlinear least squares problems. By integrating with PyTorch, the package allows one to learn and solve many tasks in computer vision and robotics in an end-to-end and deep fashion. The library provides support for common objectives, robust functions, optimizers (*e.g.*, GN, LM), as well as useful utilities (*e.g.*, Lie-algebra). The underlying implementation is carefully designed such that it is memory and computationally efficient.\n **Strength**\n- I am personally a big fan and a practitioner of deep structure models. Many of my previous work have combined deep neural networks with optimization (some are NLS while some are not). In order to train the whole model end to end, I had to write all these things myself, such as unrolling GN step, lie-algebra transformation, etc. It was fun, but indeed a bit cumbersome. It is thus very exciting to see that there is a flexible and modularized library that can greatly improve the speed of our future development. I can foresee the library being adopted by a wide variety of the community.\n- The authors provides several case studies (which is just the tip of the iceberg) across computer vision and robotics and showcase how they can be implemented easily and cleanly with the task-agnostic interface.\n- Theseus provide additional support/integration for sparse linear solvers, which can be used independently as standalone pytorch functions.\n- Thorough analysis on computational cost and memory usage.\n- I also like how the library integrates many (latest) techniques, such as projection operator for Lie-algebra, implicit differentiation, etc. It allows one to experiment with more crazy stuff such as unrolling tons of steps, or obtain more stable results with gradient explosion.\n\n\n**(Minor) Weakness**\n- While the aim of the package is to support generic nonlinear optimization, the current state seems to focus majorly on least square problem (*e.g.* GN solver). The title is thus a bit mis-leading imo.\n- Following above, many state-of-the-art algorithms in vision and robotics adopt LM solver with learnable, data-driven $\\lambda$. I don't see why this function is unavailable, or what's the major difficulty/block on this.\n\n**Correctness** \n- I'm not aware of any correctness issue in this paper.\n\n\n**Minor**\n- I personally gave it a try and use Theseus to replace my personal implementation on GN solver and lie-algebra (for 3D pose estimation). While I didn't observe significant speedup (which aligns with the analyses in the paper), the code is indeed much cleaner ;) Please see the above weakness section. The limitations are properly discussed.", " This paper presents Theseus, a software library allowing for a new layer in pytorch models based on differentiable nonlinear least squares (DNLS) solves. That is, the input to the layer specifies a NLS problem which in the forward pass the layer solves and in the backward pass, the layer provides the adjoint derivates, i.e. derivatives for the solution to the NLS problem in terms of the problem parameters. This creates a nested optimization problem in which an inner NLS solver iterates to find the NLS solution as part of the outer optimization of a pytorch model by gradient descent. \n\nThe authors are clear that they are not introducing this technique but rather provide an extensive list of citations for its use in robotics and vision communities for a solving an array of problems in which combining the flexibility of the deep learning with the constrained structure of NLS leads to good solutions. However, the authors of this work note that in other works this problem was solved using custom application specific implementations which were in many cases inefficient. They remedy the problem by providing an efficient and scalable package which can work for many applications.\n\nThe paper contains many examples of use cases for the method, explanations of the many options provided for both the forward and backward modes, and empirical profiling comparing the different options and showing improved efficiency versus the previous NLS solver at large scale. ## Strengths\n\n- The authors make a compelling case for the usefulness of the method implimented by their package, giving an extensive bibliography of uses in robotics and vision.\n- They also implement two novel (in this context) methods for computing the adjoint derivatives for DNLS: Implicit differentiation and Direct Loss minimization. Experiments in Sec. 5.1 show an improvement in efficiency and accuracy relative to unrolling or truncated differentiation. \n- The library is very flexible providing two different sparse NLS solvers: CHOLMOD and cudaLU, and explaining the advantages and drawbacks of each. Four methods for the backward mode are provided. There is also support for optimizing variables in Lie groups such as orientations in SO(3) which are quite important in robotics and vision and tricky to optimize over. \n- Support for batching and automatic vectorization gives the DNLS layer similar levels of parallelism to other pytorch layers. \n- The supplementary material includes the complete code of the package including scripts and instructions to run several different examples in the paper. The appendix includes nice explanations of the examples and proofs justifying the novel backward modes. Given that the purpose of the paper is provide a solution which works flexibly across different applications, I found seeing these examples script and explanations helpful to understanding this. \n\n## Weaknessess\n- Some of the empirical evaluations are somewhat hard to interpret. Figure 2 left is not a very clear plot and it is hard to find a strong conclusion of when to prefer either sparse solver (although the preference over dense is clear.) \n- I understand that it is a prior assumption from the literature that the combination of deep learning and NLS afforded by this method is a worthwhile and superior approach in many applications relative to either DL or NLS independently. It still would have been convenient if this comparison could be made explicitly for one of the examples. \n- Figure 4, right shows that the choice of backward method inside Theseus have an impact on the ultimate performance of the model. The authors note this is probably application dependent. This seems like a critical aspect for end users and should probably be explored more. \n\n ## Minor Point\n- Line 74: $\\in$ should be $\\subset$. Do the subsets need to be disjoint? \n- Line 76: parallelism issue. ``Euclidean vector or a matrix Lie group element''\n- Line 91: maybe a small semantic point, but this does not really seem like a second-order method since the 2nd derivatives do not need to be computed, which seems like an advantage. I have seen the derivation and I understand that $J^T J$ is the second order term of the objective after linearizing the model, but it seems one should be careful to be precise here.\n- Line 106: \"the lastest\"\n\n## Questions\n- Figure 1: It seems the larger batch has smaller speed up. Why do you think that is? \n\n## Post-Response Edit\nI have read the other reviews and author responses. These strengthen my positive assessment and I maintain my score. The paper discusses limitations of various alternatives throughout the work, for example, the fact that the CHOLMOD spare solver is tied to the CPU. A limitations section at the end lays out other limitations, for example, incompatibility with hard constraints. ", " The paper presents Theseus, a library for optimizing through differentiable nonlinear least squares. The library allows for end-to-end learning for various structured learning problems like pose estimation, and homography estimation among others. The library is task agnostic, and provides an efficient implementation for dense and sparse problems, along with a variety of optional backprop methods for the underlying second-order optimizer. **Strengths**: \n1. The proposed library is task-agnostic allowing for end-to-end learning across a variety of robotics and vision problems.\n2. The implementation supports a variety of backpropagation approaches for taking gradients including autodiff.\n3. The paper shows either comparable or better results as compared to Ceres solver.\n4. The motivation is well supported with several examples and has value to the community.\n\n\n**Weaknesses** \n1. Technically, there do not seem to be any flaws in the proposed approach.\n2. The authors cite several papers that already implement related approaches. It will be good to compare a general purpose solver like Theseus with application specific implementations.\n3. The writing needs 1. Reiterating from above, I would like to see comparisons with existing task specific implementations to see differences if any.\n2. In terms of the optimization, the approach builds on a two step optimization scheme. However, this may lead to instabilities in optimization especially with the choice of wrong hyperparams. How much does the choice of hyperparameters affect the overall performance of the proposed approach? The authors have been upfront about the limitations and have clearly addressed them in the settings.", " This paper describes a convenient, systematic, and clean DNLS library. It could be possibly used to develop many differentiable algorithms.\n\nIt has several useful features, such as Differentiable Lie groups and kinematics. \n\nAlthough it’s not novel, this feature makes optimization of matrices and robots kinematics more easily in pytorch. It could be useful when optimizing non-Euclidean variables, for example, joints in robotics, pose matrices in multi-view geometry like SLAM and SfM.\n\nAutomatic Vectorization: It could possibly be one novelty, but was not described in detail. In L232, “we make use of the single instruction-multiple-data (SIMD) protocol by automatically detecting and vectorizing operations of the same type, significantly reducing the overhead for forward and backward passes.” \n\nGPU Acceleration for a Solver: They design and implement a differentiable cudaLU solver, which itself could be useful. Cuda solver is usually closed-source. Making a differentiable version of it takes effort.\n\n Four Differentiation Strategies: In Sec 4.3, they provide 4 different strategies for users, suitable for different problems. It helps the user to select the most suitable one. STRENGTH: potentially high utility for the ML community interested in differentiable programming paradigm\n\nWith this library, researchers can more easily design differentiable programming systems while spending less time on the differentiation part (or at least can quickly code up \"proof of concept\" systems using this general tool), esp. considering that the optimization is one of the hardest parts when making a system differentiable.\n\nWEAKNESS: novelty in this paper is unclear, if not low, as it is currently presented and described.\n\nAnother possible weakness is that, similarly to other methods that achieve differentiation by pytorch, the overhead could be high compared to simple forward C++ code, especially when the data size is small and the advantage of parallelization is not significant. An example is in Figure 3, where the existing Ceres (black dashed) outperforms most of the methods in this new library on small data. \n\n\n Can you highlight or give more detail on the key novelties of the design choices & algorithms in the library itself? Not discussed clearly." ]

[ -1, -1, -1, -1, 7, 8, 8, 6 ]

[ -1, -1, -1, -1, 3, 2, 3, 3 ]

[ "3JQPwPGiLCn", "piQcOLT4Vkv", "hf5NeA1B9_l", "QHCL1WOEYtn", "nips_2022_K48UYo0glaJ", "nips_2022_K48UYo0glaJ", "nips_2022_K48UYo0glaJ", "nips_2022_K48UYo0glaJ" ]

[ "KsDw-wpGpZ", "_VGELRxW2zA", "7MUtGSMTyre", "pihWp54Dqgz", "2tP79gRUzAR", "jm669frnFzs", "6EmKglXS1z", "GD9yWj9EvuX", "m68yJcLOE1d", "d8JMWd3UVaQ" ]

[ "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I vote for accepting this paper as I think that it proposes a great approach and presents an improvement in the performance and learning time.", " Dear reviewers,\n\nwe first thank you again for your valuable comments and suggestions. In the previous replies, we have tried our best to address your questions point by point.\n\nWe are sincerely looking forward to your reply to our responses and we are open to any discussions to improve our paper.\n\nBest wishes!\n\nThe authors.", " - **About the difference between our method and Diff-AE.**\n\nFrom the perspective of auto-encoder, both our method and Diff-AE employ an encoder to learn a representation $z$ from $x_0$. The key difference is on the decoder side. For Diff-AE, it trains a conditional DPM $\\epsilon^c_\\theta(x_t,t,z)$ from scratch to reconstruct $x_0$. For our method, we leverage a pre-trained unconditional DPM $\\epsilon^u_\\theta(x_t,t)$ and employ a gradient-estimator $G_\\psi(x_t, z, t)$ to model the mean shift to fill the gap between the predicted posterior mean $\\mu_\\theta(x_t,t)$ (derived by $\\epsilon^u_\\theta(x_t, t)$) and the true posterior mean $\\widetilde{\\mu}_t(x_t,x_0)$. In this way, we can reconstruct $x_0$ using our gradient-estimator $G_\\psi(x_t, z, t)$ based on pre-trained $\\epsilon^u_\\theta(x_t, t)$.\n\nCompared with Diff-AE, our method doesn't need to re-train a DPM from scratch, which is very time-consuming. Furthermore, by redesigning the weighting scheme of training objective, our method can learn richer representations from images.\n\n\n\n- **About the qualitative comparison and the imrpovements.**\n\nIn autoencoding reconstruction contexts, both Diff-AE and our method achieve the MSE of $1e^{-5}$ order and it's difficult to detect macroscopic differences among samples. In unconditional sampling contexts, it's also difficult to perceive the sample quality of the models with different FID scores. They all generate plausible samples. Therefore we only list the quantative comparison to the Diff-AE baseline.\n\nIn quantitative results, we think that the improvement of more than 0.5 on FID score should not be underestimated, especially for big and high-resolution datasets. Otherwise, our method only needs about $\\frac{1}{5}$ and $\\frac{1}{10}$ of the representation-relevant training times and time compared with Diff-AE. We think the improvements are not limited.\n\n\n\n- **About the confusion in Figure 1.**\n\nSorry for the vague description in Figure-1 that confused you. Your interpretation is correct. $x_0 \\rightarrow x_t$ means the forward process of DPM, i.e., $x_{t}=\\sqrt{\\bar\\alpha_{t}}x_{0}+\\sqrt{1-\\bar\\alpha_{t}}\\epsilon$, which does not involve any pre-trained parameters.\n\n\n\n- **About the stochastic variations in samples.**\n\nWe add an example in Appendix D.3 to illustrate the stochastic variation in our method. Please see our revised appendix file in **Supplementary Material**. It's on page 4~5.\n\nDDPM sampling method and DDIM sampling method (random $x_T$) always involve the stochastic variations, expressed in hair, skin and so on. With $x_T$ inferred from DDIM forward ODE, DDIM sampling method can almostly reconstruct the input image, without macroscopic difference. This also can be proved by the MSE metric in our **Autoencoding Reconstruction** experiments (section 4.2). DDIM sampling method with inferred $x_T$ achieves a much lower MSE than that with random $x_T$, for both Diff-AE and our method.\n\n\n\n\nWe sincerely hope you can reconsider the novelty and contributions of our method.", " - **About the sampling algorithm.**\n\nWe add an algorithm section in Appendix A.3 to explain how the sampling step works. Please see our revised appendix file in **Supplementary Material**. The additional algorithm section is on page 2~3.\n\n\n\n- **About the figure layout and overall proofreading.**\n\nWe will optimize the layout and proofread the paper in following revision to make our paper readable.\n\n\n\n- **About L116.**\n\nSorry for the inaccurate statements that confused you. Your interpretation is correct.\n\n\n\n- **About the experiments in section 3.4.**\n\nAs you suggested, we discard our encoder and directly incorporate the class label of MNIST sample as one-hot vector into $G_{\\psi}(x_{t}, y, t)$ to learn a mean shift by filling the posterior mean gap, i.e., optimize $\\psi$ by minimizing $E_{t,(x_{0},y),\\epsilon}\\bigg[ \\lambda_{t} \\big\\| \\epsilon - \\epsilon_{\\theta}(x_{t}, t) + \\frac{\\sqrt{\\alpha_{t}} \\sqrt{1-\\bar\\alpha_{t}}}{\\beta_{t}} \\cdot \\Sigma_{\\theta}(x_{t}, t) \\cdot G_{\\psi}(x_{t}, y, t) \\big\\|^{2} \\bigg]$.\n\nThen we carry out the mixed sampling procedure described in section 3.4 and get the same results. Please see our revised appendix file in **Supplementary Material**. The supplementary experiment is in Appendix D.1, on page 4. It's not surprising we see some effect. The mean shift during critical-stage actually contains more crucial information to reconstruct the class information in samples than the other two stages.\n\n\n\n- **About the meaning of \"one-step\".**\n\n\"the prediction of $x_{0}$ is done from $x_{t}$ in only one step\" means that:\n\nGiven a sample $x_{0}$ and a timestep $t$, we first calculate $x_{t}=\\sqrt{\\bar\\alpha_{t}}x_{0}+\\sqrt{1-\\bar\\alpha_{t}}\\epsilon$.\n\nThen for pre-trained DPMs, we directly predict the noise in $x_{t}$ as $\\hat{\\epsilon} = \\epsilon_{\\theta}(x_{t}, t)$ and output $\\hat x_0 = \\frac{x_{t} - \\sqrt{1 - \\bar\\alpha_{t}}\\hat\\epsilon}{\\sqrt{\\bar\\alpha_{t}}}$.\n\nFor our method, we directly predict the noise in $x_{t}$ as $\\hat\\epsilon = \\epsilon_{\\theta}(x_{t}, t) - \\frac{\\sqrt{\\alpha_{t}} \\sqrt{1-\\bar\\alpha_{t}}}{\\beta_{t}} \\cdot \\Sigma_{\\theta}(x_{t}, t) \\cdot G_{\\psi}(x_{t}, E_{\\varphi}(x_{0}),t)$ and output $\\hat x_0 = \\frac{x_{t} - \\sqrt{1 - \\bar\\alpha_{t}}\\hat\\epsilon}{\\sqrt{\\bar\\alpha_{t}}}$.\n\nThrough the comparison of $\\hat x_0$ between these two methods, we want to show that our method:\n\n1. actually fills the posterior mean gap so that it can output $\\hat x_0$ significantly similar to $x_{0}$ for only one-step denoising, even for large $t$.\n2. can generate high-quality samples with fewer sampling steps than pre-trained DPMs. After all, it can generate a plausible sample in only one step. That's why our method can be applied as an auxiliary booster of pre-trained DPMs to significantly improve the sample quality in few sampling steps, as shown in our unconditional sampling experiments (section 4.6).\n\n\n\n- **About the training time.**\n\nA fair and intuitive comparison of the training time between Diff-AE and our method is difficult. Unlike our method, the training of Diff-AE involves both diffusion denoising and representation learning, while ours resolves them separately. We only claim that our method needs less representation-relevant training times (i.e., the number of images used to train the representation learner, not time).\n\nNevertheless, we still calculate the training time of different models on our devices. For saving time, we only re-train the pre-trained DPM and Diff-AE with 13M images and multiply their running time by 10.\n\npre-trained DPM: **FFHQ128-130M** 248h\n\nour method based on above pre-trained DPM: **FFHQ128-130M-z512-22M** 36.4h\n\nDiff-AE: **FFHQ128-130M-z512** 307h\n\nWe can find that 248+36.4<307, which means that our method actually takes less training time and performs better than Diff-AE. If someone has alreadly had a pre-trained DPM, our method must be the preferred option for representation learning, which will save much more time than retraining a DPM (36.4<307).", " - **About Diff-AE with classifier-free guidance.**\n\nFor a Diff-AE $\\epsilon_\\theta(x_t,t,z/\\varnothing)$ trained by classifier-free method, i.e., randomly discard conditioning with some probability, we can use the pre-trained unconditional DPM $\\epsilon^u_\\theta(x_t,t)$ to simulate $\\epsilon_\\theta(x_t,t,\\varnothing)$ and the trained Diff-AE $\\epsilon^c_\\theta(x_t,t,z)$ to simulate $\\epsilon_\\theta(x_t,t,z)$. In theory, this substitution at least performs not worse than that trained by classifier-free method. For the unconditional DPM with classifier guidance, we use modified diffusion score estimator $\\epsilon^u_\\theta(x_t,t)+(1+s)\\cdot [\\epsilon^c_\\theta(x_t,t,z)-\\epsilon^u_\\theta(x_t,t)]$. Here we use $(1+s)$ because uncondtional DPM needs at least $1 \\times$ classifier guidance to achieve conditional sampling. For the conditional DPM with classifier guidance, we use modified diffusion score estimator $\\epsilon^c_\\theta(x_t,t,z)+s\\cdot[\\epsilon^c_\\theta(x_t,t,z)-\\epsilon^u_\\theta(x_t,t)]$, which is equivalent to above unconditional one.\n\nMoreover, we also adapt our method to classifier-guided form with the modified diffusion score estimator: $\\epsilon_\\theta(x_t,t)-(1+s)\\cdot\\frac{\\sqrt{\\alpha_t}\\sqrt{1-\\bar\\alpha_t}}{\\beta_t}\\cdot\\Sigma_\\theta(x_t,t)\\cdot G_\\psi(x_t,E_\\varphi(x_0),t)$. Then we perform the unconditional sampling on FFHQ-128 with DDIM (T=10) sampling method (same with section 4.6) for different strengths. The FID scores are shown in the following table:\n\n| Method | s=0.0 | s=0.1 | s=0.2 | s=0.3 | s=0.4 | s=0.5 | s=1.0 | s=5.0 |\n| :-----: | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- |\n| Diff-AE | 21.95 | 21.93 | 22.06 | 22.01 | 22.19 | 22.58 | 22.96 | 23.14 |\n| ours | 19.39 | 19.42 | 19.53 | 19.58 | 19.56 | 19.49 | 19.96 | 20.71 |\n\nAs you can see, FID scores almost remain unchanged and large-strength classifier guidance will decrease FID scores.\n\nWe think there are two reasons:\n\n1. Classifier guidance are used to achieve the truncation-like effect, i.e., decrease the diversity of the samples while increasing the quality of each **individual** sample. The whole quality of samples, such as FID metric, will not necessarily improve, like the curve in Figure-4 of classifier-guided paper [1] and Figure-4 of classifier-free paper [2]. \n2. Our topic is totally different with those in classifier-guided [1] and classifier-free [2] paper. The classifiers they use are based on the class label of data, which is a kind of incomplete information of data. Therefore, reinforcing the strength of classifier guidance can compel samples to contain more information of class. But Diff-AE and our method use the classifiers that contains almost all information of data, i.e., $z$. Reinforcing the strength of classifier guidance is non-meaningful because they can have already reconstructed the data that $z$ corresponds to. We illustrate this by an experiment. Please see our revised appendix file in **Supplementary Material**. The supplementary experiment is in Appendix D.2, on page 4~5. Compared to the Figure-3 in classifier-guided [1] paper, where reinforcing the strength of classifier guidance extremely improve the sample quality, while in our topic, generated samples guided by different strengths are almost the same.\n\nSo we think our improvements are given by the novel formulation $G_\\psi$​ and redesigned weighting scheme, not the usage of classifier guidance. Also, classifier-guided and classifier-free methods introduce prior knowledge of data to fill the posterior mean gap (ends), while in our method, we learn the knowledge from data by filling the posterior mean gap (means). This is a novel contribution.\n\n- **About conditioning both the diffusion model and the gradient-estimator.**\n\nOne of our main contributions is to use pre-trained DPMs for representation learning, so conditioning the DPMs with the representation $z$ means that we need to retrain both the DPM and gradient-estimator. In so doing, $G_\\psi$ no longer models the gradient because its target is no longer the posterior mean gap. Actually there is no longer posterior mean gap between $\\mu_t(x_t,x_0)$ and $\\mu_\\theta(x_t,t,z)$. The method transforms to Diff-AE.\n\nIn practice, we train a model by optimizing $L(\\theta,\\psi,\\varphi)=E_{t,x_0,\\epsilon}\\bigg[\\lambda_t\\big\\|\\epsilon-\\epsilon_\\theta(x_t,t,E_\\varphi(x_0))+\\frac{\\sqrt{\\alpha_t}\\sqrt{1-\\bar\\alpha_t}}{\\beta_t}\\cdot\\Sigma_\\theta(x_t,t)\\cdot G_\\psi(x_t,E_\\varphi(x_0),t)\\big\\|^{2}\\bigg]$. Although we can perform DDPM sampling with $\\epsilon_\\theta(x_t,t,E_\\varphi(x_0))-\\frac{\\sqrt{\\alpha_t}\\sqrt{1-\\bar\\alpha_t}}{\\beta_t}\\cdot\\Sigma_\\theta(x_t,t)\\cdot G_\\psi(x_t,E_\\varphi(x_0),t)$, we cannot use $G_\\psi$ as gradient for DDIM sampling, which makes the generated samples totally messy. Even it works, as we illustrate and explain above, the sample quality will be similar to our method.\n\n[1]: Diffusion Models Beat GANs on Image Synthesis\n\n[2]: Classifier-Free Diffusion Guidance", " - **About the start and end of the critical-stage.**\n\nWe grid $1000$ timesteps with a step size of $50$ and perform grid-search for $(t_{1}, t_{2})$ paris to find the shortest critical-stage that can ensure high accuracy of conditional generation. For the DPM pre-trained on MNIST, it is $(400, 600)$. A shorter one will make the conditional guidance be eliminated by the stochasticity of reverse process. Different DPMs pre-trained on different datasets/domains may have different critical-stage, such as the critical-stage of $(350,700)$ for CIFAR-10 in our investigations.\n\nWe originally worked without redesigning the weighting scheme, but found the training to be extremely unstable, resulting in slow/non convergence and poor performance. We supposed that the posterior mean gap in different stages may contain different levels/degrees of information and substantiated it through the experiments noted above. We then tried to redesign our weighting scheme to adjust the relative loss weighting of different timesteps, which is surprisingly well performed. \n\nDue to different critical-stage that different DPMs have, perhaps our method can be further improved by carefully redesigning the dataset/domain-dependent weighting scheme. We leave the investigations of this aspect as future work. Now in this project, our proposed weighting scheme applies and performs well for all pre-trained DPMs we use.\n\n\n\n- **About the writings.**\n\nThanks for your suggestions and we will correct such awkward phrasing in following revision to make our paper readable.\n\n\n\n- **About modeling the generative distribution $z$.**\n\nActually we tried to model the generative distribution $z$ with a normalizing flow model, for which we just use a stack of affine coupling layers [1]. It can achieve similar performance with DPM, but its network is more complicated and training is more time-consuming than DPM. We also tried VAE to model the generative distribution $z$. However the training is unstable and the model cannot reach convergence. The sample quality is also under-performance. This may be due to its limited capacity or prior-hole problem. Perhaps deep hierarchical vaes, such as NVAE [2], can work.\n\nWe try your idea that employs a simple auto-encoder with a post-fit GMM over the latent vectors. However we find that the parameter estimates of GMM is difficult. Many generated samples (GMM $\\rightarrow$ $z$ $\\rightarrow$ $G_\\psi$ $\\rightarrow$ $x_0$) are blurry or corrupted. We think this is because the generative distribution is complex and the gradient-estimator $G_\\psi$ is sensitive to $z$, so that the auto-encoder+GMM cannot model it accurately and the variations of the latents of auto-encoder greatly affect the generated samples.\n\nMoreover, the DPMs we use to model the generative distribution are lightweight (stack of MLP layers) and easy to train. DPMs have advantages of stable training and excellent performance compared to other counterparts. We think that it's a good choice.\n\n\n\n- **About the domain problem.**\n\nWe try your idea on MNIST. Specifically, we train a DPM on the images of 5 digital classes and use it to learn representations on the images of the other 5. It works well. \n\nHowever, when we use the DPM pre-trained on FFHQ to learn representations on LSUNBedroom, the training of our method is very unstable and the model cannot converge. The samples are totally messy.\n\nDespite the success on MNIST, we think that is because the simplicity of MNIST. Our method cannot handle the domain shift problem.\n\nIn theory, the pre-trained DPM $\\epsilon_{\\theta}$ only recognize the noisy samples belonging to the distribution it is trained on. With some out-of-distribution $x_t$, the gap between $\\epsilon$ and $\\epsilon_{\\theta}(x_{t}, t)$ will become non-meaningful (because $\\epsilon_{\\theta}(x_{t}, t)$ is non-meaningful) and our method will fail to learn useful representations from it.\n\nDiffusionCLIP [3] propose to fine-tune the pre-trained DPMs to adapt it to other domains, which means that we actually need a new $\\epsilon_\\theta$ for a new domain.\n\n\n\n[1]: Density estimation using real nvp\n\n[2]: NVAE: A deep hierarchical variational autoencoder\n\n[3]: DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation", " Whereas prior work (DiffAE) uses a conditional DPM as the decoder in an auto-encoder setup, this work attempts to leverage pretrained unconditional DPMs instead. The proposed formulation extends the classifier-guidance solution for latent autoencoder semantic codes z. However, instead of explicitly training classifiers p(z | x_t), taking its corresponding score, they propose to directly fit to the posterior mean gap of the pretrained, unsupervised, and frozen DPM. Results demonstrate higher quality reconstruction than DiffAE, with an overall simpler training setup. strengths\n- paper was clearly written. Formulation was easy to follow\n- prior works using classifier guidance had some issues regarding the scale of the guidance vector being used, but I believe the proposed formulation gets around that issue by fitting to the posterior mean gap instead.\n\nweaknesses\n- In section 3.4, it's not clear how the start and end of the critical stage are determined.\n- L124 Except the latent code z (awkward phrasing)\n- One thing that would've been nice to see is whether it's truly necessary to use another DPM for modeling the generative distribution $z$. DiffAE justifies their choice of a DPM by stating that a VAE's objective would have been difficult to tune, but perhaps a simple auto-encoder with a post-fit GMM over the latent vectors might suffice?\n - See weaknesses\n- How does the closeness between the pretrained DPM's domain and the target domain affect the efficacy of this method? If the pretrained DPM were from a completely unrelated domain, would this just mean that the posterior gap is larger and that the training time of this method would take much longer? Limitations were not discussed. Example topics would include deep fakes etc.", " This paper presents a method of learning representations out-of pretrained unconditional diffusion models. Different from DiffusionAE which learns the encoder and condition DPM together, this paper proposes to keep a pretrained unconditional diffusion models unchanged, and learn the gradient of classifier guidance which takes a latent variable as the additional input, and the latent variable in encoded by a learnable encoder. Empirical results show that this method leads to better reconstruction and few-shot conditional generation results compared to DiffusionAE with less training expense. Qualitatively the method learns meaningful representations, and it can also improve the sample quality of unconditional diffusion models with a learned latent DPM on the latent variables. Strength:\n\n- This paper is well written and easy to follow. It clearly states its connection with the previous close related work, DiffusionAE, and points out the advantage over the previous work. \n- The proposed method is technically sound and naturally combines learning representation and classifier guidance. \n- Various experiments are carried out and results are compared with baseline methods, making the method more convincing. \n\nWeaknesses: \n- IMO the novelty of this work is kind of limited. Compared to DiffusionAE, this work includes the classifier guidance and the latent codes are embedded into the learnable guidance term instead of the diffusion model, expect for which all other components remains the same as DiffusionAE, such as reversing DDIM sampler for latent code and learning latent DPM for z. Technically speaking I don't think there's a significant novel method proposed here.\n- Compared to DiffusionAE, this method includes guidance term so it is not quite surprising to me that it can outperform DiffusionAE. It's not clear to me whether the improvement is due to the guidance mechanism or due to the novel formulation $G_\\psi$. - One baseline worthwhile to compare is DiffusionAE + classifier-free guidance. If the proposed method can beat this baseline, it will be more convincing that the improvement is given by the novel formulation $G_\\psi$, instead of the guidance formulation which is not the contribution of this paper. \n\n- For classifier(-free) guidance, it is known that results are better if the diffusion models are also conditional, i.e., the modified score is given by $\\nabla_{x_t} [\\log p(x_t|c) + \\omega \\log p(c|x_t)]$ instead of $\\nabla_{x_t} [\\log p(x_t) + \\omega \\log p(c|x_t)]$. I'm wondering if similar conclusion applies here. I.e., if you condition both the diffusion model and the classifier gradient $G_\\psi$ with the latent variables $z$, whether you can get better performance than the current formulation. No limitation and potential negative social impact are discussed . ", " The paper presents a new learning framework for diffusion probabilistic models. Unlike the most existing diffusion probabilistic models, which mainly embed the data into a predefined distribution through the Markov chain, the proposed framework aims to learn a robust representation feature through a pre-trained diffusion models. The authors also introduce a weighting scheme redesign function to further improve the representation learning in the diffusion models. Extensive experiments are conducted on multiple scenarios (e.g. FFHQ, CelebA, Bedroom). ### Strengths\n- The task of representation learning via diffusion probabilistic models is novel and interesting.\n- The overall idea and the approach towards addressing it seems reasonable. \n\n### Weaknesses\n- The paper is not well written and hard to read.\n- The technical novelty is limited. Neither the designed network nor the theory are new. \n- The qualitative results are poor, and the quantitative improvement is limited. - What's the key difference between the proposed framework with the latest state-of-the-art diffusion autoencoders (Diff-AE) [21]. While the authors consider Diff-AE as a baseline, the two works seem to be similar. The authors should clearly explain what is the difference between them.\n- Besides, The qualitative comparison to the Diff-AE baseline is missing, even after considering the results in the Appendix. What's more, the quantitative improvement in Tables 1, 2, and 3 is limited compared to the Diff-AE baseline.\n- It takes me a hard time buying the $x_0\\to x_t$ in Figure 1. If I understand correctly, this should be a diffusion processing in general. Then, does this contain any pre-trained parameters?\n- Could please the authors illuminate the difference between these results shown in Figure 5? While the authors claimed to \"some stochastic variations\", it seems to be very hard to capture such a conclusion. Limitations are not discussed.", " The authors propose an unsupervised method for data representation and reconstruction, utilizing a pre-trained unconditional diffusion probabilistic model (DMP) in order to avoid the long training time of such models.\nThe method incorporates a gradient estimator, that learns the posterior mean shift, which is then used as a condition in order to guide the sampling process towards the image reconstruction. The authors also propose a new weighting scheme for training the objective function. Learning the gradient estimator encourages the encoder to learn meaningful data representation, and the sampling process to produce better data reconstruction.\nThe authors provide quantitative and qualitative evaluations showing improvements in representation learning, image reconstruction, and image sampling. Strength:\n\n- The problem is known to be valid and challenging, and the level of novelty is reasonable.\n\n- The method, idea, and motivation are well explained in the paper. The authors provided a good intuition about their proposed network architecture.\n\n- The authors well-explained their weighting method by describing their insights from an experiment that shows differences in the result with and without the classifier-guided sampling\n\nWeaknesses:\n\n- There is no algorithm that explains how the sampling step works in the author's method (how does the sampling-guided method is employed when using the model described in the paper).\n\n- I suggest showing Figures 1,2 in separate locations (figure 2 should be closer to the text that describes it, along with figure 3).\n\n- According to the quantitative results, the improvement of data representation is not significant. However, there is an improvement in the rest of the experiments, such as in unconditional sampling.\n\n- Overall proofreading is required. - Line 16: \"and train it like a normal DMP\": this causes some confusion, as the DMP part of the model is fixed. Also, the objective function aims to learn image reconstruction rather than image generation.\n\n- It would be nice to see the results of the experiment shown in section 3.4, but when using the gradient-estimator as classifier-guided sampling, instead of a separate classifier, as done on MNIST.\n\n- In the experiment section, the prediction of x_0 is done from x_t in only one step. What does this \"one-step\" mean? Isn't the whole reverse process required in order to retrieve x_0?\n\n- It would be great to have an experiment that supports the claim that this method requires less training time than its competitors. The author did not address their method's limitations.\nThe described work has no potential negative societal impact." ]

[ -1, -1, -1, -1, -1, -1, 7, 5, 5, 6 ]

[ -1, -1, -1, -1, -1, -1, 3, 5, 3, 3 ]

[ "pihWp54Dqgz", "nips_2022_IiCsx9KNVa0", "m68yJcLOE1d", "d8JMWd3UVaQ", "GD9yWj9EvuX", "6EmKglXS1z", "nips_2022_IiCsx9KNVa0", "nips_2022_IiCsx9KNVa0", "nips_2022_IiCsx9KNVa0", "nips_2022_IiCsx9KNVa0" ]

[ "OveTOV07DNq", "pnahU-9ewT6", "_YDZpSg3qov", "I4ww292c6ai", "0Ze815vMyjm", "aAXgXXanf6", "bblpeRhwe-E", "2aBjkzcQuBz", "E2t6mp6qHH", "XgLwZoTfZv", "Gahens_EyLU", "Pfoz2XPoKJS", "YXkTr588ypS", "1vf2858IZIr", "6FX9lkwtct5" ]

[ "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We sincerely thank the reviewer for willing to update the rating to weak accept (6) after the discussion period. We appreciate the reviewer for clarifying the above particular issue. We understand that the use of pre-trained DGCNN for evaluation and comparison may still be a concern. In recent works on semantic instance completion like [A, B], researchers take RGB-D images of indoor scenes as inputs, and they focus on producing completed 3D models with segmentation results for particular objects in that scene (e.g., chair, table, etc.). During the evaluation, these works also compare to methods particularly designed for scene completion or instance segmentation only. More specifically, when comparing to SOTAs for scene completion, they also apply pre-trained instance segmenter to produce the semantic labels for the completed outputs. In other words, the above evaluation protocol has been conducted (as what we did in Table 2). We will be happy to include the above discussions in the revised version, and we hope this would address the raised concern.\n\n[A] RfD-Net: Point Scene Understanding by Semantic Instance Reconstruction, CVPR 2021\n\n[B] RevealNet: Seeing Behind Objects in RGB-D Scans, CVPR 2020", " Regarding my Q1, maybe I didn't express it clearly enough. The paper seems to directly use the evaluation of the segmentation results of DGCNN as a quality assessment for part generation. This evaluation method is somewhat reasonable, but not intuitive or common enough without explanation.\n\nHowever, after reading the authors' responses and the other reviewers' Q&As, almost all of my concerns have been addressed. I'll change my rating to 6: Weak Accept.\n", " Thanks the authors for responding to my concerns.\nMy rating for this submission remains the same (6: Weak Accept).", " The authors addressed all of my concerns in the rebuttal, and I decide to change my rating to weak accept.", " **Q6: Compared to the SOTA completion methods (e.g. VRC-Net), the improvement of completion is small but requires more labor for data labeling. Moreover, the proposed method requires a model for each category. Do we really need to introduce the semantic information in point cloud completion?** \n\nA6: We thank the reviewer for pointing out these two issues and we are glad to clarify these two issues. \n\nFor the requirement for ground truth semantic labels during training, as discussed in Q3, we are able to alleviate this limitation by utilizing a pre-trained semantic labeler (i.e. DGCNN) for assigning point cloud labels. With promising and favorable results presented in Q3, the practicality of our proposed work can be confirmed. \n\nOn the other hand, Reviewer Bq58 also points out the concern of training one model for each object category. In fact, as stated in L97 of our main paper, we suggest that this can be achieved by increasing the total number of semantic parts M. To better address this issue, we conduct additional experiments to assess whether our SPoVT can be trained across object categories. More specifically, we conduct a new experiment that our SpoVT is trained on both “Airplane” and “Car” categories together in a unified model. The results are shown below: (CD: x$10^4$, mIoU: %)\n\n\n| | Airplane | | Car | |\n|-----------------|:--------:|:----:|:----:|:----:|\n| | CD | mIoU | CD | mIoU |\n| Ours (Original) | 0.73 | 82.6 | 2.86 | 82.5 |\n| Ours (Unified) | 0.84 | 84.6 | 3.39 | 80.6 |\n\nFrom the above table, we observe that a unified SPoVT (trained for two object categories) exhibited slightly degraded completion and segmentation performances when compared to the original SPoVT, which is expected. Nevertheless, both models still performed favorably against SOTA methods listed in Table 2 (in which SOTA methods are trained for each category). We will be glad to add the above experiments and discussions to our revised version.", " **Q3: All competitive methods use DGCNN for part segmentation for a fair comparison. However, it is still not fair because the proposed method does not use DGCNN. Moreover, DGCNN is a very old baseline.**\n\nA3: We thank the reviewer for raising this concern. We understand that, with the use of ground truth segmentation labels for our proposed SPoVT and the use of those produced by pre-trained DGCNN for the SOTAs, the comparison in Table 2 would be less informative. And, ground truth segmentation labels might not always be available during training. \n\nTo address and alleviate this issue, we conduct an additional experiment, in which segmentation labels predicted by pre-trained DGCNN are used for training our SPoVT (denoted as Ours* in the updated Table 2, as listed below). From the results shown in Table 2, we see that while Ours* degraded the performance when compared to the original version (Ours), it still performed against SOTA methods for both completion and segmentation tasks. This suggests that our proposed model is able to utilize pre-trained segmenters for assigning point cloud labels for completion/segmentation purposes. Thus, the effectiveness and practicality of our proposed model can be verified.\n\nTable 2: Quantitative evaluation on PCN in terms of L2-Chamfer Distance (CD×$10^4$) and mIOU (%). Note that $N^{GT} = 16384$ for all methods across different categories.\n\n| Method | Airplane | | Car | | Chair | | Lamp | | Table | | Avg. | |\n|-----------------|:--------:|:----:|:----:|:----:|:-----:|:----:|:----:|:----:|:-----:|:----:|:----:|:----:|\n| | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU |\n| PCN | 1.26 | 67.4 | 10.8 | 38.1 | 5.77 | 79.3 | 11.4 | 62.1 | 5.22 | 76.6 | 6.88 | 64.7 |\n| PMP-Net++ | 1.80 | 70.3 | 3.82 | 48.6 | 3.42 | 75.3 | 7.93 | 66.3 | 7.87 | 59.3 | 4.97 | 64.0 |\n| VRC-Net | 0.84 | 69.7 | 3.15 | 60.6 | 3.50 | 82.2 | 4.90 | 75.5 | 4.76 | 74.1 | 3.43 | 72.4 |\n| PoinTr | 1.88 | 53.6 | 3.73 | 50.8 | 3.01 | 79.2 | 4.55 | 60.5 | 2.97 | 76.1 | 3.23 | 64.0 |\n| Ours* | 0.75 | 82.1 | 2.99 | 76.9 | 2.97 | 77.0 | 4.50 | 86.1 | 3.04 | 84.1 | 2.85 | 81.2 |\n| Ours (Original) | 0.73 | 82.6 | 2.86 | 82.5 | 2.36 | 85.2 | 4.12 | 91.5 | 2.50 | 86.5 | 2.51 | 85.7 |\n\n**Q4: Why the mIoU of PointTr are much worse than the rest methods? All of these methods adopt DGCNN for part segmentation.**\n\nA4: We thank the reviewer for pointing this out, and we are glad to provide an additional explanation. As shown in Fig. 5 in our supplementary material, PoinTr generally fails to complete part details (e.g., wings of the airplane). With Chamfer Distance as the only training objective, PoinTr tends to produce outputs whose shape is similar to the ground truth one. PoinTr is not designed to handle or preserve particular parts (as ours does). This explains why PoinTr was not able to reach satisfactory mIoU scores.\n\n\n**Q5: The experimental results are only compared on the synthetic dataset, how about the results on real-world scenarios?**\n\nA5: Please kindly refer to L13-20, Fig. 2, and Fig. 3 in our supplementary material. We presented experiments on KITTI cars, ScanNet tables, and ScanNet chairs, which are all real-world datasets. With pre-trained DGCNN for predicting labels for the partial inputs (no ground truth labels available for such real-world point cloud data), we see that our model is able to produce impressive completion results and performs favorably against the SOTA ones.\n\n", " We thank Reviewer QsJ3 for the critical comments and suggestive remarks. Please see our responses below for each raised issue.\n\n**Q1: The motivation for introducing semantic labels in the point cloud completion is not clear. In other words, the proposed method can be regarded as point cloud completion + part segmentation.**\n\nA1: We sincerely thank the reviewer for giving us the opportunity to clarify/strengthen the motivation of our work. As pointed out in [16, 17], semantic labels have been exploited for scene-level point cloud completion. While such information is shown to be complementary to the task of completion (L29-34 and Sec. 2.2 in our main paper), most existing works for object point cloud completion do not utilize such information as the input. This motivates us to exploit point cloud labels into the task of object point cloud completion, with additional objectives for object reconstruction and part segmentation. Thus, we agree that our work can be viewed as performing joint point cloud completion and part segmentation.\n\nWe further note that, existing works on object point cloud completion are not able to perform part-based point cloud manipulation, since they do not have the ability to model particular object parts during their learning process. Nevertheless, we understand the concern that observing point cloud labels might not always be practical. As later discussed in Q3, we conduct additional experiments in which with semantic labels are obtained from a pre-trained semantic labeler (i.e., DGCNN), not the ground truth ones. From the detailed results later presented and discussed in Q3, the practicality of our SPoVT can be verified.\n\n\n\n\n**Q2: The experiments are only conducted on the five categories of the PCN dataset, which is not enough. PCN is a very old dataset. I suggest conducting experiments on the ShapeNet34/55 and MVP datasets.** \n\nA2: We thank the reviewer for the constructive suggestions, and we are more than happy to conduct additional experiments. As requested, we now consider the categories of ‘Car’ and ‘Guitar’ from ShapeNet55, and we compare the outputs to those produced by PoinTr. The completion results (CD x $10^4$) are listed below: \n\n| | Car | Guitar | CD-Simple (avg.) | CD-Medium (avg.) | CD-Hard (avg.) |\n|--------|:----:|:------:|:----------------:|:----------------:|:--------------:|\n| PoinTr | 8.11 | 2.46 | 3.79 | 5.21 | 7.51 |\n| Ours | 4.61 | 2.34 | 1.96 | 3.15 | 5.31 |\n\nNote that we directly apply the official implementation of PoinTr (https://github.com/yuxumin/PoinTr ), and the results are listed in the above table. Following the evaluation procedure, performances are evaluated in three difficulty categories: Simple (CD-Simple), Medium (CD-Medium), and Hard (CD-Hard), where the partial point clouds are cropping off 25%, 50%, and 75% from the ground truth point clouds. From the above table, it can be seen that our proposed SPoVT performed favorably against PoinTr across all categories. This confirms the effectiveness of our proposed model on the suggested dataset.", " \nWe thank Reviewer Z3zB for the positive comments and suggestive remarks. Please see our responses below for each raised issue.\n\n**Q1: The comparisons in Table 2 showed the advantages of the proposed method. However, it is not clear to me whether the comparison is apples-to-apples. For example, is the semantic label information used in other baselines (such as PCN)? It would be nice to explicitly mention which methods used such additional input, and which methods did not. That way, we would know where the improvement comes from (from the semantic label, or from the model architecture).**\n\nA1: We thank the reviewer for raising this critical issue. We understand that, with the use of ground truth segmentation labels for our proposed SPoVT and the use of those produced by pre-trained DGCNN for the SOTAs, the comparison in Table 2 would be less informative. And, ground truth segmentation labels might not always be available during training. \n\nTo address and alleviate this issue, we conduct an additional experiment, in which segmentation labels predicted by pre-trained DGCNN are used for training our SPoVT (denoted as Ours* in the updated Table 2, as listed below). From the results shown in Table 2, we see that while Ours* degraded the performance when compared to the original version (Ours), it still performed against SOTA methods for both completion and segmentation tasks. This suggests that our proposed model is able to utilize pre-trained segmenters for assigning point cloud labels for completion/segmentation purposes. Thus, the effectiveness and practicality of our proposed model can be verified.\n\nTable 2: Quantitative evaluation on PCN in terms of L2-Chamfer Distance (CD×$10^4$) and mIOU (%). Note that $N^{GT} = 16384$ for all methods across different categories.\n\n| Method | Airplane | | Car | | Chair | | Lamp | | Table | | Avg. | |\n|-----------------|:--------:|:----:|:----:|:----:|:-----:|:----:|:----:|:----:|:-----:|:----:|:----:|:----:|\n| | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU |\n| PCN | 1.26 | 67.4 | 10.8 | 38.1 | 5.77 | 79.3 | 11.4 | 62.1 | 5.22 | 76.6 | 6.88 | 64.7 |\n| PMP-Net++ | 1.80 | 70.3 | 3.82 | 48.6 | 3.42 | 75.3 | 7.93 | 66.3 | 7.87 | 59.3 | 4.97 | 64.0 |\n| VRC-Net | 0.84 | 69.7 | 3.15 | 60.6 | 3.50 | 82.2 | 4.90 | 75.5 | 4.76 | 74.1 | 3.43 | 72.4 |\n| PoinTr | 1.88 | 53.6 | 3.73 | 50.8 | 3.01 | 79.2 | 4.55 | 60.5 | 2.97 | 76.1 | 3.23 | 64.0 |\n| Ours* | 0.75 | 82.1 | 2.99 | 76.9 | 2.97 | 77.0 | 4.50 | 86.1 | 3.04 | 84.1 | 2.85 | 81.2 |\n| Ours (Original) | 0.73 | 82.6 | 2.86 | 82.5 | 2.36 | 85.2 | 4.12 | 91.5 | 2.50 | 86.5 | 2.51 | 85.7 |\n\n**Q2: It has been reported in the literature that the VAE inference is prone to posterior collapse, which greatly degrades the quality of model inference. Have the authors encountered such problem in the VAE inference in this paper? Any procedures taken to alleviate this problem (e.g., through weight annealing)?**\n\nYes, we apply cyclical annealing [A] to the weight of KL-divergence loss to avoid the potential posterior collapse problem (see L185-190 in our main paper). After two cycles, the weight of KL-divergence loss is set to 1e-5 as stated in L218 in our main paper. We thank the reviewer for raising this issue and allowing us to clarify it. We will be happy to include the above remarks in our revised version.\n\n[A] Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing (NAACL 2019)\n\n\n\n\n\n\n**Q3: The model uses semantic labels as additional input for point cloud completion. A natural question is, what if such additional input is not available in practice? Is it practical to run a separate semantic labeler on the point cloud?**\n\nA3: We thank the reviewer for giving us this chance to clarify this issue. As we explained and confirmed in Q1, we follow the suggestion and take DGCNN as the pre-trained segmenter (i.e., semantic labeler) for all methods. This removes the requirement of observing ground truth labels during training for our proposed method. In Sect. A of our supplementary material, we run a separate semantic labeler for the real-world point cloud data to obtain their segmentation labels. This is to verify that, since ground truth labels are not available for real-world point cloud data, utilizing an additional segmentor for producing point cloud labels would be a feasible solution. As confirmed by our experiments, our model is shown to produce satisfactory completion results on such real-world data.", " We thank Reviewer fQ4M for the positive comments and suggestive remarks. Please see our responses below for each raised issue.\n\n**Q1: The motivation of using Transformer-structure for the encoding part for point cloud semantic completion seems not sufficient. Although the authors mentioned in the Introduction section that the reason is to better refine local geometry, in fact, point-based convolution methods such as PointConv provide such utility and graph-based methods such as DGCNN are also suitable for such task. A detailed discussion and comparisons in Related Works section are desired.**\n\nA1: We greatly appreciate the reviewer for giving us the opportunity to further clarify our motivation, especially on the use of Transformer-based architectures as our network backbone.\n\nOur SPoVT is designed to derive prototypes for each semantic part, which guides the point cloud completion with the associated semantic information. The Transformer architecture allows us to assign and learn such part tokens, and thus association (i.e., self-attention) of point cloud features within/across object parts can be performed accordingly. Moreover, the above self-attention mechanism further allows us to observe and preserve geometry features for each semantic part during both encoding and decoding processes. The above remarks can be seen in L102-103 and L116-123.\n\nAs for recent methods like [1, 11, 12, 14], either point-based or graph-based convolution are utilized for point cloud completion. They generally apply pooling layers to aggregate the features during encoding, which might not be able to preserve fine-grained or detailed features from the input point cloud data. It is worth repeating that, as shown in Fig. 2 and Table 2, our SPoVT is shown to preserve more part details during completion and performs favorably against SOTA methods on both completion and segmentation tasks. And, we have ablation studies in Table 3 to verify the model design of our SPoVT.\n\n\n**Q2: From Line 259 on Page 8, the authors perform an evaluation on the setting of varying resolution, I’m curious about the memory usage and runtime comparisons. It seems there’s a lack of evaluation on the model runtime in the paper and supplemental. It’s suggested to provide it for objective evaluation.**\n\nA2: We thank the reviewer for pointing this out, and we are glad to clarify this issue. As stated in L195-201, since we produce such results by repeating the inference process multiple times, the inference time only grows linearly with the point cloud resolution (but not the memory usage). Please see the table below, in which we conduct extra experiments on varying point cloud resolutions and list the required inference times and memory requirements.\n\n\n| Output point cloud resolution | Inference time (ms) | Memory usage (GB) |\n|:-----------------------------:|:-------------------:|:-----------------:|\n| 2048 points | 50.0 | 1.923 |\n| 8192 points | 145.6 | 1.923 |\n| 16384 points | 277.2 | 1.923 |\n\n", " **Q4: Just to be sure, like other completion methods, SPoVT needs to train the model separately for each category of objects, and you can't mix parts of different categories of objects, right?** \n\nA4: We are glad to further clarify this issue. As explained in Q3, all methods including ours are trained for each object category for fair comparisons. However, with the suggestion from the reviewer, we now assess whether our SPoVT can be trained across different object categories. In fact, as stated in L97 of our main paper, we suggest that this can be achieved by increasing the total number of semantic parts M. \n\nWe now conduct a new experiment that our SpoVT is trained on both “Airplane” and “Car” categories together in a unified model. The results are shown below: (CD: x$10^4$, mIoU: %)\n\n\n| | Airplane | | Car | |\n|-----------------|:--------:|:----:|:----:|:----:|\n| | CD | mIoU | CD | mIoU |\n| Ours (Original) | 0.73 | 82.6 | 2.86 | 82.5 |\n| Ours (Unified) | 0.84 | 84.6 | 3.39 | 80.6 |\n\nFrom the above table, we observe that a unified SPoVT (trained for two object categories) slightly degraded the completion and segmentation performances when compared to the original SPoVT. Such degraded performances can be expected (due to the need to handle more object categories and parts in one model). Nevertheless, both models in the above table still performed favorably against SOTA methods listed in Table 2 (in which SOTA methods are trained for each category).\n\n\n\n**Q5: Some suggestions for figures. a) Figure 1 is too cluttered, lacks annotations, and has a different style for each block. This is confusing. b) In Figure 3, It might be better to mark the number of points in red. The writing of the paper needs to be improved a little bit. a) Some paragraphs are a little cluttered, like the Semantic VAE part, ablation studies part, etc. b) Typos, like “Tranformer-based” in the Introduction, “SWiVT” on Table 2, “mIOU”s , etc.**\n\nA5: We sincerely thank the reviewer for helping us improve the presentation. We will revise the figures and make them more readable, and the typo/errors will be corrected in the revised version (see below):\n\n* “Tranformer-based” in L47 -> “Transformer-based”\n* “SWiVT” on Table 2 -> “SPoVT”\n* “mIOU” on Table 2, Table 3, L231, L235, L270 -> “mIoU”\n* remove “Please refer to our supplementary for calculation details of T during the training process.” in L181-182\n\n\n**Q6: Please consider adding a discussion section to the paper to describe the limitations of the method as possible, such as the need for additional semantic annotations, inference speed, complex training process, etc.**\n\nWe thank the reviewer for the valuable suggestion, and we feel that it is necessary to point out the limitations of our SPoVT below.\n\nAs raised in Q1, our SPoVT requires ground truth semantic labels for the point cloud data during training, which might not be practically available. As discussed in Q1, we are able to alleviate this limitation by utilizing pre-trained segmentors for assigning point cloud labels. \n\nAs for the concern about inference time, we do expect its increase when producing completion results with higher resolution. As stated in L195-201, since we produce such results by repeating the inference process multiple times, the inference time only grows linearly with the point cloud resolution (but not the memory usage). Please see the table below, in which we present the inference time and memory usage under different point cloud resolutions.\n\n\n| Output point cloud resolution | Inference time (ms) | Memory usage (GB) |\n|:-----------------------------:|:-------------------:|:-----------------:|\n| 2048 points | 50.0 | 1.923 |\n| 8192 points | 145.6 | 1.923 |\n| 16384 points | 277.2 | 1.923 |\n\nFinally, training our SPoVT includes the pre-training of encoder and decoder for partial point cloud reconstruction, followed by completion and segmentation objectives. The details of our training process are presented in L185-194 in our main paper, which allows others to reproduce our model (if training his/her own models is of interest).\n\nWe sincerely thank the reviewer again for the constructive suggestions, which make our work more complete and sound. We will add the above discussions in our revised version.", " We thank Reviewer Bq58 for the constructive comments and suggestive remarks. Please see our responses below for each raised issue. \n\n**Q1: In Table 2, pre-trained DGCNN is used for semantic segmentation for each completion method for comparison. Under this condition, the comparison of the segmentation metric is not too meaningful, it just means that the segmentation of those methods + DGCNN is worse than the proposed method.**\n\nA1: We thank the reviewer for raising this concern. We understand that, with the use of ground truth segmentation labels for our proposed SPoVT and the use of those produced by pre-trained DGCNN for the SOTAs, the comparison in Table 2 would be less informative. And, ground truth segmentation labels might not always be available during training. \n\nTo address and alleviate this issue, we conduct an additional experiment, in which segmentation labels predicted by pre-trained DGCNN are used for training our SPoVT (denoted as Ours* in the updated Table 2, as listed below). From the results shown in Table 2, we see that while Ours* degraded the performance when compared to the original version (Ours), it still performed against SOTA methods for both completion and segmentation tasks. This suggests that our proposed model is able to utilize pre-trained segmenters for assigning point cloud labels for completion/segmentation purposes. Thus, the effectiveness and practicality of our proposed model can be verified.\n\nTable 2: Quantitative evaluation on PCN in terms of L2-Chamfer Distance (CD×$10^4$) and mIOU (%). Note that $N^{GT} = 16384$ for all methods across different categories.\n\n| Method | Airplane | | Car | | Chair | | Lamp | | Table | | Avg. | |\n|-----------------|:--------:|:----:|:----:|:----:|:-----:|:----:|:----:|:----:|:-----:|:----:|:----:|:----:|\n| | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU | CD | mIoU |\n| PCN | 1.26 | 67.4 | 10.8 | 38.1 | 5.77 | 79.3 | 11.4 | 62.1 | 5.22 | 76.6 | 6.88 | 64.7 |\n| PMP-Net++ | 1.80 | 70.3 | 3.82 | 48.6 | 3.42 | 75.3 | 7.93 | 66.3 | 7.87 | 59.3 | 4.97 | 64.0 |\n| VRC-Net | 0.84 | 69.7 | 3.15 | 60.6 | 3.50 | 82.2 | 4.90 | 75.5 | 4.76 | 74.1 | 3.43 | 72.4 |\n| PoinTr | 1.88 | 53.6 | 3.73 | 50.8 | 3.01 | 79.2 | 4.55 | 60.5 | 2.97 | 76.1 | 3.23 | 64.0 |\n| Ours* | 0.75 | 82.1 | 2.99 | 76.9 | 2.97 | 77.0 | 4.50 | 86.1 | 3.04 | 84.1 | 2.85 | 81.2 |\n| Ours (Original) | 0.73 | 82.6 | 2.86 | 82.5 | 2.36 | 85.2 | 4.12 | 91.5 | 2.50 | 86.5 | 2.51 | 85.7 |\n\n\n\n**Q2: Is the dataset the complete PCN dataset, or the intersection of PCN and ShapeNetPart? Does the intersection contain the annotations of all GT objects in the PCN?**\n\n\nA2: We thank the reviewer for giving us the opportunity to clarify the dataset used in our experiments. The PCN dataset [1] is composed of 30,974 point cloud object instances across 8 categories. For each object, 8 partial observations are obtained from virtual cameras with random poses. As for the part segmentation dataset ShapeNetPart [28], 16,881 objects across 16 categories are available. And, for each object, ground truth part segmentation labels are provided. Note that both PCN and ShapeNetPart are subsets of a larger dataset ShapeNet [29]. To obtain point cloud objects with both partial observations and segmentation annotations, we consider the intersection objects of these two datasets, followed by normalizing/matching the ground truth point clouds for each object extracted. Then, the ground truth semantic labels (from ShapeNetPart) are assigned to each complete point cloud object and its partial versions. As a result, the intersection dataset contains 11,262 point cloud objects across 5 categories. Each object has 8 partial observations, while both complete and partial point clouds are with ground truth segmentation annotations. The above details can be seen in L2-12 of our supplementary materials and L208-214 in our main paper. \n\n**Q3: I noticed that you reproduced other methods for fair comparisons. I wonder if these methods are trained under the default configuration of the official implementation? Besides, both PMP-Net and PoinTr provide pre-trained models on PCN, how do these compare to your trained models?**\n\nA3: Yes, we implement and reproduce SOTA models under their default configurations, including learning rate, weight decay, etc. However, for fair comparison purposes, we train with one model for each category for all methods in our experiments, using the data explained in the above Q2. The above remarks are available in L223-225 in our main paper.", " A Transformer-based network for point cloud completion called Semantic-Prototype Variational Transformer (SPoVT) is proposed. Firstly, SPoVT learns point cloud distributions for each semantic part by taking partial point cloud and additional associated part labels as inputs, allowing resampling point features for decoding and generation point clouds with varying resolutions. Secondly, A ratio predictor is deployed in SPoVT for predicting point number distributions for each segment part, which serves and guidance for point cloud completion and alleviates potentially dense or sparse completion for particular object parts. Finally, by learning prototypes and feature distributions for object parts, SPoVT is able to perform point cloud completion and manipulate at instance or part levels. Strengths:\n1.\tThe authors found an efficient way to introduce semantic label information in point cloud completion. Unsurprisingly, the performance is better than methods that only use partial point clouds as input.\n2.\tI like the idea of Semantic VAE, which can manipulate parts or objects with different point count distributions, making point cloud generation more flexible.\n3.\tThe experimental content is sufficient.\n\nWeaknesses:\n1.\tIn Table 2, pre-trained DGCNN is used for semantic segmentation for each completion method for comparison. Under this condition, the comparison of the segmentation metric is not too meaningful, it just means that the segmentation of those methods + DGCNN is worse than the proposed method.\n2.\tSome writing problems. Please see the suggestions below.\n Questions:\n1.\tPlease address the above Weakness 1.\n2.\tIs the dataset the complete PCN dataset, or the intersection of PCN and ShapeNetPart? Does the intersection contain the annotations of all GT objects in the PCN? \n3.\tI noticed that you reproduced other methods for fair comparisons. I wonder if these methods are trained under the default configuration of the official implementation? Besides, both PMP-Net and PoinTr provide pre-trained models on PCN, how do these compare to your trained models?\n4.\tJust to be sure, like other completion methods, SPoVT needs to train the model separately for each category of objects, and you can't mix parts of different categories of objects, right?\n\nSuggestions:\n1.\tSome suggestions for figures.\na)\tFigure 1 is too cluttered, lacks annotations, and has a different style for each block. This is confusing.\nb)\tIn Figure 3, It might be better to mark the number of points in red.\n2.\tThe writing of the paper needs to be improved a little bit. \na)\tSome paragraphs are a little cluttered, like the Semantic VAE part, ablation studies part, etc.\nb)\tTypos, like “Tranformer-based” in the Introduction, “SWiVT” on Table 2, “mIOU”s , etc.\n No.\nSuggestions: Please consider adding a discussion section to the paper to describe the limitations of the method as possible, such as the need for additional semantic annotations, inference speed, complex training process, etc.\n", " This paper proposes the Semantic-Prototype Variational Transformer model for the 3D point cloud semantic completion problem. Experiments on benchmark datasets show that the proposed method outperforms existing methods. Strengths:\nThe proposed approach applies transformer-like structures with a semantic VAE module for 3D point cloud semantic completion problem. The authors also apply a coarse-to-fine strategy for improving the semantic completion, with the learning prototypes and feature distributions for each object part. The ablation analysis validates the efficacy of the proposed network structure.\n\nWeaknesses: \nThe motivation of using Transformer-structure for the encoding part for point cloud semantic completion seems not sufficient. Although the authors mentioned in the Introduction section that the reason is to better refine local geometry, in fact, point-based convolution methods such as PointConv [1] provide such utility and graph-based methods such as DGCNN [2] are also suitable for such task. A detailed discussion and comparisons in Related Works section are desired.\n\n[1] Wu, Wenxuan, Zhongang Qi, and Li Fuxin. \"Pointconv: Deep convolutional networks on 3d point clouds.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2019.\n[2] Wang, Yue, et al. \"Dynamic graph cnn for learning on point clouds.\" Acm Transactions On Graphics (tog) 38.5 (2019): 1-12.\n From Line 259 on Page 8, the authors perform an evaluation on the setting of varying resolution, I’m curious about the memory usage and runtime comparisons. It seems there’s a lack of evaluation on the model runtime in the paper and supplemental. It’s suggested to provide it for objective evaluation.", " The authors proposed a Semantic-Prototype Variational Transformer approach for the dense point cloud semantic completion problem. In addition to the partial input, the paper also used the semantic labels as input for the completion task. An encoder-decoder Transformer architecture is used to leverage both the pixel level input and the semantic label input, so that the semantic label can guide the completion task. The Variational AutoEncoder (VAE) is used for model training and inference. Empirical results showed that the semantic label helped to improve the completion quality, outperforming other baselines. Strengths:\n1) The paper proposed to use semantic label from other sources as additional input to the point cloud completion problem. With this extra source of information, the model is able to infer the ground truth point cloud with better accuracy.\n2) The paper leveraged an encoder-decoder Transformer architecture to consume both the pixel level input and the semantic label input, so that the semantic label information can effectively guide the point cloud completion process. \n\nWeaknesses:\n1) The comparisons in Table 2 showed the advantages of the proposed method. However, it is not clear to me whether the comparison is apples-to-apples. For example, is the semantic label information used in other baselines (such as PCN)? It would be nice to explicitly mention which methods used such additional input, and which methods did not. That way, we would know where the improvement comes from (from the semantic label, or from the model architecture). It has been reported in the literature that the VAE inference is prone to posterior collapse, which greatly degrades the quality of model inference. Have the authors encountered such problem in the VAE inference in this paper? Any procedures taken to alleviate this problem (e.g., through weight annealing)?\n\n The model uses semantic labels as additional input for point cloud completion. A natural question is, what if such additional input is not available in practice? Is it practical to run a separate semantic labeler on the point cloud?", " The authors propose Semantic-Prototype Variational Transformer for semantic point cloud completion, which combines the tasks of point cloud completion and part segmentation. The experimental results on the five categories of the PCN dataset demonstrate that the proposed method outperforms the state-of-the-arts methods. **Strengths**\n\n- The paper is clearly written and well organized.\n\n**Weaknesses**\n\n- The motivation for introducing semantic labels in the point cloud completion is not clear. In other words, the proposed method can be regarded as point cloud completion + part segmentation.\n- The experiments are only conducted on the five categories of the PCN dataset, which is not enough. PCN is a very old dataset. I suggest conducting experiments on the ShapeNet34/55 and MVP datasets.\n- All competitive methods use DGCNN for part segmentation for a fair comparison. However, it is still not fair because the proposed method does not use DGCNN. Moreover, DGCNN is a very old baseline.\n- Why the mIoU of PointTr are much worse than the rest methods? All of these methods adopt DGCNN for part segmentation.\n- The experimental results are only compared on the synthetic dataset, how about the results on real-world scenarios? Please refer to the weaknesses. Compared to the STOA completion methods (e.g. VRC-Net), the improvement of completion is small but requires more labor for data labeling. Moreover, the proposed method requires a model for each category. Do we really need to introduce the semantic information in point cloud completion?" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 6, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 3, 5 ]

[ "pnahU-9ewT6", "XgLwZoTfZv", "2aBjkzcQuBz", "0Ze815vMyjm", "aAXgXXanf6", "bblpeRhwe-E", "6FX9lkwtct5", "1vf2858IZIr", "YXkTr588ypS", "Gahens_EyLU", "Pfoz2XPoKJS", "nips_2022_JVoKzM_-lhz", "nips_2022_JVoKzM_-lhz", "nips_2022_JVoKzM_-lhz", "nips_2022_JVoKzM_-lhz" ]

[ "dwc8TcUG5pi", "PK7b310vOC6", "-jM4PNItdVq", "Th5iiD2PgIQ", "CwkZtvpTZ8I", "9C6cG7sPmQx", "CMissa5zgmZ", "sWQ_Pe4tjFN", "1Bw8upTML-Z" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Due to time constraints with respect to today’s deadline, we included in the appendix the discussion on inference time (App. G), an extended comparison with other DL skeleton approaches (App. H), as well as the ablation studies (App. E). We commit to integrate them as well as possible to the main paper in the camera ready version, if the paper gets acceptance. \nWe would like to thank the reviewer for changing his score, as well as providing a set of questions that will give more impact to our work.\n", " Thank you for adding the comparison with other approaches and the ablation study. If the final submission does contain such changes, I would be happy to raise my score.", " We thank the reviewer for their valuable comments and strong endorsement of our paper. Please find our response below.\n\n***Though being a new SR paper that pushes the SOTA, this paper upscales the dimension from (<=3) only to (<10), as the author mentioned in line 287. Hence the method still remains improvable in scaling to larger dimensions*** \nWe agree with this assessment, and will mention this limitation more explicitly. The reason we restricted our model to dimension <=10 is that the input sequence length becomes prohibitively long beyond, and that generating high-dimensional functions in an unbiased way becomes increasingly tricky.\nNonetheless, since the objective of SR is to output interpretable formulas, we argue that SR is most useful for moderately low dimensional problems. For example, 1- 10 dimensional problems already cover a large class of physical systems : for instance, point objects can be represented by their position, speed and mass, 7 parameters.\n\nAdditionally, in many real world problems where more than 10 features are available, some of the features are often irrelevant or heavily correlated. To mitigate this, one typically carries out feature selection before modeling the data. Motivated by this comment, we tested our model on the high-dimensional problems of SRBench, by feeding to our model only the the 10 features most correlated with the output. This naive strategy already obtained encouraging results (with a median R2 score of 0.72, to compare with 0.58 for DSR and 0.55 for gplearn, but still well below Operon which stands at 0.91​​), which we shall include in the main paper. \n\n***Other limitations dwell in the evaluation of the pre-training data generation procedure, which is critical to this sequence prediction type of SR formulation, but is under-evaluated***\nFor the dimensions considered here, the data generation procedure is rather standard, and has been used in most previous work. Our out-of-domain results on SRBench, suggest that it is sufficient to achieve good performance on black-box datasets. \nHowever, we agree that a better understanding of the role of data generation procedure is an important next step, if we want pre-training based approaches to SR to become better – we will add a discussion on this in the future work section.\n\n***It would be better to explicitly show how different is the OOD symbolic samples differ from the pre-training data generation params? Better demonstrate this with concrete examples of OOD symbolic ground truth and pre-training examples.***\nThis is a very good point, and we acknowledge that concrete examples would help a lot the reader. Hence, we added a section in the Appendix (section F), where we provide two tables comparing typical expressions from our random generator with some from the Feynman dataset. From this, it is clear that our expressions tend to be more complex ; note that to remain unbiased towards the OOD datasets, we did not explicitly design our generator to “look like” the Feynman expressions.\n\nWe would like to emphasize the fact that the generalization of our model cannot be attributed to mere memorization. Indeed, (i) the number of possible skeletons is much larger than the number seen during training as shown in App. C ; (ii) even when a skeleton has already been seen, the function surely differs by the value of the constants, which affect the shape of the function significantly ; (iii) even for two identical functions, the points at which they are observed are never the same. \n\n***It is helpful but not mandatory to show that modifying the pre-training dataset distribution could positively contribute to but not greatly impact the OOD result***\nWe agree that a better understanding of the role of data generation procedure is an important next step, if we want pre-training based approaches to SR to become better – we will add a discussion on this in the future work section.\n\n***It is better to compare with prior works in this domain, which are symbolicGPT and NSRS. I am aware that official implementations seems to be not yet available, hence I'm not posting this as a must-have. One way is to alter the E2E implementation so as to only predict skeletons, then apply coeff optimization to un-officially simulate the symbolicGPT.***\nWe actually do provide results of the skeleton-only counterpart to our model in tables 1 and 2 (for in-domain) and Fig. 1 and 5 (for out-of-domain, see \"Ours (skel)”), which perform significantly less well that the E2E model.\n\nNote that symbolicGPT and NSRS are currently limited to very low-dimensional problems, so it is impossible to evaluate them on SRBench. However, even in dimension <=3, NSRS seems to perform less well than our model : the authors report an accuracy (R2>0.95) of ~0.75 on the feynman datasets in their appendix (Fig. 9), whereas we get ~0.84 (R2>0.99) on all dimensions. ", " ***Comparison with other end-to-end approaches and with NSRS***\nTo the best of our knowledge, no other end-to-end (E2E) approach for SR existed at the time of submission – all existing methods predicted skeletons. Another end-to-end technique [4] (without our inference tricks) was released two months ago, after the submission deadline.\nAs for NSRS [5], it is only applied to problems with dimension <=3, which means one can only test it on a very small subset of SRBench. Note however that even at these low dimensions, NSRS seems to perform less well than our model : the authors report an accuracy (defined at R2>0.95) on the feynman datasets of ~0.75 in their appendix (Fig. 9), whereas we get ~0.84 on R2>0.99 on all dimensions. \n\nThe benchmark we used for our comparison, SRBench, is currently the most extensive and up-to-date benchmark for SR, and provides comparisons with other DL-based methods such as DSR [1]. Note also that the ablation of Tables 1 & 2 (in-domain) and Figures 5 & 11 are provided to show the benefit of the E2E approach over methods such as NSRS.\n\n[4] Vastl, Martin, et al. \"SymFormer: End-to-end symbolic regression using transformer-based architecture.\", 2022.\n\n[5] Biggio et al. \"Neural symbolic regression that scales.\", 2021.\n\n***Ablation of (1) mixture of distributions and (2) input points scaling at inference time.***\nWe thank the reviewer for bringing up this important point, which indeed needs to be expanded. It is generally observed that Transformers struggle to generalize out-of-distribution, especially in mathematical tasks [6]. Hence, (1) and (2) are necessary to handle datasets involving input distributions that are (1) neither gaussian nor uniform, and (2) vary across wide ranges of scales. \n\n[6] Welleck et al. \"Symbolic Brittleness in Sequence Models: on Systematic Generalization in Symbolic Mathematics\", 2021.\n\nFor (1), we will add complete ablations in the camera ready copy as the corresponding experiments are too long to be run during the rebuttal period (we need to train a model without mixture from scratch). \nHowever, we used a model trained on a generator with uniform input distribution for only a few epochs to provide a qualitative example that shows how distribution-shift at test time can cause failure (see figure “rebuttal/mixture_ablation.pdf” in the SM). \n\nConsider the function cos(x0+x1)*x1. Recall the model was trained on distributions either N(0,1) or U([-1,1]). As we sample 100 datapoints from U([0,6]), we see the E2E model makes good predictions, whereas, adding 100 datapoints, sampled uniformly between U([-7,5]), degrades the model prediction.\n\nFor (2), since the rescaling happens at inference, we ran the SRBench evaluation for our E2E model without scaling, and as expected got worse results (see table below, which shall be added to the Appendix). We also added the figure “rebuttal/rescale_ablation.pdf” in the SM to provide a qualitative example of failure when the scaler is not used.\n\n|Refinement|Scaler|Feynman [mean R2>0.99]|Black-box [median R2]|\n|-|-|-|-|\n|With|With| 0.84|0.87|\n|Without|With|0.78|0.70|\n|With|Without|0.53|0.64|\n|Without|Without|0.06|0.46|", " We thank the reviewer for their constructive comments and suggestions. Due to space limitations, we split our answers in two different comments.\n\n***On the importance of inference time***\nWe would like to thank the reviewer for pointing out the need for a discussion on inference time. This property has been neglected by the SR community, because the inference time for most GP algorithms is both long and unbounded (the longer, the better the results). Yet we are convinced that it is important for two reasons. \n\nFirst, recall that the search space in SR is very large. A first pass through a fast symbolic regressor could reduce the search space, by performing feature or operator selection, or serve as an initialisation step to a GP approach (by populating its initial guesses). Such an approach has been proposed in DSR [1].\n\nSecond, SR is still a research topic with just a few practical applications, but we believe it will eventually be used on a wider range of tasks. It is already a viable alternative (with better interpretability) to current algorithms on regression tasks, as SRBench showed some SR techniques outperformed classical ones e.g. decision trees, XGBoost or NN on black-box datasets. The importance of inference speed will grow as SR is applied to real-time tasks. For instance, in control or reinforcement learning (RL), an agent might want to estimate (via SR) a model of its environment to optimize future actions (see [2,3]). We will include this discussion in the main paper.\n\n[1] Petersen et al. \"Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients.\", 2019.\n\n[2] Kubalík et al. \"Symbolic regression methods for reinforcement learning\", 2021.\n\n[3] Derner et al. \"Symbolic regression for constructing analytic models in reinforcement learning\", 2019. \n\n***Comparison with [d’Ascoli et al., 2021]***\nAlthough the general pre-training method is similar, there are a number of differences, which we will better develop in the revised version. \n\nFirst, the tasks are very different. [D’Ascoli et al., 2021] focuses on the one-dimensional case only, but they study a harder problem : inferring recurrence relations from small sets of points, while we estimate functions of many variables over larger sets of points. \n\nSecond, we introduce novel methods to handle high-dimensional data - an embedding module to compress the inputs, the mixed numeric-symbolic vocabulary for constant prediction, as well as various other tricks. \n\n\n***The accuracy is still lower than state-of-the-art GP approaches***\nWe believe that our model, while not strictly SOTA in terms of raw accuracy, is the first DL-based approach to strike an excellent balance between the desirable properties of a SR algorithm (accuracy, simplicity, inference time). As Fig. 5 shows, we are close to the best GP algorithms in terms of overall accuracy. On the Feynman dataset, we achieve high accuracy while producing simpler functions than many GP approaches (see Fig. 11).\n\n", " We thank the reviewer for their useful comments and suggestions. Please find our answers below.\n\n***For example, how is it pretrained? I couldn’t find any statement about the setting for the pretraining. Or is the method written in Section 2.1 for the pretraining? If so how is the post-training performed?***\nWe acknowledge that the term “pre-training” can cause confusion, and we will change the wording. To clarify : our model is not pre- and then post-trained – there is only one training phase, which is performed on synthetic (i.e. randomly generated) data, where for each example the model learns to predict a function from its values at a set of points. At inference, a new set of points is presented and the trained model is tasked to predict the corresponding function. \nThe synthetic training data and its generation are described in section 1. The model and its training are described in section 2.1. Finally, the inference (evaluation of unknown functions with the trained model) is described in section 2.2. \n\n***The computational time written in line 66 is for what?***\nThis is the average training time for one epoch (300k examples). Training lasts 50 epochs, at which point the accuracy on the validation set saturates. The inference time (time needed for the trained model to predict a single function) depends on the size of the input data, but is usually around 1 second. We will clarify this.\n\n***It was also not clear for me how the refinement of the parameter is performed in the end-to-end manner.***\nOur end-to-end denomination refers to the following fact. Previous methods predict a function skeleton, e.g. A cos(Bx+C), where A,B,C are free parameters which must then be determined by external tools. Our model provides an estimate of both the skeleton and the parameters (e.g. 2.1 cos (0.5 x +3) ), which makes it end-to-end. Parameter refinement is an optional step which improves accuracy. We will also clarify this.\n\n***The author’s claim the advantages of the proposed approach over the top performance approaches in its inference time. However, it was not evaluated whether this comes from the trick described in Section 2.2 or it is intrinsic to the approach using Transformer.***\nPrediction is faster with a transformer because it is trained in advance, on many synthetic examples, to predict a function from its values.\nAt inference, it only needs to evaluate (a single forward pass) the learned model on the set of points it is given: a very fast process.\nGenetic algorithms, on the other hand, have no such pre-inference training phase. They predict any new function from scratch, and do not capitalize on past examples. This results in a much slower process.\nThe improvements proposed in section 2.2 actually make inference slower, by resorting to external minimization techniques (BFGS) and working on ensembles, but the overall inference time remains orders of magnitude smaller than that of genetic algorithms (see figure 1).\n\n***Although the checklist says the code is available, I couldn't find the pointer to the code in the main text. It would always be nice to have a pointer to the code, even if it is included in the supplementary.***\nThanks for pointing this out. We will add a reference to the code in the introduction (pointing to supplementary material during the review, then to an online repository should the paper be published).\n", " This paper proposes a symbolic regression model using Transformers. It enables to pre-train the model using datasets from the other domain, which is helpful when the target domain dataset is relatively small. Moreover, this approach performs the parameter refinement with BFGS to further enhance the performance. Compared to the state-of-the-art approaches, which are mainly genetic programming based, this approach achieved not superior but competitive performance on benchmark tasks, and showed significantly smaller inference time.\n Clarity\n\nThe motivation of each algorithmic component is described well. However, as I am not an expert in SR, it was hard for me to understand this paper in details. Probably it is because of my lack of the common knowledge in the SR community. For example, how is it pretrained? I couldn’t find any statement about the setting for the pretraining. Or is the method written in Section 2.1 for the pretraining? If so how is the post-training performed? The computational time written in 166 is for what? It should depends on the dataset, right? It was also not clear for me how the refinement of the parameter is performed in the end-to-end manner. \n\nSignificance\n\nBased on the authors’ statement, this approach is the first one that reaches competitive performance to GP-based approaches. Although the performance is not superior, the advantage of using pre-training over GP-based approach is promising.\n\nThe author’s claim the advantages of the proposed approach over the top performance approaches in its inference time. However, it was not evaluated whether this comes from the trick described in Section 2.2 or it is intrinsic to the approach using Transformer. \n Please see the comment above. Although the checklist says the code is available, I couldn't find the pointer to the code in the main text. It would always be nice to have a pointer to the code, even if it is included in the supplementary. \n\nAlgorithmic description of the proposed approach would help readers understand.", " This paper proposed a transformer-based approach to perform end-to-end symbolic regression, that is, predicting simultaneously the function and the values of numerical constants. The trained model is augmented with several tricks at inference, including refinement, scaling, and bagging, etc. Experimental results show that the accuracy approaches to the state-of-the-art GP approach and the inference time is significantly reduced by several orders of magnitude. Symbolic regression is well studied with various machine learning technique. In contrast to addressing the problem in a two-step manner, the proposed approach directly predicts the function along with the value of constants. Such an end-to-end model is not surprisingly new. The key innovation is the employed tricks for improving the performance of trained model, and the employed techniques are technically sound.\n\nAs the accuracy is still lower than state-of-the-art GP approaches, the main benefit of the proposed approach is the reduced inference time. However, I am not sure whether inference time is the key factor of symbolic regression. It would be helpful to introduce more background on the importance of inference time.\n\nBesides, more comparison with other end-to-end symbolic regression approach and ablation studies would be quite helpful to demonstrate the effectiveness of the proposed approach. 1. Could you make a further comparison with [29] instead of just mentioning “[29] infers one-dimensional recurrence relations”? It seems that both of them have the same architecture and similar tasks.\n\n2. Could you please provide more ablation studies to demonstrate the effects of: (1) mixture of distributions and different distribution shapes; (2) input points scaling at inference time.\n\n3. Could you please compare with other deep learning symbolic methods like [5] in experiments? It seems that [5] performs well on both running time and accuracy. Please see questions listed above.", " This paper provide a novel sequence prediction based solution to symbolic regression (SR). Compared to search-based SR methods, the proposed method is more efficient in inference and generalize to new tasks effortlessly. Compared to privious sequence based SR methods, the proposed E2E is able to scale to larger dimensions. \nSymbolic regression is one challenging, theoretically and practically important task that incorperates pattern recognition, rule based reasoning, sequence modeling, discrete optimization, and beyond. \n\nCompared to GP based SR, the sequence prediction based SR scales to novel unseen problems effortlessly. Compared to previous works in the sequence prediction based SR such as symbolicGPT and NSRS, this work scales better, capable to deal with > 3 dimensional problems and is with better accuracy. This paper claims that using the proposed dataset generation scheme, the pre-trained E2E SR could generalize to both in-distribution and OOD problems.\n\nIn the formulation of sequence based SR, the most critical issue is how to sample the pre-training tasks such that the model learned on the generated samples could capture symbolic knowledge, while not overfit to the pre-training dataset. To address this, the authors provided a principled dataset generation workflow, and showed via experiments that E2E could generalize to OOD. The author also provided in the supples additional series of experiments on whether the E2E is memorize the data.\n\n\nThe authors provided implementations which helps the reproducibility.\n\nThough being a new SR paper that pushes the SOTA, this paper upscales the dimension from (<=3) only to (<10), as the author mentioned in line 287. Hence the method still remains improvable in scaling to larger dimensions.\n\nOther limitations dwell in the evaluation of the pre-training data generation procedure, which is critical to this sequence prediction type of SR formulation, but is under evaluated.\n\nI haven't checked the provided implementations carefully. If the results are fully reproducible and more evaluations could be given to pre-training data generation on OOD, based on my limited assessment, this paper could be given high merit.\n One important issue for the sequence based SR is that people need to know to what extent the model is learned to overfit the pretraining data. The authors provided OOD evaluations in the exp section and the dataset generation controlling params in the supples, which is helpful to this question. However, it would be better to 1) expliclitely show how different is the OOD symbolic samples differ from the pre-training data generation params? Better demonstrate this with concrete examples of OOD symbolic ground truth and pretraining examples. And 2) it is helpful but not mandatory to: show that modifying the pre-training dataset distribution could positively contribute to but not greatly impact the OOD result.\n\n\nAs a new method targeting at sequence based SR, it is better to compare with prior works in this domain, which are symbolicGPT and NSRS. I am aware that official implementations seems to be not yet available, hence I'm not posting this as a must-have. However, since the E2E SR and symbolicGPT are similar in many ways, it would still be beneficial if we could see the simulated results: one way is to alter the E2E implementation so as to only predict skeletons, then apply coeff optimization to un-officially simulate the symbolicGPT. This work does not explicitely show potential negative societal impact.\n" ]

[ -1, -1, -1, -1, -1, -1, 6, 5, 7 ]

[ -1, -1, -1, -1, -1, -1, 1, 3, 5 ]

[ "PK7b310vOC6", "Th5iiD2PgIQ", "1Bw8upTML-Z", "CwkZtvpTZ8I", "sWQ_Pe4tjFN", "CMissa5zgmZ", "nips_2022_GoOuIrDHG_Y", "nips_2022_GoOuIrDHG_Y", "nips_2022_GoOuIrDHG_Y" ]

[ "bN4-nwtggcX", "R9kn6E8lrJH", "5jRE-IPDjv9", "ZQ3sC4ZbkCX", "gxRNgwxI958", "u0grOrh2eq", "jvfabJMTqqN", "3aJ0kWAeCbw", "5rdN57ilJuk", "qPjoYjNMK_2", "rQH8Czcpsu", "ccQQl2RPvFS", "m6FFNP7VFp", "WKEs49JhlEF", "62wT0gu6Gbt", "OiW-mZgUHHJ", "tJ3Se8vODd", "Mdx2L7jO5-R" ]

[ "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for your answer and the proposed developements. I will need some time to fully process this discussion, thank you very much for the interaction!", " Thank you for your kind words.", " Thank you for your thoughtful answer and your willingness to improve your rating. We have worked toward the changes you suggested. We updated the appendices to add definitions of the tools used.\n\n> a collection of unsurprising (it is not a bad thing!) facts about Lipschitz Deep Neural Networks\n\nOur experience on the matter is that it depends on the mathematical culture of the reader. Some researchers are surprised by these results. To the best of our knowledge, the link between cross-entropy temperature and accuracy/robustness tradeoff have not been studied before. The ill-posed problem of BCE minimization on AllNet is often not addressed or mentioned. We would not qualify those facts as unsurprising.\n\n> that are kind of all network as stated from Definition 1\n\nIt's true that 1-Lipschitz networks are a subset of conventional networks. The key difference is in what the optimization process yields. Crucially, our work shows that\n\n$$\\bar f = \\arg\\min_{f\\in\\text{LipNet1}} \\mathbb{E}_{(x,y)\\sim P} [\\mathcal{L}(f(x),y)] \\text{ (exists under mild assumptions per Prop 2)}$$\n\nis very different from\n\n$$\\begin{aligned}f &= \\arg\\min_{f\\in\\text{AllNet}} \\mathbb{E}_{(x,y)\\sim P} [\\mathcal{L}(f(x), y)] \\text{ (assuming it exists, not always per Prop 5)},\\\\\\\\\n\\bar f &= \\frac{f}{\\text{Lip}(f)}\\end{aligned}$$ \n \nboth theoretically and empirically.\n\n> which Lispchitz constraint technic should be used for which problem, and can we distinguish Lipschitz network from one another.\n\nThank you for opening the discussion on possible extensions of our work. This is a good remark that highlights the importance of exploring this field, by keeping in mind both the role of architecture and the role of the loss.\n\nFirst, let's recall some facts from literature.\n \n* ReLU based networks suffer from expressiveness issues (pointed out by [11]) and should be replaced by GroupSor (known to be superior [36]).\n* The quality of robustness certificate depends on the tightness of the upper bound on Lipschitz constant. So methods based on regularization (such as spectral regularization [38] or gradient penalty [37]) should be avoided since they do not allow precise control of the Lipschitz constant.\n* Frobenius normalization or weight clipping is better [6, 39] but it often yields loose upper bounds wrt l2 distance. Spectral normalization [14] leads to tighter bounds. \n\nWe can share a preliminary answer in the context of classification.\n\n* To ensure tightness of robustness certificate, the robustness radius at $x$ must fulfill $\\epsilon = |f(x)|$ which implies $\\|\\nabla_x f(x)\\|=1$. It is possible per Prop 1 and Corollary 2. This property can be enforced with orthogonal layers (including GroupSort), and orthogonal affine layers (in particular their spectral norm is equal to 1). Or by using hKR loss whose solution verifies this property by design [8] without explicit orthogonal constraints.\n* hKR and hinge yield VC bounds per Prop 6 because they separate samples based on margins. Ubiquitous in C-SVM, hinge loss and its variants are not frequently used for NN training. Our work may help rehabilitate them: the margin must be tuned (not possible with default implementation in Tensorflow framework). \n* The role of $\\tau$ in cross-entropy is to control the accuracy-robustness tradeoff (illustrated by fig 2) - and sensitivity to noise (as in fig 1.b).\n* Please take a look at the discussion with reviewer jRZ5 for additional insights regarding other architectures.\n\nWe plan on exploring those questions in future work. We will add a “Perspectives” section that contains this discussion in the additional page of the camera ready version. \n\n", " Honestly, I could not read the whole paper again but I trust my fellow reviewers that its coherence has improved. I am hopeful to see this work accepted at NeurIPS 2022.", " Thank you very much for your answer and sorry for the delay. I read the updated version and it is indeed style-wise much much better. I would improve my grade following this improvement, but in a limited way: despite your clear answer about the objective of your paper, I still fail to find a definite general purpose to your work that I still see as a collection of unsurprising (it is not a bad thing!) facts about Lipschitz Deep Neural Networks (that are kind of all network as stated from Definition 1).\nAn interesting potential direction in my opinion would be to shed some light on which Lispchitz constraint technic should be used for which problem, and can we distinguish Lipschitz network from one another. Could you work tackle this kind of problem?", " We appreciated the thoughtful review, and are available to answer any question regarding the modifications we made.", " Thanks for your interest. In fact CNN do fall under the scope of this paper, both on the theoretical and practical side: convolutions can be seen as a special case of a dense layer with sparse and repeated weights. But as you pointed out, CNN comes with it's own variety of building blocks: others layers must be analyzed independently: average pooling can be seen as a special case of convolution, skip connections must be followed by a 0.5 multiplicative factor, and so on... This (non-exhaustive) list motivated our choice for the deel-lip library (more information in appendix D), which allowed us to run large scale experiment with CNN on CIFAR-10/100, Mnist and Fashion-Mnist. We expect that our results still hold as this field evolves, so improvements can be expected on the experimental side (higher pareto front in fig 3, and convergence at an higher accuracy in fig 4 for instance). The importance of the CNN width is illustrated in fig 16 for example. ", " Thank you for your response. I would be interested in looking at the results for CNNs if you could share them.", " Thank you for your detailed comments and questions. \n\n> There is no comparison with SotA certifiable networks in the current manuscript. \n\nPlease see our general response regarding this remark. \n \n> Isn’t the requirement in Eq. (3) too conservative? Does changing the min over x to an expectation help here? \n \nIt is too conservative for practical purposes: with the “min” we enjoy the nice geometric interpretation (Signed Distance Function), whereas the “expectation” is a lot harder to analyze. \n \n> Can you provide an example of the behavior discussed at the end of Sec. 5.2 for conv nets trained on datasets like CIFAR-10 or MNIST? \n \nWe added an experiment that confirmed our remark: see please our general response. \n \n> Adversarial training of regular networks leads to a large gap between training and test losses. Should we expect this gap to disappear for adversarial training of 1-Lipschitz networks? \n \nThanks for this question, as you pointed out adversarial training can be combined with LipNet1 networks. However, as this method attempts to do empirically what LipNet1 does with usual training, combining the two might be redundant. When the loss parameters are not tuned properly LipNet1 networks can also have a large generalization gap, as shown in fig 4. \n \n> Do the authors think that playing with the temperature of 1-Lipschitz networks is enough to build certifiable robust classifiers? \n\nIt is necessary, but not sufficient. The robustness certificate exists by design (Property 1). The temperature will define the nature of the optimum (see figures 1.b, 2). For the certificate to be tight, the upper bound on Lipschitz constant must be tight. Hence, the architecture plays an important role in the final quality of the certificates, as does the overall optimization process. For instance, designing orthogonal convolutions is still an active research area. \n\n> The observation made in this paper bears some similarities to other publications, such as (On Calibration of Modern Neural Networks, Guo et al., ICML 2017) and (How Good is the Bayes Posterior in Deep Neural Networks Really?, Wenzel et al., ICML 2020). \n\nThanks for the additional references ! Note that the LipNet1 network is not necessarily calibrated : the value of the probability sigma(f(x)) is more an indication of the distance to the boundary (a lower bound at least), than a confidence like the one encountered in calibration. \n\n> The extent to which certain observations of this paper hold in practice is not clear enough \n \nWe hope that experiments we added on Fashion-Mnist with different architectures (appendix N), in addition to the ones already present on CIFAR-10 and CIFAR-100, can convince you the phenomenon we exhibit holds broadly. We also added an experiment on Mnist to show that Example 1 continues to hold. \n \n> Are you sure about Lines 182 and 183; Some typos: L137, cannot guarantees; L138, “is not” repeated twice; L154: an unified. \n \nWe have corrected these typos, thanks for your careful reading.\n", " Thank you for your comment regarding typography rules. We do appreciate that you found our results nice, we are also convinced that such a paper is important for the NeurIPS community to increase interest on LipNet1 networks.\n\nConcerning the general writing style of this paper, we invite you to read the general response. \n \n> the biggest problem is the writing style \n \nWe modified definitions 1&2 (we added a remark), we added a definition before corollary 1. We rewrote some equations. We moved the footnotes into the main flow. We are confident that the remaining remarks regarding typography can be easily resolved in the respect of the 9 pages limit, upon acceptance. \n\nConcerning the proof readability, we are prone to rework on the proofs. Can you elaborate on the style you would like to read? \n \n> - the proofs rely on many technical tools such as Lebesgue measure but the pre-requisite (Borel space etc) are never explicitly given. \n \nThanks for your remark. We will add definition /or references in the appendix in order to make the paper self consistent with regards to these classical concepts of measure theory. \n \n> Lipchitz neural networks are \"often perceived as not expressive\", which I do not remember ever reading in the literature \n \nThe citation given at the end of the first page “Lipschitz-based approaches suffer from some representational limitations that may prevent them from achieving higher levels of performance and being applicable to more complicated problems” comes from a peer reviewed paper [9]. \n \n> The paper is full of references and it costs the readability of the arguments \n \nThis is something we discussed during the writing. We wanted to support every claim by citing appropriately prior works. We are advocating for the appealing properties of those networks: it requires a lot of tools and we cannot afford to put them all in the main paper. We had to choose the most significant parts to leave space for the main message, and give pointers to allow the reader to navigate the remainder in references or appendix. \n \n> most reference are incomplete (many article are reference as arxiv instead than the published and peer-reviewed version) \n \nIndeed 12 out of the 84 citations were referenced as arxiv. Among them for 5 papers [32, 38, 54, 68, 73] we couldn’t find a peer reviewed equivalent on the authors webpages. For the others we amended the manuscript, including the ones published this year like [44, 48, 67]. \n \n> l94: one needs additional hypothesis on AllNet to claim that they have finite Lipschitz constant (Lipschitz activation would do). \n \nWe amended the manuscript. The vast majority of activations have a finite lipschitz constant (ReLu, Softplus, Sigmoid, Tanh, GeLU, etc). All details related to this result can be found in the paper [16] we are referring to. \n \n> l216: the reference to cor 1 seems dubious: it is a definition of \\epsilon separation rather than about bias. \n \nWe are referring to the bias/variance tradeoff in learning. Corollary 1 is saying that under the \\epsilon separation hypothesis, 100% accuracy is achievable by LipNet1 networks. It implies that the LipNet1 class does not suffer from any bias. We rewrote the Corollary to make it more clear.\n", " Thank you for your careful reading and detailed questions. \n \n> the authors do not cite any experimental study or theoretical work, where someone claimed that 1-Lipschitz neural networks are inherently less accurate or less expressive than unconstrained neural network models. \n \nWe gave a citation line 34 from paper [9]: “Lipschitz-based approaches suffer from some representational limitations that may prevent them from achieving higher levels of performance and being applicable to more complicated problems”. \n \n> the provided evidence that LipNet1 models are not prone to overfitting unlike conventional models is not conclusive \n \nBenefitting from generalization guarantees does not exactly imply that lipschitz networks are not prone to overfitting. Proposition 4 proves that once the loss parameters are fixed, the generalization gap vanishes to zero *in the limit* of large sample size. Figure 4 shows that this phenomenon can be observed in practice. For the practitioner, this means that generalization gap can be reduced by: \n* increasing the number of samples once tau is fixed (or other loss parameter).\n* decreasing tau once the number of samples is fixed \n \nWe added curves of AllNet networks in Fig 4. to illustrate their generalization gap. \n\n> the authors should expand the experimental section to compare LipNet1 models and conventional models \n \nWe added an experiment with an AllNet network in Section 5.2 (fig 12) and in fig 4. Please see our general answer. \n \n> Can the authors include experiments where LipNet1 model robustness with tuned L or tau is tuned and compared with current state-of-the-art methods? \n\nPlease see our general response regarding this remark. \n \n> How does the choice of the loss function affect the training dynamics and generalization? \n \nThis is an interesting question. Our results (figure 3) reveal that the studied losses share a similar behavior at global scale at least from the point of view of accuracy, robustness and generalization. Whether these losses differ at a local scale is still an open question. We give insights about this in fig 14.\n \nThe remarkable stability of LipNet1 training can also be observed in the additional experiment on fashion-mnist (fig 15).\nDifferences regarding other criterions (such as explainability) might be expected. hKR enjoys a nice optimal transport interpretation [8]. However, hKR and hinge are piecewise affine (like LipNet1 networks), so they cannot be trained with order-2 methods. \n \n> We do not know how many samples are required for the convergence of the LipNet1 models: \n \nfig 4 shows that this convergence can be observed empirically (see fig 8. for detailed results). We believe we can obtain convergence rates using Donsker’s theorem, since Lipschitz functions are a Donsker’s class [90] under mild assumptions [91], but we leave this for future work.\n\n[90] Aad W. Van Der Vaart et Jon. A. Wellner, Weak convergence and empirical processes with applications to statistics, Springer, p. 127 \n \n[91] Giné, E. and Zinn, J., 1986. Empirical processes indexed by Lipschitz functions. The Annals of Probability, pp.1329-1338.\n\nWe add details in Section 5.1 about this limitation of our work.\n\n> The initial VC dimension bounds are rather vacuous:\n \nWe emphasize that existing proofs that assume elementwise activation, are not applicable to GroupSort which is widely used in LipNet1. As expressed in l267, we are pretty confident that future works could improve this bound.\n", " Thank you for your comprehensive reading, we answer your questions here, and we invite you to read the general response where the additional experiments are listed.\n\n> How does this analysis extend to other types of networks apart from feed forward networks? \n \nThanks for your question which opens nice perspectives for future works.\nEffectively the focus of this paper was on feed forward networks which are the most common networks for computer vision (including convolutional layers). We have some preliminary results that we can share in this rebuttal.\n\nSelf-attention layers are not Lipschitz (see [40]) so they do not fit in our analysis. Lipschitz Recurrent layers (such as LSTM) have been recently studied by [42]. Recurrent layers are useful for inputs that are given as sequences. Sequences of bounded length (<= l) can be embedded into euclidean space, eventually by padding sequences that are too short. If the latent space is big enough, the Lipschitz recurrent unit can carry the whole input and additional information, so we recover universal approximation. Hence, our work generalizes to Lipschitz recurrent units that take in input sequences of lengths <= l. \n\nHowever, for arbitrarily long sequences, we cannot embed them easily in euclidean space of finite dimension. Recurrent units can be used to simulate a Turing Machine [88] which might have huge implications on expressivity.\n\nIn the case of Deep Equilibrium models [89] LipNet1 networks are contractive operators : the fixed point is guaranteed to exist by Banach fixed-point theorem. So they would be more sound (mathematically) with this implementation.\n\n[88] Hyötyniemi, H., 1996. Turing machines are recurrent neural networks. Proceedings of step, 96. \n \n[89] Bai, S., Kolter, J.Z. and Koltun, V., 2019. Deep equilibrium models. Advances in Neural Information Processing Systems, 32.\n\n> a lot of prior knowledge is assumed.\n \nWe agree on that, especially about the practical implementation of LipNet1 networks, and mathematical tools. We hope that appendix D, E and F can help with practical implementation. We will add definitions in the appendix for the different tools we use such as VC dimension or optimal transport.\n", " Please find below the modifications we made to the paper.\n\nWe added three experiments:\n1. We extended exemple 1 in section 5.2 to show that this phenomenon is also observed on Mnist. Results were added in fig 12. We see that the norm of the weights increases continually during training (both with SGD and Adam). This is coherent with the empirical observations made about the high Lipschitz constant of AllNet networks [23]. \n2. We now report generalization gap of AllNet networks in figure 4 for better comparison between AllNet and LipNet1.\n3. We introduce a new experiment on Fashion-Mnist to show sensitivity of Pareto front with respect to architecture size. This experiment also shows the stability of the training with respect to Tau (fig. 15 and 16 in appendix N).\n\nWe hope those additional large scale experiments can convince you that our theoretical results also hold in practice. \n\nOther modifications:\n* Better separation of results and definitions, reformatting of some equations\n* References formatting\n* Typo + minor remarks", " We would like to thank the reviewers for their instructive feedback about our paper. From their review, it seems that the results of this paper are understood, including by reviewers who claimed to be “unfamiliar with some pieces of related works”. If we could convince you about the nice properties of LipNet1 for classification, we will have already reached our first goal.\n\n## About the style of the paper\nThis paper aims to be at the intersection between theoretical ML and (empirical) deep learning. Lipschitz constrained networks allow to directly put in perspective mathematical proofs with empirical experiments on large scale vision datasets. The style is meant to be understandable by practitioners from the deep learning community, while staying mathematically rigorous. This motivated our choice to articulate each message with:\n* theoretical result that carries the message of the section (Proposition 1, Proposition 2, Proposition 4)\n* a toy experiment for pedagogical purposes (figures 1&2, example 1)\n* a large scale experiment (figures 3, 4, 12, 15, 16) \n \nEach message is carried by its own section, and summarized in Table 1. This organization is also reflected in the table of content given in the appendix, where each subsection title carries a message.\n\nThis structure allows us to show that, with LipNet1, theory matches the practice remarkably well (figures 2, 3 and 4), including on large scale experiments (fig 12, 15, 16). Some results (such as the consistency result of Proposition 4) have important consequences for the community of robust learning, and for practitioners interested in Deep Learning with formal guarantees (for safety critical applications in health or industry for example). Control of Lipschitz constant and training with LipNet1 extends further than the robustness community only, for example in fields like Differential Privacy [85], optimal transport [6], density estimation with orthogonal normalizing flows [58]. \n\n[85] Abadi, M., Chu, A., Goodfellow, I., McMahan, H.B., Mironov, I., Talwar, K. and Zhang, L., 2016, October. Deep learning with differential privacy. In Proceedings of the 2016 ACM SIGSAC conference on computer and communications security (pp. 308-318).\n\n## About the research line of this paper\nWhile the question of the LipNet1 architecture is often in the spotlight, the loss is overlooked. Our research line is to point out its tremendous importance (see sections 3.2, 4.2 and 4.3). In personal communications across different teams and labs, it became apparent that some teams assigned the poor results of their LipNet1 networks to an intrinsic limit of the architecture, without questioning their loss, and abandoned the tool before ever reaching production or publication stage. We feel that there is a gap in literature that must be filled. \n \nThis paper also provides a toolbox of results and experiments to serve as a basis for future works. We aim to open new research directions, and to encourage the community to use LipNet1 networks more, including outside the field of robust learning. We also believe it provides insight on what is going on in AllNet networks training: their Lipschitz constant grows uncontrollably during training (see fig 12), which is like using cross entropy with high Tau.\n\n## About comparison with SOTA:\nComparing with state of the art methods in provable robustness has been discussed while redacting this paper. However doing so would have been counterproductive as:\n1. All the networks in figure 3 (resp fig 4) share the same architecture, and training procedure. This allows a fair comparison. We explained in appendix D why we chose the Deel-Lip library, among other implementations of LipNet1 networks.\n2. The conclusions of the paper does not depend on the exact architecture used to parametrize LipNet1 convolutions. By adding sota methods in the graphs, there is a risk of misleading the reader into thinking that we advocate a new method or a specific LipNet1 architecture. \n \nIn fact the results in fig 3 questions the way we evaluate the state of the art: it seems that a rigorous comparison between two methods can only be achieved by comparing their Pareto front. However none of the papers on LipNet1 convolutions [ 53, 54, 3, 8, 55, 56 , 57] does this to evaluate robustness. An extensive comparative study between architectures is an important future work that deserves its own 9 neurips pages.\n\nThe experiment we added in fig 16 (appendix N) shows that changing architecture size shifts the Pareto front: we expect similar behavior for other LipNet1 architectures.", " The paper studies 1-Lipschitz constrained neural networks, and prove some results for this class of networks. The paper defines 1Lip nets as those networks for which the output function is Lipschitz constrained with a Lipschitz constant of 1. They cite a way to construct such feed forward networks based on the norms of the weight matrices. They then show that for any binary labelling function, one can get an equivalent 1-Lipschitz function which agrees with the labelling function on all points of the domain. They then empirically show that tuning the temperature hyper-parameter while learning with BCE loss is important, and imply connections between this hyper-parameter and the lipschitz constant. They then show that 1Lip network are certifiably robust to adversarial attacks, and that the discriminator of a WGAN, which is also a 1Lip network is the optimally robust classifier. Finally, they give generalization results of 1Lip networks, showing that this class of networks is PAC learnable with a VC dimension independent of the architecture. Strengths - \n1. The results in the paper are novel, interesting and important.\n2. The generalization guarantees and robustness results can open up a new line of research into these architectures. \n\nWeaknesses - \n1. More empirical evaluation could benefit the paper.\n2. The writing could be improved, in particular, a lot of prior knowledge is assumed.\n How does this analysis extend to other types of networks apart from feed forward networks? Some of the limitations are listed in the weaknesses above. A more thorough empirical evaluation on other tasks and adversarial perturbations would be appreciated. ", " The authors theoretically studied several properties of 1-Lipschitz neural networks (LipNet1). They showed that LipNet1 can learn and approximate any classification decision boundary. Secondly, they showed that LipNet1 is certifiable robust and not prone to overfitting, unlike conventional unconstrained models. They showed that by varying margin for hinge loss or temperature for binary cross-entropy, one can control the trade-off between robustness and accuracy. **Originality:**\n\n- The paper derives several theoretical results. Yet, I am not confident to say that all the results presented here are original.\n\n**Quality:**\n\n- The authors state that the purpose of this paper is to address the common misconception that “they (1-Lipschitz neural networks) remain commonly considered as less accurate”. However, the authors do not cite any experimental study or theoretical work, where someone claimed that 1-Lipschitz neural networks are inherently less accurate or less expressive than unconstrained neural network models.\n- The authors provide an interesting analysis of 1-Lipschitz neural networks and show that LipNet1 can have certain advantages over conventional neural networks.\n- The theoretical analysis, however, is not very useful as 1) we do not know how many samples are required for the convergence of the LipNet1 models; 2) the initial VC dimension bounds are rather vacuous, see proposition 7, where VC bounds depend exponentially on the number of neurons.\n\n**Clarity:**\n\n- The paper at times is difficult to follow its main story is fragmented without sharing a common theme. The expanded experiments (not just toy experiments) should be included to expand the paper and confirm the main theoretical results.\n\n**Significance:**\n\n- The paper provides an analysis of the properties of LipNet1 models, which recently become of interest in the community recently. However, to highlight its significance, the authors should expand the experimental section to compare LipNet1 models and conventional models. At the present moment, the provided evidence that LipNet1 models are not prone to overfitting unlike conventional models is not conclusive. - Can the authors include experiments where LipNet1 model robustness with tuned $L$ or $\\tau$ is tuned and compared with current state-of-the-art methods?\n- How does the choice of the loss function affect the training dynamics and generalization? The authors briefly discussed the limitations of their work: lack of convergence speed bounds. The limiations of this work can be expanded. The authors should describe all the assumptions in detail and clearly state their limitations when providing their theoretical results.", " The paper proposes many theoretical statement Lipschitz neural network for classification and show that these specific networks follows attractive properties. AllNet networks are defined as any neural networks without any constraints. This class does not produce Lipschitz function without any further hypothesis (such as activations are Lipschitz).\n\nThe paper is all over the place and the main research line is unclear. Most of the theoretical results are rather common or \"trivial\". The whole paper seeks for internal coherence and lacks of general purpose. As a reader, it is difficult to grasp what is the objective.\nThe present paper seems to be more adequate for a journal publication than to a conference.\n\n* Global style as the biggest weakness\n\nThe main assumption behind the development of the theory is the fact that Lipchitz neural networks are \"often perceived as not expressive\", which I do not remember ever reading in the literature. Most of the paper seems fuzzy: it goes from BCE to robustness certification to a (trivial) convergence proposition (prop 4) to consideration about float32/64 (ex 1)... it is just too much. There are no transitions and at no moment the reader understands what is the point.\n\nOne of the biggest problem is the writing style that makes the paper hard and annoying (sorry...) to read.\nFor example among many other problems:\n\n - sentences must contain a verb and end with a '.'(even when it ends with a formula);\n - theorem should be self contained, exterior references should remain exceptional;\n - organize the equations in order to be easily readable;\n - separate definitions and remarks (e.g. def 1 & 2 contains definitions and remarks);\n - separate propositions and definitions (e.g. corollary 1 contains a definition and a proposition);\n - the proofs rely on many technical tools such as Lebesgue measure but the pre-requisite (Borel space etc) are never explicitely given.\nMost of the proofs in the appendix should be re-written. More personal but I think the footnotes in the paper could be avoided.\nThe paper is full of references and it costs the readability of the arguments. The reader gets overwhelmed very quickly for the wrong reasons.\n\n* References\n\nmost reference are incomplete (many article are reference as arxiv instead than the published and peer-reviewed version)\n\n* Others\n\nl94: one needs additional hypothesis on AllNet to claim that they have finite Lipschitz constant (Lipschitz activation would do).\n\nl216: the reference to cor 1 seems dubious: it is a definition of \\epsilon separation rather than about bias. I suggest that the other should carefully rewrite the paper with a clear objective, the typography should be respected.\nThe different results of the paper are nice, but in order to be published they should be properly articulated. Yes", " This paper challenges the common belief that 1-Lipschitz natural networks are less generalizable than regular networks. It accomplishes this by proving a series of claims. The authors first demonstrate that any classification problem, under mild assumptions, has a 1-Lipschitz solution, and that the error is zero if the distributions of classes are well separated. They go on to show that 1-Lipschitz models can always minimize a tempered cross-entropy loss, while the generalization performance depends heavily on the temperature value. This paper suggests that the low performance of 1-Lipschitz networks in the literature can be attributed to the wrong choice of temperature. One positive thing about 1-Lipschitz networks is that one can certify the output margin $\\|f(x)\\|$ rather than the input margin, as the former is a lower bound of the latter. The paper demonstrates that the WGAN discriminator maximizes an average of the signed output margin, thus it is optimally robust in this respect. The WGAN discriminator has the disadvantage of not ensuring a very high level of accuracy. There are even classification problems for which the WGAN discriminator's accuracy can be arbitrarily low. Nevertheless, implicit/explicit regularizations with 1-Wasserstein distance can be used for a trade-off between accuracy and “certifiable” robustness in 1-Lipschitz networks. Finally, the paper discusses some guarantees on the learnability of 1-Lipschitz networks. This is a thought-provoking paper that questions certain overlooked aspects of 1-Lipschitz networks that are associated with adversarial robustness. It contains many interesting insights as well as simple illustrations to demystify some myths about these networks. While discussing interesting aspects of Lipschitz networks, the paper does not present its results in a unified manner, rather it provides nuggets of understanding. I am pleased to learn that 1-Lipschitz networks may not be as weak as previously thought, but I would like to know how these insights can be used to build robust and accurate models. Additionally, the paper could have better positioned itself compared to previous studies. - Isn’t the requirement in Eq. (3) too conservative? Does changing the min over x to an expectation help here? \n- Are you sure about Lines 182 and 183? The MCR for Q is not missing here?\n- Can you provide an example of the behavior discussed at the end of Sec. 5.2 for conv nets trained on datasets like CIFAR-10 or MNIST?\n- There is no comparison with SotA certifiable networks in the current manuscript.\n- Adversarial training of regular networks leads to a large gap between training and test losses. Should we expect this gap to disappear for adversarial training of 1-Lipschitz networks?\n- Do the authors think that playing with the temperature of 1-Lipschitz networks is enough to build certifiable robust classifiers?\n- The observation made in this paper bears some similarities to other publications, such as (On Calibration of Modern Neural Networks, Guo et al., ICML 2017) and (How Good is the Bayes Posterior in Deep Neural Networks Really?, Wenzel et al., ICML 2020).\n- Some typos: L137, cannot guarantees; L138, “is not” repeated twice; L154: an unified. The extent to which certain observations of this paper hold in practice is not clear enough." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 5, 3, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 3, 4, 3 ]

[ "5jRE-IPDjv9", "ZQ3sC4ZbkCX", "gxRNgwxI958", "5rdN57ilJuk", "qPjoYjNMK_2", "nips_2022_BRIL0EFvTgc", "3aJ0kWAeCbw", "ccQQl2RPvFS", "Mdx2L7jO5-R", "tJ3Se8vODd", "OiW-mZgUHHJ", "62wT0gu6Gbt", "WKEs49JhlEF", "nips_2022_BRIL0EFvTgc", "nips_2022_BRIL0EFvTgc", "nips_2022_BRIL0EFvTgc", "nips_2022_BRIL0EFvTgc", "nips_2022_BRIL0EFvTgc" ]

[ "kfAKFgwsxp7", "VipxkskhMt7", "XDdH1dKm8GX", "RqA1yQ1duaH", "092RU8AosP", "cbl6gaPu18", "yNtiSijn2Fr", "9icFk68Lfdh" ]

[ "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I would like to thank the authors for their response. Some questions are addressed properly, including the efficiency evaluation and the comparison between initialized kernels and trained kernels, which improve the completeness. \n\nHowever, the claimed main contribution that solving the multiple image fusion problem as a reverse filtering process is limited. Although the authors argued that they tailor the classical reverse filtering in an alternating iteration manner, it’s much closer to a reasonable implementation rather than an inspiring innovation. Besides, the stability and convergence of the iterative process totally benefit from the classical reverse filtering. Considering all the related demonstration have been given thoroughly in “Zero-order Reverse Filtering”, the authors oversell the theoretical contribution.\n\nOverall, I feel the work is a good engineering approach, but the novelty is a bit limited. \n\nTherefore I will keep my score unchanged.", " We appreciate the positive and constructive comments, including novel alternating update deep convolution network, the state-of-the-art results of our method, and clear writing and easy to follow. The raised concerns are addressed as follows.\n\n**About the the iteration number set in the ablation study.**\n\nIn the ablation study of different initialization methods, we set the iteration number to 5 for a fair comparison. For the baseline models, we change only one parameter or component, and keep the other parameters and components the same.\n\n**About the performance improvement from the learned kernels.**\n\nCompared with the model that is initialized by fixed Gaussian kernels (III), our model with the learned kernels (ll) can gain large performance improvement. The comparison results are listed as follows:\n\n| Methods | PSNR↑ | SSIM↑ | SAM↓ | ERGAS↓ | SCC↑ | Q↑ | Dλ↓| Ds↓| QNR↑|\n| :-----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: | :----: |\n| (ll) | 41.7587 | 0.9691 | 0.0229 | 0.9540 | 0.9749 | 0.7731 | 0.0631 | 0.1184 | 0.8285 |\n| (lll) | 40.4161 | 0.9612 | 0.0261 | 1.0668 | 0.9667 | 0.7316 | 0.0684 | 0.1275 | 0.8123 |\n\nAlthough the learned kernels are close to the initialized Gaussian kernels, a large number of multi-scale Gaussian kernels can still bring performance improvements. We will add these experimental results in the revised version.\n\n**About the recent method.**\n\nBecause the related work mentioned by reviewer have not released the code when we submitted the paper, there is no comparison with this method in our paper. \n\n**About the computation cost and efficiency.**\n\nThe floating-point operations (FLOPs) and the number of parameters of the compared models are provided in the following table:\n\n| Methods | PNN | PANNet | MSDCNN | SRPPNN | GPPNN | Ours |\n| :-----: | :----: | :----: | :----: | :----: | :----: | :----: |\n| Flops | 1.13 | 1.12 | 3.92 | 21.11 | 1.40 | 2.58 |\n| #Params | 0.69 | 0.69 | 2.39 | 17.11 | 1.12 | 1.66 |\n\nAs can be seen, PNN and PANNet have the fewest FLOPs and parameters, but the performance is the worst. SRPPNN exhibits large increases in the number of parameters and FLOPs as the number of convolutional layers and the complexity of the network design rise. Notably, it achieves the second highest performance at the expense of massive model computation and storage. Additionally, the most comparable solution to ours, GPPNN, is organized around the model-based unrolling principle and has comparable model parameters and flops reductions but inferior performance. In summary, our network achieves a favorable trade-off between calculation, storage, and model performance compared with other methods.\n\n**About the related citation for definition and theorem.**\n\nTake the reviewer's suggestions into account, we will add the related source citation for the definition, the theorem and reverse filtering formulation. Specifically, Definition 3.2 and Theorem 3.2 can be found in reference [*1]. \n\n[*1] Banach, S, “Surles operations dans ensembles abstraits etleur application aux equations integrales,” Fundamenta Mathematicae, 3. 51-57. 1922.\n\n**About the subtraction and addition symbols.**\n\nThanks for your careful reading and suggestions.The position of the legend about subtraction and addition is reversed. We will revise it in a revision.\n\n**About the novelty.**\n\nReverse filtering is a classical algorithm, which inspired a lot of works. However, our approach is significantly different from classical reverse filtering. To be specific, (1) the classical reverse filtering can only solve the inverse problems of single image such as denoising, deblurring and super-resolution. Our approach tailors the classical reverse filtering in an alternating iteration manner based on the theortically feasible fixed point equation system for multispectral image fusion. As mentioned in our paper, with such theoretical support, the proposed algorithm can also be extended to other image fusion tasks that involve multiple images. (2), the classical reverse filtering needs to select a suitable and fixed filter function, such as adaptive manifold filter, rolling guidance filter, wlsFilter and so on. For this problem, we introduced the multi-scale Gaussian kernels to approximate arbitrary functions and combine them into deep networks. By doing so, the data-driven deep neural networks can help our model to obtain an appropriate function rather than a fixed and manually defined one, improving the model’s generalization and applicability. ", " We thank reviewer for the feedback. We are encouraged that the reviewer confirms the good writing of our paper and convincing and sufficient experiments. The raised concerns are addressed as follows.\n\n**About originality of this work is limited.**\n\n1)Reverse filtering is a classical algorithm, which inspired a lot of works. As the research background, the introduction of reverse filtering is provided, to make readers better understand the background of reverse filtering. However, our approach is significantly different from classical reverse filtering. To be specific, (1) the classical reverse filtering can only solve the inverse problems of single image such as denoising, deblurring and super-resolution. Our approach tailors the classical reverse filtering in an alternating iteration manner based on the theortically feasible fixed point equation system for multispectral image fusion. As mentioned in our paper, with such theoretical support, the proposed algorithm can also be extended to other image fusion tasks that involve multiple images. (2), the classical reverse filtering needs to select a suitable and fixed filter function, such as adaptive manifold filter, rolling guidance filter, wlsFilter and so on. For this problem, we introduced the multi-scale Gaussian kernels to approximate arbitrary functions and combine them into deep networks. By doing so, the data-driven deep neural networks can help our model to obtain an appropriate function rather than a fixed and manually defined one, improving the model’s generalization and applicability. \n\n2)In addition, our fusion network is quite different from [63]. (1), the model solving processes between our network and [63] are quite different. [63] employs the gradient projection method to solve their assumptions with penalized optimization. The penalty term is approximated by a proximal operator which is set empirically without constraints. The whole process is constrained in the following steps. At each iteration, it is necessary to perform down-sampling and blurring to obtain the residual map. And then the residual map is added back to the H by inverse down-sampling approximate operation. In comparison, in our approach, there are no penalized priors in the solution process of the fixed-point equation system, and we do not need to design various approximation operators. (2), as both networks are interpretable, we can see that the interpretation represented by the various parts of the two networks is also different. For example, the convolutional operators in the MS Block [63] represent the down-sampling matrix, circular convolution matrix, transpose matrix approximation operator and proximal operator corresponding to penalty. However, there is only a multi-scale Gaussian convolution module in our model that represents the low-passing filter.\n\n**About Clarity.**\n\n1)As shown in Figure 1, network g(•) and network f(•) have the same structure that is based on the multi-scale Gaussian convolution module. The multi-scale Gaussian convolution module consist of a series of Group Convolutions which are already widely used in previous works [*1, *2]. We use Gaussian kernels to initialize the kernels in Group Convolutions. The code in PyTorch is implemented as ```F.conv2d(x, Gaussian_kernels, padding, groups=input_channels)```. The sizes of Gaussian kernels are different, so there are different Group Convolutions. The outputs of different Group Convolutions are added, and the combined coefficients are learnable. \n\n2)Take the work we mentioned in the related work as an example, the CSC model [*3] is based on a strong assumption that there are common and private features between PAN and MS that can be represented by the dictionary. The two types of features can be expressed independently is the pre-defined exact prior in the CSC model. In fact, the two types of features cannot be completely separated. Solving such ideal assumptions may cause system model error. Similarly, the reviewer mentions [63] establishes a pre-defined image generation process as priors: P=SH，L=DKH. Based on these priors, the model needs to be obtained transpose DK during the solution process. But the DK and transpose DK cannot get a strict correspondence in the process of optimization. In contrast, our approach does not explicitly establish these priors that avoids the dependency on pre-defined exact priors. Additionally, our approach does not need to involve the calculation of transpose DK or the pseudo inverse DK in the process of solving the fixed-point equation system to obtain HRMS. \n\n[*1] ImageNet classification with deep convolutional neural networks, Communications of the ACM, pp. 84-90, 2017.\n\n[*2] \"ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices,\" IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018.\n\n[*3] \"PanCSC-Net: A Model-Driven Deep Unfolding Method for Pansharpening,\" in IEEE Transactions on Geoscience and Remote Sensing, 2022. ", " **About the Quality.**\n\n1)Sorry for our carelessness. When transcribing the data to Table 2, I inverted the last two digits of the data (The 0.8251 should have been 0.8215.) . We will correct this in a revised version. The proposed method still achieves the best result in two metrics in bold. In addition, according to the calculation formula of QNR and the relationship among QNR, Ds and D_lamda [*1], we can tell that the QNR of MSDCNN should not have such a high value (0.8251). \n\n2)In the visualization results of the Brovey method in Figure 3, there is obvious spectral distortion, which is because the CS-based methods replace the separated spatial component with the PAN image. Therefore, the results of Brovey look more like the PAN image in spatial texture. However, such spectral distortion is unacceptable in this task. In general, our method achieves better performance than the Brovey methods. \n\n[*1] Multispectral and panchromatic data fusion assessment without reference. Photogrammetric Engineering & Remote Sensing, 74(2):193–200, 2008.\n\n**About the parameter numbers and inference time.**\n\nThe floating-point operations (FLOPs) and the number of parameters of the compared models are provided in the following table:\n\n| Methods | PNN | PANNet | MSDCNN | SRPPNN | GPPNN | Ours |\n| :-----: | :----: | :----: | :----: | :----: | :----: | :----: |\n| Flops | 1.13 | 1.12 | 3.92 | 21.11 | 1.40 | 2.58 |\n| #Params | 0.69 | 0.69 | 2.39 | 17.11 | 1.12 | 1.66 |\n\nAs can be seen, PNN and PANNet have the fewest FLOPs and parameters, but the performance is the worst. SRPPNN exhibits large increases in the number of parameters and FLOPs as the number of convolutional layers and the complexity of the network design rise. Notably, it achieves the second highest performance at the expense of massive model computation and storage. Additionally, the most comparable solution to ours, GPPNN, is organized around the model-based unrolling principle and has comparable model parameters and flops reductions but inferior performance. In summary, our network achieves a favorable trade-off between calculation, storage, and model performance compared with other methods.", " We appreciate the positive and constructive comments, including interesting ideas, a new method, a well-designed module with sufficient theoretical analysis, and convincing quantitative and qualitative experiments. The raised concerns are addressed as follows.\n\n** About the structure loss function.**\n\nThank you for the insightful question. We have already conducted some experiments to explore how to design the loss function for the multispectral image fusion problem at the very beginning of the research. The comparison experiment mentioned by the reviewer also has been done before. For the story flow of the paper, we did not provide these experiments in the paper. As suggested, we provide the experimental results in the table below, where the configurations (I) and (II) are the loss Ls using structural similarity loss and L2 loss, respectively.\n\n| Config | PSNR↑ | SSIM↑ | SAM↓ | ERGAS↓ |\n| :-----: | :----: | :----: | :----: | :----: |\n| (l) | 41.7587 | 0.9691 | 0.0229 | 0.9540 |\n| (ll) | 41.7913 | 0.9677 | 0.0234 | 0.9569 |\n\nAs presented in this table, if the loss function Ls uses the same L2 loss function as the reconstruction loss, the performance in terms of the PSNR metric will be improved, but the other metrics (such as SSIM) will be decreased slightly. Based on the comprehensive consideration, we choose to use the structure loss Ls based on the structural similarity. In addition, we found that the best results could be obtained when both structure loss and L2 loss are used. However, in this case, the hyperparameter needs to be carefully adjusted. Hence, we did not adopt such a combination strategy.\n\n** About supervision at each alternate iteration output.**\n\nIn the previous works[*1-*3], the loss function of the training process is usually supervised at the output of an unrolling-based deep network. To make a fair comparison, we did not add the supervision at each alternate iteration output. To answer the reviewer’s question, we carried out the experiments following the same strategy of the unrolling-based work[*4], in which each alternate iteration output is supervised with losses. The experimental results on the WordView-II dataset are presented in the following table.\n\n| Config | PSNR↑ | SSIM↑ | SAM↓ | ERGAS↓ |\n| :-----: | :----: | :----: | :----: | :----: |\n| (l) | 41.7587 | 0.9691 | 0.0229 | 0.9540 |\n| (ll) | 41.7843 | 0.9698 | 0.0228 | 0.9523 |\n\nConfiguration (I) is the original model configuration while Configuration (II) represents that the loss is supervised at the output of each alternate Iteration. As the table shows, the losses are supervised at the output of each alternate iteration, giving the model a performance boost.\n\n[*1] Denoising prior driven deep neural network for image restoration. IEEE transactions on pattern analysis and machine intelligence, 41(10):2305–2318, 2018.\n\n[*2] Pancsc-net: A model-driven deep unfolding method for pansharpening. IEEE Transactions on Geoscience and Remote Sensing, pages 1–13, 2021.\n\n[*3] Deep gradient projection networks for pan-sharpening. In IEEE Conference on Computer Vision and Pattern Recognition, pages 1366–1375, June 2021.\n\n[*4] Memory-augmented deep unfolding network for com409 pressive sensing. In ACM International Conference on Multimedia (ACM MM), 2021.\n\n** About the number of iterations K.**\n\nObserving the results from Table 6 of the main paper, the model’s performance has improved considerably as the number of stages increases until reaching 5. When increasing the number K, there is still a slight increase in the performance in terms of some metrics (such as PSNR). Due to limited time, we only added one experiment (that is, K=8), and present the experimental results in the table below:\n\n| K | 5 | 6 | 7 | 8 |\n| :-----: | :----: | :----: | :----: | :----: |\n| PSNR↑ | 41.7587 | 41.7614 | 41.7603 | 41.6671 |\n| SSIM↑ | 0.9691 | 0.9690 | 0.9688 | 0.9680 |\n\nAs shown in this table, the results show that a descending trend, which may be caused by the difficulty of gradient propagation. Therefore, we set K to 5 as default to balance the performance and computational complexity. \n\n** About the K used in GPPNN.**\n\nIn the work [*3], the authors demonstrate that the GPPNN model can achieve the best performance when the value of K is set to 8. Therefore, in our comparison experiments, the GPPNN model is also set with K=8. To ensure a fair comparison of the two unrolling models, we use the best parameter settings of each model separately, instead of using the same value of K. Specifically, for the GPPNN model, the K is set to 8, and our model adopts K=5.\n\n** About the parameters for initializing the Gaussian kernel.**\n\nIn our implementation, the parameters of the initialized Gaussian kernel vary with the sizes of the kernel. The sigma of the Gaussian function is set to ks/4, where ks denotes the kernel size. We will add the details of the parameters for initializing the Gaussian kernel in the revised version.", " This paper proposes an alternating reverse filtering network for multi-spectral image fusion. Motivated by classical reverse filtering, the authors develop an unrolling network based on alternating fixed-point iterations and the learnable multi-scale Gaussian kernel module, which is interpretable. Unlike existing model-driven methods, the proposed iterative network avoids the dependency on pre-defined exact priors and its convergence can be guaranteed theoretically. In addition, this paper introduces a new perspective to solving the image fusion problems. Extensive experiments on diverse scenes to thoroughly verify the performance of the proposed method. Strengths:\n1. The authors innovatively propose a new multi-spectral image fusion method without requiring well-designed priors. The exploration of tailoring classic methods for multi-spectral image fusion and combining them with deep networks is worth trying and encouraging.\n2. In the image fusion community, the idea that formulating pan-sharpening as an alternately iterative reverse filtering process is interesting. Other researchers could utilize it for further exploration in the field of image fusion.\n3. The learnable multi-scale Gaussian kernel module is well designed and the convergence of the iterative process is sufficiently supported by theoretical analysis. \n4. Quantitative and qualitative results clearly verify the effectiveness and scalability of the proposed method.\n\nWeaknesses:\n1. More ablation results about the loss functions and iterations should be provided. Please refer to the detailed Questions part.\n2. The parameters such as sigma for initializing the Gaussian kernel should be given in line 239. 1. The structure loss $L_s$ is based on structural similarity, what will happen if loss function $L_s$ uses the L2 loss function?\n2. If each alternate iteration output is supervised with losses, would it be better?\n3. In the ablation study about the number of iterations K, why does the performance seem to decrease slightly when K reaches 7 compared with K=5? What happens to the model's performance in the case of the larger K? \n4. As far as I know, the GPPNN network compared in the manuscript is also based on an unrolling method. What is the K used in GPPNN here? If the settings of K are different, how to ensure fair comparisons of the two unrolling methods?\n5. As mentioned in the Weaknesses, the authors are suggested to provide specific parameters for initializing the Gaussian kernel. The limitations and potential negative social impact of their work have been addressed.", " The authors propose an alternating reverse filtering network for pan-sharpening. Specifically, a learnable multi-scale Gaussian kernel module is designed to ensure the convergence of the iterative process. The experiments on diverse scenes show that the proposed network achieves better results compared to other pan-sharpening methods. Strength:\nThe paper is well-written. The experiments show that the method can perform well in terms of quantitative analysis and qualitative comparison.\n\nWeakness:\n1. Originality\nThe originality of this work is limited. The reverse filtering is derived from [23] and the fusion network is derived from [63]. The description in 3.2, 3.3, and 3.4 sections looks quite similar to [23]. \n2. Clarity\n-The multi-scale Gaussian convolution is a group of convolutional layers initialized by 2D Gaussian kernels, but the detailed architecture of these layers is missing. What are the exact architectures of g and f?\n-The contribution states that ‘In contrast to existing model-driven methods, our iterative network can obtain HR MS without the need for pre-defined exact priors or assumptions’. It is confusing and more explanations are needed. What does the pre-defined exact prior mean in existing model-driven methods? How does the proposed method obtain HR MS without the need for pre-defined exact prior, compared to prior methods? \n3. Quality\n-In Table2, the MSDCNN achieves 0.8251 in QNR and the result of proposed method is 0.8236. However, the result 0.8236 is in bold instead of 0.8251. The proposed method only achieves the best result in one metric.\n-Observed from Figure 3, the Brovey method achieves better fusion results in spatial texture compared to proposed method.\n How about the parameter numbers and inference time for the proposed network and competing networks? Yes", " The manuscript first formulate the pan-sharpening problem as a reverse filtering process and propose an alternating reverse filtering network (ARFNet) to solve it. Besides, the authors develop multi-scale Gaussian convolution modules to obtain better filtering effect. Experimental results on both simulated and real-world scenes show that the proposed ARFNet outperforms other methods. Strengths: \n1.\tThis manuscript combines the deep unrolling model and the reverse filter process, and proposes a novel alternating update deep convolution network for pan-sharpening task.\n2.\tExperimental results show that this manuscript set up some new state-of-the-art results in both simulated and real-scene datasets.\n3.\tThe writing is clear and easy to understand.\nWeakness:\n1.\tThe reverse filter method has been already applied in super-resolution, deconvolution in [1], the Gaussian filter and its convergence condition has also been analyzed. Overall, the novelty is limited.\n 1.\tAs stated in [1], the optimal iteration number is different for variant filters and needs to be set empirically. Is the iteration number set equally in the ablation study of different initialization methods? \n\n2.\tThe learned kernels are close to the initialized Gaussian kernels as stated in Line 241, can the learned kernels gain large performance improvement compared with the initialized ones? \n\n3.\tThe authors cited the recent method[2], but not compared the experimental results with it.\n\n4.\tHow about the computation cost and efficiency compared with other methods?\n\n5.\tIt’s better to include related source citation for the definition, the theorem and reverse filtering formulation.\n\n6.\tPlease check the subtraction and addition symbols in Fig. 1, they are a bit confusing.\n\n[1] Xin Tao, Chao Zhou, Xiaoyong Shen, Jue Wang, and Jiaya Jia. Zero-order reverse filtering. In 2017 IEEE International Conference on Computer Vision (ICCV), pages 222–230, 2017.\n[2] Man Zhou, Xueyang Fu, Jie Huang, Feng Zhao, Aiping Liu, and Rujing Wang. Effective pan-sharpening with transformer and invertible neural network. IEEE Transactions on Geoscience and Remote Sensing, 60:1–15, 2022.\n There is no potential negative societal impact mentioned. Considering the paired dataset is expensive to obtain, the authors could also explore methods in unsupervised manner." ]

[ -1, -1, -1, -1, -1, 7, 4, 5 ]

[ -1, -1, -1, -1, -1, 4, 5, 4 ]

[ "VipxkskhMt7", "9icFk68Lfdh", "yNtiSijn2Fr", "yNtiSijn2Fr", "cbl6gaPu18", "nips_2022_hH9ohGbhyv", "nips_2022_hH9ohGbhyv", "nips_2022_hH9ohGbhyv" ]

[ "b9XM4mNTjP1", "i2wcOzaE5IL", "Zrx-TsL8PL1", "O1dYLZVUEOC", "gtP4QqVQZuh", "6cmx0ukY_rM", "5jE4Hgt8dZT", "Br-T4-9FgGU", "i1LujlxnxhI", "7B_mEA__h7L", "mHIQkinxLeT", "9K24YaJZe0u", "gqZk_jLYlzh", "6IXpA48XML5", "UvCMz6rsSMg", "IvlOaJMq0WH", "5tTteeERxQN", "ytB6xUGp7f6O", "nlwUP-QFiSv", "4x35Ky8_7eI", "009daQaPBk", "2ggTWRWEulj", "5jCPk6pD-3n", "QzV_YTyqiHV" ]

[ "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " My recommendations to the authors are:\n1) Make clear up front about the sources of error in the batch acquisition function: the potential of error from the lower bound (this error relative to true batch acquisition function seems possibly quite large), MC error and submodularity error (the latter two really only apply to approximating the lower bound). \n2) Draw a clearer boundary between the previous work and the new contributions. Currently, a careful read is required to distinguish between the two in the manuscript's current form.\n3) Move the weighted hypervolume indicator to the appendix or include d_GHV results in the main text. Currently, the weighted hypervolume discussion seems out of place.\n4) I second the AC that more comprehensive noise and batch experiments are warranted.", " Thank you for your detailed answer to my questions.\nMy concern was whether the assumption that Y is a finite set affect the practical performances, but I was convinced that experiments have already confirmed that this is not the case in practice.\nAfter reconsidering the comments I have received, together with the comments of the other reviewers, I would like to increase the score by one.", " Thank you for your reply. We will further clarify the difference between the single-objective and multi-objective problem in the paper. As pointed out by the reviewer, we use the Pareto partial ordering in the multi-objective setting and the standard total ordering in the single-objective setting. Computationally, the main difference occurs when computing the region of integration. Specifically, in the single-objective setting, the box-decomposition of the dominated region (Step 4 of Alg 1) is (-infty, y*], where y* is the maximum. ", " Thank you for the replies. \n\n- R1 (batch acquisition function): The lower bound batch acquisition function and its approximation are principled acquisition functions because they can be written as determinantal point processes (DPPs) (Kulesza et al 2012). This property was derived and used in the proof of submodularity. As discussed in the BO literature (references below), batch acquisition functions based on DPPs are powerful because they can promote diverse batches in high-quality regions. The trade-off between diversity and quality (Section 3.1 in Kulesza et al 2012) is evident in the form of the DPP kernel, Km_{i,j} = q_i q_j A_{i, j} (line 821), where q_i = exp(zeta_i/M) can be interpreted as the quality of item i, whilst A_{i,j} corresponds to a notion of similiarity. The Monte Carlo error arises in estimating the expectation in zeta_i (equation 31) and it contributes only to the relative quality assigned to each point in the batch. The optimal batch for the approximation might differ slightly due to the error present in the quality term, but the diversity of the batch will still be high because of the matrix A. The sequential greedy optimization of this acquisition function is arguably necessary because maximizing the original expression is known to be NP-hard (Ko et al. 1995).\n\n - Ko et al. (1995) - An exact algorithm for maximum entropy sampling.\n\n - Contal et al. (2013) - Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration\n\n - Kathuria et al. (2016) - Batched Gaussian Process Bandit Optimization via Determinantal Point Processes\n\n - Wang et al. (2017) - Batched High-dimensional Bayesian Optimization via Structural Kernel Learning\n\n- R2 (more experiments): We are conducting more experiments similar to the ones listed in order to demonstrate the performance trade-off with different amount of noise and batch sizes. As the wall-time plots might suggest, our ability to generate these results within the rebuttal period are limited.", " Hi authors,\n\nQtD3 and WzLK raise some important points with respect to statistical significance of the results with respect to alternative methods. Your work is notable in its extensive evaluation of high-quality implementations of entropy-based methods for MOBO. However, some of the evaluation is less transparent due to seemingly arbitrary choices of noise and parallaelism. Plots that are devised to more directly quantify how well the AFs can handle increasingly higher levels of parallelism or noise are important for understanding the tradeoffs between different methods. For example, in the qNEHVI paper, the authors consider final log HV regret as a function of batch size (Fig 4) and noise (Fig 14). Something similar could be helpful here. It is not necessary for JES (or the other ES) methods to strictly dominate any other methods, but it is important to investigate and clearly state when there are and are not practically significant differences between methods. How do you plan to address these concerns?", " Thanks for the detailed response from the authors! There seems to be some work needed to be done for the comparison and making a more compelling case for this method, so I am sticking with the score.", " Thank you for the detailed response. \n\nMost of my concerns were addressed, especially from a presentation perspective. \n\nThe parts that I still disagree with/were not addressed are the following: \n\n* The acronyms of different algorithm names would not be problematic in the general case; however, in this specific case, PES and MES actually refer to two famous acquisition functions for single objective optimization, so I still think this should be changed across the paper. Adding two letters for each acronym will not complicate anything and will serve the context. This is especially true for this paper, where there are plots involving single objective experiments. \n\n* DGEMO was compared to qNEHVI only in the noisy setting while it was not built to support the noisy setting. This means that it is not expected to perform well. This does not mean that it will not outperform other algorithms in the non-noisy setting. DGEMO is a very strong baseline, recent and relevant. I believe it is very common to compare methods that are not necessarily built with the same library, most papers do not reimplement other baselines from scratch. \n\n > The algorithm is valid for both the single-objective and multi-objective setting as can be a random vector-valued function with M components. This is registered at the beginning of Section 2.\n\n* I totally disagree with this statement. The inequality relationship in the case of a single objective and multi-objective are totally different. This has been already shown and discussed in the extension of MES to MESMO and PFES and also PES to PESMO. So assuming that this is straightforward is concerning. \n", " Thanks to the authors for the thorough response!\n\n> W1 (in sample results): \n\n Thanks for adding these\n\n> W2 (error bars):\n\nThanks for adding these. Unfortunately, it shows that in general on the test problems considered, JES is not statistically significantly better than other methods---even with 100 replicates and on a log scale. Furthermore, since not clearly faster than alternative approaches that are competitive w.r.t. to hypervolume, it is not clear why one should use JES\n\n> W3 (computation cost): Our approaches, MES-LB and JES-LB results in competitive wall times with other competing methods even without using parallelization, which could improve the run time further.\n\nIt is worth noting that NEHVI for example is much faster on a GPU than a CPU (and measurements in this paper are made on a single CPU_, so while runtime of MES-LB/JES-LB might be improved by exploiting parallelism, the same is true of alternative approaches.\n\n> W4 (many approximations):\n\nThanks for reducing the number of methods in the plots. They are much clearer.\n\n> W5 (weighting the hypervolume): \n\nI agree that alternative evaluation metrics are interesting to consider, but including such a discussion in the main text strikes me as out of place---especially considering that no alternative metric is used for evaluation in the main text.\n\n> Q4 (independent models): \n\nMakes sense. Figure 3 seems out of place of place to me though because it is never even discussed in the paper\n\n> Q5 (batch lower bound): … We agree that the estimation error and role of batch size should be investigated further. \n\n Thanks for confirming this. Unfortunately, this reaffirms my concerns about the critical potential failure modes of the batch approximation.\n\nI have increased the confidence of my review, but I will leave my score as is. The lack of statistically significant improvement in any test problem *even on a log scale with 100 replicates* makes it clear that the method does not offer a significant improvement in optimization performance. Since it isn't faster than alternatives, the question is when should this method be used. Furthermore, it is surprising to jump to the multi-objective setting with JES rather than the single objective setting---\"In preliminary investigations to single-objective optimization, we noticed little difference between the many different acquisition functions for single-objective BO.\"---given that there are not significant differences in the multi-objective setting.\n\nThe response to my critique about the suboptimal batch formulation confirmed my concern that the estimation error can be quite large and is not captured in their sub-modularity argument, which makes the batch formulation and sub-modularity argument not very confidence inspiring.", " Thanks for the response and for making the editorial changes and adding the variance to the plots. Unfortunately, in a lot of these examples it's hard to discern the performance of at least some of the methods given the relatively high variance. It would be good to consider evaluations that make the performance differences more clear. I never considered the performance of the method a particularly compelling aspect of the paper, but the paper does have other sufficiently many other strengths and so I am sticking with my score. ", " - It unavoidable that numerically the Pareto frontier approximation will be be constructed on a finite set of points. This is a standard assumption in the literature and we believe is also sensible given the interest here is on approximations with finite number of observations. In addition, in Appendix J.3 our sensitivity analysis suggests that there is no visible improvement as the number of points approximating the Pareto frontier increase beyond a moderate number of points (around 10 points for ZDT2 with 2 objectives on 6 dimensions).\n\n- Regarding computational cost increase w.r.t number of points, this increases moderately when computations are performed in sequence on one processor (Figure 15). Notably, some of these calculations can benefit from parallelization in order to get a speed-up.", " - Q5 (Reference Konakovic Lukovic et al. 2020): Many thanks for pointing this out, we have now added this reference. All the algorithms used in our comparison were implemented using the same set of python libraries for both the modelling and acquisition. The DGEMO implementation uses different dependencies, which we believe will result in an unfair comparison. Nevertheless, a recent benchmark by Daulton et al (2021) showed that DGEMO has comparable or weaker performance on the standard hypervolume compared to qNEHVI and qNParEGO, which we did compare with.\n\n- Q6 (error bars): We have now restructured the plots and added error bars everywhere.\n\n- Q7 (performance): In the many of the test cases our method was among the best performers in terms of the standard hypervolume. The few cases where this did not occur (e.g. Penicillin example) was when specific parts of the Pareto frontier were isolated. The improvements the method offers are indeed marginal, but this is over many methods and on a variety of problems that had received significant attention in the past.\n\n- Q8 (Penicillin): The Penicillin objective function is obtained by solving a set of differential equations using a discretization scheme. As a result, the change in the hypervolume of the proposed points varies in a noisy manner.\n\n- Q9 (single-objective plots): Figures 1, 6-10 are there just to aid in terms of intuition, so we opted for the simple choice of single objective. We agree this intuition should be used with caution in the multi-objective case, but we still believe that the plots can be useful to illustrate some differences between MES, PES, and JES. \n\n- Q10 (several metrics): We completely agree and this was our motivation for including additional visualizations of the Pareto front and performance results over the different regions of the objective space (Appendix J5 and J6).\n\nTypos:\n\nAll typos have been corrected, many thanks for spotting.", " - W1 (some ad hoc design choices): This is indeed an ad hoc approximation and is meant to provide more intuition. This should have been better clarified in the text to avoid any confusion. We moved this result to Appendix D and added a further discussion, which we will briefly summarise here. In the zero observation noise setting, the JES-0 acquisition function can be written as $\\mathbb{E}[-\\log(W)]$ + other terms, where as a reminder $W = p(y \\preceq Y^* | D_{n*})$ i.e. the probability that y is dominated by the sample Pareto front Y* conditioned on the augmented data set. The expectation here is over the distribution of optimal inputs and outputs. The first term $\\mathbb{E}[-\\log(W)]$ can be interpreted as the exploitation term because it computes the expectation of the negative log-probability of being dominated by the front. The other terms can be interpreted as an exploration term. The ad hoc correction can be viewed as a way to maintain the right amount of exploration even in the presence of noise. This correction demonstrates decent numerical results that are in-line with the other approximations. The contour plots in Appendix G demonstrates that this approximation is close for a single-objective example where the noise in this experiments is set to around 5\\%.\n\n- W2 (reference to prior work): This is true, our analytical computations makes use and extends the results in these works. We have now further emphasized this in the main text and have also included mention in the contributions section.\n\n- W3 (presentation): Based on feedback from the reviewer we have updated the proofs with background notation and numbering where necessary. We have included the statement of the result before the proofs to improve the reader experience. We also used color-coded references and links throughout the document for ease of navigation.\n\n- W4 (experiments): Please see below. \n\n- W5 (familiarity with information-theoretic acquisitions): We agree that there is limited discussion on information theoretic acquisition functions, but at the same time this is a very well studied topic in Machine Learning as well as traditional Statistics and experimental design. For the notation, we tried to compromise between being close to previous works, readability and smooth exposition. For the algorithm we present standard mathematical pseudo-code and will make Python code available. \n\n- W6 (acronyms use): We agree that we deviated from using PESMO, MESMO etc and opted for notation such as PES, MES for simplicity. We have now added a mention at the end of section 2 to alert the reader on this. \n\nApproximations \n\n- Q1 (dealing with 0 variance assumptions): This has been discussed in W1 above.\n\nWriting and presentation\n\n- Q1-4: We have followed most suggestions from the reviewer - thanks for the feedback. In the Appendix we have added the statements proposition and lemmas before the proof and repeated the necessary equations with numbers. \n\n- Q5 ($f(x) \\preceq Y^*$ notation): We have included a definition on the partial ordering relation on sets in the paragraph on Pareto domination in Section 2.\n\n- Q6 (pseudo-code): The algorithm is valid for both the single-objective and multi-objective setting as $f$ can be a random vector-valued function with M components. This is registered at the beginning of Section 2.\n\nExperiments\n\n- Q1 (batch sizes): This is a fair point. We note that the batch case was meant as an extension and had we had more time would have tested additional batch sizes.\n\n- Q2 (experiments): We believe we have a variety of cases with different dimensions and number of objective. More synthetic examples would indeed be useful but we preferred to focus more on standard benchmarks and more challenging problems.\n\n- Q3 (noise choice for different examples): The choice was based on what noise level we felt could potentially be more realistic in practice based on the context of the application. In numerical work not presented we did experiment with different noise levels and the results were rather similar.\n\n- Q4 (on Figure 13): The point here is all methods perform very similarly to the hypervolume criterion even when the number of Monte Carlo samples S varies and believe both ways of plotting will achieve this. Here we were more interested to check how each method performs with S separately. Since all plots are in the same scale so we believe that comparisons between methods are also possible here but differences are marginal. ", " - Q5 (batch lower bound): In general, the optimizer of a lower bound might not be an optimizer of the original quantity. Batch size experiments can be very expensive and the lower bound approximations are necessary from a practical point of view. We agree that the estimation error and role of batch size should be investigated further. This is part of current work that look into this in more detail and use also ideas from stochastic control and dynamic programming. \n\n- Q6 (single-objective): We found the vector optimization setting to be more interesting and challenging because we also have to consider the multi-objective trade-off. In preliminary investigations to single-objective optimization, we noticed little difference between the many different acquisition functions for single-objective BO. The acquisition functions mainly differ in how they balance the exploration-exploitation trade-off. This was the motivation of the contour plots in Appendix H.\n\n- Q7 (invariance): In addition to introducing JES a general aim in the paper is to highlight how information theoretic criteria can be improved and what benefits they provide compared to other approaches. As such we believe it is worth including here.\n\n- Q10a (nadir points): This point is correct and we clarified this in the revised main text. The reference point in the evaluation for the experiments did indeed use a reference point that is slightly worse than the nadir for the whole function (not just the Pareto front).\n\n- Q10b (error bars): Thank you for the suggestion, we have now restructured the plots to focus solely on the lower bound estimate and have modified the figures to include error bars.\n\n- Q11 (noiseless): Noiseless results were similar to what is presented in the paper and hence we did not include them.\n\n- Q12 (incorporating preferences): We would not go as far as suggesting that this is drawback for entropy based methods (or any method), simply because not all methods are designed to do this. If this is of interest all methods should be modified and extended for such a scenario. For example, to extend entropy based methods we could redefine the optimal front as one which is Pareto optimal and dominates a specified reference point. Computationally, this modification will result in different bounds for the box-decomposition for MES and JES.\n\n- Q13 (warm start): We have not tried this form of initialisation near the Pareto frontier. This is an interesting suggestion and we believe this could improve the efficiency of all methods. Better understanding how to effectively solve the inner optimization problem in BO is an interesting line of inquiry which we leave for future work. Some interesting references we are aware of include Gramacy et al. (2021) and Grosnit et al. (2021) - Are we Forgetting about Compositional Optimisers in Bayesian Optimisation.\n\nMinor points: \n\nWe agree with most points and have taken onboard the reviewer suggestions. Regarding input or output dimension, the answer is both are challenging for random scalarization. In the work by Paria et al (2020), they proved a cumulative Bayes regret for an acquisition strategy based random scalarization, which depended on both the input dimension and number of objectives. We have rephrased accordingly. Regarding gradients as the reviewer hints it is the form the expression rather than analytical tractability per se. We have also rephrased this accordingly. ", " - W1 (in sample results): In the revision, we have included the results for the in-sample experiments in Appendix J.4. We have also included a discussion in the main text. The in-sample results reveal that the information-theoretic algorithms have tendency not to directly select the best performing points and instead opt to query more informative points that have higher uncertainty. This can result in a behaviour where the in-sample performance appears to stagnate, whilst the out-of-sample performance improves. We mention that if directly querying high performing points is useful, taking an epsilon greedy approach where one occasionally picks points by maximizing a greedy criterion might be a useful modification.\n\n- W2 (error bars): We have now restructured all the plots and have included error bars.\n\n- W3 (computation cost): We have been quite thorough about testing the wall times of our different conditional entropy approximations and acquisition functions using a single processor (Appendix J.3 and J.7). Our approaches, MES-LB and JES-LB results in competitive wall times with other competing methods even without using parallelization, which could improve the run time further. \n\n- W4 (many approximations): We have indeed proposed multiple implementations for JES. Our intention was to be methodical and thorough on how JES can be implemented and made more efficient. The main observation is that the JES approximations can perform similarly for the same number of Monte Carlo samples and sampled Pareto optimal points. The best choice can be selected based on wall-times. Our experiments showed the benefit of using the lower bound estimates for both the multi-objective MES and JES when only using CPU computations. Some routines could parallelized for further speed gains. For example, the vector optimization (step 4 in Algorithm 1) was executed serially using a gradient-free optimization method. Potentially this can be solved in parallel using gradient-based optimization such as the one proposed by Liu et al. (2021).\n\n- W5 (weighting the hypervolume): Our impression is that there is over-emphasis in the recent literature on maximization of the hypervolume. This can be misleading in some cases, so the aim of Section 4 and Figure 4 is to highlight this and propose a more complete assessment and comparison. Clearly our intention is to focus more on information theoretic methods (and hence include Prop. 3 on invariance to reparameterization) but we believe that the point of working towards more diverse comparisons is valuable for all methods. Interestingly our probabilistic weighting idea can be viewed as an extension of Zitzler et al (2007), who identified this issue from their early work (Zitzler et al 1998) that first introduced the hypervolume criterion.\n\nAs regards to the overall assessment, we respectfully disagree with a) and b) but understand the reviewer's point of view and thank them for the feedback. Regarding point c) on empirical evaluation, we believe our revisions has addressed this. \n\n- Q1 (constraints): Early numerical results with constraints are encouraging, but more work is needed to report concrete conclusions. \n\n- Q2 (noise levels): In the paper we used different noise levels in the different examples, but in numerical work not presented here we did try different noise levels for each example and noticed fairly similar results.\n\n- Q3a (incremental and references): Input and output entropy are well studied, but until this paper have not been used jointly. We believe is a natural but not straightforward extension. We have now further emphasized the connection with earlier work in the main work. In particular, we have added additional references to Moss et al. (2021) and Suzuki et al. (2020) throughout the paper and especially in the contributions section. Moreover, we have emphasized that Lemma 1 and the box-decomposition strategy are standard results in multi-objective optimization dating back to earlier work by Keane (2012), Couckuyt et al. (2014), Picheny (2015) and Suzuki et al. (2020).\n\n- Q3b (BAX): The BAX acquisition function (Neiswanger et al 2021) is subtly different to the one considered here. The probability density of observations in the BAX paper (Equation 5 in Neiswanger et al 2021) conditions only on the \"execution path\", which in our setting is the augmented data set. In contrast, the probability density of the observations in our work (Equation 6) conditions on both the \"execution path\" and the optimality condition $f(x) \\preceq Y^*$. We have now included this point in the related work section and cited Neiswanger et al (2021).\n\n- Q4 (independent models): We accept the criticism that the different objectives are modelled as independent. The probability density in Figure 3 conditions on the points, data, and the optimality condition. The latter causes the correlations and this can also be seen in the results in Prop. 2.", " - W1 and Q1a (why JES): In general, the best acquisition function is dependent on both the problem and the decision maker's goal. We recommend using JES when the goal is to obtain a good posterior distribution over the optimal points. The experiments indicate that JES is indeed a good choice when that is the goal.\n\n- Q1b (JES vs MES): Our main result concerning the lower bound conditional entropy estimate (Prop. 2) benefits both the MES and JES acquisition function. The cost of JES is indeed slightly greater than the MES because of the conditioning step in Algorithm 1, but in turn leads to a strategy that queries points which are more informative for both the optimal inputs and outputs.\n\n- Q1c (cost performance trade-off): Investigating the cost-performance trade-off in multi-objective Bayesian optimization is certainly an interesting research question that we are also looking in to. As Section 4 suggest, it is unclear how to define performance from the get-go and this choice will naturally have an effect on any analysis we conduct to compare between cost and performance.\n\n\n- Q2 (example): Our initial investigation into this resulted in the contour plots in Appendix H. We observed that JES strikes a different balance on the exploration-exploitation trade-off compared to the PES and MES. For a single-objective problem, where the posterior mean is bi-modal, the JES opts for one mode whilst the PES and MES opts for the other. For this particular set up, the mode that JES picks is marginally better.\n\n- Q3 (motivation): This is a very good suggestion and is something we tried to accomplish as we discussed above. In the end, we opted for Figure 1, which we believe is sufficient as an initial way to motivate the difference between the acquisition functions.\n\n- Q4 (approximation): We observed very little difference when increasing the number of samples in Appendix J.3. Our results indicate that setting the number of Monte Carlo samples moderately to 10 seems to work well. We observed that increasing the number of Pareto optimal points tended to result in an improvement in performance (up to a certain point) at the expense of computational cost, we also set this to 10 as a compromise. Developing theoretical results in order to justify these choices, such as Theorem 4.1 in Takeno et al. (2021), is something we are also looking into.", " - W1 (error bars): We agree that this was an omission from our part, we have now restructured the plots and included error bars in all the figures. We also included some more discussion in the experiments section to guide practitioners.\n\n- W2 (independent models): Regarding independence and GP modelling, this is a valid point and we accept this criticism. Our main focus here was on improving the acquisition and hence chose this standard setting. As the reviewer points out, further work is needed to adapt our methodology as well as other competing methods based on GPs for the correlated case.\n\n- W3 (discussion): We also agree with the reviewer that more details were needed in the experiment section. We have now moved a proposition to the Appendix, which allowed us to augment and improve the discussion of the main results and findings.\n\n- Q1 (scalar utility): Multi-objective optimization algorithms are usually assessed using performance metrics defined over the space of subsets of vectors. One acquisition strategy is to directly optimize the performance metric directly e.g. the hypervolume. An algorithm that does this will likely perform well under this specific performance metric, but may not appear to do well under another performance metric, which might assess other features of the Pareto front. We believe that working to improve the quality of a posterior distribution is more convenient and sidesteps these issues. We also tried to include different measures of performance to emphasize this. We agree that this statement was confusing and have now rephrased this accordingly.\n\n- Q2 (probabilistic perspective): We agree and have removed the phrase.\n\n- Q3 (cancellation): This is a fair point. It is correct the cancellation only occurs when computing the MES-0 estimate. As discussed in another review, this is an ad hoc modification in order to maintain the exploration-exploitation trade-off. We have now relegated this result and discussion to the Appendix D as it caused confusion and drew attention away from the main results.\n\n- Q4 (property of the model): We meant to say any function of the model f, for example the argmax(f) or max(f) in the case of PES and MES. We have now rephrased this.\n\nTypos:\n\nThanks for spotting the typos, they have now been sorted.", " Many thanks for the positive feedback.", " We thank all the reviewers for their comments and the effort to assess our paper. In our revised manuscript, we have addressed the most common and important points:\n\n- We have clarified that the modification to the noiseless conditional entropy estimate was meant as an ad hoc adjustment to account for the amount of exploration when there is observation noise. As this result caused some confusion, we have relegated it to Appendix D in favour of emphasizing our main result in Prop. 2 (previously Prop. 3), which gives a more principled and better performing estimate.\n\n- We have further emphasised the connection to existing work in the main text.\n\n- We have provided error bars in the plots. \n\n- We have added an in-sample standard hypervolume comparison (Appendix J.4) as requested by one of the reviewers.\n\n- We have augmented the discussion of the experiments with additional points raised by the reviewers.\n\n- We have sorted all typos and minor errors.\n\nBelow we provide a point-by-point response to each reviewer separately. ", " In this paper, a Bayesian optimization algorithm using Joint Entropy Search (JES), a new entropy search type acquisition function, is proposed to efficiently estimate the Pareto solution set for multi-objective optimization problems. JES is defined as the mutual information between the pair of optimal solution set and the optimal value set, (X^*, Y^*) and the new query point (x, y). While PES and MES, the main conventional entropy search type acquisition functions, focus only on the marginal distribution of the optimal solution and optimal value, respectively, JES determines the next acquisition point by considering their joint distribution. \n\nJES can be expressed as the difference of two differential entropies as in other entropy search type acquisition functions. For its optimization, the authors proposed a method to approximate the expected value of entropy for the pair (X^*, Y^*) of the optimal solution set and the optimal value set that appears in the second term of the JES acquisition function. Specifically, when there is no observation noise, entropy can be calculated analytically since the argument distribution is a multivariate truncated normal distribution, and when there are observation error, the entropy of the multivariate normal distribution that bounds it from above can be used as an approximation. Specifically, when there is no observation noise, entropy can be calculated analytically since the argument distribution is a multivariate truncated normal distribution. When there are observation errors, a multivariate normal distribution whose 1st and 2nd moments are equivalent to the argument distribution can be used as an approximation. This is because the entropy of latter distribution is bounded above by the entropy of former one.\n\nThe proposed method, the JES acquisition function, is also extended to the batch optimization setting. Specifically, the authors proposed a method in which the entropy of the joint distribution for the batch points is bounded from above by the sum of entropies for each point, and the latter is used to select each point independently.\n\nIn the experiments, the proposed method is compared with existing multiobjective Bayesian optimization methods for different optimization problems with 2-, 3-, and 4-objectives, using the difference of hypervolumes as an evaluation criteria. Strengths\n\n- The proposed new entropy-search type acquisition function, JES, considers the joint distribution of optimal position x^* and optimal value y^*, and is expected to provide more information about the optimal solution than PES, which considers only the former, or MES, which considers only the latter. \n\n- Different computation methods have been proposed for the entropy of the second term in JES, with and without noise. Both are derived in an analytic form, and the advantage is that costly numerical computations can be avoided.\n\n- As a method for obtaining batch points, the joint conditional distribution for a batch is upper bounded by the sum of the conditional distributions for each point, avoiding the intractable computations of the former. With respect to the goodness of this upper bound, the authors show that by showing the submodularity of the acquisition function, an iterative method of sequential acquisition at each point achieves a regret upper bound of e^-1.\n\n- While the hypervolume of the Pareto set (e.g., its expected reduction), which is often used as an acquisition function in multi-objective optimization, is not invariant with respect to monotonic transformations of the output, the proposed method, JES, is shown to be invariant to the same transformation.\n\nWeakness\n\n- The assumption is made in Lemma 1 that the true Pareto optimal value set Y^* is a finite set, which appears to be a strong condition given that in general there are an infinite number of Pareto solutions. \n\n- The computations of the conditional distribution for the Pareto set and the computations for acquiring batch points are each broken down into a computations for each point, which is expected to become a computationally expensive method when the number of elements in the Pareto solution set increases as iteration progresses. - As pointed out in Weakness, the assumption that Y^* is a finite set, as placed in Lemma 1, seems to be a strong one; it seems to be the key lemma for the approximate computation of the JES acquisition function, but is it not an issue?\n\n- As pointed out in weakness, since the proposed method decomposes all computations into point-by-point computations, I think that it needs to be carefully evaluated in terms of computational cost compared to existing methods. Have you done any comparison of actual computational costs? The authors adequately addressed the limitations and potential negative societal impact of their work.", " The paper proposes a new information gain acquisition function for multi-objective Bayesian optimization. The method selects the input that maximizes the joint information gain about both input and output space. The paper provides several approximations of the acquisition function using lower bound and assumptions about the observed variance. The method is extended to batch selection accompanied by a submodularity study. The paper provides an analysis of the sensitivity of the hypervolume performance metric to functions transformations. Strengths:\n+ The paper is technically rich and provides an extensive study of the problem space with several approximations and derivations\n+ The idea of the use of joint information gain is novel and interesting. \n+ The extension to batch setting seems naïve however, the discussion of submodularity of the acquisition function is interesting \n+ The paper provides a thorough cost analysis in terms of analytical complexity and wall clock time of optimization \n\nWeaknesses:\n+ Some design choices made in the approximation are not justified and seem ad hoc, including the cancellation of variance effect in the first approximation and choice of noise in experiments. \n+ Many parts of the derivation in the main paper and the appendix are inspired by [50] and [68]. However, this does not seem to be properly acknowledged in the paper. \n+ The paper has a significant presentation issue. In general, the derivations are very hard to follow, both in the main paper and the appendix. This is not due to the extensive mathematical formulation of the acquisition function but rather to the lack of smoothness in the writing and the assumption that the reader can easily follow all the equations and substitutions. I provide more details in the questions box. \n+ The experimental setup has several weaknesses that I discuss more in detail in the questions and comments box\n+ The writing of the paper assumes the reader is familiar with previous work on Information-theoretic acquisition functions, which is not necessarily true. Several steps of the algorithm are not described thoroughly and have confusing notations.\n+ The paper uses “incorrect” acronyms to refer to previous work. This is problematic because the acronyms used in this paper are usually used to refer to different algorithms in SOO. For example, MES and PES are usually used to refer to a single objective acquisition function. In MO, they are referred to as PESMO and MESMO. The EHVI is usually used to refer to the sequential EHI method. The method discussed in this paper is the recently developed batch approach qEHVI and qNEHVI. \n Approximations\n+ How is the 0 variance assumption made, and what are the consequences of this on the selections made by the acquisition function? Canceling the effect of the predictive variances can lead to more exploitation in the acquisition function. It seems to be a little ad hoc just to add an additional term to cancel the variance effect. The transition is not explained well or justified. \n\nWriting and presentation: suggestions for readability enhancement: \n+ Several equations and inequalities are written in the text without any numbering and then used in the derivation without a referral. \n+ I suggest adding all the equalities/inequalities and definitions of variables used in separately numbered equations. I am aware of the space constraint, but several definitions can fit in one line, and white space reduction can also be used. \n+ Adding the propositions/lemmas written in the main paper near their corresponding proofs in the appendix would make it easier to follow the derivations. The reader won’t need to jump back and forth between the main paper and the appendix. \n+ The connections and substitutions used in the derivations should be detailed, at least in the appendix. \n+ f(x) <= Y* is a notation used repeatedly in the paper. However, the relation between two Pareto fronts is not always quantified as higher or equal and would depend on the tradeoff between several functions. A more rigorous notation should be used. \n+ The confusion between SO and MO surfaces in the names used for algorithms and in the notation used in the paper. For example, in algorithm 1, line 3 can be confused as a single objective sampling or sampling from a single multi-task GP while each of the objectives is sampled separately. \n\nExperiments: \n+ Only batch sizes of 1 and 8 are used. Typically batch BO papers include extensive experiments on different batch sizes\n+ More synthetic experiments can be useful to show the behavior of the algorithm when the number of functions and number of dimensions is varied \n+ The noise choice for each experiment is different. How is this choice made? \n+ Figure 13 does not easily provide the needed information. It would be more informative to plot all the algorithms using the same number of samples in the same figure and have different figures for different numbers of samples \n+ Some relevant and important baselines were not cited or compared to: Diversity-Guided Multi-Objective Bayesian Optimization With Batch Evaluations, Neurips 2020\n+ The standard errors are not plotted. The use of quantiles is unconventional and do not substitute or provide the same interpretation as the error. A light-colored error plot can still be readable.\n+ The performance improvement is minor, and the baselines sometimes work better. \n+ In the Penicillin experiment, the hypervolume progress seems unstable for all algorithms; what is causing the fluctuation, and how is this interpreted? \n+ Figure 1 provides an analysis based on single objective optimization, which does not necessarily hold in the multi-objective case. This figure is not discussed or analyzed anywhere in the text. The same issue applies to Figures 6, 7, and 10. I suggest removing these studies. They are not relevant, and they add to the confusion between SO and MO.\n+ The discussion on the sensitivity of the hypervolume as a metric is insightful. However, it is important to note that it is a common practice to fit the Gaussian processes to normalized data, and therefore the scale issues between the objectives become less problematic. Additionally, several other distance-based metrics overcome some of the weaknesses of HV when comparing equivalent Pareto fronts. Therefore, evaluating the performance using more than one metric is encouraged.\n\nTypos:\n+ Typo in line 186 “because the cost of evaluating”\n+ The structure of the sentence in line 176,177 is incorrect\n The paper discussed some of the work's limitations.", " This work proposes a novel acquisition function JES for multi-objective Bayesian optimization based on the joint entropy of the optimal inputs and outputs. Previously works have studied input and output entropy independently. The work proposes novel entropy approximations—particularly one based on moment-matching, which has been previously used in the single objective setting but not the multi-objective setting. The work extends the proposed JES acquisition function to the batch setting using an additional approximation. In addition, this work analyzes potential for negative pathologies when using the hypervolume indicator for evaluation and proposes an alternative weighted hypervolume evaluation criterion. Although this paper is largely well-written and provides precise detail on the empirical setup and evaluation, the contributions are limited. Multi-objective BO is an important but well-studied space. Hence, the work can, inherently, at best be incremental. Furthermore, entropy-based methods have been studied in multi-objective BO. The contributions of a novel joint input/output entropy acquisition function and a new multi-objective entropy approximation show improvement over previous ES methods, but these are small contributions that leverage well-studied ideas from the literature. Although JES approximations show good empirical performance, the evaluation is limited to evaluating the out-of-sample model predicted Pareto frontier. This evaluation technique favors and is well-suited to information theoretic methods, but as the paper states often time decision-makers would prefer to launch a previously evaluated design (regardless of whether this is observation noise). Therefore, it is not clear that JES approximations outperform alternative approaches such as DGEMO and NEHVI when the decision maker is only interested in choosing a final design at implementation time from the set of previously evaluated designs. Evaluation of the performance using this in-sample Pareto frontier (under the noiseless objectives) would help provide more clarity. Furthermore, the absense of error bars in the empirical evaluation makes it impossible to determine which differences in performance are statistically significant. Moreover, the paper does not propose one single JES approximation to use. There are numerous JES methods and many confusing acronyms, and the empirical evaluation does not obviously indicate a single best JES method (even based on the mean performance, without accounting for uncertainty). In addition, JES is computationally intensive and is slower than even EHVI-based methods---which are known to be computationally demanding.\n\nThe additional contributions of an analysis of the HV indicator and the proposed weighted HV metric are a bit orthogonal to the new JES method and feel out of place with the rest of the paper, which focuses on JES. It seems like the weighted HV metric should be de-emphasized in the main text (specifically, the contributions), since it is not actually used in the main text and it is unclear what distribution is appropriate for sampling scalarization weights. The weighted HV and HV analysis are not JES specific, but is a general comment on multi-objective optimization that is out-of-place with the JES-focus of the paper.\n\nIt is worth noting that code is provided and well-documented. This is particularly notable because PES is known to be difficult to implement and most BO papers leverage an old Spearmint implementation with now unsupported dependencies. A high-quality PES implementation is of value to the community.\n\nOn a whole, a) the contributions are scattered (results on JES, results on ES methods handling monotonic transformations, an analysis of using HV for evaluating multi-objective optimization algorithms), b) the JES-specific contributions are incremental (a new joint entropy and a new application of an approximation techniques from the single objective setting), and c) the empirical evaluation is difficult to interpret (which JES method is best/should be used, what does performance look like if only in-sample---rather than out-of-sample---designs can be used in the Pareto frontier) and lacks measures of statistical significance. * How well does the constrained version work empirically?\n* How robust is the performance to the noise level? \n* The JES approach seems quite incremental. \n * The input entropy and output entropy are well-studied\n * The moment-matching approximation is well-studied in the single objective case [50]\n * The box decomposition-based entropy computation is proposed in [68]\n * Lemma 1 is not novel. It comes directly from [68] and is used in [68] which should be made more prominent\n * The whole JES computation algorithm is an incarnation of BAX with a different acquisition function than PES and a different approximation method.\n* JES does not support modeling correlated outcomes---independent GPs models are assumed to be used. Why then distinguish equations (10) and (11)? Also, Why does Figure 3 show correlation between outcomes? Aren’t the covariances matrices across outcomes for a single point always diagonal under the assumption of the independent GP models?\n* The batch extension follows [50] and is “suboptimal” (L193) and approximates the joint JES across a batch of points with the sum of the independent entropies of each point. Why would the best batch of `q` points not be the same point `q` times using this acquisition function?\n * Also, sequential greedy batch selection is common practice. While the submodularity proof is neat, it applies to 1) approximating true batch JES with sequential greedy or 2) approximating the coarse approximation (sum of independent entropy) of batch JES with sequential greedy. It makes no guarantees about how well the coarse approximation (12) approximates batch JES (or some approximate version of JES without the batch independent entropy approximation (12)). This error seems like it could be quite large.\n * How does JES scale with increasing batch size both in terms of wall time and in terms of optimization performance? It is hard to draw conclusions from q=1 and q=8 alone.\n* Why does this paper focus on multi-objective JES and not a single objective JES?\n* Being invariant to component-wise monotonic transformations of the objectives is a nice property of entropy-based methods (prop 4). But this is not specific to JES, and therefore seems a bit odd to include.\n* Page 7 footnote: “The reference point is typically chosen to be the nadir…”. Typically the reference point is typically chosen to be *slightly worse* than the nadir of the *Pareto frontier*, *not the entire objective space* as stated in the footnote. Using the nadir of entire objective space (as described) would often be a poor choice of reference point because it would be very far from the pareto frontier. Was this strategy used for evaluation purposes (hypervolume computation) in the experiments? Also using the nadir of the Pareto frontier directly would be a poor choice because it gives zero hypervolume to the end points, which is why the reference point is typically chosen to be slightly worse than the nadir (see Ishibuchi et al., 2011).\n * L954/983: using a nadir over all observed points as the reference point is also is likely a poor choice for solving the MOOP problem for recommendation and for use in NEHVI and EHVI. A point that is slightly worse than the nadir point over the pareto frontier across the observed designs is likely a much better choice because it 1) will ensure that it is not very far from the current pareto frontier, which could be the case with using the nadir across all observed points and 2) gives non-zero hypervolume to the endpoints of the pareto frontier and beyond the endpoints, which is likely very important for discovering designs outside of the currently observed Pareto frontier with EHVI/NEHVI. \n * It is very hard to distinguish the trend lines in Figure 5. I would recommend focusing on one JES method. This would also help the reader understand which JES method is best and should be used. Currently, this is very hard to parse. The colors for TSEMO and LB-JES-0 are very similar.\n * Also, can you provide error bars please? Currently, it is not clear which differences in performance are statistically significant\n* How does the performance look on noiseless problems?\n* L288: Regarding being able to specify a preferred region (via the reference point) with hypervolume-based methods, this seems like a positive. It seems like a major drawback of entropy-based methods to only be able to identify the entire Pareto frontier and not just an area of interest.\n* For problems such as the ZDT family, the optimal designs lie in a small region of design space. This means that the heuristic for selecting the initial points for gradient-based acquisition optimization is particularly important for improvement-based acquisition functions since they can be 0 over a large portion of the design space. In L903, the paper says that initial points were not sampled near the Pareto frontier, which would have led to faster convergence for entropy-methods. I think it would be even more important for improvement-based methods. Can you provide empirical results were the initialization heuristic does sample points near the current best (pareto optimal) for acquisition optimization?\n\nMinor comments\n\nL24: “trade-off” -> “trade-offs”\n\nL31: “might suffer when the scale of the objectives is unknown apriori”. A common approach is simply to rescale the objectives to the unit cube based on the observed outcomes\n\nL32: “or when the input space is high-dimensional”. Wouldn’t high-dimensional output spaces be more problematic for random scalarizations? \n\nL50: “analytically available, which enables the use of gradient-based optimization”. It is not clear here why analytic availability implies differentiable\n\nL73: should be \\subseteq instead of \\subset\n\nL196: These acronyms are very confusing\n\nL298: it would be good to clarify that “multi-objective optimization” refers to the fact that computing JES requires solving a set of multi-objective optimization problems of optimizing GP function samples.\n Some limitations are discussed in the last section, but further discussion around when to use which method would be useful. Additionally, characterizing drawbacks of the approach and sensitivity of the approach and entropy-based methods more generally to model-specification would be useful. Negative societal impacts are not discussed.", " A new acquisition function for Bayesian Optimization (JES) is proposed in this paper. It considers the joint information gain for the optimal set of X and Y. Several analytical approximations to the acquisition function are also introduced. Strength: A new information-theoretic acquisition function for Bayesian Optimization is presented, and approximation methods are also discussed and analyzed in this paper.\n\nWeakness: It is not quite clear why this new method is superior to the existing methods (for example PES and MES as mentioned in the paper) with respect to its cost-performance trade-off. - It is not quite clear from the paper why this new method is superior to the existing methods (for example PES and MES as mentioned in the paper) with respect to its cost-performance trade-off. The amount of work involved in using this new acquisition function may be large, especially compared to MES. \n- Maybe it is good to identify certain specific settings or scenarios where this joint information gain acquisition function has an advantage over both PES and MES. \n- For motivation and illustration purposes, maybe in the introduction, some small examples on a small instance can be worked out where this new method can be easily compared with PES and MES. In this way, this method can be better motivated.\n- The approximation methods can achieve different accuracy levels using a different number of samples, if possible, some discussion or guidance on that will be helpful in that section. Not applicable.", " The paper proposes a new information-based acquisition function for multi-objective Bayesian optimization that combines the approaches from the known PES and MES acquisition functions. The authors derive various approximations to efficiently compute this acquisition function and provide a comparison of their performance characteristics against a number of baselines.\n # Strengths:\n- The paper is well written, in particular Section 2 provides a nice buildup of background to understand JES in relation to (P)ES and MES.\n- The motivation for studying the new acquisition function and the theoretical contributions (in terms of JES and the various approximations) are solid; I view them primarily as well crafted technical work on top of a large body of existing literature in the field rather than a surprising or particularly novel set of contributions (which is not a bad thing).\n- The main strength of the paper beyond this solid execution is that it provides a comprehensive comparison and ablation studies of various state-of-the art acquisition functions.\n- The authors also provide a full implementation of the methods in a popular and maintained python library for Bayesian Optimization. This in itself is a significant contribution to the community, which can now easily use not just JES but also the other implemented baselines (without trying to get an unmaintained library such as spearmint running in a modern software environment...).\n- Pointing out the potential issues with HV w.r.t. rescaling objectives is valuable, and the fact that JES is invariant to that is nice and useful (though not surprising as one would expect that from an information-based acquisition function).\n- The supplementary material is very comprehensive and goes into lots of detail. This is very useful to the reader. For instance, I found the illustrations of the acquisition function in the contour plots instructive.\n\n# Weaknesses:\n- One shortcoming of the work is this that there aren't any variance estimates of the performance of the different algorithms in the empirical evaluation. The checklist states that \"We do not include the error bars directly on the plots because it made it difficult to visually compare between the different algorithms.\", but as a reader I would have hoped to see a more thorough analysis of this in the supplementary material. The quantile versions of the plots are useful to some extent, and by comparing the performance of the suggested methods across the detailed results of the benchmarks the reader can get a sense that the proposed algorithms may indeed improve over existing methods. However, this is a lot of work to require from the reader, and I would ask the authors to add a more comprehensive discussion to help practitioners understand in which the proposed methods are most useful and computationally feasible.\n- The information gain estimates rely crucially on the assumption that the different objective functions are modeled by independent GPs. If the objectives are correlated, then this assumption could result in poor performance. Other approaches, such as Monte-Carlo based EHVI methods are not subject to these limitations since their methodology applies in the same fashion to multi-output GPs. In fact, as they are based on MC sampling from the model's posterior, such methods are also compatible with other probabilistic models, which is not the case for the approach proposed in this paper.\n- Overall, I found the experimental section of the paper in the main text too brief to be able to get a good sense for the empirical performance of the JES approach in comparison to the baselines (both in terms of sample efficiency and computational footprint). I would suggest the authors move some of the mathy and notation-heavy details of Section 3 (e.g. Proposition 3) to the appendix, potentially streamline the exposition in other parts of the paper, and include additional results / discussion of the empirical performance in the main text. - l34: \" The main drawback of these approaches is that the performance of these methods are biased towards a single scalar utility criterion, which can be inadequate to assess the multi-objective aspects of the problem\". I don't really understand this point; after all, the scalar utility is defined specifically in order to capture the multi-objective aspects. In a sense your formulation is no different in that ultimately you optimize a scalar function, the information gain. Can you please clarify?\n- l38: This sentence makes it seem as if other papers do not consider a \"probabilistic perspective\", which of course they do (this is BO after all).\n- l156: what does \"cancelling out\" mean here? JES is computed on the covariance using the augmented set of observations so there shouldn't be any cancelling in the strict sense. Please clarify.\n\nNits / Typos:\n- l28/29: it enables -> they enable\n- l47: set-up -> set up\n- l89: \"and a property of the probabilistic model.\" <- not sure what is meant by this, please clarify\n Yes. ", " This paper proposes a novel information-theoretic acquisition function for BO called Joint Entropy Search (JES), which considers the joint information gain for the optimal set of inputs and outputs. The authors present several analytical approximations to the JES acquisition function and also introduce an extension to the batch setting. The authors show the effectiveness of this new approach on a range of synthetic and real-world problems in terms of the hypervolume and its weighted variants Strength 1, it identifies the problem of predictive entropy search (PES) method, i.e., the acquisition function is heavily dependent on the approximation of p(y|x, Dn, X∗), which is difficult to implement and optimize. Besides, it also shows that the max-value entropy search (MES) method, though comes with closed-form expressions, does not directly dealing with the maximum Y∗. JES combines the advantages of both methods.\n\nStrength 2, it gives several theoretic property of the JES function, with in-depth study.\n\nStrength 3, the experiments are very detail, and have a good overall design. No the authors adequately addressed the limitations of their work. i.e., the computational complexity of JES." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 7, 4, 6, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 5, 5, 3, 4, 5 ]

[ "009daQaPBk", "7B_mEA__h7L", "5jE4Hgt8dZT", "gtP4QqVQZuh", "Br-T4-9FgGU", "UvCMz6rsSMg", "mHIQkinxLeT", "gqZk_jLYlzh", "IvlOaJMq0WH", "nlwUP-QFiSv", "9K24YaJZe0u", "4x35Ky8_7eI", "6IXpA48XML5", "009daQaPBk", "2ggTWRWEulj", "5jCPk6pD-3n", "QzV_YTyqiHV", "nips_2022_ZChgD8OoGds", "nips_2022_ZChgD8OoGds", "nips_2022_ZChgD8OoGds", "nips_2022_ZChgD8OoGds", "nips_2022_ZChgD8OoGds", "nips_2022_ZChgD8OoGds", "nips_2022_ZChgD8OoGds" ]

[ "fdRTzTh5IYfn", "QmtUsr1cx2ZK", "o9KlftyyJUp", "9G4heUKrxa9", "2qDQI0589s7", "FhIl8macL16", "P4aQgeusq3V", "pk-p9nwMETe", "GbKOG8TMbYp", "-LeYm67kwv" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks a lot for checking our response and the updated paper. We are glad that our response and updated presentation have resolved your concerns regarding the motivation, contribution, and clarity of the paper. Your valuable comments have improved our presentation a lot and made the paper more readable. Thank you very much!", " Thank the authors for the comprehensive response and updated paper! The detailed response addressed my concern, and I am happy to raise my rating.", " Dear Reviewer c3r2, thanks for your positive comments and helpful suggestions! We made several small revisions, according to your suggestions. Please see the revised paper and supplementary materials for details. \n\n>**Q1:** “ Lack of explanation of failure cases, such as StanfordCar in Fig.3. A good illustration and discussion on failure cases can help the community know better about your method and the problem.”\n\n**A1:** Thanks very much for this helpful suggestion. On the StanfordCar dataset, as you mentioned, learning multiple prompts didn’t significantly improve the performance over a single prompt. It may be because the discriminative characters in this dataset coincide with each other, such that one global prompt and one global visual feature can work well. We have updated this explanation on page 7 of the revised version. To further discover the reason behind this phenomenon, we visualize the attention maps of some failure cases. Specifically, in Figure 1 in the updated version of supplementary materials, we showed two failure examples with class \"2000 AM General Hummer\" in the StanfordCars dataset. Although the number of prompts is set as 4, we found the learned prompts can be roughly divided into two classes: Foreground and Background, where some of the prompts coincide with each other. For example, in both images, \nprompt 2 (right top) and 3 (left down) focus on the foreground car, while the others focus on the background. It demonstrates that not all classes have multiple complementary attributes, which motivates us to go further to learn the dynamic local prompts numbers to reduce the computational load in the future. We included the results and discussions in the updated supplementary materials (Section F on pages 4 and 5).\n\n>**Q2:** “Lack of visualization of the learnt prompt. Although it is understandable that it is difficult to print the learnt prompt out into a completed sentence, some words in the prompt can still reveal what the prompt is about. For example, in CoOp, the learnt prompt in OxfordPets has some words like fluffy, paw, etc. Hope PLOT can show more clues about its intrinsic mechanism.”\n\n**A2:** Thanks very much for these suggestions. We produced the visualization results of the learned prompt and the corresponding discussion, but could not put them in the main paper due to the page limits. Please kindly refer to Section E and Table 4 in the supplementary materials. We found some interesting relations between the learned prompts and corresponding optimal transport plans, which help to understand the semantic attributes of different local prompts. If you think it is essential to show such results in the main paper, we will find a way to achieve it.\n\n>**Q3:** “The authors do not include a discussion on the limitation of the method. We hope the authors can provide more analysis on its weakness in the discussion.”\n\n**A3:** Thank you! We have explicitly included the limitations in Section 4.4 of the updated version based on previous discussions. There are two main limitations of our method. First, PLOT still needs few-shot data for optimization, which cannot be directly applied in the zero-shot setting. It is because that CLIP is trained by matching the global visual feature and text, while our method applies the local visual features which need few-shot data for optimization. Second, The method needs more computing costs than CoOp. \n", " We thank all reviewers for their thoughtful and constructive review of our manuscript. We were encouraged to hear the reviewers think PLOT is “effective”(Reviewer fGe6), “reasonable”(Reviewer c3r2), and “well-motivated” (Reviewers bMB5 and c3r2), and that the effectiveness can be demonstrated with “comprehensive experimental analysis”(Reviewers fGe6, bMB5, and c3r2). We provide a general response here to summarize the modifications of the manuscript.\n\n- To reviewer fGe6: We have clarified the motivation and advantage of using Optimal Transport on page 2.\n- To reviewer fGe6: We have added the experimental comparison with CoCoOp in Figure 3.\n- To reviewer fGe6: We have added a subsection on page 5 to introduce the inference strategy of PLOT.\n- To reviewer fGe6: We have split Table 2 into 2 tables for ablation studies and parameters analysis respectively.\n- To reviewer fGe6: We have refined Figure 4 for clarity.\n- To reviewer bMB5: We have clarified our optimization strategy on page 5.\n- To reviewer bMB5: We have highlighted the capability of optimal transport for misalignment on page 2.\n- To reviewer bMB5: We have corrected the typos accordingly. \n- To reviewer c3r2: We have updated the explanation for the failure cases on page 7 and included more visualization results of the failure cases in Section F of the supplementary materials.\n- To reviewer c3r2: We have explicitly included the limitations in Section 4.4 based on previous discussions. ", " Dear Reviewer bMB5, we are sincerely grateful for your careful reading and valuable feedback, which has helped improve our paper. We provide the point-to-point response below and have updated the paper and appendix accordingly.\n\n>**Q1**: \"The proposed method is a two-stage optimization strategy, which is a bit difficult to balance the two steps of optimization. Could it be end-to-end training?\"\n\n**A1**: Thanks very much for this valuable question. There are two points to this question. First, thanks to the Sinkhorn algorithm[1], the optimizations of optimal transport and prompt learning can be integrated. Though it is a two-stage optimization strategy, we find it is natural and relatively easy to the optimization. We have added this into page 5 of the revised paper to reflect this point. Thanks for your question.\n\nSecond, we also updated the paper to make it more explicit that though the optimization strategy is two-stage, the whole training flow is end-to-end. It is because the transport plan is computed using a small number of matrix multiplications using the iterative Sinkhorn algorithm as one feedforward module of the neural network. The gradients of these matrix multiplications are taped for backpropagation for end-to-end optimization, which makes the whole system fully differentiable (including the iterative algorithm) and easy to implement using an autograd library like PyTorch. \n\nBesides, the optimization of the transport plan with the Sinkhorn algorithm is very efficient. As shown in lines 303-305 of the original paper and Section D in the supplementary material, we demonstrate that this optimization process only costs around 10% inference speed and 5% training time. \n\n[1]Cuturi M. Sinkhorn distances: Lightspeed computation of optimal transport[J]. Advances in neural information processing systems, 2013, 26.\n\n>**Q2**: \"After optimization, for different images and classes, are they sharing the same prompts? If so, there might be issues. Because different images have different local patterns, like a dog lying on the ground' v.s. 'a bird in the forest'. They have different local patterns (positions).\"\n\n**A2**: Thanks for this valuable question. First, the **prompts** are shared for different images and classes, and the **prompt features** are only shared for different images of the same class (prompt features contain the information of the class label). It requires the distance between prompt features and visual features to be intra-category robust even if the images in the same class are misaligned. In this paper, we learn a transport plan T to align prompt features and local visual features. Let us explain why the optimal transport helps solve this intra-category misalignment problem below. \n\nSuppose we have two prompts “head” and “tail” for the class “bird”, given two images with position shifts where **Image A** is “left head and right tail” and **Image B** is “right head and left tail”. It will provide a wrong similarity score if we directly match the prompt “head” with the left region and prompt “tail” with the right region. To deal with this problem, we leverage optimal transport, which optimizes a transport plan to adaptively match the prompt feature and visual feature. The optimal transport can acquire the optimal matching flows with minimal distance. In this example, the optimal transport will match prompt “head” with the left region for **Image A** and match prompt “head” with the right region for **Image B**. Thus, even though the prompt features are shared for all images in the same class, the optimal transport can provide the adaptive matching plan to solve the misalignment problem. We have highlighted this capability of optimal transport on page 2 of the revised paper. \n\n>**Q3**: \"Typos.\"\n\n**A3**: Thank you very much! We have corrected the typos in the revised paper. \n\n\n", " >**Q2**: \"It seems that this work is just an application work on a specific model and a specific task, which limits the contribution.\"\n\n**A2**: Recently, large-scale pre-trained models have achieved great success and attracted a lot of attention. As a parallel paradigm with “pretraining-finetuning”, prompt learning shows the great potential to efficiently adopt pre-trained knowledge into downstream tasks. In this paper, we propose learning multiple comprehensive prompts for a more representative prompt learning. It is a plug-and-play module that can be easily extended to any baseline prompt learning method such as CoOp[3] or Tip-adapter[5]. It can achieve orthogonal and complementary improvement over the baseline methods as shown in Table 2 and Table 3. \n\nMost existing methods[3,4,5] exploring how to adapt the pre-trained vision-language knowledge apply the few-shot recognization as the evaluation metric. It is because that few-shot recognization can effectively evaluate the adaptation ability of the method when only few-shot downstream data is available. Besides, the same few-shot recognization setting can provide a fair comparison with existing methods, such as CoOp[3]. Some recent progress shows that the pre-trained vision-language knowledge can also be applied to other tasks, e.g. DenseCLIP[6] applies the pre-trained model to visual detection and segmentation. Our method also has potential for these applications. \n\n[3]Zhou K, Yang J, Loy C C, et al. Learning to prompt for vision-language models[J]. arXiv preprint arXiv:2109.01134, 2021.\n\n[4]Gao P, Geng S, Zhang R, et al. Clip-adapter: Better vision-language models with feature adapters[J]. arXiv preprint arXiv:2110.04544, 2021.\n\n[5]Zhang R, Fang R, Gao P, et al. Tip-adapter: Training-free clip-adapter for better vision-language modeling[J]. arXiv preprint arXiv:2111.03930, 2021.\n\n[6]Rao Y, Zhao W, Chen G, et al. Denseclip: Language-guided dense prediction with context-aware prompting[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022: 18082-18091.\n\n>**Q3**: \"The recent related work CoCoOp is not compared in the experiments. \"\n\n**A3**: Thanks very much for this suggestion! We have added the performance comparison in the experiments of the revised paper. Please see updated Figure 3 for the details. In the original submission, we didn’t add CoCoOp[7] in the experiments because the experimental settings of CoCoOp and our method were different: CoOp[3] and our method focus on the few-shot recognition task, while CoCoOp focuses on the generalization for the unseen new classes. For a fair comparison, we re-run CoCoOp in our experimental settings with the same backbone network. The performance on all 11 datasets is shown in the updated Figure 3. We found that in most datasets, our method achieved better performance than CoCoOp. Besides, since CoCoOp focuses on \"from base to new\" setting, its performance is even lightly slower than CoOp. \n\n[7]Zhou K, Yang J, Loy C C, et al. Conditional prompt learning for vision-language models[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022: 16816-16825.\n\n>**Q4**: \"In the approach method, there lacks a separate part or subsection to introduce the inference strategy.\"\n\n**A4**: We appreciate this suggestion to help improve our paper. We have added a subsection of inference strategy on page 5 of the updated version. Below we give a more detailed introduction of the inference strategy. \n\nDuring inference, the goal of the method is to classify the query images given the learned prompt and the pre-trained model. Given one image, we first feed it into the image encoder to obtain a set of local visual features. Then, we combine the learned prompts and the names of classes to get a set of prompt features. Specifically, the visual feature set contains M=HxW, which is 7x7, feature vectors, while the prompt feature set contains NxC feature vectors, where N is the number of local prompts and C is the number of classes (C=1000 in Imagenet). Then, we calculate the distance between the visual feature set and the prompt feature set of each class. To calculate the distance, we optimize the transport T to reweight the distance matrix. This transport T helps align the local visual features and multiple prompts for a fine-grained cross-modal matching. After obtaining the OT distance for each class, we sort the distance and classify the image into the class with minimal OT distance. \n\n>**Q5**: \"It would be great if Table 2 can be split into several tables according to the analyzed component.\" & \"The visualization in Figure 4 is not clear.\"\n\n**A5**: Thank you! This suggestion helped a lot to improve the readability of the paper. We split Table 2 into 2 tables for ablation studies and parameters analysis respectively. Then we darkened the color of the attention map in Figure 4 for clarity. Please kindly see pages 7 and 9 in the revised paper for details.\n\n", " Dear Reviewer fGe6, we appreciate your time dedicated to reviewing this paper and the valuable comments, which have helped improve our work. We revised our manuscript accordingly (please see the updated paper and supplementary materials for details), and provide a point-to-point response below.\n\n>**Q1**: \"it is not clear enough to me why Optimal Transport is better than other distances. Especially, the insight behind the application of Optimal Transport is not clear. I would like to see more analysis and explanation on why Optimal Transport works well.\"\n\n**A1**: Thanks for your valuable question! In light of your comments, we added more comparisons between Optimal Transport and other distance to show the insight of using Optimal Transport in the revised manuscript. \n\nConventional prompt learning methods (e.g. CoOp) adopt the **Euclidean distance** to measure the similarity between **single (global) prompt feature vector** and **single (global) visual feature vector**. In contrast, PLOT proposes to use the **Optimal Transport** to calculate the distance between **multiple (local) prompt features** and **multiple (local) visual features**. Before we discuss the differences between Optimal Transport and conventional Euclidean distance, we would mention the differences between PLOT and conventional prompt learning methods in three folds: multiple (local) prompt features v.s. single (global) prompt feature; multiple (local) visual features v.s. single (global) visual feature; and using Optimal Transport to calculate set-to-set distance v.s. Euclidean distance.\nLet’s discuss them one by one:\n\n**1, Multiple (local) prompt features v.s. single (global) prompt feature:** Prompt is used to represent the classes. One class can be described with many intrinsic characteristics and extrinsic context relations. It motivates us to use multiple prompt candidates which focus on different attributes to replace one global prompt. Compared with a single prompt, multiple local ones can comprehensively represent the class and thus facilitate classification.\n\n**2, Multiple (local) visual features v.s. single (global) visual feature:** Compared with the single global visual feature, the information provided by local features are more discriminative and transferable. These local features are more robust to visual misalignment such as within-class position shift. \n\n**3, Using Optimal Transport to calculate set-to-set distance v.s. Euclidean distance:** As shown in lines 44-48 in the original manuscript, if we use multiple prompt features and single visual feature, all prompts are encouraged to be closer to one single point and thus tend to learn the same characteristics. It calls for multiple prompt features and multiple local visual features. Given the motivation that we use multiple local prompt and visual features to replace the global one, we further need to calculate the distance between the two feature sets. The conventional solution is to calculate the pairwise Euclidean distance and take the mean of all pairs. However, this distance is not robust for the feature shift. In this paper, we propose to apply the optimal transport to align the visual features and prompts, whose insight is to adaptively align different visual features for each local prompt, which is more robust to the visual misalignment and tolerates well feature shift[1]. It is because Optimal Transport distance can represent the data structure by learning an adaptive transport plan for the fine-grained alignment. Besides, some theoretical analyses [2] also show that Optimal Transport distance space is more flexible than Euclidean spaces. Here we show a toy example to show the advantage of the Optimal Transport distance. Given two prompts whose values are 2 and 0, and two visual feature sets of the same class with feature shift (1,1,1,-1) and (1,1,-1,-1). In the mean Euclidean distance space, we get the distances of 1.5 and 1.25 respectively, while with optimal transport, we get the same distance of 1.\n\n[1]Rubner Y, Tomasi C, Guibas L J. The earth mover's distance as a metric for image retrieval[J]. International journal of computer vision, 2000, 40(2): 99-121.\n\n[2]Frogner C, Mirzazadeh F, Solomon J. Learning Embeddings into Entropic Wasserstein Spaces[C]//International Conference on Learning Representations. 2019.\n\n\n", " This paper focused on adapting large-scaled pre-trained vision-language model (i.e., CLIP) to downstream datasets under the few-shot setting. Compared to the recent related work CoOp, this work (1) learns multiple prompts, (2) uses both local features and global features, and (3) measures the similarity of prompts and visual features using optimal transport. Experiments on 11 benchmark visual recognition datasets show that the proposed method outperforms the baseline CoOp. Ablation studies further more analysis on the contribution of each component.\n\n----------------------\n\nUpdated after rebuttal:\n\nReasons to accept:\n\n+ The motivation for this work is clear. Single prompts may lose the details of local attributes or contexts.\n\n+ The idea of applying optimal transport to prompt learning makes sense and meets well with the motivation.\n\n+ The experiments and analysis are comprehensive. The improvement is significant.\n\nI am satisfied with the authors' responses to my comments and concerns, and I increased my rating from 6 to 7. I have read other reviewers' concerns on (1) two-stage training, (2) sharing of prompts, and (3) failure analysis and visualization. I think these questions are not severe for rejection and the authors have responded to these concerns. Overall, considering both strengths (simple but effective pipeline, comprehensive experimental analysis) and weakness (insight and contribution), my initial rating is borderline. \n\nStrengths:\n\n\\+ The problem of adapting CLIP under few-shot setting is recent. Compared to the baseline method CoOp, the improvement of the proposed method is significant.\n\n\\+ The ablation studies and analysis in Section 4.4 is well organized and clearly written. It is easy to follow the analysis and figure our the contribution of each component. Also, Figure 2 is well designed and clear to illustrate the pipeline.\n\n\\+ The experimental analysis is comprehensive. The analysis on computation time and inference speed is also provided.\n \nWeakness:\n\n\\- (major concern) The contribution is somehow limited. The main contribution is applying optimal transport for few-shot adaptation of CLIP. After reading the paper, it is not clear enough to me why Optimal Transport is better than other distance. Especially, the insight behind the application of Optimal Transport is not clear. I would like to see more analysis and explanation on why Optimal Transport works well. Otherwise, it seems that this work is just an application work on a specific model and a specific task, which limits the contribution.\n\n\\- The recent related work CoCoOp [1] is not compared in the experiments. Although it is a CVPR'22 work that is officially published after the NeurIPS deadline, as the extended version of CoOp, it is necessary to compare with CoCoOp in the experiments.\n\n\\- In the approach method, there lacks a separate part or subsection to introduce the inference strategy, i.e., how to use the multiple prompts in the test stage.\n\n\\- Table 2 mixed different ablation studies (number of prompts, visual feature map, constraint). It would be great if the table can be split into several tables according to the analyzed component.\n\n\\- The visualization in Figure 4 is not clear. It is not easy to see the attention as it is transparent.\n\nReferences\n\n[1] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Conditional prompt learning for vision-language models. In CVPR, 2022.\n\n\n------------\n\nAfter reading the authors' response and the revised version, my concerns (especially the contribution of introducing the optimal transport distance for fine-tuning vision-language models) are well addressed and I am happy to increase my rating. Please see weaknesses in the above. The authors have adequately addressed the limitations.", " The authors propose a new prompt learning method, which learns multiple prompts to describe diverse characteristics of categories. To optimize the model effectively, they apply optimal transport to match vision and language modalities. The experiments demonstrate its effectiveness and achieve improvement on few-shot learning tasks. Strengths:\n\t1. The motivation is innovative. Conventional methods use a single prompt which is not able to capture multi-grained features. The authors therefore aim to learn multiple comprehensive prompts to describe different categories. \n\t2. An interesting combination between optimal transport theory and prompt learning.\n\t3. The experiments are comprehensive and demonstrate the effectiveness of introduced method.\n\n\nWeaknesses:\n\t1. The proposed method is a two-stage optimization strategy, which is a bit difficult to balance the two steps optimization. Could it be end-to-end training? \n\t2. Although it is intuitive that including multiple local prompts helps, for different categories, the features and their positions are not the same.\n Questions\nAfter optimization, for different images and classes, are they sharing the same prompts? If so, there might be issues. Because different images have different local patterns, like 'a dog lying on the ground' v.s. 'a bird in the forest'. They have totally different local patterns (positions).\n\nTypos: \n\t1. Line 55, prompts learning -> prompt learning\n\t2. Line 75, simultaneously several items -> several items simultaneously\n\t3. Line 90, filed -> field\n\t4. Line 110, 111: improve -> improves, achieve -> achieves\n\t5. Line 135, vectorss -> vectors\n\t6. Line 158, is same as -> is the same as\n\t7. Line 232, summarize -> summarizes\nLine 274, we obtain -> We obtain N/A", " This paper focuses on the few-shot prompt learning for vision-language model CLIP.\nOn the top of the recent work CoOp who only learns one single prompt, this work proposes a novel method called PLOT, which learn multiple prompts to leverages more fine-grained information from image's feature map. The key motivation of PLOT is to generate a set of prompts so that each prompt can help the model to focus on some specific areas on the feature map. To realize the idea, optimal transport method is used to contrast the effects of each prompt.\nThe experiment shows that PLOT can achieve better performance over CoOp in most of the datasets. Pro:\n+ The motivation of PLOT is strong. Figure 1 clearly states the main idea.\n+ Using optimal transport to learn distinguishable prompt is reasonable and simple.\n+ The experiment shows the effectiveness of the proposed methods.\n+ Implementation details are clearly stated.\n+ Analysis is comprehensive and strong.\n\n\nCon:\n- Lack of explanation of failure cases, such as StanfordCar in Fig.3. A good illustration and discussion on failure case can help the community know better about your method and the problem.\n- Lack of visualization of the learnt prompt. Although it is understandable that it is difficult to print the learnt prompt out into a completed sentence, some words in the prompt can still reveal what the prompt is about. For example, in CoOp, the learnt prompt in OxfordPets has some words like fluffy, paw, etc. Hope PLOT can show more clues about its intrinsic mechanism. None The authors do not include the discussion on the limitation of the method. We hope the authors can provide more analysis on its weakness in discusssion." ]

[ -1, -1, -1, -1, -1, -1, -1, 7, 6, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, 5, 3, 5 ]

[ "QmtUsr1cx2ZK", "P4aQgeusq3V", "-LeYm67kwv", "nips_2022_b9APFSTylGT", "GbKOG8TMbYp", "pk-p9nwMETe", "pk-p9nwMETe", "nips_2022_b9APFSTylGT", "nips_2022_b9APFSTylGT", "nips_2022_b9APFSTylGT" ]

[ "rQgzh4B9ui", "9pkawbgfbCV", "iyab_oHosrW", "0AJNwpRfZbo", "HgbtnaAIJFy", "Ob6gQFg2MK", "AmxPEWv_t80u", "pJT1XxZ220m", "o8XW_AWYMIy", "KUfDHslwyRP", "vuZtZZx9iuw", "0CAc7e-R8Su", "Cf3zn1xk6br", "5S1y4w8nq8D", "6eYjbLNtUW", "21KaTFRC6KD", "9fajU1YZK6A", "IC0WdkM92H_", "BpKJv8eLxs-", "bloyOSjfIy" ]

[ "author", "official_reviewer", "author", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your further response and acknowledging our efforts. Intuitively, $K$ for ADE20K should be larger than that of VOC, since one image is often with more classes in ADE20K. However, it is worth noting that the number of future classes in ADE20K is of the same order of magnitude as in VOC in a single image based on the current setting, which is also shared in prior CISS works [4, 5, 11]. We show the comparison in the table below. In this case, the accuracy of historical classes will mainly dominate how to select $K$. We hope this observation can further help address your concern.\n\n\n| Dataset | Avg all classes | Avg future classes |\n|:-------:|:---------------:|:------------------:|\n| ADE20K | 10.58 | 1.67 |\n| VOC | 2.76 | 1.04 |", " Thanks for the detailed response. I think the response addresses part of my concerns. But my concern on $K$ still remains. $K$ denotes the the number of future classes. So intutively $K$ for ADE20K should be larger than that of VOC, since ADE20K usually has more classes in one image. Therefore, the setttings of $K$ for different datasets are quite counterintuitive, though I can understand that a smaller $K$ may be better if the prediction of historical classes is not accurate enough. I think this indicates a defect of the proposed micro mechanism.\n\n", " Thank you for your feedback! For your remaining concern:\n\n\n**[Concerns about hyper-parameters]**\n\nThere may be a misunderstanding. $N$ is the number of the mask proposals, which is inherited from Mask2Former and fixed as 100 for all experiments. Therefore, only the hyper-parameters $K$ and $\\tau$ will influence the performance of MicroSeg. For $K$, we agree that it is sensitive to the difficulty of the given dataset. However, we consider that an expected $K$ is easy to be found according to some experimental analysis (more details are given in the following response). The value of $\\tau$ represents the threshold of pseudo-label, we have provided the results of different settings in the table below, and the fluctuation range of performance is from 68.3 to 69.8. This range is actually reasonable since the worst one (68.3 as $\\tau$ = 0.1) still outperforms the previous SOTA (67.6, compared to SSUL).\n\n| $\\tau$ | base | novel | all |\n|:------:|:----:|:-----:|:----:|\n| 0.1 | 79.7 | 30.7 | 68.3 |\n| 0.3 | 81.1 | 31.3 | 69.2 |\n| 0.5 | 80.8 | 33.1 | 69.4 |\n| 0.7 | 80.1 | 36.8 | **69.8** |\n| 0.9 | 80.0 | 32.5 | 68.7 |\n\n**[Can Micro mechanism still work when K is 1? & Detailed explanation about the choice of $K$]**\n\nFirst, we would like to clarify the definition of $K$, which is the number of *future classes*. When the prediction of the historical classes is accurate (i.e., high accuracy like 82.7 for VOC 15-1), the remaining uncertainty regions are mainly future classes, and as a result a larger $K$ can better distinguish different future classes. But if the prediction of historical classes is not that accurate (e.g., 43.8 as for the ADE 100-10), many historical classes would be mis-classified and grouped into the remaining future class regions. In this case, if the $K$ is still set to a large value (>1), pixels belonging to the same historical class will be forced to be separated into different categories and as a result confuse the model learning. In this case, a smaller $K$ (i.e., $K = 1$) would be safer and less harmful. We agree that the Micro mechanism is indeed incomplete with $K = 1$: the unsupervised contrastive loss does not work for $K = 1$, but there is still supervised BCE loss to constrain $c_{\\hat{u}}$ in the Micro mechanism. And it is worth noting that even in this case, the proposed MicroSeg still achieves SOTA performance (i.e., 36.3 v.s. 33.1, compared to SSUL, in ADE 100-10).\n\nOn the ADE20K dataset, in order to conduct a fair comparison with prior CISS methods [4, 5, 11], we choose to use the ResNet101 and DeeplabV3. But we assume a more advanced model (e.g. the Swin Transformer) with a larger $K$ would lead to a different conclusion. Due to the time limit of the rebuttal, we will include this experiment in the revised version to better illustrate the choice of $K$.\n", " The authors respond well to most questions and the new ablation adds to the substance of the paper.\n\nThe fact that K=1 works best for ADE seems to indicate a problem with the formulation of the micro mechanism, although ADE is a bit special and one might have not much use of large Ks.", " Thanks for the authors' clear response. I have read the response from authors and comments from other reviewers. \n\nMy remaining concern is about the hyper-parameters. It seems the proposed method relies on a lot of hyper-parameters ($N$, $K$, $\\tau$). Moreover, the method performance seems to be quite sensitive to $\\tau$, ($\\tau$ from 0.7 to 0.9, performance from 69.8 to 68.7 ).\n\nI also have a concern about the $K$ for ADE20K, where it is set as 1. The proposed micro mechanism seems to rely on assembling multiple logits of different $c_{\\hat{u},k}$. So can it still work when $K$ is 1? I notice a similar concern by Reviewer uMp6. However, I think the authors' response not clear enough. Is there any further explanation?\n", " Dear Reviewers,\n\nThanks for the comments and suggestions for this paper. We have tried our best to address all concerns. We would appreciate receiving your feedbacks, as the discussion deadline is approaching. If you have additional questions, we would be happy to reply.\n\nSincerely yours,\n\nAuthors", " \nDear Reviewers,\n\nThank you for reviewing this paper. Since authors have submitted their rebuttal, please check if the rebuttal addresses your concerns. Please also check the comments from other reviewers, and if you have any question, please discuss with authors in OpenReview soon.\n\nBest Regards, \n\nAC", " Following your kind suggestions, we have finished the experiments of generating proposals by RPN in Mask R-CNN combined with class-agnostic segmentation head (denote as RPN+Seghead). As shown in the following table, using RPN+Seghead as a proposal generator does not significantly affect the performance, comparing to the original setting of MicroSeg. We conduct the experiment on VOC 15-1. We will include the result into the revised version and hope it can help address your concerns in weakness #3.\n\n||base|novel|all|\n|:--:|:-:|:-:|:-:|\n| RPN+Seghead|80.5|33.0|69.2|\n| MicroSeg|80.1|36.8|69.8|", " Thanks for the quick response. We will follow your suggestions and provide the corresponding results here as soon as possible.", " Thanks for the response. I give one quick comment here. It's true that RPN can only output bounding boxes, but it can output masks when combing with the class-agnostic mask head. Please refer to Figure 4 (mask visualization) and implementation details of [a]. ", " ### *Responses to weaknesses*\n\n\n0. **[My main concern of this work is the writing. I believe it would be a good work if the writing is clearer]**\nThanks for acknowledging the contributions of our paper and the valuable suggestions! We will carefully proofread and polish the paper to address the writing issues in the revised version.\n\n1. **[More details about proposal generator]** \nThe structure of the proposal generator is identical to Mask2Former. As we described in L210 to L212 in the main paper, we use the off-the-shelf Mask2Former pretrained on MS-COCO to generate proposals. It is not optimized during the training stage. MicroSeg aims to accomplish the CISS with regional objectness information rather than the mask proposal generator. We will consider explaining it clearly in a revised version.\n3. **[Detailed descriptions of proposal reorganization]** \nThanks for the suggestion, we will reformulate it by following words:\n\n\n The logits $p \\\\in \\\\mathbb{R}^{N \\\\times | \\\\mathcal{C}_{1:t} | }$ is generated by classification. \n\n While proposal is a group of binary masks ${P} \\\\in \\\\{0,1\\\\}^{N \\\\times H \\\\times W}$ where $N$ is the number of masks and $H, W$ denote height and width. Proposal reorganization is a matrix multiplication of logits and proposal, to obtain probability map of image, with the shape of ${| \\\\mathcal{C}_{1:t}| \\\\times H \\\\times W}$. We will make the description of proposal reorganization clearer in the revised version.\n\n \n\n \n4. **[Detailed descriptions of contrastive loss]**\nDue to the length limitation of the paper, we only briefly introduce the contrastive loss in Sec. 3.4 in main paper, and we will add more descriptions about the component:\nContrastive loss is used to keep the effectiveness of Micro mechanism. In Micro mechanism, we represent future classes $c_{\\hat{u}}$ as a set of K classes to better cache the feature diversity in those loose future classes. To avoid model degradation caused by $c_{\\hat{u},k}$ characterizing the same features, we use unsupervised contrastive loss to force them to capture the diverse concepts, thus ensuring the effectiveness of the Micro mechanism. *Cluster* columns of Fig. 2, in Supplementary Material, show the qualitative performance of $c_{\\hat{u},k}$ to capture diverse contexts. \n6. **[The value of hyper-parameter $\\tau$ in Equation 3]**\n$\\tau$ is set to 0.7 in our experimental setting. We will add the hyper-parameter to implementation details of our paper in the revised version.\n8. **[Extra ablation experiments]** \nWe have conducted the ablation studies of $\\mathit{K}$, $\\mathit{N}$, $\\tau$. All experiments are done in VOC 15-1.\n The ablation study for the hyper-parameter $\\mathit{N}$:\n\n | $\\mathit{N}$ | base | novel | all | #params. |\n |:------------------:|:----:|:-----:|:----------:|:--------:|\n | 100 | 80.1 | 36.8 | 69.8 | 107M |\n | 200 | 80.4 | 37.3 | 70.1 | 216M |\n\n As the proposal generator model size grows, the performance of MicroSeg improves as well. We choose Mask2Former(N=100) as a better trade-off between model size and performance.\n \n The ablation study for hyper-parameter $\\mathit{K}$ in Micro mechanism: \n\n | $\\mathit{K}$ | base | novel | all |\n |:------------:|:----:|:-----:|:----:|\n | 1 | 78.6 | 30.9 | 67.2 |\n | 3 | 79.7 | 34.0 | 68.8 |\n | 5 | 80.1 | 36.8 | **69.8** |\n | 7 | 80.4 | 32.8 | 69.1 |\n\n So we choose $\\mathit{K}$ = 5 in VOC2012 for best performance.\n \n\n\n The ablation study for hyper-parameter $\\tau$: \n\n | $\\tau$ | base | novel | all |\n |:------:|:----:|:-----:|:----:|\n | 0.1 | 79.7 | 30.7 | 68.3 |\n | 0.3 | 81.1 | 31.3 | 69.2 |\n | 0.5 | 80.8 | 33.1 | 69.4 |\n | 0.7 | 80.1 | 36.8 | **69.8** |\n | 0.9 | 80.0 | 32.5 | 68.7 |\n\n We choose $\\tau$ = 0.7 for best performance. \n", " ### *Responses to weaknesses*\n1. **[Some claims of novelty require revision/clarification]** \nThanks for pointing out this, we will revise the descriptions and add references accordingly. The structure of our proposal generator is identical to Mask2Former. It should be noted that we only use an off-the-shelf pretrained Mask2Former model as a proposal generator. It is not optimized during the training stage. And proposal classification is not related to Mask2Former, as shown in Fig. 2 in the main paper.\n\n2. **[Ablation study of $\\mathit{K}$ and choice of $\\mathit{K}$ in ADE20K]** \nAs suggested, here we provide the ablation study of $\\mathit{K}$ in Micro mechanism in VOC 15-1: \n\n |$\\mathit{K}$|base|novel|all|\n |:-:|:-:|:-:|:-:|\n |1|78.6|30.9|67.2|\n |3|79.7|34.0|68.8|\n |5|80.1|36.8|**69.8**|\n |7|80.4|32.8|69.1|\n\n So we choose $\\mathit{K}$ = 5 in VOC dataset.\n The choice of $\\mathit{K}$ = 1 in ADE20K is due to that ADE20K is an admittedly difficult dataset, which makes the pseudo-label generated by the old model inaccurate. Many historical classes would be mis-classified into the future class regions. Choosing a larger $K$ will exacerbate the misleading of inaccurate pseudo-label: pixels belonging to the same historical class will be forced to be separated into different categories. As a result, it confuses the model learning. Under the condition, we set $\\mathit{K}$ = 1 for better performance. \n\n3. **[How the performance varies for different class orders on ADE20K]** \nThis is indeed an interesting idea. In fact, we have conducted similar experiments on VOC dataset with 20 different orders in our paper, as shown in Fig. 3 \\(c\\). However, due to time constraints, we are not able to provide results for swapping training orders on ADE20K (as it requires 40 days running on single NVIDIA GeForce RTX 3090 GPU for 20 different orders), but this could be an interesting future work.\n\n### *Responses to questions*\n1. **[Description about disjoint setting]** \nSorry, this is just a description error. We will fix it in the revised version.\n2. **[Are the joint results on ADE20k based on the proposed architecture, including the Mask2Former or for the base DeepLabv3 model?]** \nThe joint results on ADE20k are based on the proposed model using proposals. The reason for the identical/low results is that we only adapt Mask2Former as a frozen pretrained proposal generator. It does not fine-tuned or fit ADE20K dataset. Besides, this precisely illustrates that MicroSeg actually addresses the problem of incremental learning, rather than improving CISS results by boosting the performance of the basic semantic segmentation.\n3. **[Details of pretrained ResNet101]** \nThe pretrained weight we used for the ResNet-101 network was acquired from the PyTorch official site by using the torchvision package. Please refer to L10 in the supplementary material.\n4. **[How does the proposed split of segment proposals and classification differ from [8]? And is the splitting of the task into segment proposal and classification novel for semantic segmentation or for CISS?]** \nSegment proposals are generated by proposal generator, which is identical to Mask2Former. While proposal classification is not related to Mask2Former. To the best of our knowledge, this method is novel in CISS.\n5. **[Performance difference between classes present and absent in MS-COCO]** \nYes, it differs between classes present and absent in MS-COCO. Although it is a bit infeasible to directly evaluate the segment proposal, we designed the following experiment to show the difference. We counted the classes that were shared in MS-COCO and ADE20K (20 in our experiment), to observe the variation of the mIoU performance of these classes with/without proposal classification branch on ADE20K dataset. The experiments are conducted on ADE 50-50.\n\n ||shared|non-shared|all|\n |:--:|:-:|:--:|:---:|\n |w/o proposal|34.9|30.2|30.7|\n |with proposal|38.0 (+3.1)|32.1 (+1.9)|32.9 (+2.2)|\n \n Compared to non-shared classes, shared classes have better performance improvement with proposal classification branch. It also can be observed that the performance of both shared and non-shared has been improved, which shows the robustness of our method, even on the unseen classes to proposal generator.\n6. **[Details of the contrastive loss]** \nYes, contrastive loss is only applied for the background. It is used for the background after the pseudo-labeling, i.e. $c_{\\hat{u}}$.\n8. **[Which losses are applied to the baseline in Tab 3?]** \nOnly the BCE loss was applied to the baseline. The better performance comes from the applied *freeze strategy*, described in Line 208. This was also validated in SSUL.\n", " ### *Responses to weaknesses*\n1. **[The claim in Line 175~176 is not validated]**\nIn the Micro mechanism, we represent it as a set of K classes to better cache the feature diversity in those loose future classes. The statement in Line 175~176 can be proved with the following evidence:\n\t- From the ablation studies on the Micro mechanism in Tab. 3, the performances of both base classes and novel classes are improved with Micro mechanism(+9.9% in total, comparing the experimental setting of with and without Micro mechanism of Tab. 3).\n\t- Focused on historical classes, we further measure the probability of being incorrectly assigned to a historical class by: $$Err = 1 - Precision = \\frac{FalsePositive}{TruePositive+FalsePositive}$$ We have completed experiments with and without the Micro mechanism in VOC 15-1, step 2, to observe the variation of $Err$. As a result, the historical classes have a mean $Err$ of 9.2% and 13.5%, for methods with and without the Micro mechanism, respectively. It indicates that the Micro mechanism does help to reduce error rate of being classified into historical classes.\n\t- This phenomenon can also be observed from the comparison of the qualitative analysis in Fig. 4. Taking the {*TV*} set (row 2 & 4 of Fig. 4, referring to SSUL and MicroSeg respectively) as an example, the potential future class (*TV*) is not incorrectly classified into the past class by MicroSeg, obviously superior to the result of SSUL.\n2. **[MicroSeg gets inferior performance compared with SSUL (Tab. 1 & 2), the reason should be explained]**\nMicroSeg achieves better performance than SOTA method (SSUL) in most (4 of 6 scenarios in VOC, 3 of 4 scenarios in ADE20K) incremental scenarios. The reason why the other experimental results of MicroSeg in VOC are slightly lower than those of SSUL may be due to the small number of categories in some steps (e.g., step 2 of 19-1 has only 1 category). The lack of diverse samples makes model trained not well. ADE20K is an admittedly difficult dataset. The performance of MicroSeg on ADE 100-50 does have a trivial drop (-0.5% to SSUL). It is also worth pointing out that SSUL does not outperform all previous methods in ADE20K, e.g. ADE 50-50, compared with PLOP. It also shows that the task of CISS is still hard, especially on more challenging datasets like ADE20K. Thus, CISS research is valuable. We will add the analysis to the revised version.\n\n3. **[Is it fair to compare with other methods? Besides, could the proposed technique promote existing Class incremental semantic segmentation methods?]**\nWe have conducted a related experiment (L27-44) in Table 3 of the Supplementary Material to illustrate the fairness of the comparison, by replacing the saliency detector of SSUL with Mask2Former. Here are experimental details: we compared the performance of the original SSUL (1st row) and SSUL with the proposal generated by Mask2Former (2nd row) (i.e., *SSUL+mask proposal*). mask proposal for SSUL is obtained by binarization of the mean of queries in Mask2Former, which can measure the attention of all queries to a region, and we suppose that it is reasonable to use it as a saliency map. All experiments are done in VOC 15-1.\n- As a result, SSUL with Mask2Former obtains mIoU of 67.5, while MicroSeg achieves 69.8. Our proposed method performs better than SSUL, though SSUL also adopts Mask2Former.\n- Besides, the SSUL with Mask2Former achieves a comparable performance to the original SSUL (67.5 for SSUL + Mask2Former v.s. 67.6 for the original SSUL). \n- The result shows that the performance gain of MicroSeg was not mainly derived from the positive impact of Mask2Former on semantic segmentation (otherwise, applying it to SSUL should also result in a significant improvement). The key of our proposed method is proposals with the Micro mechanism, trying to address the problem of background shift in incremental learning. \n\n As the application of segment proposal was not considered in previous CISS methods, the proposed method may not be able to naturally applied to them to address CISS. However, MicroSeg, serving as a simple baseline, provides an idea of mining unseen classes in the CISS task. We believe it will inspire and motivate following-up research in this direction.", " ### *Responses to weaknesses*\n1. **[Limited contribution of MicroSeg. Region proposal network (RPN) is already widely used, such as [a]]**\n\n- First, [a] studied the open-set object detection task, while our work focuses on semantic segmentation in the class incremental learning (CISS) setting. The proposal generator in MicroSeg is different to RPN in object detection, since our method requires class-agnostic masks while RPN only can produce bounding boxes. We will cite the suggested paper and revise the description of our proposal generator part.\n- Second, MicroSeg aims to accomplish the CISS with regional objectness information rather than the mask proposal generator.\n- Finally, we use proposals not as a simple appropriation, but with careful consideration of the characteristics of the CISS task, in which there are potential categories in the background, and these categories can be mined by proposals. To the best of our knowledge, MicroSeg is the first application of regional objectness to CISS.\n\n2. **[Off-the-shelf saliency detector for SSUL compared to Mask2Former in the paper]**\nThanks for the suggestions. We have conducted a related experiment (L27-44) in Table 3 of the Supplementary Material to illustrate the fairness of the comparison, by replacing the saliency detector of SSUL with Mask2Former. Here are experimental details: we compared the performance of the original SSUL (1st row) and SSUL with the proposal generated by Mask2Former (2nd row) (i.e., *SSUL+mask proposal*). mask proposal for SSUL is obtained by binarization of the mean of queries in Mask2Former, which can measure the attention of all queries to a region, and we suppose that it is reasonable to use it as a saliency map. All experiments are done in VOC 15-1.\n- As a result, SSUL with Mask2Former obtains mIoU of 67.5, while MicroSeg achieves 69.8. Our proposed method performs better than SSUL, though SSUL also adopts Mask2Former.\n- Besides, the SSUL with Mask2Former achieves a comparable performance to the original SSUL (67.5 for SSUL + Mask2Former v.s. 67.6 for the original SSUL). \n- The result shows that the performance gain of MicroSeg was not mainly derived from the positive impact of Mask2Former on semantic segmentation (otherwise, applying it to SSUL should also result in a significant improvement). The key of our proposed method is proposals with the Micro mechanism, trying to address the problem of background shift in incremental learning. \n\n For the other suggested experiment about GGN[b], we use their official pretrined model as a saliency detector: we extract masks after PA and Grouping of GGN, and choose top 20 objects to generate saliency maps. Here is the comparison with original SSUL on VOC 15-1. It can be observed that there is a performance drop for SSUL when using [b].\n\n ||base|novel|all|\n |:--:|:--:|:--:|:--:|\n |SSUL|77.3|36.6 |67.6|\n | SSUL + [b]|75.1|26.5|63.5|\n\n We would be happy to conduct additional experiments to illustrate the fairness of the comparison, if there are any other possible suggested settings.\n\n3. **[Experiments of using other region proposals networks such as RPN in Mask R-CNN]**\n There might be a misunderstanding. Proposals generated by RPN cannot be directly applied to our MicroSeg, since our method requires class-agnostic masks while RPN can only produce bounding boxes. To address the concerns, we conduct additional experiments using other types of mask proposals. Specifically, we generate proposals with MaskFormer and Mask2Former. We also explore the number of proposals $\\mathit{N}$.\n\n ||base|novel|all|#params.|\n |:--:|:-:|:-:|:-:|:-:|\n | MaskFormer($\\mathit{N}$=100)|79.3|34.1|68.5|44M|\n | Mask2Former($\\mathit{N}$=100)|80.1|36.8|69.8|107M|\n | Mask2Former($\\mathit{N}$=200)|80.4|37.3|70.1|216M|\n\n It can be observed that the quality of the proposal affects the experimental results to some extent, but MicroSeg still achieves SOTA performance, even with MaskFormer($\\mathit{N}$=100) (68.5 v.s. 67.6, compared to SSUL, in VOC 15-1). \n\n4. **[Missing speed comparison and model parameters with other methods]**\nAs suggested, we provide a comparison of the performance (mIoU) of VOC 15-1, computational complexity (GFLOPS) and model size (#params) of the three methods.\n\n ||mIoU|GFLOPS|#params.|\n |:-:|:--:|:-:|:-:|\n |PLOP| 54.6 |677|58M|\n |SSUL| 67.6 |211|60M|\n |MicroSeg (Ours)|**69.8**|234|65M|\n\n MicroSeg achieves performance gains of 2.2% at similar model sizes and GFLOPS. In addition, the model size of Mask2Former that we use for proposal generator is 107M. However, it is frozen to generate proposals without training. Note, even with a smaller scale MaskFormer (44M of model size), our proposed MicroSeg still achieves SOTA performance(68.5 for MicroSeg v.s. 67.6 for SSUL, in VOC 15-1).", " ### *Responses to weaknesses*\n1. **[Meaning of symbols in Label Remodeling (Sec. 3.3)]**\nThe symbol `∧` represents the co-taking of conditions, i.e. the satisfaction of two conditions. That is, both the conditions of (1) being labeled as background in ground truth and (2) having high confidence in the predictions of the $f_{t-1,\\theta}$ belonging to the past category, are satisfied. The symbol `\\` means the difference of the set, i.e. the part of the background that does not belong to the past categories. \n2. **[Description of MiscroSeg-M (the memory sampling strategy [5])]**\nThanks for the suggestions. The version of MicroSeg with memory (MicroSeg-M) was mainly presented for a fair comparison with SSUL-M. We will revise the paper to make it more clear.\n3. **[Formatting issues (missing full stops)]**\nWe appreciate the reviewer pointing this out, and will carefully and thoroughly check and revise the paper.\n\n### *Responses to questions*\n1. **[Label Remodeling symbols]**\nPlease refer to the response to the above weakness #1.\n2. **[How is the Proposal Generator trained? pretrained model from [8]?]**\nYes, we use the off-the-shelf Mask2Former pre-trained model to generate the proposals.\n", " This paper proposes a novel framework called MicroSeg for the catastrophic forgetting problem caused by the semantic shift of the background class. This paper pioneered the idea of considering unknown categories that may occur in the future in advance in background learning. More specifically, the idea is quite interesting with the assumption that background regions with strong objectness possibly belong to those concepts in the historical or future stages. Experiment results show promising results on Pascal VOC and ADE20K datasets. Strengths\n1. Overall the paper is well written, well illustrated, and subsequently pleasant to read.\n2. The method itself is clear and proposed contributions are really intuitive.\n3. The contributions and experiments are decent and clearly shows improvement over the state-of-the-art. Ablations are okay.\n\nWeakness\n1. The author proposes pre-learning for future categories, so the labeling of unknown categories that may appear in the future will be the key to this paper. However, Label Remodeling in Section 3.3 is not explained clearly. See the the Questions part for details.\n2. There are few descriptions of MicroSeg-M in the paper. It just shows that it uses the memory sampling strategy [5]. In my opinion, simply migrating other methods to this task may not be a contribution. If authors have no special design on MicroSeg-M, I suggest to remove it, since MicroSeg itself is interesting enough.\n3. There are several formatting errors in the article. For instance, there are no full stops on lines 42 and 66. The authors are desired to read the paper thoroughly and revise them carefully. 1. In the Label Remodeling part (i.e., Equation 3), what is the meaning of symbols, such as ^ and \\ ?\n2. The Proposal Generator has the ability to generate a binary map. How is it trained? Is it a pretrained model from [8]? The authors have well addressed the limitations.", " The paper proposes MicroSeg for class incremental semantic segmentation. The region proposal generator is used to detect the potential objects with strong objectness in the background. The these identified proposals are grouped into a new defined label during the optimization. Experiments are performed on both Pascal VOC and ADE20K to validate the idea. **Strengths**:\n\n1.The paper has a good motivation, where incremental semantic segmentation is a meaningful to explore and the discussed background shift problem is also difficult for existing models.\n\n2.The experiments show an obvious improvement to existing methods. Table 3 shows the effect of Proposal and Micro respectively.\n\n3.The paper is organized well with good writing and figures.\n\n**Weakness**:\n\n1.The tech contribution of MicroSeg is very limited. Region proposal network for class-agnostic detecting novel objects is already widely used, such as [a].\n\n2.SSUL uses the off-the-shelf saliency-map detector to detect unseen classes while the paper uses the pretrained Mask2Former to produce the region proposals. This may introduce an unfair comparison in both data and model size. Mask2former is additionally trained on COCO and has much larger parameters than the off-the-shelf detector. What if SSUL also adopts Mask2Former to detect unseen classes? Or what if SSUL can generate the object proposals in an unsupervised way w/o additional lots of data or heavy model, such as [b].\n\n3.Missing experiments of using other region proposals networks instead of using Mask2Former, such as the RPN in Mask R-CNN? Will it influence the final model performance a lot?\n\n4.Missing the speed comparison and model parameters with other methods. What are the model sizes of the proposed MicroSeg combined with Mask2Former?\n\n[a] Gu, Xiuye, et al. \"Open-vocabulary object detection via vision and language knowledge distillation. ICLR, 2022.\n\n[b] Open-World Instance Segmentation: Exploiting Pseudo Ground Truth From Learned Pairwise Affinity. CVPR, 2022.\n I will consider to raise the rating if my concerns in the above weakness section can be well addressed. Yes.", " This work address the \"semantic shift of the background class\" problem where some concepts learned at previous stages are wrongly assigned to the background class at the current training stage, in Class incremental semantic segmentation task. The authors first splits the given image into hundreds of segment proposals with a proposal generator pretrained on MSCOCO. Then the segment proposals with strong objectness from the background are clustered and assigned newly-defined labels during the optimization. Combining such supervision into a conventional dense prediction framework, the proposed method could relieve the catastrophic forgetting caused by the semantic shift of the background class accordingly. Experiments on Pascal VOC and ADE20K datasets show competitive results with state-of-the-art. Strength:\n\n1. The motivation is clearly presented and the method is straightforward to address the \"semantic shift of the background class\" problem where some concepts learned at previous stages are wrongly assigned to the background class at the current training stage, in Class incremental semantic segmentation task.\n\n2. The paper is well written and easy to follow.\n\n3. The overall performance of the proposed method is good and sufficient to verify the effectiveness of the proposed method.\n\n\nWeakness:\n\n1. The claim in Line 175~176 is not validated which it is valuable to see whether the proposed method could prevents potential classes from being incorrectly classified into historical classed.\n\n2. In Tab. 1, for VOC 2-2 (10 tasks) and VOC 19-1 (2 tasks) MicroSeg gets inferior performance compared with SSUL, the reason should be explained. It also appear in ADE 100-50 (2 tasks) in Tab. 2.\n\n3. The proposed method adopts a proposal generator pretrained on MSCOCO which aggregates more information. Is it fair to compared with other methods? Besides, could the proposed technique propmotes existing Class incremental semantic segmentation methods.\n Please see the weaknesses.\n\n------------------------------------------\nThe authors have addressed my major concerns. I would stick to my original score. The authors adequately addressed the limitations and potential negative societal impact of their work.", " The authors propose a novel way to cluster the unseen classes present in the background using K different background components and a pre-trained class-agnostic mask proposal generator (Mask2Former). The results show a clear improvement from pixel-wise methods, which is further improved by the micro mechanism.\n Strengths:\n- Clear improvement in the benchmarks over current SOTA\n- Interesting approach for mining unseen classes and perform pseudo clustering of these\n- Good comparison of how stable the performance is under different class orders on Pascal (Fig 3c).\n\nWeaknesses:\n\nSome claims of novelty seems exaggerated and require revision/clarification, i.e.\n- Experimental settings:\n - The different settings that are \"introduced\" are not new, i.e. \n - Pascal VOC 10-1 and ADE20k 100-5 were used in PLOP [11]\n - Pascal VOC 10-1 + 5-3 and ADE20k 100-5 were all used in SSUL [5] \n - \"RECALL: Replay-based Continual Learning in Semantic Segmentation\" (ICCV2021) has not been referenced in the paper though they also proposed the 10-1 setting as well as 10-10 and 10-5.\n- Mask2Former:\n - Partly unclear which parts of the proposal generation and classification that differs from Mask2Former for semantic segmentation.\n\nNo ablation study of how the number of components in the Micro mechanism affects the results, which would be interesting since this is the main contribution of the paper. The choice of K=1 for ADE20k seems conter-intuitive, since ADE20k contains much more classes than Pascal and clustering these into a single component would enforce similar feature representations for all unseen classes.\n\nIt would have been interesting to see how the performance varies for different class orders on ADE20k since the class-frequency decreases drastically between stuff and things and as the original index increases. (As done in MiB and SDR)\n - The disjoint setting as it is described would allow future classes unlabeled in the background contrary to the definition of disjoint in MiB [4]. Is this an actual change of the setting or just a mistake in the description?\n- Are the joint results on ADE20k based on the proposed architecture, including the Mask2Former or for the base DeepLabv3 model (the results are identical to those reported in [4], which seems low if the Mask2Former also is used since they achieve 47.7 using ResNet50 by training on ADE20k)?\n- Please specify which pre-trained weights that are used for the ResNet-101 network for facilitating reproducibility\n- How does the proposed split of segment proposals and classification differ from [8]? And is the splitting of the task into segment proposal and classification novel for semantic segmentation or for CISS?\n- Does the performance of the proposal generator differ between classes present and absent in MS-COCO? \n- Is the contrastive loss only applied to the background? And if so, is this the background before or after pseudo-labeling?\n- Which losses are applied to the baseline in Tab 3? It seems to perform better than all methods except for SSUL by only using pseudo-labels? Yes, though there would be room to further discuss the importance of the pre-training of the proposal generation and possible limitations of it when studying data which differs more than COCO/Pascal/ADE20k.", " This paper proposes a new method for class-incremental segmentation. Based on the assumption that background regions with strong objectness possibly belong to those concepts in the historical or future stages, this paper introduces a proposal generator for generating multiple segment proposals. Also, some tricks including label remodeling and the new loss functions are designed. The proposed method gains good performance on Pascal VOC and ADE20K. I appreciate the motivation of this work, which is well presented in the introduction. Also, I believe the proposed method makes sense and is somehow novel. \n\nMy main concern of this work is the writing. I suggest the authors to reconstruct this paper in a clearer form. Many parts of this paper are quite confusing and hard to understand. Also, it lacks a lot of details, so that it is hard for others to follow. Below are some of the weaknesses:\n\n1. This paper proposes a proposal generator. However, the detailed structure of the generator is not clear. \n\n2. In Line 142 to Line 143, 'Then $P$ is *reorganized* to the original shape and the prediction scores are assigned accordingly'. I can understand this after checking Figure 2. However, I think it may be better if the authors illustrate this step more clearly by words or equations. \n\n3. Why the contrastive loss (Equation 7) is used for optimization? The motivation and prupose are not clear. \n\n4. What's the value of $\\tau$ in Equation 3? It is not illustrated in the implementation details. \n\n5. Some ablation experiments are missed. For example, how the settings of hyper-parameters $N$, $K$ and $\\tau$ affect the performance?\n\n Please refer to the weaknesses part for details.\n\nI cannot recommend accepting this work at its current version considering the high standards of NeurIPS. However, considering the interesting motivation and the relatively novel method, I suggest the authors to carefully revise the paper. I believe it would be a good work if the writing is clearer. NA" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 4, 7, 7, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 5, 4, 4 ]

[ "9pkawbgfbCV", "iyab_oHosrW", "HgbtnaAIJFy", "0CAc7e-R8Su", "vuZtZZx9iuw", "nips_2022_G1vrYk9uX-_", "nips_2022_G1vrYk9uX-_", "o8XW_AWYMIy", "KUfDHslwyRP", "5S1y4w8nq8D", "bloyOSjfIy", "BpKJv8eLxs-", "IC0WdkM92H_", "9fajU1YZK6A", "21KaTFRC6KD", "nips_2022_G1vrYk9uX-_", "nips_2022_G1vrYk9uX-_", "nips_2022_G1vrYk9uX-_", "nips_2022_G1vrYk9uX-_", "nips_2022_G1vrYk9uX-_" ]

[ "9jLNNFAoyOi", "6S6TyTKN74r", "mw1pMJDfTbG", "xBNx6nOPkuY", "ct6tRWNXfj1", "LNfHalPt0y9", "IhT0cGJ_okD", "lZByZKH5iqP" ]

[ "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " **Q6**\n*In Equation (10), it is not clear why learned weights are needed to transform both the class tokens and the modality specific features. Is it not equivalent to just transform the features? That is $Ax\\cdot By = x^TA^TBy = B^TAx\\cdot y = Wx\\cdot y$, where $W=B^TA$.*\n\nYes, they are theoretically equivalent. \nHere, we just adopt a common practice that uses individual learnable linear projections for transforming query and key in the multi-head attention operation.\nIn our CUG block, query and key refer to the features and class tokens of each individual modality.\n\n\n**Q7**\n*In Equation (12), the notation is not clear. The $\\mathbf{1}$ is not clear to me. I was expecting to see a label for the presence of the class. I'm probably misunderstanding something, but in any case, I think this needs to be better explained. Perhaps writing out the CE formula element by element would clarify. Also, maybe (13) should come before (12) for clarity.*\n\nIn Equation (12), $\\mathbf{1}$ should be one-hot encoding and only its element for the target entry $i$ is 1.\nWe follow your suggestion and re-write the formula element by element as\n$\\mathcal{L}_{cls} = \\sum_i \\mbox{CE}(\\mathbf{h}_i, \\mathbf{e}^a_i)+\\mbox{CE}(\\mathbf{h}_i, \\mathbf{e}^v_i)$,\nwhere $\\mbox{CE}(\\cdot)$ refers to cross-entropy loss; $\\mathbf{h}_i$ is an one-hot encoding vector and only its element for the target class entry $i$ is 1;\n$\\mathbf{e}^a_i, \\mathbf{e}^v_i$ are category predictions of learned tokens for each individual modality.\n\nIn Equation (13),\n$\\mathbf{p}^a, \\mathbf{p}^v$ are video-level event category predictions for audio and visual inputs of the video. Thus, there is no a direct relation between Equation (12) and Equation (13). \nPreviously, we used $\\mathbf{p}_i^{a}$ and $\\mathbf{p}_i^{v}$ to denote the token class probabilities, which causes the concern. \nNow we have used $\\mathbf{e}$ to replace $\\mathbf{p}$ in Equation (12). \n\nWe have clarified these in the revision (Line 152-157).\n\n\n**Q8**\n*Errata:\nIn order to explicitly group~ing~ class-aware…*\n\nWe have fixed the typo in the revision (Line 134).\n", " **W1**\n*The performance on audio events is not improved.*\n\nAs we discussed in Sec 4.4, although the proposed MGN achieves superior results on visual events and audio-visual events, the gains of audio event parsing are not significant compared to the visual modality. We observed that audio content is much nosier in videos. Different visual objects are naturally separated in video frames. However, multiple audio sources can be mixed together at the same time, and not all of the sources are visually appeared, which makes it challenging to disentangle noise-free features for grouping. Thus, to improve the new multi-modal grouping-based architecture, one promising direction is to further enforce separating individual audio sources in the grouping mechanism.\n\n\n**W2**\n*The analysis of false positives in Figure 3 is useful, but it seems like the models are just biased to different operating points, since their F-scores in table 1 are similar. So the reduction of false positives in Figure 3 must come at the cost of a decrease in recall. It would be better to show both numbers, or calibrate to the same operating point.*\n\nThanks for the suggestion! We have added the comparison of recall to Sec.D in the appendix.\nThe reduction of false positives by the proposed MGN over baselines indeed comes at the cost of a decrease in recall for audio, visual or audio-visual events.\n\n**Q1** \n*The paper is a bit difficult to understand due to notational issues.*\n\nWe have proofed each line and fixed notational issues below in the revision.\n\n\n**Q2**\n*\"These methods without explicit grouping suffer from false predictions due to the modality and temporal uncertainties.\"\nIt is not clear to me why that should be at this point in the paper. Is this an empirical finding or a hypothesis?*\n\nThis is an empirical finding obtained after looking at results of previous models (e.g., HAN [3]) on the LLP dataset. \n\n\n**Q3**\n*Re: Equation (6), cross entropy is usually from labels to estimates, so I would expect $CE(p,\\hat{p})$, but here it seems to be used the reverse way. Also this looks like a vectorized version with binary probabilities in the elements. It might be good to define it since technically cross entropy is defined over a distribution, rather than a vector of distributions. That is, I think what is meant is something like $CE(\\mathbf{y},\\mathbf{p}) = \\sum_{i}CE(y_i,p_i)$. If not please clarify.*\n\nSince it is a multi-label multi-class problem, the CE($\\cdot$) in Equation (6) is a binary cross-entropy function-based loss term, which summarizes binary cross-entropy for all categories.\nThus, $CE(\\mathbf{y},\\mathbf{p}) = \\sum_{i}BCE(y_i,p_i)$.\nTo avoid confusion, we replaced the CE($\\cdot$) with $\\mbox{O}(\\cdot)$ in Equation (6).\nWe have clarified it in the revision (Line 123-125).\n\n\n**Q4** \n*In the cross-modal attention $\\phi_{ca}(q, K, V)$, my understanding is that the key and value should be of the same modality, and the query of the other modality.\nSo if I understand correctly, in equation (1) $\\phi_{ca}(f_t^{v}, F_v, F_a)$ is probably supposed to be $\\phi_{ca}(f_t^{a}, F_v, F_v)$, and in equation (2) $\\phi_{ca}(f_t^{a}, F_a, F_v)$ should be $\\phi_{ca}(f_t^{v}, F_a, F_a)$.*\n\nThanks for pointing this out.\nYour understanding is correct, as we defined in Equation (4) for $\\phi_{ca}(f_t^{a}, F_v, F_v)$.\nThis is a typo, and we have fixed it in the revision (Line 113).\n\n\n**Q5**\n*From equation (7) on, the notation for self-attention changes without warning from a three-argument function to a one argument function , which I assume in the notation of (3) would be $\\{\\phi_{sa}(x_i, X, X)\\}_{i}$, but it would be kinder to the reader to just define it.*\n\nThanks for your kind suggestion!\nWe have modified it in the revision (Line 138-139).", " **W1**\n*However, it is heavily inspired from recently proposed GroupViT for image segmentation. Though the authors outline the differences between proposed approach and GroupViT in supplementary material, they are very nuanced and not significant.*\n\nYes, our method is inspired by the recent image segmentation method: GroupViT. However, not simply using GroupViT to solve the audio-visual video parsing problem, there are three significant differences between GroupViT and the proposed MGN in the grouping mechanism design as mentioned in the supplementary material:\n\n1) **No Constraint on Class Tokens**: the number of learned group tokens in GroupViT is a hyper-parameter and there is no constraint on it. However, we propose to learn categorical tokens with a semantic-aware constraint, i.e., each class token does not have semantic overlapping information among each other.\n\n2) **No Modality-aware Cross-modal Grouping**:\nwe involved the audio modality in the modality-aware cross-modal grouping to eliminate the modality uncertainty caused by the weakly-supervised setting in the task.\nBut GroupViT does not incorporate the text modality into the grouping stage and utilizes a contrastive loss to match with the global visual representations.\n\n3) **No Class-aware Unimodal Grouping**:\nGroupViT only leverages the unimodal grouping on visual patch tokens without class tokens involved, while we introduced the class-aware unimodal grouping with learnable class tokens for mitigating the temporal uncertainty in each individual modality.\n\n\n**Q1**\n*The model uses pre-trained ResNet and VGGish net for model input, both of which are very good feature extractors. What is the importance/requirement of using such feature extractors on the final result. More specifically, LLP dataset is derived from Audioset and VGGish net is trained in a supervised fashion using AudioSet, which makes it an ideal feature extractor. Can the author's comment if the unimodal grouping network would still be effective if not for such feature extractor.*\n\n(1) The proposed MGN is not dependent on a specific audio feature extractor, and there is no assumption on unimodal grouping for using what kinds of audio features.\n\n(2) We want to clarify that the adopted audio feature extractor: VGGish model was trained on YouTube-8M instead of AudioSet (https://github.com/tensorflow/models/blob/master/research/audioset/vggish/README.md). So, the used VGGish model might not be an ideal feature extractor for LLP and the grouping network should still be effective even not using this feature extractor. \nBut we do agree with the reviewer that a VGGish trained using the full AudioSet should be more powerful. \n\n\n**Q2**\n*How does the model perform with event scaling? (Any reason to limit the study to LLP and not use full AudioSet)?*\n\nThis is a good question! \nAlthough the AudioSet is a video dataset containing both audio and visual tracks, it was organized and collected only regarding audio content. The dataset only has audio event labels and lacks of visual event annotations (audio and visual events are not always in the same categories in real-world videos). \nFor our audio-visual video parsing model, the weak labels should reflect both audio and visual events in videos. So, we need additional visual event annotations for training our network. Besides, there is no segment-level annotations for evaluation.\n\n\n**Q3** \n*Regarding implementation (line 188), How low can the time-resolution go? (ie., instead of 1s snippets, can 0.1s snippets be used?*\n\nToo short audio events are hard for neural networks, even for human beings, to perceive the event category. As suggested in a sound event detection challenge (https://dcase.community/challenge2018/task-large-scale-weakly-labeled-semi-supervised-sound-event-detection), the time-resolution can be lower to 0.25s.\n\n\n**Q4**\n*in Table2, why does using CUG only makes “Audio” result worse when compared to not using ? (row1 vs row2)*\n\n In the LLP dataset, audio content is noisier compared to the visual modality. \n So only using CUG may propagate noisy segment-level features.\n But leveraging the visual information as a condition in MCG boosts the Audio result, which demonstrates the necessity of integrating both CUG and MCG.\n\n\n", " **W1**\n*The introduction of this paper is not strongly motivated, but only with a general and brief description. The introduction lists several related papers but the relations of these papers to the proposed model are not well illustrated.*\n\nOur key motivation is to learn compact and discriminative audio and visual representations by explicit multi-modal grouping for mitigating the modality and temporal uncertainties in the weakly-supervised audio-visual video parsing problem.\nExisting approaches [3,4,5] usually focus on learning to leverage the unimodal and cross-modal temporal contexts from weak supervisions. During training, segment-wise event labels are unavailable for audio and visual temporal segments in videos. Thus, the multi-modal temporal modeling in these methods might aggregate and implicitly group irrelevant semantic information due to lacking of fine-grained supervision, which causes false positives for predicting categories of events, as shown in Figures 3 and 4. Different from past approaches, we propose a new Multi-modal Grouping Network, namely MGN, to explicitly group semantic-aware multi-modal contexts, which enables learning more compact and discriminative audio and visual representations. We have modified our introduction accordingly (please kindly check the highlighted red texts in the revised paper). \n\n\n**W2**\n*L63: \"The experiments can demonstrate the superiority of our MGN over state-of-the-art AVVP approaches and its generalizability to contrastive learning and label refinement.\" When the authors first mention \"contrastive learning and label refinement\" [4] in the introduction, these two concepts are not explained but directly appear with citation to another paper, which makes the paper reading confusing.*\n\nThanks for pointing this out! Contrastive learning and label refinement are proposed in [4], where they adopted a contrastive loss to enforce the temporal alignment between the audio and visual features at the same timestamp and augmented training data with modality-aware event labels generation.\nWe have clarified them in the revision (Line 32-35).\n\n\n**W3**\n*For the results in \"Table 2: Ablation studies on Class-aware Unimodal Grouping (CUG) and Modality-aware Cross-modal Grouping (MCG) blocks, each of CUG block and MCG block is ablated as a whole. What about the effects of the design choices in each block? E.g. the effect of concatenating class labels in Class-aware Unimodal Grouping (CUG) block?*\n\n1) Thanks for the suggestion! We explored different design choices inside each block in the appendix, such as depth in Sec.B and grouping strategy in Sec.C.\n\n2) For the effect of concatenating class labels, this design choice is not feasible.\nThis is because we can only access video-level event labels during training, and we do not know which temporal segments contain and which modalities perceive these events.\nIf we concatenate video-level event labels in CUG block, those labels leak cross-modal clues in the unimodal grouping process, which deteriorates the discriminativeness and compactness of unimodal representations.\nTo learn compact and discriminative audio and visual representations, we extract event-aware unimodal features through unimodal grouping in terms of learnable categorical embedding tokens for each individual modality.\n\n\n**W4**\n*Only one dataset is experimented on.*\n\nTo the best of our knowledge, the LLP dataset is the only existing benchmark for the audio-visual video parsing problem.\nBut it is large and indeed challenging as it comes from more than 11,000 YouTube video clips of 10-seconds long from 25 different event categories.\n\n\n**Q1**\n*L58: \"We propose a new audio-visual video parsing baseline.....\" Why is the proposed model called a \"baseline\"?*\n\nRecent audio-visual video parsing methods usually adopt HAN [3] as a baseline and add new modules and losses over it. Our MGN as a novel audio-visual video parsing architecture can flexibly integrate these advanced designs to boost performance. Thus, we call the proposed MGN as a new \"baseline\".\n\n\n**Q2**\n*For the results in Table 1, the best result for \"Event-Level\"-\"A\" is not highlighted. Why?*\n\nIn Table 1, we only highlighted the result when our method surpasses the baseline in terms of same-level comparisons, such as 60.8 and 60.0 in \"Segment-Level\"-\"A\". To keep the notation consistent, we now highlight all of the best results in the modified Table 1. \n", " We thank all the reviewers for carefully reading our paper and providing constructive comments! \nWe address concerns from the three reviewers as below. \n", " This paper tackles weakly-supervised audio-visual video parsing, and proposes a Multi-modal Grouping Network to explicitly group class-aware matching semantics with class-aware unimodal grouping module and modality-aware cross-modal grouping module. Experimental results are shown on the Look, Listen and Parse (LLP) Dataset with the generalizability to the audio-visual contrastive learning and label refinement. - Strengths:\nThis paper tackles weakly-supervised audio-visual video parsing considering the asynchronous possibility of the two modalities.\n\n- Weaknesses:\n1. The introduction of this paper is not strongly motivated, but only with general and brief description. The introduction lists several related papers but the relations of these papers to the proposed model are not well illustrated.\n\n2. L63: \"The experiments can demonstrate the superiority of our MGN over state-of-the-art AVVP approaches and its generalizability to contrastive learning and label refinement.\" When the authors fist mention \"contrastive learning and label refinement\" [4] in the introduction, these two concepts are not explained but directly appear with citation to another paper, which makes the paper reading confusing.\n\n3. For the results in \"Table 2: Ablation studies on Class-aware Unimodal Grouping (CUG) and Modality-aware Cross-modal Grouping (MCG) blocks, each of CUG block and MCG block is ablated as a whole. What about the effects of the design choices in each block? E.g. the effect of concatenating class labels in Class-aware Unimodal Grouping (CUG) block?\n\n4. Only one dataset is experimented on.\n\n\n\n 1. L58: \"We propose a new audio-visual video parsing baseline.....\" Why is the proposed model called a \"baseline\"?\n2. For the results in Table 1, the best result for \"Event-Level\"-\"A\" is not highlighted. Why? The authors list the model limitations of limited data, and worse performance with deeper network, and point out the possible solutions of semi-supervised training and incorporating more intermediate supervision. The authors also point out the case of rare events in real deployment, which is practical and has corresponding techniques focusing on the case.", " The authors present a new baseline architecture for video parsing. Using learnable categorial embedding tokens they propose class-aware unimodal grouping network in conjunction with a cross-modal grouping network to time-stamp audio, visual and audio-visual events using only video level labels. They show improved results compared to other baselines on LLP dataset. The manuscript discusses the important problem of video parsing with very coarse labels. It is well written and easy to read through. The limited number of experiments presented are through and insightful. The proposed method if effective compared to other baselines as evident from the qualitative and quantitative results. However, it is heavily inspired from recently proposed GroupViT for image segmentation. Though the authors outline the differences between proposed approach and GroupViT in supplementary material, they are very nuanced and not significant. - The model uses pre-trained ResNet and VGGish net for model input, both of which are very good feature extractors. What is the importance/requirement of using such feature extractors on the final result. More specifically, LLP dataset is derived from Audioset and VGGish net is trained in a supervised fashion using AudioSet, which makes it an ideal feature extractor. Can the author's comment if the unimodal grouping network would still be effective if not for such feature extractor. \n- How does the model perform with event scaling ? (Any reason to limit the study to LLP and not use full AudioSet)?\n- Regarding implementation (line 188), How low can the time-resolution go? (ie., instead of 1s snippets, can 0.1s snippets be used?)\n- in Table2, why does using CUG only makes “Audio” result worse when compared to not using ? (row1 vs row2) see *Questions* section.", " This paper addresses the problem of predicting event labels over time in audio visual data with weak labels. A method is proposed that uses attention between audio visual features and learned class embeddings, and extracts class-specific embeddings for use in event detection. The model is evaluated on the Look, LIsten, and Parse dataset, using 11K video clips with video labels for training, and around 2K video clips with both audio and video labels for evaluation. \nStrengths:\nThe proposed method is an interesting idea, and seems to help with the task. \nSmall improvements are achieved on a challenging task evaluated on a sufficiently large test set. \n\nThe ablations in Table 2 are informative. \n\nWeaknesses: \nThe performance on audio events is not improved.\n\nThe analysis of false positives in Figure 3 is useful, but it seems like the models are just biased to different operating points, since their F-scores in table 1 are similar. So the reduction of false positives in Figure 3 must come at the cost of a decrease in recall. It would be better to show both numbers, or calibrate to the same operating point. \n\n\nClarity: \n\nThe paper is a bit difficult to understand due to notational issues\n\n> These methods without explicit grouping suffer from false predictions due to the modality and temporal uncertainties.\n\nIt is not clear to me why that should be at this point in the paper. Is this an empirical finding or a hypothesis?\n\nRe: equation (6), cross entropy is usually from labels to estimates, so I would expect $CE(p,\\\\hat{p})$, but here it seems to be used the reverse way. Also this looks like a vectorized version with binary probabilities in the elements. It might be good to define it since technically cross entropy is defined over a distribution, rather than a vector of distributions. That is, I think what is meant is something like $CE(\\\\mathbf{y}, \\mathbf{p}) = \\\\sum_i CE(y_i, p_i)$. If not please clarify. \n\nIn the cross-modal attention $\\\\phi_{ca}(q,K,V)$, my understanding is that the key and value should be of the same modality, and the query of the other modality. \nSo if I understand correctly, in equation (1) $\\\\phi_{ca}(f^v_t, F^v, F^a)$ is probably supposed to be $\\\\phi_{ca}(f^a_t, F^v, F^v)$ , and in equation (2) $\\\\phi_{ca}(f^v_t, F^a, F^v)$ should be $\\\\phi_{ca}(f^v_t, F^a, F^a)$.\n\nFrom equation (7) on, the notation for self-attention changes without warning from a three-argument function to a one argument function $\\\\phi_{sa}(X)$, which I assume in the notation of (3) would be $\\\\{\\\\phi_{sa}(x_i, X, X)\\\\}_i$, but it would be kinder to the reader to just define it. \n\nIn equation (10), it is not clear why learned weights are needed to transform both the class tokens and the modality specific features. Is it not equivalent to just transform the features? That is $Ax \\\\cdot By = x^T A^T B y = B^T A x \\\\cdot y = W x \\\\cdot y $, where $W = B^T A$. \n\nIn equation (12), the notation is not clear. The $\\\\mathbf{1}$ is not clear to me. I was expecting to see a label for the presence of the class. I'm probably misunderstanding something, but in any case, I think this needs to be better explained. Perhaps writing out the CE formula element by element would clarify. Also, maybe (13) should come before (12) for clarity. \n\n\nErrata:\n\n> In order to explicitly group~~ing~~ class-aware...\n\n\n See Weaknesses above for some questions. The authors acknowledge that performance on audio events is not improved." ]

[ -1, -1, -1, -1, -1, 4, 6, 6 ]

[ -1, -1, -1, -1, -1, 4, 3, 4 ]

[ "6S6TyTKN74r", "lZByZKH5iqP", "IhT0cGJ_okD", "LNfHalPt0y9", "nips_2022_zfo2LqFEVY", "nips_2022_zfo2LqFEVY", "nips_2022_zfo2LqFEVY", "nips_2022_zfo2LqFEVY" ]

[ "tDD6FC8249", "3-K8RnSHNX", "PnCPScbqvZ", "a73dv8IIqFm", "ZGdTXTs7Yxl", "REekGxlmnge", "GIj57bviwux", "3YHsS2z31C8T", "V-W9UZRuazp", "vTN8dcV8Nm", "DJ7YBXUfiqR" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer" ]

[ " Thanks for responding to our rebuttal, we would like to further discuss some of the details as follows.\n\n1. **`The definition of optimal padding`**\n - To clarify, Eq (1) and Eq (2) are the definitions of paddings, following how images are captured from the physical world. It is not clear to us why the definition is questionable. Could the reviewer clarify which part of the definition is questionable or counter-factual? We would like to know what the reviewer means and address the issues, as the definition of PPP is entirely based on such a definition.\n - Regarding the misunderstanding of randn padding is optimal padding, we will add an additional note to Section 2.4 that randn padding is algorithmic padding. Please note that Sections 2.1 to 2.3 have already given out a complete definition of optimal padding (Section 2.1), PPP (Section 2.2), and PPP metrics (Section 2.3). Section 2.4 does not have any argument or symbol that establishes it is optimal padding, or alternates any of the definitions that were already given in previous sections.\n\n2. **`What the \"optimal\" is?`**\n - Eq (2) has defined what the optimal padding should be, based on how images are captured from the physical world. It is the original pixels on S* without the S* -> S’ cropping (i.e., image capturing process). Since they are the ground truth pixels, therefore they are the optimal padding pixels.\n\n - **`it is a little challenging to convince myself this cropped image can be considered the optimal`** The cropped image (S’) is not the source of optimal padding, the uncropped images (S*) define the optimal pixels (in Eq (2)). We use the satellite images to simulate the uncropped S* set, as they are much larger than the receptive field of the CNN models tested in the paper.\n\n3. The terminology of using SNR-PPP and MAE-PPP\n - Could the reviewer specify the alternative terms intended for us to switch to? The response seems to agree the terms MAE and SNR are not the main issues the reviewer intends to discuss. Instead, the main concern is still on the definition of “optimal” padding, which has no relation to the terminology of MAE-PPP and SNR-PPP. We would like to know what the reviewer means and address the issues. \n", " Thank the authors for this explanation. However, this explanation makes the draft even harder to understand.\n1. Following the draft, from Section 2.1, Eqs(1) and (2) show the definitions of the \"optimal\" padding scenario(this is questionable). Then Section 2.2 discusses PPP, section 2.3 shows the \"proposed\" metrics, then Section 2.4 shows the \"proposed\" padding strategy. This organization is very misleading. \n\nThe whole paper is built on top of the fundamental question for formulation Eqs(1) and (2), without a proper explanation or statement, the first proposed method is shown in Section 2.4, so naturally this would be considered related to the problem formulation Eq(2). Line 42-43, \"To weaken the effect of PPP,.. Section 2.4\", also misleads to this understanding.\n\n2. I read lines 86-91 again, but it simply shows how to \"calculate\" the \"optimal\" padding, instead of explaining what the \"optimal\" padding should be. Line 86-91 and Eq(3) only show the PPP is defined as the \"difference\" between the \"optimal\" padding and an algorithmical padding, no explanation on what the \"optimal\" is, as introduced in Eq(2). This question is the most important and fundamental to this study, if this this question is not clearly defined, then all the proposals are a little lame. \n\nBack to your explanation on the satellite images, there is no discussion or explanation about this in Section 2.1. More importantly, it is a little challenging to convince myself this cropped image can be considered the \"optimal\". If that was \"optimal\"(I personally doubt this), why wouldn't use that (or cropped images for vision tasks) but the proposed Randn?\n\n3. The authors agree that they did not intend to emphasize the terms, but from the paper and the responses to other reviewers, MAE-PPP and SNR-PPP are still widely used to show their efficacy, this \"contribution\" can be simply interpreted as this paper applies MAE and SNR to measure the difference between the proposed \"optimal\" and an algorithmic padding, while why the proposed padding can mimic the \"optimal\" is not properly discussed and the definition of the \"optimal\" is omitted in this draft. Thus no matter what metrics are applied, (other than SNR or MAE), it can not solid measure the PPP.", " Dear reviewer,\n\nThanks for the comments. We have replied to your questions and wonder whether you have additional comments or not. We would like to address all the questions that you have.\n\nThanks,\n\nNeurIPS 2022 Conference Paper924 Authors", " \nDear Reviewer MMJm,\n\nThanks for the comments. We have replied to your questions and wonder whether you have additional comments or not. We would like to address all the questions that you have.\n\nThanks,\n\nNeurIPS 2022 Conference Paper924 Authors", " Dear reviewer,\n\nThanks for the comments. Please read our response to your questions and let us know if you have additional questions as the discussion phase ends on August 9.\n\nThanks,\n\nNeurIPS 2022 Conference Paper924 Authors", " 1. **`Evaluate on only one dataset`**: \n - For the number of samples, we want to highlight that our PPP metrics already achieve extremely low deviation with 480 images, therefore the number of samples is not an issue for the evaluation. \n - We add two additional datasets to evaluate PPP metrics on all models presented in the paper. Finding a dataset with a large field-of-view with diverse content (as we want the optimal-padding features to be realistic) is non-trivial. Therefore, we collect 1024 images at 2048x2048 pixels, synthesized by InfinityGAN [1] trained on Flickr-Landscape and LSUN-tower. The evaluation results are attached with the following *anonymous* links:\n\n - **Comparisons among three datasets**: https://i.imgur.com/hSv7YaW.png\n - (red denotes the strongest, blue denotes the weakest)\n\n - **Comparisons of randomly initialized networks**: https://i.imgur.com/hDtBlLf.png\n\n The results show that (a) PosENet still maintains an unacceptable high deviation, (b) the significant PPP gain over model training is consistent with our previous observations, (c) MAE-PPP shows significantly better cross-dataset consistency than all other metrics, and (d) SNR-PPP sometimes recognizes certain models with high peak signal with relatively low MAE-PPP (which measures the average differences of PPP). A solution toward addressing PPP should suppress both SNR-PPP and MAE-PPP. We will include the additional results in the paper and add corresponding discussions.\n\n\n2. **`Can the authors add some discussion on the implications of Fig. 5 and Section 4.3?`** \n Thanks for the suggestion, we will add the following description to Section 4.3. \n\n - “The results show that the network progressively learns to reinforce PPP as a favorable representation. Therefore, future methods in addressing PPP should be focusing on debiasing such a learning process (e.g., design paddings invisible to the network, or make the position-information less favorable with other replaced representations).“\n\n\n3. **`What can be more quantitative metrics to justify a good PPP metric?`** \n - For a metric, it is **essential** to have a low deviation. Otherwise, the numbers are not meaningful or comparable. PosENet is trivially dissatisfactory from this perspective, and shall not be used in any future studies.\n - Could the reviewer provide more details on the expected other ways to compare the quality of a metric? From our perspective, the question implies a high deviation is not sufficient to prove PosENet is not a valid metric, where an additional metric is needed to address the issue. Some additional details on the issue can help us address the concern.\n\n[1] “InfinityGAN: Towards Infinite-Pixel Image Synthesis”, ICLR’22.\n", " This paper proposes a novel metric for measuring and visualizing the encoded positional information arising due to padding in Convolutional Neural Networks. They formally define the encoded information as PPP (Position-information Pattern from Padding) which measures the distance between feature maps arising from an algorithmic padding (such as zero padding) and an optimal notion of padding (i.e. the ground truth pixels that would be around the image). They demonstrate that PPP is a more reliable metric (low variance) than alternate metrics and hence it is useful for measuring the effectiveness of methods debiasing PPP due to padding. They show that PPP is a representation that the network develops as a part of its learning process. ## Strengths\n1. The paper is well-written, and contains sufficient details.\n2. The proposed problem of determining the amount of position information encoded due to padding is important as it can be interfering to actual cues and degrade model performance.\n3. The proposed metric is motivated well, and the analysis of PPP and prior works is thorough.\n4. The idea of using an optimal padding scheme to quantify PPP is sound and reveals consistent patterns in experiments.\n​\n## Weaknesses\n1. The evaluation is conducted on only one dataset of just 480 images. A more thorough investigation can be done by incorporating diverse datasets and observing the consistency of PPP as a metric over PosENet.\n2. Fig. 5 and Section 4.3 demonstrate that PPP is a representation that the network favorably develops as a part of its learning process. Can the authors add some discussion on the implications of this? What new insights can be drawn from this experiment? What can be more quantitative metrics to justify a good PPP metric? Currently, the majority of the focus is on the large standard deviation of PosENet. However, there must be other ways to compare which metric is a better representative of measuring the result of padding. The authors already mention an important limitation of PPP being linked to the architecture of the network as it is evaluated on the outputs of a model.", " We sincerely thank the comprehensive review. Here, we discuss the raised weaknesses and questions:\n1. **`I can only guess the “optimal” refers to the randn padding.`**\n - No, randn padding is also algorithmic padding as defined in Eq (1), which is different from optimal padding (defined in Eq (2)). We simulate the behavior of optimal padding with the satellite dataset introduced in Line 205. More specifically, the dataset is served as the S* set described in Line 64. And therefore all variables in Eq (1), (2), and (3) can be derived, as long as all images of S* are large enough.\n\n - Here we describe one of the possible realizations of Eq (1), (2), and (3) below. Note that any implementations following the same definition will obtain the same results.\n\n - Given a collection of satellite images at KxK pixels. Following Eq (1) and Eq (2), after a model is fully trained at NxN pixels, we can calculate the second term of Eq (3) (i.e., algorithmic padding part) by cropping NxN regions from the satellite images. Meanwhile, for the first term of Eq (3) (i.e., optimal padding part), we crop a much larger MxM region from the satellite images and set the model to no-padding mode. With such, the model automatically pads the features with realistic features produced by the pixels between the MxM region and the NxN region and follows the definition of optimal padding in Eq (2). \n\n - Note that K can be any number larger than or equal to M (note M>N), and its value does not affect PPP as long as K>=M. The M value is architecture-dependent, and we obtain the values in Appendix A.\n\n - We acknowledge that it may not be straightforward to derive such an implementation from the symbols in Eq (1), (2), and (3). We will add a section in Appendix to explicitly describe the aforementioned realization of the equations.\n\n2. **`I suggest a more thorough study on how the “optimal” padding can be achieved.`** The procedure of obtaining optimal padding is described between lines 86-91. We describe one of the possible implementations above. Any approach following Eq (1), (2), and (3) will yield the same results.\n\n3. **`SNR and MAE are not the main focus.`** Indeed, we did not emphasize these two functions as the core contribution, they are just a prefix of PPP. They are two simple functions aggregating the information reported by PPP, as PPP is a complicated and high-dimensional signal. Any reasonable aggregation (e.g., L2) can serve the purpose.", " We sincerely thank the comprehensive review. Here, we discuss the raised weaknesses and questions:\n\n1. **`How will this technology actually be used?`** The padding-related exploration is a fundamental building block to any existing or future architectures. Recently, researchers started to pay attention to paddings and the effect paddings induce. To better evaluate the efforts made in this field, we show that existing metrics are problematic, and we propose an improved metric. The proposed PPP metric serves as a better evaluation for any future methods related to positional information from padding. Furthermore, our results show that changing the padding scheme does not completely resolve the issue. The observation is a reminder to existing and future users adopting this workaround that the problem is not resolved yet.\n\n2. **`A solution is not discussed.`** \n - The major focus of the paper is to provide a reasonable metric to any future attempt toward understanding or removing positional information caused by paddings. To this end, the proposed PPP is the solution. A correct metric for the problem is required, especially when there are misunderstandings and erroneous conclusions drawn from previous publications in top-tier conferences (CVPR and ICLR). Without the correct understanding, improving the wrong metrics can never resolve the issue we are discussing. As shown in our paper, the proposed PPP metrics are improved replacements for previous metrics. \n\n\n - As for the solution to the position information encoded by paddings, we believe the solution cannot be developed without reasonable metrics. Therefore, our whole paper aims at showing the problems of existing metrics, and demonstrating the new PPP metrics indeed resolve the issues.\n\n3. **`Can the authors explicitly explain what type of understanding one reaches by looking at the PPP maps?`** \nDirectly looking at the map only shows how strong PPP is, and how well our method can clearly extract it. SNR-PPP and MAE-PPP aggregate the PPP map into a score that can be used in comparing different models. We show and prove PPP is reliable (PPP is casted from the definition of padding, and shows a substantially lower deviation) compared to previous metrics. And discuss some observations in Section 4.\n\n4. **`How will this actually improve the practice or our understanding?`** \n - A reliable metric is always the first step to solving or understanding anything. Any information from an unreliable metric should be considered meaningless. Without any meaningful metrics, the severity of the problem cannot be correctly measured, and none of the solutions can claim it addresses the issue. \n\n - Let’s say, the `accuracy` function in image classification has a 50% deviation without a reason (perhaps some ground truth classes are randomly swapped for some reason). Then it becomes obvious that we should fix the metric first, before starting benchmarking model performance on it.\n\n5. **`What is the value of quantifying the strength of position encoding?`** First, a good metric should report a smooth and continuous value to express the property of interest. Second, if a problem cannot be analytically solved, a continuous value quantifies how well an alternative solution (e.g., a normalization or regularization) performs. To our understanding, the positional information problem is unlikely to be analytically resolved.\n\n6. **`which layer one should look at`** As shown in Figure 5., PPP is progressively reinforced and becomes the strongest in the deepest layer (closest to the network prediction). The problem is caused by paddings throughout the network, therefore a genuine solution should reduce PPP in all layers.\n\n7. **`at which layer would cause the biggest problem for prediction accuracy?`** In Figure 5., PPP is strongest in the final output layer, while being closest to the model prediction at the same time. Therefore, it is the last layer. But, again, PPP is not a problem of a particular layer, it is a problem caused by paddings throughout the whole network.\n", " Authors present a novel metric for detecting the presence and quantifying the strength of positional information encoding due to padding. They define PPP as a spatial statistic, i.e., expected absolute difference between algorithmically padded and optimally padded images’ activations, and summary statistics are defined from the spatial ones, i.e., SNR and MAE for PPP. In addition, they propose a new padding strategy, which aims to preserve local variability around a boundary when padding. The proposed metric is applied on pre-trained networks as well as those that are trained from scratch at different epochs. Results suggest that the position information encoding gets stronger with training, and very strong for pre-trained models. Compared to two existing alternatives, the proposed metric has lower variance, and therefore seems to be a more reliable metric. Strengths:\n1.\tThe investigated concept is intriguing and potentially affect all application of CNNs. \n2.\tThe proposed measure is very intuitive and easy to compute. \n3.\tResults suggest that the proposed metric shows lower variability compared to alternatives, and show that almost all networks encode position to some extent. \n4.\tResults showing emphasized position encoding for pre-trained models is interesting. \n\nWeaknesses: \n1.\tA solution towards removing the position encoding is not discussed. \n2.\tImportance of quantifying the strength of PPP is not clear to me. \n3.\tAuthors state that reliable PPP metrics are important for understanding PPP effects in different tasks. While this point is surely intriguing, such an explanation or understanding is not explicitly given in the article. Can the authors explicitly explain what type of understanding one reaches by looking at the PPP maps? \n4.\tThe conclusion of the article remains a bit vague. While the proposed metrics have some more desirable attributes, value of these attributes for applications is unclear to me. How will this actually improve the practice or our understanding? \n 1.\tMy main suggestion is to better motivate the investigation and the developed metrics for applications of CNNs. How will this technology actually be used? A roadmap towards improving the current state of things using the PPP is unclear. \n2.\tWhat is the value of quantifying the strength of position encoding? Better explanation towards this end would substantially improve the article. \n3.\tIt is shown in figure 5, that proposed metrics are different at different layers. In this setting, it may be important for authors to provide some guidelines telling which layer one should look at. More specifically, difference (quantified with PPP) at which layer would cause the biggest problem for prediction accuracy? \n Yes, they have. ", " This study investigates position information patterns learned due to the use of padding. A new evaluation method has been proposed by taking the difference between an optimal padding strategy and the “algorithmically-padded features”. The difference pattern becomes more recognizable when more samples are applied. Then signal-to-noise ratio and mean absolute error are proposed to measure the layer-wise difference between the two paddings. This whole system is claimed to be a better measure for the position information.\n Strengths: The proposed idea of randn padding is plausible, a window is used to compute the mean and deviation values within. Then we can sample padding values based on the learned normal distribution. Addressing the effect of strided convolution also makes the investigation more comprehensive. The proposed randn padding can deliver less position information than other padding strategies.\nWeakness: This study also has some essential problems that need to be addressed, please see the questions below.\n The two metrics SNR-PPP and MAE-PPP, proposed in this paper are questionable. The use of signal-to-noise ratio and mean absolute error is not new, the new metric is essentially the proposed “optimal” padding, which can be used to compare against other paddings and compute differences, including SNR and MAE or any other metrics. Then let’s focus on the basic question, what the “optimal” padding is.\n\nThis proposed position measure is conducted at feature level, which is more difficult to draw conclusions than those studies at output level. Accuracy on the BHV test from [1] can be considered a measure against human perception, which is a golden standard in CNN understanding, e.g., why the classifier behaves differently than human and what could be the factor behind (absolute position). Similarly, the artificial ground-truth used in [2] can validate CNNs in a human readable way, if the model can output the wanted pattern based on position. This type of validation has also been applied in other CNN understanding papers[3,4].\n\nThe measure proposed in this paper is computed at the feature level, which is not human readable, or is still under exploration. Then the defined “optimal” padding becomes a golden standard to compare, which is very questionable. The paper also agrees with the “optimal” padding shown in Eqs. (1) and (2) “In practice, such an optimal-padding scheme is difficult to achieve.” I personally doubted if such padding exists in practice. Without further explanation, Sec2.2(Fig 1., line 81) directly shows the visual difference between the “optimal” and the “algorithmical” padding, this is really important but looks confusing. I can only guess the “optimal” refers to the randn padding from sec 2.4(please correct me if I am wrong), and the large difference to zero-padding is not surprising. The padded value by zero-padding is very different from other content-based, e.g., circular, reflect, replicate, which has been already studied in previous studies[1,5]. (In addition, the finding in Fig 3 and Table 1 that background color matters can already be found in previous study[5].) More importantly, I am still seeking an explanation why this randn padding could be the “optimal” to compute the two metrics, it looks more like another well-designed “algorithmical” padding. The “optimal” golden standard needs to be set and studied thoroughly, then the resulting findings (Table 2 and 3) can be analyzed reliably. Otherwise, it makes less sense no matter how high or low values a metric can achieve.\n\nTherefore, I suggest a more thorough study on how the “optimal” padding can be achieved before computing metrics on top. And based on Table 1, the proposed randn padding behaves similarly to the replicate padding, which can be considered a special case drawn from the same distribution as randn padding.\n\nBased on the questions above, I would suggest this study can be further improved for a better presentation and less confusion, the use of SNR and MAE is not main focus. More importantly, the design of \"optimal\" padding should be better addressed.\n\n[1] Kayhan, Osman Semih, and Jan C. van Gemert. \"On translation invariance in cnns: Convolutional layers can exploit absolute spatial location.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2020.\n[2] Islam, Md Amirul, Sen Jia, and Neil DB Bruce. \"How much position information do convolutional neural networks encode?.\" arXiv preprint arXiv:2001.08248 (2020).\n[3]Geirhos, Robert, et al. \"ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness.\" arXiv preprint arXiv:1811.12231 (2018).\n[4]Geirhos, Robert, Kristof Meding, and Felix A. Wichmann. \"Beyond accuracy: quantifying trial-by-trial behaviour of CNNs and humans by measuring error consistency.\" Advances in Neural Information Processing Systems 33 (2020): 13890-13902.\n[5]Islam, Md Amirul, et al. \"Position, padding and predictions: A deeper look at position information in cnns.\" arXiv preprint arXiv:2101.12322 (2021). The paper can be further polished and re-organized to reduce misleading. The applicability of randn can be further discussed, the previously studied findings can be omitted. " ]

[ -1, -1, -1, -1, -1, -1, 4, -1, -1, 3, 4 ]

[ -1, -1, -1, -1, -1, -1, 2, -1, -1, 3, 4 ]

[ "3-K8RnSHNX", "3YHsS2z31C8T", "V-W9UZRuazp", "3YHsS2z31C8T", "GIj57bviwux", "GIj57bviwux", "nips_2022_MG3YN3z1J4M", "DJ7YBXUfiqR", "vTN8dcV8Nm", "nips_2022_MG3YN3z1J4M", "nips_2022_MG3YN3z1J4M" ]

[ "CZ2C-yBniTI", "V9Gb5hi6Jt", "EQmP0aJoFzA", "KkVjMl-CXmT", "yZpFeAgvjo", "e13RZp4XWBs", "decxuukYx16", "FQWnocYFKU", "vNAv6jjZVN7", "GColPEnaGjq", "IbhBUT8m8F1", "QDx8QlCs77A" ]

[ "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I acknowledge that I have read the authors’ responses and thank them for positively addressing my comments.", " I have read the response, and the authors have addressed my concerns.", " **Q1. Add empirical results of various meta learning methods at first to show whether benign overfitting phenomenon will occur in more meta-learning tasks.**\n\nThanks for the great suggestion! Following your suggestion, we have provided some empirical results in **General Response-Q1**. The empirical results demonstrate that the benign overfitting phenomenon will occur in more practical meta-learning tasks such as few-shot meta learning for image classification. \n\nWe will include this in the revision of the main text if additional page is allowed.\n\n\n**Q2. Real examples where the number of meta training data is smaller than the number of parameters.**\n\n\n\nAs suggested, we have provided real examples in **General Response-Q1**.\n\n\nWe greatly appreciate your helpful comments. We hope these can resolve your concerns. ", " ## Response to Reviewer TRZn\n\nWe thank the reviewer for the support and the careful review. Our response to your comments follows.\n\n**W1. Explain the experimental results in more depth and add some numerical results in a tabular format.**\n\nThanks for the suggestion. We have added more explanation in the revised version of the paper and we also included numerical results in the tabular format. See Section E. Additional experiments in the appendix.\n\n\n\n\n**Q1. Why the cross-task variance upper bound primarily depends on $1/M$ asymptotically?** \n\n\nSince we assume the tasks are sampled from an underlying task distribution, as the number of tasks $M$ grows larger, the average statistics across tasks converge to the expected statistics across tasks. Intuitively, sample average of independent but non-identical random variables has variance that decreases with the number of samples, which is proportional to $1/M$.", " ## Response to Reviewer FrXq\n\nWe thank the reviewer for the support and the careful review. Our point-to-point response to your remaining concerns follows next.\n\n\n**Q1. Empirical example that supports benign overfitting for meta learning and very over-parameterized neural networks for MAML.**\n\n\nWe provide example in the answer to **General Response-Q1**.\n\n\n**Q2. Personally I would recommend explicitly state how they resolve these issues in their proof outline. How you handle different eigen-vectors from different tasks? Can you provide some intuition.**\n\n\nThanks for the suggestion. Due to space limitation, we highlighted some proof rationale in the appendix. Indeed, including them in the proof outline will improve readability. \n\n\n\nIn particular, the challenge of handling multi-task data matrices with different eigenvectors mainly appears in the proof of Lemma 3. We have highlighted some key steps in the appendix, but will add more and move them to the main paper. Roughly speaking, the proof needs to deal with the trace of the product of symmetric postive semidefinite (PSD) matrices with different eigenvectors. For example, we need to bound $\\mathrm{tr}(AB)$ where $A,B$ are symmetric PSD matrices with eigenvalues $a_1\\geq a_2\\geq \\dots \\geq a_d > 0$ and $b_1\\geq b_2\\geq \\dots \\geq b_d > 0$, respectively. We use the Von Neumann’s trace inequality (and other basic properties of the trace) in Lemma 7. Von Neumann’s trace inequality gives that $\\mathrm{tr}(AB) \\leq \\sum_{i=1}^d a_i b_i$, which shows that the trace of the product of symmetric PSD matrices with different eigenvectors are bounded by the sum of the product of their ordered eigenvalues.\n\n\n\n\nWhen the additional page allows in the final version, we will promise to make corresponding changes by explicitly stating how we resolve these issues in the proof outline in the paper.\n", " ## Response to Reviewer WJZn\n\nWe thank the reviewer for the support and the careful review. Our response to your remaining concerns follows next.\n\n**W1 & Q2. Not clear how the benign overfitting condition in (13) can be used to determine whether certain settings are benign or not. For example, $M, d$ in the settings of Example 1 and Example 2 are finite while (13) expresses the condition in the form of limit.**\n\nIndeed, the equation (13) in its current form presents the benign overfitting condition in the asymptotic case. In the finite-dimensional case, we essentially require the corresponding benign overfitting condition \n\n$$\n r_ {0}(\\overline{\\mathbf{W}}_ {M}^{\\mathcal{A}}) = o({MN}),\n \\quad k^* = o({MN}),\n \\quad R_ {k^*}(\\overline{\\mathbf{W}}_ {M}^{\\mathcal{A}}) = \\omega \\big( MN \\big).\n$$\n\nNote that in the finite dimensional case, $r_ 0(\\overline{\\mathbf{W}}_ {M}^{\\mathcal{A}}) = \\Theta(1)$, the first and second conditions are satisfied. To satisfy the third condition above, the smallest $d - k^*$ eigenvalues of $\\overline{\\mathbf{W}}_ {M}^{\\mathcal{A}}$ need to be at least as large as a small constant or slowly decaying. \n\n\nRegarding when it violates the benign overfitting condition，we can modify the example from Theorem 6 of [5] (in the submission). Denote the model dimension as $d_{MN}$ which is changing with $MN$. If the eigenvalues of ${\\mathbf{W}}_{m}^{\\mathcal{A}} = {\\mathbf{W}}^{\\mathcal{A}}$, denoted as $\\mu_i$, follow the form $\\mu_i = i^{-\\beta}$, then the necessary and sufficient condition for benign overfitting in this special case is either one of the two: \n\n$$\n\\textrm{I}:\\beta \\in (0,1), d_{MN} = \\omega(MN), d_{MN} = o\\big((MN)^{1/(1-\\beta)}\\big)\n\\quad\n\\textrm{II}:\\beta=1, d_{MN} = e^{\\omega(\\sqrt{MN})}, d_{MN} = e^{o(MN)}.\n$$\n\n\nIf the above condition does not hold, it violates the benign overfitting condition.\n\n\n\n**W2. \"Nested meta-learning\" is confusing.**\n\n\nThanks for the suggestion. We introduce this term to distinguish from \"representation-based meta learning\". Following your suggestion, we have changed \"nested meta learning\" to \"gradient-based meta learning\".\n\n\n**W3&Q4. Gap between theoretical analysis and practical meta-learning methods in terms of the data, model architecture, and prediction task. Show the possible connection via discussion or experiments.**\n\n\nThanks for the suggestion. We discuss the connection of theoretical analysis and practical meta-learning methods via both similarity and differences. \n\n1. *Common between theory and practice.*\nOne connection is to show the benign overfitting phenomenon also exists in practical meta-learning settings. For more details, please see **General Response-Q1**.\n\n2. *Gap between theory and practice.*\nPlease see **General Response-Q2**.\n\n\n\n**Q1. How to change the analysis to multi-step MAML?**\n\nWe believe the analysis can be extended to multi-step MAML. For $t$-step update, the resulting mapping from ${\\theta}_ {0}$ to ${\\theta}_ {m}$ can be obtained in closed form by the applying the gradient update $t$ times.\n\nIn this case, the closed form solution of $\\hat{{\\theta}}_{0}$ can still be obtained, and thus the similar analysis as the one-step case can be conducted. In addition, the larger $t$ is, the closer the solution is to the solution of iMAML. We will pursue this in our future work.\n\n\n\n\n**Q3. Why larger data heterogeneity makes it more difficult for the benign overfitting condition to be satisfied for both MAML and iMAML?**\n\nLarger data heterogeneity results in larger excess risk error bound based on our theory.\nIn the examples we assume the cross-task data heterogeneity $\\mathbb{V}$ is bounded. However, in practice, as number of meta-training tasks increases, $\\mathbb{V}$ can grow bigger, or even in a rate faster than the decreasing rate of $k^*/({MN})$, and $MN/\\big( R_{k^*}(\\overline{\\mathbf{W}}_{M}^{\\mathcal{A}}) \\big)$. In such case benign overfitting is not guaranteed. Therefore, the benign overfitting condition also depends on the growing rate of $\\mathbb{V}$, the larger it is, the harder for benign overfitting condition to be satisfied.\n\nIntuitively, larger data heterogeneity among the sampled tasks means the eigenvalues of the data matrices for different tasks are more different. Meanwhile the benign overfitting condition requires the eigenvalues of the average weight matrices to be controlled. The higher data heterogeneity, the more difficult for the eigenvalues to be controlled, therefore the more difficult for benign overfitting condition to be satisfied.\n\n\nWe hope the above response can resolve your concerns. Feel free to let us know if you want us to provide more clarifications. ", " ## Response to Reviewer sqGF\nWe thank the reviewer for the support and the careful review. Our response to your remaining concerns follows below.\n\n**W1. Clarify the paper only deals with meta linear regression.**\n\nThanks for the suggestion. Indeed, we have mentioned in the abstract, line 9 that \"our analysis uses the relatively tractable linear models\"; in line 150 we have mentioned that our analysis uses \"linear data model\"; in the conclusion section, line 325, we have mentioned that \"we focus on linear models\". \nFollowing your suggestion, we have further emphasized this point in several places including i) the contribution part in Section 1.2; ii) the subtitles and key proposition in Section 3.1; and iii) the key statement in Section 3.2 of the revised version.\n\n\n\n**W2. Not necessary to introduce \"nested meta learning\".**\n\nThanks for the suggestion. We introduce this term to distinguish our work from \"representation-based meta learning\". We will change \"nested meta learning\" to \"gradient-based meta learning\" which is also suggested by Reviewer WJZn. Following your suggestion, we have revised this in the revised version.\n\n\n**W3. Discuss the gap between the analysis and practice and how the analysis can be extended to practical cases or which intuitions it provide.**\n\nThanks for the suggestion. \n\n1. *Gap between analysis and practice.* \n\nPlease see **General Response-Q2**.\n\n2. *Practical case where the model works on few-shot learning with novel classes.*\n\nOur analysis does handle few-shot learning with novel tasks sampled from the same underlying task distribution. Few-shot learning means the number of training data per task $N$ is small. During meta-testing, we use the meta-trained model to predict on novel tasks sampled from the same underlying task distribution as the meta-training data. One limitation is that our analysis focuses on meta linear regression, but not classification. Extension to analysis on meta classification will be our future work. When additional page is allowed, we will clarify this in the next version of the paper.\n\n\n\n\n**W4. Difference between the tools used for the analysis in this paper and [1].**\n\n\nIn general, both [1] and our paper use random matrix theory as the main tool to study statistical properties of the meta linear regression. However, [1] focuses on sample complexity to reach certain statistical error while we focus on how the excess risk, a measure of the generalization ability, depends on the task and data distribution.\n\nNevertheless, the settings and the specific techniques in our paper differ from those in [1]. To be more specific, we list some of the major differences below.\n\n1. Referece [1] studies meta learning under mixed linear regression, which differs from our data model. For example, [1] assumes the data matrix is isotropic, i.e. $E[x_m x_m^{\\top}]=I_d$. \nIn contrast, our paper does not assume the data matrix is isotropic. In fact, isotropic data matrix does not satisfy the asymptotic benign overfitting condition. We show that when the eigenvalues of the data matrix satisfy certain conditions, the overparameterized model can still generalize well. And how the excess risk changes with the eigenvalue distribution of the data matrix is therefore the focus of our study. \n\n2. Referece [1] also assumes that the sufficient meta-training tasks are given, or the overparameterization happens, if any, only in the per-task level. The focus of their work is to study when can abundant tasks with small data compensate for lack of tasks with big data. And they identify sufficient conditions for this. To achieve this, the key technique they use is the concentration inequality when sufficient number of tasks or sufficient number of data per task are given.\n\n3. Referece [1] assumes the task parameters come from a discrete distribution of a fixed support size while we do not assume a discrete distribution of the task parameters. And [1] develops an algorithm that first clusters these tasks and then estimates the task parameters. The algorithm is different from MAML, which is the focus of our study.\n\nTo summarize, they mainly focus on analyzing sample complexity in isotropic data case without overparameterization in the meta level, while we focus on studying the benign overfitting condition in the overparameterized case. We have also included comparison with this work in Table 1 in Section 1.2 of the revised paper.\n\n>[1] Kong et al. Meta-learning for Mixed Linear Regression. ICML, 2020.\n\n", " ## General Response\n\nWe thank the reviewers for their constructive comments! We will first address the common questions raised by several reviewers and then respond to each reviewer.\n\n**Q1. Connection to practical meta-learning cases (All reviewers).**\n\nReviewers' commments can be summarized into the following two subquestions.\n\n**Q1.1** Whether meta-learning model is overparameterized in practice given multiple tasks?\n\n**Q1.2** Does benign overfitting happen in practice?\n\n \n\nIndeed, overparameterization and benign overfitting happen in meta learning empirically. Below we list some practical data quoted from existing works on empirical study of MAML. We estimate the total number of meta-training data by the meta-training iterations times the batch size (task number for each iteration) times the number of shots.\n\n\nFor **Q1.1 overparameterization**, the following table quotes results from Table 2 in [1] and Table A5 in [2], which clearly shows that ResNet-10 and ResNet-12 are overparameterized in the meta level while conv-4 is underparameterized in the meta-training level. Please note that ResNet-10 and ResNet-12 outperform conv-4, which means overparameterization in the meta level does not harm testing performance.\n\n\n| Model (on mini-ImageNet) |MAML Conv-4 [2] |MAML ResNet-10 [2] | MAML ResNet-12 [1] |\n| :--- | :----: |:----: |---:|\n| # params | 0.07M | 6M | 8M|\n| # meta-training data (1 shot)| 1M | 1M | 0.3M|\n| # meta-training data (5 shot)| 3M | 3M | 1.5M|\n| Test accuracy (1 shot) | 46.47±0.82 | 54.69±0.89 | 51.03±0.50 |\n| Test accuracy (5 shot) | 62.71±0.71 | 66.62±0.83 | 68.26±0.47 |\n\nFor **Q1.2 benign overfitting**, we copy Figure 3 in [2] below (if the link is not visible in OpenReview, it can be viewed in a browser). Using ResNet-12 or larger model, the number of model parameters are usually orders of magnitute higher than the total number of meta-training data, especially in 1-shot learning. It can be seen that for in almost all experiments, the testing performance of MAML improves as the number of model parameters increases (e.g. ResNet compared to ConvNet). Therefore, the benign overfitting happens in these practical cases. \n\n\n\n\n\n\n\n>[1] Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond. NeurIPS, 2021.\n>\n>[2] A closer look at few-shot classification. ICLR, 2019.\n\n\n**Q2. Gap between theory and practice (data, model, and task). How the theory can be extended to practical cases or which intuitions it provide? (Reviewers sqGF, WJZn)**\n\n1. *Connection and gap between the analysis and practice.*\n**General Response-Q1** shows that overparameterization in the meta level does happen in practice such as in *few-shot* image classification. In addition, benign overfitting happens in the meta learning settings. These observations justify that the benign overfitting of meta learning that the paper studied indeed happens in practice. The gap is that our current analysis focuses on the meta linear models in the regression settings while the practical meta learning may often use nonlinear models in the classification settings. \n\n \n\n2. *How our analysis can be extended.*\nAlthough our analysis focuses on the linear models, it can still provide the fundamental insights on the benign overfitting in practical meta learning cases where we reuse the feature extractor from pre-trained models and only meta-train the parameters in the last linear layer for regression problems; see [3]. Then the feature vector $x_m$ in our analysis represents the last feature layer output from the feature extractor. In addition, linear models have been frequently used in the recent generalization analysis of MAML (e.g., [3, 9, 13, 21] in the submission) since the dynamics of SGD on overparameterized neural networks can be effectively captured by that on linear models. Going beyond the considered linear models, it is also promising and possible to extend our analysis to nonlinear cases via means of random features and neural tangent kernels. In addition, while our current analysis focuses on the regression task, it is promising to build upon our work and the recent work on benign overfitting in classification (e.g., [4]) to study the benign overfitting in the meta classification task. \n\n>[3] Few-shot Image Classification: Just Use a Library of Pre-trained Feature Extractors and a Simple Classifier. ICCV, 2021.\n>\n>[4] Benign overfitting in multiclass classification: All roads lead to interpolation. NeurIPS 2021", " This paper explores the generalization of overparameterized meta-learning models with a nested structure, specifically model-agnostic meta-learning (MAML) and implicit MAML (iMAML). Under some theoretical assumptions, the authors derive an upper bound for the excess risk of MAML and iMAML in the overparameterized setting. Further, they derive conditions for benign overfitting in nested meta-learning and provide hyperparameters for MAML and iMAML that preserve the benign overfitting. The paper does a good job of explaining the motivations for studying the problem. In addition, the authors present their contributions clearly and provide a proof outline of their main result, which contributes to the clarity of the paper.\n\nThe main weakness of the paper is in the discussion of the experimental results. I believe that the significance of the theoretical results could be further emphasized by explaining the experimental results in more depth (and adding some numerical results in a tabular format). Is there an intuitive way to explain why the cross-task variance upper bound primarily depends on 1/M asymptotically? The authors adequately address the limitations of their work. Specifically, they acknowledge that their current analysis is limited to the non-Bayesian setting and the linear model assumption.", " This paper analyzes the “benign overfitting” phenomenon of nested meta-learning, where an over-parameterized model can still work well in the meta linear regression setting. Both MAML and iMAML are covered by the analyses. Numerical simulations validate the results of the theoretical analysis.\n The paper analyzes an interesting phenomenon in meta-learning in the meta linear regression setting. The authors need to clarify the paper only deals with the meta linear regression, which simplifies the analysis with a different thread of tools. BTW, the \"nested meta-learning\" is just the bi-level optimization in meta-learning. Since most meta-learning methods adopt the bi-level form, it is not necessary to introduce a new term.\n\nIn addition, the authors need to discuss the gap between the analysis and the practical MAML/iMAML, since the latter methods work on few-shot learning with novel classes. Some discussions on how the analysis can extend to practical cases or which intuitions it provides are welcome.\n\nThe difference between the tools used for the analysis in benign overfitting and [1] should be discussed.\n\n[1] Kong et al. Meta-learning for Mixed Linear Regression. ICML 2020. Please refer to the weakness in the previous parts. \n\nTo better show what it the “benign overfitting\" in meta-learning, the authors may consider showing some empirical results of various meta-learning methods at first (even not fully consistent with the assumptions in the paper). Based on the final results of the paper, we can see the benign overfitting in the meta linear regression, but we are not sure whether the same phenomenon will occur in more meta-learning tasks.\n\nSince the analysis is based on the case where the total number of meta-training data is smaller than the number of parameters in the model, which is not always the case in meta-learning, the authors may provide more real examples where we will meet the case. The authors have adequately addressed the limitations and potential negative social impact of the work.\n", " The paper aims to answer whether overparameterized nested meta learning models would lead to overfitting or not. As a first step, the paper theoretically analyzes the generalization performance of relatively tractable linear models in the meta linear regression problem with the minimum norm solution. By decomposing excess risk into three individual terms and bounding them separately, the bound for the excess risk can be obtained. Based on the bound, condition for benign overfitting in meta learning is derived. Numerical experiments validated the theoretical findings. Pros:\n\n+ The paper demonstrated how the analysis of benign overfitting in linear regression can be extended to meta linear regression problems. The analysis provides understanding on how data data heterogeneity, model adaptation affect benign overfitting in meta-learning. The derived bound of the excess risk is verified by showing the same trend as the simulated excess risk in numerical simulations.\n\n+ The paper is well organized. It clearly shows the assumption of the derivations and highlights the key difference between different methods, e.g. Figure 1 and Table 2. The contents in the paper are easy to follow. \n\nCons:\n\n- It is not clear how the benign overfitting condition in (13) can be used to determine whether certain settings are benign or not. For example, the parameters M, d in the settings of Example 1 and Example 2 are finite while (13) expresses the condition in limit form. More explanations are needed to demonstrate the significance of the derived benign overfitting condition. \n\n- The use of \"nested meta-learning\" is confusing since meta-learning itself indicates a nested structure. Using \"nested\" before meta-learning may refer to a new method where multiple (more than two) levels of optimization are used. However, the paper actually analyzed MAML and iMAML, which are gradient-based meta-learning methods using two-level optimization.\n\n- There is a large gap between the theoretical analysis and and the meta-learning methods used in practice in terms of the data, model architecture, and prediction task. Although the setting in this paper facilitates theoretical analysis, it would be better to show the possible connection between derived results and real meta-learning applications via discussion or experiments.\n\n\n--------------------- Post rebuttal --------------------- \nI have read the rebuttal and all my concerns have been addressed. - The MAML analyzed in the paper only uses one gradient step in adaptation, while a more realistic scenario is to use multiple gradient descents in the adaptation phase. How does this change affect your analysis? \n\n- Example 1 and Example 2 show the settings that satisfy the benign overfitting condition. What setting can violate such condition?\n\n- Why larger data heterogeneity makes it more difficult for the benign overfitting condition to be satisfied for both MAML and iMAML?\n\n- What's the connection between the derived results and real meta-learning applications? How can the derived results help understand more practical meta-learning settings? Yes.", " The paper provides generalization bounds for overparamterized linear model in meta learning, for three different methods: empirical risk minimization (ERM), model agnostic meta learning (MAML) and implicit model agnostic meta learning (iMAML).\n\nModel. In a meta learning problem, there are M tasks and labeled data $\\{(x_{i, m}, y_{i,m})\\}_{i \\in [N], m \\in [M]}$ are drawn i.i.d. from each distribution. The paper considers linear model, where the goal is to come up a share $\\theta^{*} \\in \\mathbb{R}^{d}$ that fits M tasks: For ERM, it just minimizes the square loss; while for MAML and iMAML, it reduces to minimize certain regularized square loss. The paper considers the ``overparameterized'' regime where $d\\geq MN$, and the generalization bound explain the the benign overfitting phenomena in certain angle.\n\nResults. It is hard to summarize the generalization in a few words. But it follows the seminal work of [Barlett et al. PNAS 2020], but with an extra term that characterize the cross-task data heterogeneity, which is defined as the maximum discrepancy between data covariance matrix of each task, which is unique to meta-learning or multi-task learning.\n\nMethods. The method generally follows the work of [Barlett et al. PNAS 2020] with extra effort handling the cross-task data heterogeneity, i.e., data coming from different task could have different eigenvector. I feel it is non-trivial to deal with this factor. Strength. The paper provides the first generalization bound for meta learning under over-parameterized linear model, the proof handles data coming from different source with different covariance matrix (eigenvector especially) is non-trivial to me. The paper is very well-written.\n\nWeakness. There is no major weakness of the paper. Here is one minor question. \n\nThe data assumes overparameterized model for multi-task learning and the benign overfitting somewhat motivates from empirical observation of double descent. Are these valid? E.g. does double descent happen for meta learning, and does the neural network for MAML very over-parameterized when data comes from multi-task are available? It would be good to have some discussion later.\n\n--------------------- Post rebuttal ---------------------\nI have read the rebuttal and keep my evaluation. The paper outline some technical difficulty in the second, and resolves nicely in the proof. Personally I would recommend explicit state how they resolve these issues in their proof outline. One technical question that appears to be non-trivial to me is that how you handle different eigen-vectors from different tasks? It seems the covariance matrix could be quite different (though the eigenvalue is assumed to aligned well). Can you provide some intuition.\n\n\nAnother minor comments is to state that all figures are numerical calculation of the generalization bound in some place, it is bit confusing to me.\n\n\n No" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 7, 6, 6, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 1, 4, 3, 4 ]

[ "KkVjMl-CXmT", "decxuukYx16", "GColPEnaGjq", "vNAv6jjZVN7", "QDx8QlCs77A", "IbhBUT8m8F1", "GColPEnaGjq", "nips_2022_oW4Zz0zlbFF", "nips_2022_oW4Zz0zlbFF", "nips_2022_oW4Zz0zlbFF", "nips_2022_oW4Zz0zlbFF", "nips_2022_oW4Zz0zlbFF" ]

[ "wBp6y53AknGa", "AqtPMtNRHEr", "tojIyrIBClP", "d0bFDXJgfNg", "v9J6Sjd-2S", "Hi6KerbCJKf", "lst4fjrKHW", "fJY4oGgJItC", "E3yH2coeRxX", "2HmoHzSiUpn" ]

[ "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " The authors' replies resolve my concerns about the method presentations and ablation studies. I would like to raise my ranking from 3 to 6.", " We appreciate the reviewer’s interest in the paper, as well as their raised suggestions and comments. Next we answer the questions they raised.\n\n**Exploring the multimodality of the prediction is not explored in the experiments section**\n\nThe multimodality and uncertainty of the prediction is indeed a key aspect of our framework, both in terms of motivation and method. We agree with the reviewer that in the initial version of our paper limited evidence was shown supporting this claim. To show that our model decodes diverse (plausible) trajectories given a segment, we added two different figures in our revised paper.\nFirst, we show some qualitative examples where we predict the future of past segments, and decode two different random samples for each of them (see Fig. 8 in the appendix), as well as showing the actual ground truth trajectory. All the decoded futures are plausible given the past, and each sample shows a different future, proving that our model learns to represent different options when there is uncertainty. \n\nSecond, we study the multimodality from a quantitative point of view, and report results for different values of $M$, which is the number of samples we use at inference time (we report the best out of these $M$ samples). There is a clear improvement as the number of samples $M$ increases, which implies that each one of the samples is different. If they were very similar or the same, decoding new samples would not lead to better solutions. The main improvement comes within the first 3-5 samples. However, improvements are seen for larger numbers of samples. \n\nThese results are also discussed in the text (Appendix E).\n\n&nbsp;\n\n**Learned representations being useful for comparing trajectories**\n\nWe agree with the reviewer that this claim has not been evaluated, and we have removed it from the paper. Quantitatively evaluating clustering methods is challenging because there is no “ground truth” to cluster assignments. Since this is not a significant claim in our paper, we have removed it to remain objective. \n\n&nbsp;\n\n**Minor errors and typos**\n\n*L141 Shouldn’t it be a division operation instead of subtraction?*\n\nYes, thank you for spotting the error! We corrected it in the updated paper (line 145). The cause of the mistake was that in practice we work in the log domain, where divisions are computed as subtractions of log-volumes.\n\n*L192 Trajectron++*\n\nThanks, we corrected it.\n\n", " We appreciate the reviewer’s interest in the paper, as well as their raised suggestions and comments. Next we answer the questions they raised:\n\n### Paper organization\n\n**About Section 2.3**\n\nThank you for the suggestions to improve the paper. We have made a significant revision to section 2.3 in the paper to clarify the details that are missing. \n\nPlease note that we are limited to nine pages during the paper submission and revision, which prevents us from including implementation details in the main text. However, the camera ready version allows us to include an additional tenth page, if accepted. We will incorporate more details, such as Figure 6, from the appendix into this tenth page. \n\nAdditionally, we revised the paper to make the details for the creation of negatives and positives more clear. Specifically, we modified the following:\n- We significantly revised section 2.3. We focused it completely on positive/negative pairs creation, including changing its title. Before it was too generic, and it didn’t convey specific information about what segments were positive/negative with which other segments. In the current version, examples are given for every new concept that is introduced, and the whole text is oriented towards the goal of positive/negative pair creation. Also, we restructured the order of the concepts, such that the base case is mentioned first, and the section builds conceptually from there. Finally, we repeat the main rule that we follow to determine positive and negative pairs (line 101), again with examples and making reference to Figure 3.\n- We show (see answer to the specific question below) that the distinction between soft and hard pairs is not crucial for our method. While it helps improve the accuracy, the main distinction to be made is between positives and negatives (which is key to our framework), not soft and hard. \n- For the previous reason, and in order not to confuse the reader, we do not mention hard/soft negatives and positives in the main text. There is only a brief reference in line 121, but it does not confuse the explanation in section 2.3. In the current version the explanation is therefore cleaner.\n- We added a very extensive explanation of soft/hard pairs and the reasoning behind them in the Appendix C.1. \n\n**Formalization of box embeddings**\n\nWe agree with the reviewer that adding the equation for the Volume (Eq 12) will help understand the concept behind the box embedding operations, so in the revised version we added it to the main paper’s explanation (line 145). Note that Eq.11 was already present in the main paper (currently in line 144), albeit with a typo (seen by reviewer 1wa9), which has been corrected.\n\n&nbsp;\n### Some sentences of the paper are not well-supported\n\n**Claim in line 165 - \"our method is generally designed for any kind of spatial trajectory\"**\n\nWe agree with the reviewer that the claim is not well supported by our experiments, so we removed the sentence. This paper already contains a number of experiments on different datasets (albeit all of them in the same domain), which quantitatively and qualitatively support that our proposed trajectory representation is effective. \n\n**Ablation of distance function D**\n\nWe have revised the paper to include these results. We report the symmetric case, implemented with Gaussian distributions, in Table 3 in the Appendix. The box embeddings implementation obtains better results, but the symmetric case with Gaussian distributions is also competitive.\n\n**Explanation of HP and SP**\n\nWe agree that some of the details about the selection of hard or soft negatives and positives between pairs of segments were missing in the paper. We added a detailed explanation in the appendix C.1, explaining the rules we followed to determine if a positive or negative pair was considered to be a hard one or a soft one. \n\n[The answer continues in the next comment]", " [Continuation of the answer]\n\n### Insufficient experiments.\n\n**Baselines and GNN-based models**\n\nOur contribution is not the architecture of the Encoder network (which we implement with a generic Transformer), but the probabilistic modeling of trajectories. Task-specific architectures for the Encoder, like a GNN-based model, would affect equally our method and the baselines, because we use the same architecture for all of them. Therefore, using a GNN-based model for the Encoder would not be considered another baseline, but a different variation of our implementation (and the baselines), and one that is orthogonal to our contribution. \n\nNevertheless, we implemented our Encoder network using ST-GCN [1], which is the most established model to process temporal skeleton data, replacing the Transformer architecture. We use the implementation in https://github.com/open-mmlab/mmskeleton . We report the results in Table 3 in the appendix, with several more ablations. ST-GCN performs worse than the Transformer network (although the results are competitive), probably because temporal information cannot be added to an out-of-the-box ST-GCN architecture. Finally, we would like to note that Transformers are a special case of graph neural networks [2].\n\n[1] Yan, Sijie, Yuanjun Xiong, and Dahua Lin. \"Spatial temporal graph convolutional networks for skeleton-based action recognition.\" Thirty-second AAAI conference on artificial intelligence. 2018.\n\n[2] Joshi, Chaitanya. \"Transformers are graph neural networks.\" The Gradient (2020): 5.\n\n**Ablations studies**\n\nThanks for the suggestions! We implemented several ablations, and reported the results in Table 3 (Appendix), for the FineGym short dataset. Among others, we included the ones suggested by the reviewer: \n- *Symmetric distance vs conditional*: we report results for the symmetric case trained with Gaussian distributions. The symmetric case works slightly worse than the conditional case with box embeddings. Nevertheless, its performance is significantly better than baselines. \n- *Removing the triplet loss* (in the table the name is “w/o trajectory loss”). Removing this loss significantly impacts the results.\n- *Choosing a different sampling strategy*. The sampling strategy we selected implied changing all soft positives to be hard positives. This results in slightly worse results, but as mentioned above, it is not a crucial design choice for our framework.\n\nAdditionally, we report ablations for different values of $\\alpha$ (see next answer), and for the case where we train using uniform time-steps.\n\n**Hyperparameter $\\alpha$ sensitivity**\n\nThe choice of $\\alpha$ is rather arbitrary. Because the range of the distance function (for the distances used in our experiments) is in $[0, \\infty)$, $\\alpha$ influences the norm of the distances, but not the relative distances between segments. We ran two experiments with different values of $\\alpha$ (0.1 and 10), and reported their results for the FineGym short dataset in Table 3 in the Appendix. The results show that indeed the model performance is not very sensitive to this hyperparameter.\n\n**Training curves**\n\nThe optimization process of our model is stable across training. We show training curves for the two losses (in Eq. 1 and Eq. 2) in Fig. 7 (appendix).\n", " We appreciate the reviewer’s interest in the paper, as well as their raised suggestions and comments. Next we answer the questions they raised:\n\n**About baselines**\n\nWe chose these baselines because they are highly competitive, state-of-the-art and established methods for representing trajectories and their uncertainty, and they serve as a foundation for many other tasks.\n\n**Typo \"Transformer++\"**\n\nThanks for spotting the error! We corrected it in the updated paper.\n", " We thank the reviewer for their thoughtful comments. Next we separately answer the questions they raised:\n\n**Ablation studies**\n\nThanks for the suggestions! We implemented several ablations, and reported the results in Appendix E - Ablations, and in Table 3, for the FineGym short dataset. Among others, we included the ones suggested by the reviewer (discussed next). Additionally, we report ablations for different values of $\\alpha$, for a different encoder network, for a version without the trajectory loss, and for a different hard/soft positives strategy.\n\n*How does the network performance vary with the number of samples, $M$?*\n\nIn Figure 9 in the updated paper (Appendix), we show the performance of the model for different values of $M$ (number of samples at inference time, from which we select the best one). The error decreases significantly as $M$ grows, especially for low values of $M$. This implies that our model is capturing the multimodal nature of trajectories, and it models the uncertainty appropriately: new samples result in *different* plausible trajectories (otherwise, increasing $M$ would result in the same trajectories, and the error would not decrease). This reinforces a key idea of the paper that trajectories are not deterministic and should be modeled as distributions.\n\n*How does the choice of the encoding distribution impact network performance?*\n\nWe report the performance of Gaussian embeddings trained with the KL divergence in Table 3 (Appendix). Gaussian embeddings work slightly worse than box embeddings. Nevertheless, their performance is significantly better than baselines.\n\n*How sensitive is the method to irregularly sampling from the distribution and how does it impact the final decoded trajectory?*\n\nWe would kindly appreciate some more detail from the reviewer on this point. By “irregularly sampling”, we assume the question is about irregularly sampling time-steps from a trajectory, but please let us know if that is not what you meant. During training, the trajectories are sampled at irregular time-steps, which helps generalize to any time $t$. We added an ablation in Table 3, where we train with uniform time-steps, and test at irregular intervals, and show that the model performs worse. In terms of decoded trajectories, each point (human pose) that is decoded from a distribution at a specific time is independent of the decoding at other times, conditioned on the representation in the latent space.\n\n**About non-compliant trajectories and repetitive trajectories**\n\nIn this answer, we assume “non-compliant” trajectories mean out-of-distribution trajectories. If this is not the meaning intended by the reviewer, please follow up with us. \nSimilar to most machine learning models, our system has no guarantee about out-of-distribution trajectories. We assume that if the input segment and the segment to be predicted are clearly out-of-distribution with respect to the training data, the model will not be able to predict its past or future accurately. Accordingly, actions such as hand waving for a few time-steps will be dealt properly by the model if they are part of the training data.\n\nThe study of special cases such as repetitive trajectories is very interesting, we appreciate the suggestion! We believe that our model does not have a structure that directly deals with these cases, so they would probably be modeled like any other case. \n\n**Other domains and context aggregation**\n\nIn this answer we address these two points jointly. We agree with the reviewer that studying other domains such as autonomous driving would be interesting. For such domains, context aggregation would be crucial, and as mentioned in the paper, and acknowledged by the reviewer, it is out of scope in our paper. However, we note that our formulation is generic enough to accept contextual information, for example as extra inputs to the Transformer. We leave these very interesting extensions to future work.", " The paper aims to develop a method for trajectory prediction/ interpolation by learning trajectory\nrepresentations in a latent space. The paper uses a transformer encoder to learn parameters of\na distribution, and decoder to reconstruct the original trajectory point from an embedding in the\nlatent space. The paper uses the conventional triplet loss to force similarity between\nembeddings from the same trajectory segment, and a reconstruction loss for the decoder. Strengths\n- The proposed method is sufficiently novel, with most previous works focusing on autoregressive predictions or the latent space representations not modeling future representations adequately.\n- The paper is generally well written, with the qualitative examples demonstrating the network’s ability to interpolate/extrapolate in diverse contexts.\n- The method allows sampling from a distribution, which comes with its benefitsirregularly spaced sampling, flexibility on the prior for \n distributions, generalizing to unobserved latent spaces.\n- The method performs better than the existing state of the art method of Trajectron++ on the human pose prediction task.\n\nWeaknesses\n- The paper lacks additional ablation studies, such as:\n - How does the network performance vary with the number of samples, M?\n - How does the choice of the encoding distribution impact network performance?\n - How sensitive is the method to irregularly sampling from the distribution and how does it impact the final decoded trajectory?\n- It would be interesting to understand how non-compliant trajectories (irregular actions such as hand waving for a few timesteps) impact the learned latent space, both for interpolation and extrapolation. Additionally if the authors could comment on repetitive trajectories (actions that repeat periodically), that would be interesting.\n- The paper evaluates the method on the single task of joint-space trajectory domain- it would be interesting to see how this translates to other domains for trajectory prediction eg. autonomous driving, crowd prediction.\u0000\n- The paper mentions the lack of context aggregation in the method, which is understandable for simplicity reasons. However, to generalize outside of the joint-space prediction problem, context aggregation would be vital. Questions have been asked along with the weaknesses mentioned above. Yes, in Appendix A.", " This paper proposes a spatial trajectory representation framework. The framework represents a partial observation of a trajectory as a probability distribution in a learned latent space. With this representation, the framework is able to perform a variety of different tasks, with examples including 1) future and past prediction, 2) continuous reconstruction given a discrete input, 3) interpolation between two segments, 4) comparison of different trajectories, and 5) modifying existing trajectories. The framework consists of an encoder and a decoder. The encoder is trained with self-supervised triplet loss. The decoder is trained with regression loss on ground-truth trajectories. The authors evaluated the method on public human movement datasets and compared its performance against VRNN and Trajectron++. The result shows that it achieves significantly better performance than the baselines. --- Strengths\n\n- The paper is well written and easy to follow.\n\n- The framework is able to perform a variety of different tasks without re-training.\n\n- The proposed method was evaluated on public datasets and achieved significantly better performance than the public baselines.\n\n\n--- Issues and suggestions\n\n- The baselines used in this work are a bit old. VRNN is from 2015, and Trajectron++ is from 2020. --- Other comments\n\n- Line 192: Typo \"Transformer++\".\n N/A", " This paper presents a new representation learning method for spatial trajectories, named by TrajRep. TrajRep is in an encoder-decoder structure and optimized based on the reconstruction loss, as well as a self-supervised triplet loss to refine the learned representations. For the self-supervised loss, the authors define the positive and negative loss by analyzing the structure of trajectories in detail and define the distance function based on the box embeddings under the conditional scenario. TrajRep is evaluated on the human movement dataset. ### Strengths\n\n1. In general, I think this paper is interesting. Concretely, I think the novelty of this paper mainly lies in two aspects:\n- The whole pipeline for trajectory modeling, namely especially Equation (2) that decodes the raw trajectory from z and t.\n- The distribution formalization method in sections 2.4 and 2.5.\n\n2. The qualitative Experiments are impressive, especially the Figure 5.\n\n3. The related work is well researched.\n\n### Weaknesses\n1. I do not think this paper is well-organized. Due to the lack of details, it is difficult to clear up the method design from the main text. Too many details are hidden in the supplementary materials, which affects the reading of the main text.\n\n2. Some sentences of the paper are not well-supported.\n\n3. The experiments are insufficient, including the aspects of comparing baselines, ablations studies, analysis of hyperparameter sensitivity and training curves.\n\nSee the next section for more details of the weaknesses. 1. Paper organization.\n- Figure 6 in the supplementary materials should be placed in the main text. Section 2.3 of the original paper does not clarify the authors' design well.\n- The formalization of box embedding (Equation (11)-(12)) should be mentioned in section 2.5 or related works. In the original version, it is hard to know the formalization of Vol in line 141.\n\n2. Some sentences of the paper are not well-supported.\n- Line 165: the authors claim that “our method is generally designed for any kind of spatial trajectory”, but the experiments only include the human movement dataset. More datasets are expected.\n- Line 148-line 150: the authors present two types of the distance function D and choose the box-embedding way without experiments of comparison.\n- Figure 6. The authors do not explain the reason why the relationship between two segments is labeled as HP or SP or others.\n\n3. Insufficient experiments.\n- Comparing baselines. This paper only includes two baselines. More baselines are expected, e.g. some GNN-based models, which are widely used in skeleton prediction.\n- Ablations studies. The design space of the paper is large. More ablations are expected, including the definition of D (symmetric distance or conditional), w/ or w/o triple loss, and the sampling strategy mentioned in line 530.\n- Hyperparameter sensitivity. Why choose $\\alpha$ as 1 (line 541)? Does the training process and model performance is sensitive to this hyperparameter?\n- Training curves. Since the extreme point may affect the triple loss, I would like to see if the training process is steadily convergent during training.\n\nConsidering the above questions, I think this paper needs much more effort in presentation and experiments.\n\n=====================\nIn the rebuttal, the author addressed the above questions well. I would like to raise my score.\n\n Yes, the authors have discussed the limitations and potential negative social impact of this paper.", " The authors propose a framework for learning representations for trajectory data from partial observations. The learnt representation is in the form of a probability distribution such that it captures the uncertainty of the unobserved segments. This distribution can be used for sampling unobserved segments of trajectories (interpolation, extrapolation, continuous time sampling), compare different trajectories or modify the given trajectory. A distance measure is defined in the latent space of distributions, and the framework is trained using a self-supervised triplet loss that maximizes distance between similar trajectory segment representations and minimizes the same between dissimilar pairs. \n\nExperiments are conducted on human pose dataset, with Variational RNN and Trajectron++ as baselines, with results for prediction and interpolation tasks. Qualitative results are also provided to show learned representation manipulation for speed change and temporal offset.\n Strengths :\n1) The paper is well written and easy to read. \n2) The idea of learning trajectory representation as a probability distribution, which can be decoded in continuous time is novel, and is of interest to the community. The various aspects of problem formulation in explored in good detail. It is interesting to see the use of box embeddings for trajectory data representation learning. \n3) The idea is presented in a fairly generic form, and it could have relevance in diverse problem domains involving trajectory data. \n\n\nWeaknesses :\n\nThe main weaknesses center around lack of experimental evidence for some of the central claims in the paper. \n1) While the authors claim the learned representation captures the uncertainty in unobserved segments, the multimodality of prediction is not explored in the experiments section. Can the framework be used to decode diverse realistic pose variations?\n2) The claim of learned representations being useful for comparing trajectories (line 160) is also not evaluated. The authors have referred to prior work on trajectory similarity detection / trajectory clustering, but the proposed approach is not compared with prior work for this task.\n\n######## EDIT after rebuttal : The authors have addressed my main concerns as well as those from the other reviewers. Hence, I would like to raise my rating. (Please see the weaknesses section.)\n\n\nMinor errors, typos:\n\nL141 Shouldn’t it be a division operation instead of subtraction?\n\nL192 Trajectron++\n Adequately addressed by the authors." ]

[ -1, -1, -1, -1, -1, -1, 6, 6, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, 4, 2, 3, 3 ]

[ "E3yH2coeRxX", "2HmoHzSiUpn", "E3yH2coeRxX", "E3yH2coeRxX", "fJY4oGgJItC", "lst4fjrKHW", "nips_2022_nJWcpq2fco3", "nips_2022_nJWcpq2fco3", "nips_2022_nJWcpq2fco3", "nips_2022_nJWcpq2fco3" ]

[ "KzLUosRug_x", "1HvdJ9S92q", "qXZ_pNXFvd_", "dvhTHbXSky", "hz1TTFxIJkj", "DMGan2Bvr0N", "yTJ0gpD46Hd", "HG90utBhjnt", "y1-Ykus1v2s" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you very much for your clarifications. I think they have addressed most of my concerns. I will rise my score to 6.", " The paper deserves to be published. I raise my score to 7.\n\n\nminor remark: The hyperlink (Section 4) in the discussion section does not work.\n", " Thank you for these clarifications! After reading these replies and the other reviews I am in favor of accepting this paper and will raise my score accordingly! ", " We really appreciate all the advice you provide to improve our paper. Please find below answers to your questions and some clarifications to other important points of your review.\n> a. A few more words [...] to the caption \nb. [...] Assumption 2, that \\rho is asymptotically continuous wrt. \\nu. \n c. The paragraph on top of page 9 [...] is very confusing. [...] \n\nThank you very much for pointing out these issues. We took into account all of them in the revised version.\n> The discussion of variance reduction methods is lacking in nuance […]\n\nFirst of all, we would like to emphasize that SGD and SGLD should not be considered as the same stochastic algorithm. In the case of GLD, noise is already intentionally added which results in a strongly noisy algorithm with the scheme of SGLD. It is thus important to reduce superfluous noises engendered by mini-batching to accelerate the convergence while keeping the benefits of SGD. In that sense, variance reduction techniques are theoretically and practically of high relevance. Furthermore, even though we processed variance reduction, stochasticity is conserved since the stationary distribution is the same. One of the biggest difficulties overcome here is precisely this balance between the noise that enables escape saddle points and variance reduction that attenuates noises. We not only realized this but also provided the scenario with the best trade-off. \nThe benefits of variance of SGD (generalization and escape from saddle points) were also mentioned in this part of review. Even though generalization is important, we focused more on the precise behavior of our variance reduction methods as numerical algorithms, as it is the case for other usual theoretical research on optimization algorithms and MCMC methods. There are many cases where rigorous calculation is needed instead of generalization such as sampling from Bayesian posterior distribution. As for saddle points escape, we showed this was possible as well. We even proved in Section 4 global convergence under the weak Morse assumption (similar to strict saddle), better than a simple escape from saddle points of SGLD. Since sampling can also be seen as an optimization problem, in both Sections 3 and 4, escape from saddle points is realized. \nAs mentioned earlier, all this is achieved as we succeeded in finding the right balance between the stochasticity and variance reduction. Therefore, we believe our result to the variance-reduced methods does not reduce the significance of the paper and shows the possibility that variance reduction methods can be successful in Langevin Dynamics.\n> There should be a better discussion of the assumption that \"the batch size and the inner loop length are set to \\sqrt{n}\". [...] \n\nMaybe we were not clear, but this is **neither an assumption nor a condition** at all. We only set the batch size and the inner loop length to $\\Theta( \\sqrt{n})$ in order to obtain the best gradient complexity. The general gradient complexity is provided in the proof of Corollary A.2.1. as $O(n+(n/m+B)/\\epsilon)$ with $mB=O(n)$. Since $B\\ge m$ was required, the optimal value is obtained with $m=\\Theta(\\sqrt{n})$ and $B=\\Theta(\\sqrt{n})$. This is of course not a necessary condition for the convergence proof as it can be seen in Theorems 1 and 2 with no assumptions of this kind on B and m. \nThis optimal value of B and m is totally standard in the literature on variance reduction algorithms. See for example, Zou et al. (2019a) for SVRG-LD, Li et al. (2019) for SSRGD. There are even papers that actually prove theoretically and experimentally that the optimal batch size is of order √n for stochastic gradient in some cases [1]. \nOn the other hand, we agree there is still a gap between theory and practice. This batch size may become impractical in the case n is really huge. One of the main goals of theoretical papers like ours is precisely to fill this gap. In this regard, our work should be viewed as an improvement since previous work on GLD and its stochastic scheme have suggested bigger batch sizes, which even depend on the accuracy \\epsilon, than ours (see for example Xu et al., 2018). \n\n> [...] if there were a few experiments, demonstrating them\n\nThank you very much for your advice. We would like to include experiments in the camera ready version.\n> I didn't understand what the \"inner loop length\" is. This concept needs some clarification in my opinion.\n\nWe apologize for not being clear. In Algorithm 1, there are two “for loops”, one inside the other. The outer loop is that with length K/m and the inner loop is that with length m. This m is called \"inner loop length\".\n\nWe hope we could address all your questions and concerns. We will be glad to provide further explanation and clarification if necessary. \n\n[1] Nitanda, A., Murata, T., & Suzuki, T. (2021). Sharp characterization of optimal minibatch size for stochastic finite sum convex optimization. Knowledge and Information Systems, 63(9), 2513-2539.\n", " Please find below answers to your questions and some clarifications to other important points of your review.\n\n> I feel the result seems to be an incremental improvement of the work by Li and Erdogdu (2020) and Vempala and Wibisono (2019).\n\nThank you for sharing this point of view. However, we would like to emphasize that our work is not a simple incremental improvement of previous work. \nNeither Vempala and Wibisono (2019) nor Li and Erdogdu (2020) discussed stochastic gradient methods with variance reduction. In fact, variance reduction methods are on their own an important and huge theme of research in the field of stochastic optimization and the study of the effect of variance reduction on existing algorithms is an important topic of research which attracts a lot of interests of the community (Johnson et al., 2013; Dubey et al., 2016). Moreover, in general, the extension of known algorithms to variance reduction schemes is also far from being straightforward. In our paper, the stochastic gradient and GLD both add important noises, and in order to find a good balance between them to assure the best convergence of SVRG-LD while keeping the advantages of the stochastic gradient such as decreased gradient computation and escape from saddle points, an adequate evaluation of the variance of the stochastic gradient and a precise estimation of the step size were crucial. One of the biggest difficulties overcome in our paper is precisely this balance between the noise that enables escape saddle points and the variance reduction method that attenuates noises. We not only realized this balance but also provided the scenario with the best trade-off. It was also not trivial whether acceleration of convergence in terms of KL-divergence, a strong criterion, was possible and needed some work on it. Therefore, we believe our contribution does not limit to an incremental improvement with regard to the whole line of research on variance reduction and Langevin Dynamics, and our paper shows the possibility that our researched variance reduction methods can be successful in Langevin Dynamics.\n\n> Wondering if the authors could comment on the scale of the learning rate. [...] the required learning rate could be quite small.\n\nIndeed, the learning rate (or step size) could become quite small in some situations. Nevertheless, this is unavoidable to compensate for the use of mini batches and is actually indispensable to obtain the benefit of variance reduction as we can observe in our proof. As overall this leads to a better gradient complexity, we believe this result on the learning rate is acceptable in our problem setting with SVRG-LD and SARAH-LD.\n\n> While setting the batch size to be √n leads to an improved gradient complexity, such batch size is very large and rarely used in practice. \n\nThank you for raising this point. We would like to first emphasize that this is totally standard in the literature of variance reduction algorithms. Many papers similarly showed the optimal upper bound is realized with this kind of batch size. See for example, Zou et al. (2019a) for SVRG-LD, Li (2019) for SSRGD. There are even papers that actually prove theoretically and experimentally that the optimal batch size is of order √n for stochastic gradient algorithms in some cases [1]. \nOn the other hand, we agree there is still a gap between theory and practice. This batch size may become impractical in the case n is really huge. One of the main goals of theoretical papers like ours is precisely to fill this gap. In this regard, our work should be viewed as an improvement since some previous work on GLD and its stochastic schemes have suggested bigger batch sizes, which even depend on the accuracy $\\epsilon$, than ours (see for example Xu et al., 2018). \n\n> What would the gradient complexity look like if using a much smaller batch size.\n\nAs long as $mB=O(n)$ and $B\\ge m$, Corollary A.2.1 tells us the gradient complexity is $O(n+(n/m+B)/\\epsilon)$, with the lowest upper bound realized when substituting $B=m=\\Theta(√n)$. A similar argument can be still constructed based on smaller batch sizes, inevitably providing a bigger gradient complexity than our optimal result. For example, when $B=m=n^{1/3}$, the gradient complexity becomes $O(n+n^{2/3}/\\epsilon)$. When $B=m=n^{1/10}$, $O(n+n^{9/10}/\\epsilon) $etc. In conclusion, for any B, we will always obtain an improvement compared to the deterministic gradient algorithm which has a gradient complexity of $O(n/\\epsilon)$. Therefore, our paper can account for the empirical success of stochastic gradient algorithms for diverse values of B as well.\n\nWe hope we could address all your questions and concerns. We will be glad to provide further explanation and clarification if necessary. \n\n[1] Nitanda, A., Murata, T., & Suzuki, T. (2021). Sharp characterization of optimal minibatch size for stochastic finite sum convex optimization. Knowledge and Information Systems, 63(9), 2513-2539. \n", " We really appreciate your comment on the presentation quality. Please find below answers to your questions and some clarifications to other important points of your review.\n\n> In the literature review the paper _\"On the Theory of Variance Reduction for SG-MC \" _ by Chetterji et al. is missing. […] the iteration complexity of Chatterji et al. is smaller than the one proposed in this paper. A discussion on this paper is required.\nHow does your work compare to the above mentioned paper?\n\nThe work of Chatterji et al. [1], which studies two sampling algorithms SAGA-LD and SVRG-LD, is indeed an important paper that we did not include in ours. Thank you for pointing out this. However, it is important to note that we clearly worked on a broader problem setting than Chatterji et al. [1] and that their gradient complexity is not smaller than ours. First, Chatterji et al. [1] assumed (smoothness (A2),) strong convexity (A3) and Hessian Lipschitzness (A4) to prove their result, and these are stricter conditions than those we imposed in our paper (only LSI and smoothness for sampling). Especially, strong convexity of Chatterji et al. [1] is a really strong assumption. On the contrary, all of our results were proved for **non-convex** functions, and we even derived global convergence. Moreover, our convergence guarantee is proved in terms of KL divergence which is a stronger criterion (i.e., can upper bound) than that used in Chatterji et al. [1], i.e., 2-Wasserstein distance. While the gradient complexity alone may seem to be better than ours, the objective function in Chatterji et al. [1] is actually different. That is, it does not have the factor 1/n before the finite sum. Zou et al. [2] re-wrote the result of Chatterji et al. [1] for our problem setting in Table 1 of their paper. It appears that gradient complexities for SVRG-LD and for SAGA-LD proved by Chatterji et al. [1] become $\\tilde O(n+n^{2/3}/\\epsilon)$ and $\\tilde O(n+n^{1/2}/\\epsilon)$ respectively, which are equivalent or worse than ours even with better assumptions in our case. Zou et al. [2] already provided an improved result of Chatterji et al. [1] for SVRG-LD. This can be found in Table 1 (of our paper), which we adjusted in the revised version. Therefore, there is a clear improvement made in our paper compared to Chatterji et al. [1]. \nWe added a reference in the revised version (see line 49). As we do not have enough space, further explanation on SAGA-LD will be added in the additional one page, if the paper is accepted. \n\n> In the statement of the theorems 1 and 2, the introduction of the constant Λ seems to be redundant as Λ=1+2Ξ.\n\nThank you for pointing out this issue. It is indeed redundant, and we have corrected this in the revised version of our paper. \n\n> The assumption 6 is restrictive as one might have multiple global minima.\n\nWe would like to first emphasize that this assumption is only used to prove Corollary 3.2 (indexes of statement have changed a bit in the revised version), and we believe it does not constitute a major limitation of our work (please notice that our main results, Theorems 1,2 and 3, do not require Assumption 6). The main concern of our paper is sampling from a probability distribution, and we only used Assumption 6 to show that an acceleration of global convergence in non-convex optimization from exponential to polynomial was possible by adding Assumptions 4 to 6. Concerning this Corollary 3.2, Assumption 6 is indeed quite restrictive and further research could be conducted to relax this condition. \n\n> The discussion on the limitations of the work seem to be absent in the paper.\n\nWe apologize for this. Please find a discussion on the limitations in the Discussion and Conclusion section of the revised version of our paper. \n\nWe hope we could address all your questions and concerns. We will be glad to provide further explanation and clarification if necessary. \n\n[1] Chatterji, N., Flammarion, N., Ma, Y., Bartlett, P., & Jordan, M. (2018, July). On the theory of variance reduction for stochastic gradient Monte Carlo. In International Conference on Machine Learning (pp. 764-773). PMLR. \n[2] Zou, D., Xu, P., & Gu, Q. (2018, January). Subsampled stochastic variance-reduced gradient Langevin dynamics. In International Conference on Uncertainty in Artificial Intelligence.\n", " The connection between Langevin sampling and optimization has been extensively studied. A line of research in literature tries to adapt the known optimization techniques to get new sampling algorithms. This paper follows the same direction. The authors studies two algorithms SVRG-LD and SARAH-LD which are respectively based on the variance-reduced stochastic optimization algorithms SVRG and SARAH. Under the smoothness and LSI conditions the convergence of both algorithms is established in the KL divergence through a descent-like inequality. Under additional conditions, they apply these algorithms for the problem of non-convex optimization. Strengths\n* The paper is very well written. It explains the problem and the setting very clearly. One of the best written papers I have reviewed this year.\n* The proposed methods work in the relaxed LSI regime instead of strong convexity. \n\n\nWeaknesses\n* In the literature review the paper _\"On the Theory of Variance Reduction for SG-MC \" _ by Chetterji et al. is missing. This paper studies a similar problem. In particular, they propose an adaptation of the SAGA algorithm to the LMC problem. After a brief overview of the results, I saw that the their iteration complexity of Chatterji et al. is smaller than the one proposed in this paper. A discussion on this paper is required. \n * How does your work compare to the above mentioned paper?\n* In the statement of the theorems 1 and 2, the introduction of the constant $\\Lambda$ seems to be redundant as $\\Lambda = 1 + 2\\Xi$.\n\n * The assumption 6 is restrictive as one might have multiple global minima.\n* The discussion on the limitations of the work seem to be absent in the paper.", " In this paper, the authors proved the convergence rate of the Stochastic Variance Reduced Gradient Langevin Dynamics and the Stochastic Recursive Gradient Langevin Dynamics. The proof is based on Log-Sobolev inequality and a relaxed assumption of smoothness and the result shows an improvement from the previous analysis.\n This paper provides a non-asymptotic analysis of the convergence of SVRG-LD and SARAH-LD to the Gibbs distribution in terms of KL-divergence. The analysis is based on the relaxed assumptions of smoothness and LSI which are weaker conditions than those used in prior works for these algorithms. Overall, the proven convergence rate of SVRG is better than in previous work. \n\n\nHowever, I feel the result seems to be an incremental improvement of the work by Li and Erdogdu (2020) and Vempala and Wibisono (2019).\n 1. Wondering if the authors could comment on the scale of the learning rate. I feel in order to have Theorem 1 and Corollary 1.1. to hold, the required learning rate could be quite small.\n\n2. While setting the batch size to be $\\sqrt(n)$ leads to an improved gradient complexity, such batch size is very large and rarely used in practice. What would the gradient complexity look like if using a much smaller batch size?\n In order to have the theorems hold, the choice of a few hyper-parameters, such as learning rate and batch size seem, seem to be far away from what has been used in practice.\n", " This paper presents improved convergence rates of SGLD with variance reduction. Also, it presents an application to non-convex optimization -- namely an upper bound on the gradient complexity necessary to reach a certain complexity, in SVRG-LD and SARAH-LD methods. The results are novel -- they take the same assumptions of Vempala et al. (2019), who also used the KL divergence as a criterion, but derive a better gradient complexity. Other works have used other assumptions or criteria. Crucially, however, this paper assumes that the batch size and inner loop length is set to \\sqrt{n}. This is theoretically a very strong paper. The main weakness is that its implications are a bit restrictive, as SVRG-LD and SARAH-LD aren't used so much in practice, as far as I know. (In fact, variance reduction is not used much in practice; instead, it has been shown recently that the stochasticity in SGD is vital for generalization and escaping minima/saddle-points.)\n\nStrengths:\nThe analysis is very detailed and technically involved. I did not read the Appendix, but could follow the exposition in the main paper. The literature review is very good and contains most relevant prior work. Table 1 is very helpful to the reader. (A few more words about the comparison with Vempala et al. (2019) could be added to the caption though.) The texts are clear and easy to read, and the authors are transparent about their assumptions. \n\nWeaknesses: \n1. The discussion of variance reduction methods is lacking in nuance: Lately it has been demonstrated the _stochasticity_, i.e. the variance, actually makes SGD so good by improving generalization. See e.g. https://arxiv.org/abs/2006.15081?context=stat or https://arxiv.org/pdf/2202.02831.pdf . Also, the variance is useful to escape saddle points and local minima: https://opt-ml.org/papers/2021/paper24.pdf and https://arxiv.org/abs/1902.04811. As far as I know, people don't really use variance reduction in practice, for precisely this reason. This is not a fundamental criticism of the paper: It is still important to study variance reduction, but there should be a discussion of the role of stochasticity and the usefulness of the studied methods in the Introduction. Also, the restriction of the results to variance-reduced method of course reduces the significance of the result.\n2. There should be a better discussion of the assumption that \"the batch size and the inner loop length are set to \\sqrt{n}\". While the other assumptions are fairly standard, this assumption is highly unusual. Also, it doesn't appear in Table 1 (why?). There should be a better discussion of this assumption, if this appears in other papers, too, and why it is necessary. \n3. Some plots or experiments demonstrating these experiments would be nice. (The proofs are very complicated and it would make the results more plausible if there were a few experiments, demonstrating them.)\n\nBottom line: If the authors provide a few experiments, I am fine with accepting this paper.\n\n 1. I didn't understand what the \"inner loop length\" is. This concept needs some clarification in my opinion. \n2. Doesn't one have to assume, in Assumption 2, that \\rho is asymptotically continuous wrt. \\nu.\n3. The paragraph on top of page 9, before \"Analysis under the weak Morse condition\", is very confusing. Why is the second term with n^{1/2} almost all the time dominant? Why does the analysis of Mattingly et al. (2002) support this? Why use \"likely\" if the work of Raginsky et al. (2017) implies it? (Not a big deal, but maybe this paragraph can be improved.) No limitations and no negative societal impact." ]

[ -1, -1, -1, -1, -1, -1, 7, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, 3, 3, 2 ]

[ "hz1TTFxIJkj", "DMGan2Bvr0N", "dvhTHbXSky", "y1-Ykus1v2s", "HG90utBhjnt", "yTJ0gpD46Hd", "nips_2022_Sj2z__i1wX-", "nips_2022_Sj2z__i1wX-", "nips_2022_Sj2z__i1wX-" ]

[ "0nr2UZoFb6E", "8uvWd-0AkYJ", "uiLK9IKLnHW", "iXnM3Pd1qwG", "3jHyJRau8Bz", "FU0wsiIjUw", "Q5Tlme3AH8JR", "mugDV_wWdTB", "tMXlL28L07", "QWJbnFtClD", "5YdHLQCVp-n", "4oeoAga8gpM", "4l-Jn0ip_Si", "tJs-Su1f-8X", "c7yV904pnEC", "Q3WfJKjMuHw" ]

[ "author", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear Reviewer 43Nu,\n\nThanks for your valuable response again. Please forgive us if you felt offended. We didn't mean to offend you or anyone. \n\nWe were trying to clear up your misunderstanding, and we bolded that sentence so that you could more clearly see our motivation for designing GPM. \n\nWe are glad we can refine the questions step by step and solve them step by step during the communication process. Regarding your further questions, we list the responses below:\n\n**New Q1**:\n\nWhy do you just believe this will contribute to the VOS community further? \n\n**A1**:\n\nIn the process of our research on DeAOT, the successful introduction of feature decoupling allowed us to further raise the SOTA performance of the VOS field. While achieving breakthroughs in performance, feature decoupling would reduce algorithm efficiency. \n\nHowever, we hope that a good framework not only achieves breakthroughs in performance but also should reach a higher level of efficiency. We thought such a framework would make more sense for the VOS field. Hence, we further tried to design the GPM module to improve DeAOT's efficiency. Finally, we end up with improvements of VOS in both performance and efficiency.\n\n**New Q2**:\n\nThe generalization ability of the proposed method has not been proved.\n\n**A2**:\n\nTo prove the generalization ability of the proposed method, we have evaluated our method in four different architectures (including STM-like architectures) with three different backbones on four benchmarks, in which a new challenging benchmark (VOT2020) was used to further prove the generalization ability of our DeAOT. \n\nWe tried our best to cover all popular settings of VOS in recent years. More details have been supplied in answer to the initial Q1. Please forgive us since we cannot list details here due to the character limitation.\n\n**New Q3**:\n\nThe performance promotion compared to AOT is moderate.\n\n**A3**:\n\nThe performance promotion of DeAOT is significant. For example, R50-DeAOT-L achieves a 1.9% improvement (from 84.1% to 86.0%) over R50-AOT-L on YouTube-VOS 2018, which is the most important benchmark of VOS. According to the progress of VOS in recent years, this improvement is not worse than the improvement made by previous SOTA methods in recent years, such as R50-AOT-L v.s. CFBI+ (1.3%, from 82.8% to 84.1%), CFBI+ v.s. CFBI (1.4%, from 81.4% to 82.8%), and CFBI v.s. STM (2.0%, from 79.4% to 81.4%). \n\nConsidering it will be harder to improve performance on a stronger baseline, we suppose it is reasonable to claim that the performance improvement of DeAOT is significant.\n\nThanks again for all your time and valuable comments. It seems that we have addressed most of your previous questions (if not, we are still happy to answer them for you), and we hope these new answers will address your new questions again.\n\nBest Regards,\n\nAuthors\n", " For A1, \nthe authors claim that **We hope the reviewer will not punish us because we have introduced the GPM module in order to improve DeAOT's efficiency. We just believe this will contribute to the VOS community further.**\n\nWow, firstly, I have never punished any ones. I just give my comments objectively.\nSecondly, why do you just believe this will contribute to the VOS community further? Is this an overclaim? This work still follows the AOT [58] framework. The generalization ability of the proposed method has not been proved. Also, the performance promotion compared to AOT is moderate. \n", " Thanks for the authors' response and I think my concerns have been adequately addressed. I will raise my score to a certain accept.", " Dear Reviewer vqMg,\n\nWe sincerely thank you for your valuable comments during the review procedure, and we are glad you recognize our DeAOT's novelty and contributions to the VOS field!\n\nBest Regards,\n\nAuthors", " Dear Reviewer 43Nu,\n\nWe sincerely thank you for your time and your response. Your comments complete our paper and make it better. \n\n**We're sorry we couldn't answer your question in more detail earlier due to the character limit.** Regarding your new questions, our new responses are listed below:\n\n**New Q1**: \n\nFor Q2, the authors claim that both the feature decoupling and GPM are effective in improving VOS performance. However, the contribution of each component (feature decoupling and GPM ) is approximate. Thus, the main contribution, i.e., feature decoupling can not be regarded as the main innovation.\n\n**A1:** \n\nThe contribution of each component (feature decoupling and GPM) is not approximate, but only the performance gains are approximate. We consider feature decoupling as the major contribution since feature decoupling is a technically original and novel innovation in the field of semi-supervised VOS. We have a clear motivation and in-depth analysis of the feature decoupling for VOS. Compared to feature decoupling, GPM is technically motivated by some latest works [23][27]. Hence, the contribution of GPM is not comparable with feature decoupling since the contribution of GPM mostly comes from the hard design of the DeAOT framework. \n\nWe tried our best to make DeAOT variants achieve the SOTA performance and efficiency across different benchmarks and model complexity. Regarding the current results, the DeAOT variants can still achieve the SOTA performance after losing half of the gains by removing GPM (but will lose some efficiency). \n\n**We hope the reviewer will not punish us because we have introduced the GPM module in order to improve DeAOT's efficiency. We just believe this will contribute to the VOS community further.**\n\n**New Q2:**\n\nFor Q3, In the task of semi-supervised VOS, it is intuitively reasonable that single-head matching/propagation processes can achieve comparable or even better performance than multi-head processes. This statement is overclaiming and questionable. The related proof or theoretical analysis should be provided.\n\n**A2:**\n\nWe didn't want to overclaim anything and were just trying to give a possible reason. In Semi-supervised VOS, most methods use single-head attention maps (STM[32], KMN[40], SST[17], HMMN[41], STCN[11]) or matching maps (CFBI[57], CFBI+[59]) to match object patches from one-frame to another-frame. Intuitively, the optimal object matching between two frames is one-to-one matching for each object, since each object can not appear at multiple different places simultaneously. Based on such a motivation, KMN[40] proposed regularizing the matching/attention maps to be approximately one-to-one using the Gaussian kernel. Following such an innovation, MiVOS [a] proposed a stronger regularization method, the top-k memory strategy. The Gaussian kernel and the top-k memory strategy are utilized by STCN[11] as key tricks, significantly improving STCN's VOS performance (more than 2%). \n\nEven if we don't consider the characteristics of VOS, in another task, NLP, [23] and [27] **have found** that the presence of gating attention allows single-head attention performs better than multi-head attention. This motivated our minor contribution, and we designed the efficient GPM module for VOS.\n\nBased on the results, analyses, and findings from the above-mentioned works, we suppose it is reasonable that single-head matching/propagation processes can achieve comparable or even better performance than multi-head ones.\n\nWe have to strengthen that the above analysis and conjecture are just based on our years of experience in the VOS field. Moreover, we are happy to discuss possible factors behind these open questions with experts in the field, and we respect all different opinions. \n\n**However, the use of a single head or multiple heads is only a small and empirical improvement of DeAOT. We hope the reviewer will not punish us since we shared some of our thoughts regarding this minor improvement.**\n\nIf you have more questions, we will be happy to address them further. \n\nBest Regards,\n\nAuthors\n\n\n[a] Modular Interactive Video Object Segmentation: Interaction-to-Mask, Propagation and Difference-Aware Fusion. CVPR 2021.\n\n", " I have read the rebuttal carefully. I still have questions after reading the rebuttal. \n1. For Q2, the authors claim that both the feature decoupling and GPM are effective in improving VOS performance. However, the contribution of each component (feature decoupling and GPM ) is approximate. Thus, the main contribution, i.e., feature decoupling can not be regarded as the main innovations. \n2. For Q3, In the task of semi-supervised VOS, it is intuitively reasonable that single-head matching/propagation processes can achieve comparable or even better performance than multi-head processes. This statement is overclaim and questionable. The related proof or theoretical analysis should be provide. \n\nOverall, according to the current rebuttal, I change my score from Weak Accept to Borderline reject.", " Thanks for the detailed response to my questions. I will stick with my original rating and recommend acceptance.", " \nDear Reviewers,\n\nThank you for reviewing this paper. Since authors have submitted their rebuttal, please check if the rebuttal addresses your concerns. Please also check the comments from other reviewers, and if you have any question, please discuss with authors in OpenReview soon.\n\nBest Regards, \n\nAC", " We appreciate you taking the time to share your comments and suggestions in the review assessment. We are glad that you and all the other reviewers recognize our contribution in decoupling object-agnostic and object-specific information, which helps DeAOT achieve state-of-the-art performance at impressive speed. All your comments are addressed point by point in the following.\n\n**Weaknesses:**\n\n**Q:** DeAOT extends the operation of STCN.\n\n**A:** STCN is a great VOS job, but DeAOT extends the hierarchical propagation based on AOT instead of STCN. The AOT framework has two novel characteristics, i.e., the identification mechanism (responsible for matching, propagating, and decoding multiple objects together) and the hierarchical propagation (responsible for scaling VOS networks). These two characteristics are the essential difference between AOT and STM-like methods (e.g., STM and STCN). Figure 1 and Table 1 show that AOT has better performance, efficiency, and scalability than STCN.\n\nAlthough AOT shows strong results, our DeAOT still achieves a comprehensive and significant improvement in performance and efficiency over AOT. The total contribution of DeAOT is not incremental but significant to the VOS field:\n\n(1) The **major contribution** of DeAOT is the feature decoupling method, which can generalize to different types (multi/single-object, long/short-term) of challenging benchmarks and different VOS models with different backbones/propagation layer numbers/inference types (CFBI-like or STM-like). We tried our best to ensure our DeAOT could generalize to all the possible VOS settings under a uniform framework. \n\n(2) The **minor contribution** is the gated propagation responsible for improving DeAOT's efficiency. Combining both feature decoupling and gated propagation, DeAOT achieves a significant improvement in performance and efficiency against previous VOS methods.\n\n**Questions:**\n\n**Q1:** Only containing ID branch is lacking.\n\n**A1:** Thanks for your suggestion. We have considered the experiment of using only the ID branch, but we found it is not applicable. When predicting the current frame mask, the initial information (which can be used to match objects) is only the visual information given by the current frame image. In other words, it is necessary and inevitable to use visual embeddings to compute matching/attention maps.\n\n**Q2:** Whether the improvement is brought by adding more parameters. \n\n**A2:** Thanks for your suggestion, and we will supply the information of parameters in the revision. Here, we show some important parameter comparisons below (all the models use ResNet-50 as the backbone):\n\n| Model | STM | HMMN | STCN | R50-AOT-L | R50-DeAOT-L |\n| ----- | --- | ---- | ---- | --------- | ----------- |\n| YouTube-VOS accuracy | 79.4 | 82.6 | 83.0 | 84.1 | **86.0** |\n| fps | - | - | 8.4 | 14.9 | **22.4** |\n| Param (M) | 34.0 | 42.8 | 54.4 | **14.9** | 19.8 |\n\nAs shown, R50-DeAOT-L significantly outperforms STCN and R50-AOT-L on accuracy and run-time speed. However, R50-DeAOT-L introduces only 5M parameters (which is inevitable due to feature decoupling) compared to R50-AOT-L and uses only 36% of the parameters of STCN (19.8M v.s. 54.4M). Besides, the careful design of GPM makes DeAOT run even much faster than AOT.\n\n**Q3:** The role of gate (δ(U)) and DW-Conv.\n\n**A3:** According to our experimental records, removing δ(U)/DW-Conv from DeAOT-S degraded the performance by 1.9%/2.7%. δ(U) is necessary for improving the ability of non-linear transformation of GPM. Without δ(U), the non-linear ability of GPM only comes from the LN modules and is not sufficient to fit complex functions. The DW-Conv is critical in enlarging the receptive fields of DeAOT and AOT (AOT uses a DW-Conv layer in each feed-forward module). Without DW-Conv, the performance of DeAOT/AOT will degrade by about 2%~3%. \n\n**Q4:** Does the problem of fading object-agnostic information exist in STM-like double backbone structure?\n\n**A4:** During the design of DeAOT, we also considered using STM-like double backbones. However, we didn't find any obvious performance gains by replacing the ID bank of DeAOT/AOT with a ResNet-18/34 backbone. In this regard, our analysis is that the information contained in the mask is not as rich as the image, and a simple ID bank can generate the mask embedding well.\n\n**Q5:** How to divide the long-term and short-term memories?\n\n**A5:** The long short-term memories are introduced in AOT and not our contribution. Their theoretical and experimental basis can be found in the original AOT paper.\n\n**Q6:** The theoretical basis of GPM.\n\n**A6:** Thanks for your suggestion. Although the GPM is only a minor contribution of DeAOT, we are glad to study the theoretical basis of GPM in future works. If possible, we will add relevant progress in the revision.\n", " We appreciate you taking the time to share your comments and suggestions in the review assessment. We are glad that you and all the other reviewers recognize our contribution in decoupling object-agnostic and object-specific information, which helps DeAOT achieve state-of-the-art performance at impressive speed. All your comments are addressed point by point in the following.\n\n**Questions:**\n\n**Q1:** The incremental contributions. \n\n**A1:** The total contribution of DeAOT is not incremental but significant to the VOS field. The contribution of DeAOT can be separated into a major contribution and a minor contribution:\n\n(1)\tThe **major contribution** of DeAOT is based on the in-depth analysis of the object-agnostic and object-specific, which gives a novel view of the VOS task, as you mentioned. Based on the analysis, we carefully design a highly effective decoupling mechanism, which can generalize to different types (multi/single-object, long/short-term) of challenging benchmarks (YouTube-VOS 2018/2019, DAVIS 2017/2016, VOT 2020) and different AOT models with different backbones/attention layer numbers/inference types (CFBI-like or STM-like). We tried our best to ensure our DeAOT could generalize to all the possible VOS settings under a uniform framework. The characteristics of the used benchmarks and models are listed below:\n\n| Benchmark | Characteristics |\n| - | - |\n| YouTube-VOS 2018/2019 | **large-scale, multi-object**, with **unseen categories**|\n| DAVIS-2017 | small-scale, **multi-object** |\n| DAVIS-2016 | small-scale, **single-object**|\n| VOT 2020 | small-scale, **single-object** with **long-term videos** (327 frames per video on average)|\n\n| Model | Characteristics |\n| -| - |\n| DeAOT-T | **STM-like structure** with only one layer of matching and propagation. |\n| DeAOT-S/B| **Multiple layers** of matching and propagation. **CFBI-like inference**, considering only the reference frame as the long-term memory. |\n| (R50/SwinB-)DeAOT-L| **Multiple layers** of matching and propagation. **STM-like inference**, increasing the long-term memory per 5 frames.|\n\n(2)\tThe **minor contribution** is the gated attention/propagation for VOS. The design of such a module is responsible for compensating for the efficiency loss when utilizing the feature decoupling. In other words, the minor contribution serves the major contribution and is not independent of the major contribution. We agree with you that the gated attention/propagation is technically motivated by previous works [23][27]. However, the contribution of the gated propagation should not be independently assessed. Only by combining both the proposed feature decoupling and gated propagation, DeAOT achieves a comprehensive and significant improvement in performance and efficiency against previous VOS methods.\n\nIn summary, the contribution of DeAOT is not incremental but significant. Besides, we have tried our best to conduct experiments on STM-like models and make all the models under a uniform framework. We believe our extensive experiments can demonstrate the generalization ability of the DeAOT framework.\n\n**Q2:** Do this paper's main innovations (i.e., decoupling features) really play an essential role?\n\n**A2:** Sorry for not getting you to understand our experimental results correctly. In Table 3 (a), replacing GPM with LSTT means removing the feature decoupling as well since the feature decoupling is a part of GPM in our default setting. When only the GPM module is replaced in AOT (without the feature decoupling), the performance drops from 81.5 to 80.3 (instead of from 82.5 to 80.3), according to Table 3 (a). Besides, according to our earlier experimental records, decoupling features in LSTT could bring a performance improvement of 1.2%, which is similar to the improvement of replacing LSTT with GPM (without the feature decoupling). In other words, both the feature decoupling and GPM are effective in improving VOS performance.\n\n**Q3:** Why the results of $N_h=1$ and $N_h=8$ are similar?\n\n**A3:** In the task of semi-supervised VOS, it is intuitively reasonable that single-head matching/propagation processes can achieve comparable or even better performance than multi-head processes. In the matching of objects in videos, it is impossible for each object to appear in multiple different locations in the same frame. In other words, the matching relationship of objects in different frames is a one-to-one correspondence, which can be represented by a single-head of attention map. Therefore, it is reasonable that single-head matching/propagation processes are capable of modeling multi-object matching and propagation. We will add the following discussion in the revision\n\n**Q4:** Typographical adjustments. The abbreviation, AOT. Grammar errors.\n\n**A4:** We sincerely thank you for your patience during the review, and we will correct all the typos in the revision.\n", " We appreciate you taking the time to share your comments and suggestions in the review assessment. We are glad that you and all the other reviewers recognize our contribution in decoupling object-agnostic and object-specific information, which helps DeAOT achieve state-of-the-art performance at impressive speed. All your comments are addressed point by point in the following.\n\n**Questions:**\n\n**Q1:** It wasn't clear to me how the gating embedding U is obtained. The authors should clarify this.\n\n**A1:** Sorry for not being able to give you a simple understanding of the meaning of the gating embedding U, and we will add more descriptions in the revision to help the readers understand it. In GPM, the way to obtain the gating embedding U is simple and similar to the way to obtain other commonly-used embeddings (e.g., Q, K, V). In attention mechanisms, Q, K, and V are obtained after linearly projecting a feature (or three different features) by their weights, $W^{Q}, W^{K}, W^{V}$ (notably, we set $W^{Q} = W^{K}$ in GPM to share the embedding space of Q and K). In GPM, the gating embedding U is also obtained after projecting a feature by a learnable weight, $W^{U}$. In the object-agnostic/specific branch of GPM, the projected feature is the visual/mask feature (I/M). $W^{U}$ is not shared among different GPM modules and different branches. More details can be found in Eq. 6, 7, 10, and 11. \n\n**Q2:** It would be interesting to see the performance of LSTT with decoupling features (i.e., an extra entry in Table 3a for completeness).\n\n**A2:** Thanks for your suggestion, and we will supply the related results in the revision. According to our earlier experimental records, decoupling features in LSTT (putting Long/Short Term Attn before Self-Attn) could bring a performance improvement of 1.2% (J&F, YouTube-VOS) to AOT-S, which is consistent with the experimental phenomena of GPM in Table 3(a). However, decoupling features in LSTT reduced run-time speed by more than 5 fps. The main reason is that the doubled multi-head propagations are computationally intensive.\n\n**Q3:** Are both the encoded visual features as well as the ID features used to obtain the target mask or only the ID features?\n\n**A3:** To predict the target mask, both the visual (object-agnostic) and ID (object-specific) features are concatenated and forwarded to the decoder network. We also tried to use only the ID features to decode the mask prediction but didn't find a noticeable improvement in performance or efficiency (the decoder network, FPN, is light-weight).\n\n**Q4:** The current approach performs a strict separation of object-specific and object-agnostic features and mainly uses the object-agnostic features to compute the attention masks. However, I imagine that certain object-specific information could also be helpful when computing attention masks. Thus would it make sense to instead have two branches, one which is used to compute the attention masks and the second used to obtain the final mask. Both of these branches can take both the image and object masks as input and determine whether to use the ID information or not during the training process.\n\n**A4:** Thanks for your detailed suggestion, which is really worth thinking about in future works. The success of DeAOT feature decoupling indicates that it is reasonable and effective to use one branch to compute attention masks and another branch to obtain the final mask (as you mentioned). But the current experimental results in Table 3(c) show that using only visual embeddings to compute attention masks leads to better performance. A possible reason is that using both visual and mask embeddings may make the networks overfitted to the training objects' shape patterns. In summary, how to effectively use both the image and object masks in computing attention masks is still an open problem and requires future studies.\n", " We appreciate you taking the time to share your comments and suggestions in the review assessment. We are glad that you and all the other reviewers recognize our contribution in decoupling object-agnostic and object-specific information, which helps DeAOT achieve state-of-the-art performance at impressive speed. All your comments are addressed point by point in the following.\n\n\n**Questions:**\n\n**Q1:** The effect of removing FFN, or whether introducing FFN would result in a better speed-performance tradeoff.\n\n**A1:** Removing FFN from the LSTT of AOT-S will significantly degrade its performance by more than 3% (J&F, YouTube-VOS) but only improve run-time speed by about 2 fps. Such a tradeoff is worthless. Without FFN, the non-linear transformations within LSTT only come from the LN modules and are insufficient to fit complex functions. By contrast, in GPM, the GP function compensates for the lack of non-linear transformations by introducing the gating embedding U, which is followed by a non-linear activation (SiLU/Swish in our setting).\n\n\n**Q2:** The impact of swapping Self-Attn (Prop) and Long/Short Term Attn (Prop).\n\n**A2:** Putting Long/Short Term Attn(Prop) before Self-Attn(Prop) is not a trick for DeAOT but is an inevitable design. The Self-Prop takes two input branches, i.e., object-agnostic visual embedding and object-specific mask embedding. Suppose we put Self-Prop before Long/Short Term Prop. In that case, there will be no object-specific mask embedding for the first Self-Prop module since the first module in GPM can only take the encoder network’s output as input, which is an object-agnostic visual embedding. But if we put Self-Prop after Long/Short Term Prop, the first Long/Short Term Prop module can generate an object-specific embedding by propagating mask embeddings from past frames to the current frame. Thus, the next Self-Prop module can have two branches of input.\n\nAlthough putting Long/Short Term Attn(Prop) before Self-Attn(Prop) is necessary for DeAOT, we were also curious about its effect on the LSTT of AOT. According to our experimental records, putting Long/Short Term Attn before Self-Attn positively affected AOT-T (about 0.4% improvement, J&F, YouTube-VOS) but showed no obvious improvement in deeper networks (AOT-S/AOT-B/AOT-L/R50-AOT-L). Overall, the swapping will not make a significant performance difference.\n\n\n**Q3:** The difference between sharing an attention map or not.\n\n**A3:** According to our earlier experimental records, decoupling features in LSTT (putting Long/Short Term Attn before Self-Attn) could bring a performance improvement of 1.2% (J&F, YouTube-VOS) to AOT-S, which is consistent with the experimental phenomena of GPM in Table 3(a). However, decoupling features in LSTT reduced run-time speed by more than 5 fps. The main reason is that the doubled multi-head propagations are computationally intensive.\n\nRegarding the discussion of different possible ways to share attention maps, we have supplied detailed ablation studies in Table 3 (c). Moreover, please refer to Table 3 (a) for the GPM without sharing attention maps.\n\n\n**Weaknesses:**\n\n**Q:** Lack of ablation studies on GPM. It is more important to explain the more subtle differences between LSTT and GPM.\n\n**A:** Thanks for the suggestion. In the above answers, we addressed all your questions about the subtle differences between LSTT and GPM. In addition, we will add all these valuable discussions into the revised version or the supplementary material.\n", " This paper proposed an improved AOT method called DeAOT. The main idea of DeAOT is to separate representation learning from identity information. This means using two GPMs instead of the original LSTT in AOT. The Gated Propagation Module(GPM) is faster than LSTT and achieves better performance. Strengths\n- Great performance on several VOS/VOT benchmarks.\n- Intuitive and effective design about disentangle the representation learning and id information.\n- GPM balances the inference speed and performance.\n\nWeaknesses\n- Lack of ablation studies on GPM. Compared to AOT, the difference between DeAOT seems to be only in the design of Propagation Module, and specifically the difference between LSTT and GPM. Therefore, it is more important to explain the more subtle differences between LSTT and GPM and to explore what really works in the design of the GPM. For example:\n- the effect of removing FFN, or whether introducing FFN would result in better speed-performance tradeoff\n- the impact of swapping Self-Attn(Prop) and Long/Short Term Attn(Prop)\n- the difference between sharing an attention map or not\n\nFrom the ablation information provided in the current experiments(Table 3), we could find that GPM still outperforms LSTT even without disentangle representation learning and id information, so it is more important to analyze the role of GPM clearly. From another perspective, GPM is the core of this paper and it would be detrimental to the quality of this paper if the mechanism of GPM could not be well explained. No but not need.", " The paper tackles the problem of video object segmentation by extending the Associating Objects with Transformers (AOT) approach. AOT uses multiple Transformer blocks to gradually integrate target information from the previous frame and masks into the current frame features. The encoded features are then decoder to obtain the target mask. The deeper Transformer blocks in AOT operate on features which are target-specific, i.e. which contain encoding of the target mask information. The authors claim that using such features to compute the attention maps inside Transformer harms performance since they contain less target agnostic visual information. To address this, the authors propose to decouple the propagation of target-specific and target-agnostic features using two parallel transformer branches. Both the branches share attention maps, computed using the target-agnostic features. Additionally, the authors propose an efficient Gated Propagation Module (GPM) instead of Long-Short term Transformer (LSTT) used in AOT to propagate the features. GPM uses single-head attention, as opposed to multi-headed attention in LSTT. Additionally it uses a gating function to modulate the propagated features. The use of GPM compensates for the extra computation incurred due to use of two transformer branches. Overall, the proposed methods consistently outperforms baseline AOT on 4 benchmarks, across 3 different backbone networks (+1.6% on YouTube-VOS 2019), obtaining state-of-the-art results on these benchmarks. The proposed method is also faster than AOT. ## Strengths\n\n**S1**: The proposed approach obtains state-of-the-art results on YouTube-VOS, DAVIS, and VOT2020 benchmarks while operating at impressive speed (>10 FPS). \n\n**S2**: The proposed approach generally outperforms the baseline AOT across YouTube-VOS, DAVIS, and VOT2020 benchmarks, when using 5 different backbones/configurations. Furthermore the proposed approach is faster then AOT.\n\n**S3**: The paper is well written, and the authors clearly introduce the issue with the baseline AOT. This claim is further experimentally validated (Figure 2, Table 3a). The proposed approach is shown to mitigate this issue.\n\n**S4**: The proposed Gated Propagation Module (GPM) is interesting and seems to provide a clear improvement over LSTT block, while being faster (Table 3a, 3b).\n\n**S5**: The authors perform a thorough analysis of the proposed approach, showing the impact of each component.\n\n## Weaknesses\nI do not have any major issues with the paper. Some minor comments to be addresses\n\n**W1**: It wasn't clear to me how the gating embedding U is obtained. The authors should clarify this.\n\n**W2**: It would be interesting to see the performance of LSTT with decoupling features (i.e. an extra entry in Table 3a for completeness).\n\n**W3**: Are both the encoded visual features as well as the ID features used to obtain the target mask, or only the ID features? \n\n**W4**: The current approach performs a strict separation of object-specific and object-agnostic features, and mainly uses the object-agnostic features to compute the attention masks. However I imagine that certain object-specific information could also be helpful when computing attention masks. Thus would it make sense to instead have two branches, one which is used to compute the attention masks, and the second used to obtain the final mask. Both of these branch can take both the image and object masks as input, and determine whether to use the ID information or not during the training process. Please see weaknesses. The authors discuss the limitations, albeit in the supplementary material.", " This paper proposes a hierarchical propagation module based on transformer which can keep the object-agnostic information in the videos. And it also proposes Gated Propagation Module for enhancing model efficiency. This method achieves high accuracy and efficiency. strengths:\nThe author alleviates the missing of object-agnostic information in deeper transformer modules by introducing hierarchical dual-branch propagation module. The GP function further improves the model efficiency while keeping high efficiency. This method has a certain originality.\n\nWeakness:\nThe object-specific information can lead to the performance degradation of memory-based methods such as STM. STCN takes two object-agnostic features as Q and K to perform attention. This method extends this operation to a hierarchical propagation module and it is a continuation of this idea. 1.The performance of only containing ID branch is lacks in table 3 (c). For experimental integrity, the contribution of every module should be shown.\n2.The author should list the module parameter and inference speed in table 3. The author needs to further demonstrate and verify whether the improvement in GPM is brought by adding more parameters.\n3.The author needs to further analyze the effectiveness of modules in GP function. I want to know if gate (δ(U)) and DW-conv actually play an important role in this module\n4.The authors mention that object-agnostic information fades in the video and use a single-backbone VOS model for hierarchical dual-branch propagation module validation. But the memory-based model such as STM takes a double backbone. Does this problem exist in the double backbone structure, and can the hierarchical dual-branch propagation module also improve the defects in the two-stage model?\n5.I am interested in how the long-term and short-term memory images are divided and what the theoretical and experimental basis for this division. In addition to the ablation experimental results and visualization results, the author also needs to analyze the effectiveness of the GPM and GP function from the theoretical basis and the feature visualization results.", " This paper introduces a feature decoupling mechanism into the VOS task to solve the problem of visual information forgetting in the AOT method. Specifically, DeAOT decouples the hierarchical propagation of object-agnostic and object-specific embeddings by handling them in two independent branches. In addition, Gated Propagation Module with single-head attention is used to reduce the computational complexity. Experimental results on YouTube-VOS, DAVIS17, DAVIS16, and VOT20 demonstrate the performance gain of the proposed method. The in-depth analysis about the object-agnostic and object-specific gives a novel view for VOS task. In addition, two independent branches of the shared attention map do not significantly increase the model parameters. \n\nThe proposed gate attention reduces multiple-head attention to single-head attention, greatly reducing computational complexity while maintaining accuracy.\n\nThe paper is well-written and easy to read and understand.\n The incremental contributions. The main innovation is to expand the AOT model through a decoupling mechanism and gate attention. However, it is a common way to improve features' expression ability through decoupling, and gate attention is proposed in previous papers [23][27]. To prove the generalization ability of decouping mechnism, the authors should also combine it with other baseline method, such as STM.\n\nDo this paper's main innovations (i.e., decoupling features) really play an essential role? In Table 3 (a), when the decoupling module is removed, the performance drops from 82.5 to 81.5, while when the GPM module is replaced, the performance drops more significant (82.5-> 80.3). This means GPM plays a more important role than decoupling feature.\n\nFor the head numbers in ablation experiment, the authors need to explain why the results of head numbers N_h=1 and N_h=8 are similar. Moreover, the performance of multiple-head is even inferior to that of single-head. This is conflict with the motivation of multiple-head mechanism. The authors may need to add other ablation results of N_h.\n\nTypographical adjustments, Fig 4 goes too far from its text description.\n\n Minors: the abbreviation, i.e., AOT, should give the total words when first used. \ngrammar errors ‘Fig. 4 give qualitative comparisons’\n Yes" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 7, 4, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 5, 5 ]

[ "8uvWd-0AkYJ", "3jHyJRau8Bz", "4oeoAga8gpM", "Q5Tlme3AH8JR", "FU0wsiIjUw", "QWJbnFtClD", "5YdHLQCVp-n", "nips_2022_DgM7-7eMkq0", "c7yV904pnEC", "Q3WfJKjMuHw", "tJs-Su1f-8X", "4l-Jn0ip_Si", "nips_2022_DgM7-7eMkq0", "nips_2022_DgM7-7eMkq0", "nips_2022_DgM7-7eMkq0", "nips_2022_DgM7-7eMkq0" ]

[ "7EbWx26R1dp", "Bv97-AJwM_w", "IHy6kYVR72v", "fYvSShGl5mW", "zp7XLw964V-", "xUXtHOzTjV", "cx6ZxTW7CNd", "eq40OcpSCKw", "82VS2tjNuPh", "3vgCF708j7", "R1973UQFvgc", "06-NbhnCi5z", "uRQ19eHwa7-", "jSIEIZkAEOq", "7lM5hTjm2d0", "Ks1jBZ2ONQ4", "sj10B557NrL" ]

[ "author", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank the reviewer for their response and second look at the paper.\n\nWe would like to respond to your comment on the quoted claim.\n\nBrain Score describes the performance of models trained to *predict neural activity recorded in primates, not humans*. In our work (and the quote) we are solely comparing DNNs with human perception. Also note that in our submitted manuscript we describe how Brain Score has changed over the years as DNNs have become more accurate (lines 82-84): \"While the original theory was that model explanations of neural representations of object images improved alongside model classification accuracy [29], recent large-scale DNNs are worse at explaining neural data than older ones with lower ImageNet accuracy [30].\" \n\nGeirhos indeed has done rigorous work comparing human and DNN classification performance on a variety of challenging tasks. His most recent paper, \"Partial success in closing the gap between human and machine vision\" aggregates most of the prior challenges together. In our original submission we summarized their findings (lines 69-73), \"On the one hand, there is evidence that DNNs are becoming better models of humans on challenging visual tasks, such as recognizing objects obscured by noise [23].\" The authors found that newer models like CLIP perform nearly on par with humans, whereas we found that CLIP is poorly aligned with human perception and visual strategies. \n\nGiven the above, we hope you agree that we do indeed provide novel insight beyond Schrimpf and Geirhos. Please let us know if you have any other references that we have missed, we would be happy to add them.\n\n\n ", " Given the feedback from all reviews and the rebuttal, I've decided to keep my score. I think the paper is making progress but it is still not ready for publication. In addition I find this claim in the general rebuttal quite strong:\n\n> \"Lastly, we want to re-emphasize that we have provided the first ever demonstration that the field of computer vision is systematically producing worse models for Human vision.\"\n\nI do not think this is true. The work that Schrimpf has pioneered through Brain-Score and through a series of papers has already shown this. Geirhos has also in parallel explored many of these pivotal ideas via rigorous human vs machine psychophysics and several other results (texture-bias, short cuts, etc...) . The Neural Harmonizer and/or the general structure of the paper should give a greater insight beyond what Schrimpf, Geirhos and other colleagues that perform work at the intersecion of human and machine vision have explored.", " Dear reviewers,\n\nThank you again for your time and effort in reading and critiquing our paper. We hope you will have a chance to read our responses to your reviews before the response period ends tomorrow, 8/9. Please find that we have addressed the concerns raised, and that if you have any others we are happy to discuss them.\n\nBest,\n\nThe authors", " We thank the reviewer for their feedback\n\n> This is a trivial finding...\n\nTo briefly restate our contributions:\n\n1. In our survey of 85 neural networks trained for object classification, the best performing model explains just under 60% of human visual strategies.\n2. Even more importantly, the alignment between DNNs and humans has worsened as their ImageNet accuracy has improved beyond the best-aligned model.\n3. We show that harmonizing DNNs with human visual strategies improves their accuracy and significantly improves their alignment with humans.\n\nReviewer *Xrpg* stated that our work \"addresses an important problem in modern ML + CV.\"\nReviewer *cZRY* stated that our work is \"timely and relevant.\"\nReviewer *cEc7* stated that we investigate an \"extremely interesting problem,\" that \"measuring if these improvements [in DNN accuracy] result in better alignment between biological and artificial intelligence is a fundamental goal for a multitude of reasons,\" and that \"the neural harmonizer module is interesting as it increases alignment significantly.\"\n\nThere is no guarantee that DNNs can learn to adopt human visual strategies in novel object images. We not only find that this is possible — across three datasets and two different measures of visual strategies (*where* humans look and *how* they integrate that information) — but also that this object is to some degree synergistic with object recognition accuracy. Our work therefore introduces a fundamental problem in computer vision, and shows that the solution is not only scalable but also useful for Brain Science and Industry applications alike since it both improves accuracy and promotes behavior that is more predictable and understandable to humans.\n\n> Evaluating which pretraining objective leads to most brain-like representations (as measured by the authors' proposed saliency alignment metric) would shed light on which learning objective the brain might be using...\n\nSorry for the misunderstanding. We plotted the alignment of 85 DNNs trained for object recognition. No model exceeds 60% alignment with humans. In our original manuscript we stated that the best-aligned model is the DenseNet 121. Are you asking for a more detailed analysis of how these off-the-self models are ordered in their alignment? \n\n> Note that the proposed \"neural harmonizer\" is not a candidate learning objective the brain might be using (this would be tautological)...\n\nOur work is focused on DNNs as a model of behavior and their alignment with human visual strategies. We are not focused on biological plausibility since it is debatable that any DNN can pass that bar. Our use of the neural harmonizer is to show that co-training on human visual strategies surprisingly yields improvement in accuracy and predictions of human visual strategies on novel images.\n\n> Similarly, evaluating which neural network architecture leads to most brain-like representations (as measured by the authors' proposed saliency alignment metric) would elucidate which parametric class the brain might be using. However the authors simply lump all models together, confounding architecture, learning objective, and data. Hence we're unable to see any systematic effects from architecture. \n\nWe clustered our analysis of 85 models according to whether they were standard CNNs trained on ImageNet, self-supervised, Transformers, adversarially-trained (Robust), trained with additional industry-level data (e.g., JIT-300M, JIT-3B, etc.), or harmonized. We did not spend much effort in the paper describing systematic differences between these architecture/training groupings because the factor that explained the most variance in human alignment was model accuracy. For instance, Transformers and models trained with extra data were less aligned with humans, but these are also the most accurate models that we tested.\n\nWe are happy to add additional and more granular analyses. Could you please advise on what additional work you would like to see?", " The authors seem to have misunderstood my comment.\n\n- The authors evaluate a host a models on their alignment with human saliency maps. They then start training networks for this same metric, and find that they improve in that regard. This is a trivial finding, and in their words, does not tell us \"anything about brains or cognition.\"\n\n- Understanding brains and cognition means understanding why and how they have gained their particular selectivity and function. Evaluating which pretraining objective leads to most brain-like representations (as measured by the authors' proposed saliency alignment metric) would shed light on which learning objective the brain might be using. Note that the proposed \"neural harmonizer\" is not a candidate learning objective the brain might be using (this would be tautological), hence finding that the neural harmonizer outperforms other learning objectives teaches us nothing about what the brain is doing. It is simply hacking a metric that should be used for evaluation only.\n\n- Similarly, evaluating which neural network architecture leads to most brain-like representations (as measured by the authors' proposed saliency alignment metric) would elucidate which parametric class the brain might be using. However the authors simply lump all models together, confounding architecture, learning objective, and data. Hence we're unable to see any systematic effects from architecture. This is an unfortunately missed opportunity. \n\nGiven that the neural harmonizer holds no scientific interest, and that the analysis section of the paper doesn't hold on its own (a more careful dissection of the results is required here), I don't think the paper belongs at NeurIPS. ", " > The code and data are propriety and will NOT be released.\n\nWe included a link to the code in the discussion of the original manuscript. We have moved it to the abstract for visibility. Here is the link: https://anonymous.4open.science/r/Meta-predictor-3791/\n\n> Some relevant recent literature is missing\n\nWe have added these references to the related work section, both of which are fantastic and we apologize for missing them the first time. \n\nNote that the “When pigs fly…” paper is about adjusting model accuracy to match humans when contextual information is available. We are not using human accuracy as the barometer in our work, but rather, human visual strategies. Our goal is to allow the field to scale model capacity as it is currently doing, to generate models with super-human accuracy that can nonetheless exploit predictably human-like visual strategies. \n\n>On the role of scene context: Human annotations highlighted lesser context areas (Page 5), but it is widely known that human visual recognition is strongly dependent on scene context. Does this suggest that what humans \"think\" of as visually important, may not essentially be the most important regions? Also may be suggested by work on minimal images, as it is counter-intuitive to humans that a few pixels can cause such large drops in accuracy. Would be good to see this discussed briefly in the limitations.\n\nHumans are indeed sensitive to context when recognizing objects, but context is of course not necessary for object recognition [1]. The *ClickMe* maps we used in this experiment contain sufficient features for accurately recognizing objects in a rapid vision paradigm that is similar to what we used in Figure 5 (see Figure 2 in [1] and our discussion with **Xrpg** on a similar question). Regarding minimal image patches, in the *Clicktionary* work they compared their feature importance maps to the minimally reducible configurations (MIRCs) of the original Ullman 2016 paper and found a strong correlation between the two. Thus, it is likely that the unifying feature of MIRCs, *ClickMe*, *Clicktionary*, etc. feature importance datasets is that they capture task-based saliency: the features that human observers rely on to recognize object images. The key difference between each of these efforts then is the ability to scale and the corresponding amount of noise that such scaling introduces. However, as the authors of *ClickMe* found, there is a strong correlation between their maps and *Clicktionary* despite capturing three orders-of-magnitude more data (and four orders-of-magnitude more data than the original MIRC study).\n\n> A broader question is that the evaluation of alignment necessarily requires a gold standard of knowing what humans rely on in the first place. How confident are we in the current measured ClickMe/Clicktionary style data? Also, how do the psychophysics data collected here improve upon these? A short discussion on this would be helpful.\n\nAs mentioned above, the authors of the *ClickMe* dataset noted that their maps have high intersubject reliability and validated their utility for object classification in psychophysics experiments. They found that *ClickMe* maps contain sufficient information for object recognition, and significantly more diagnostic information than other large saliency datasets like SALICON contain. \n\nOur psychophysics experiments rely on feature importance maps from *Clicktionary* rather than *ClickMe*, as the method used to gather the former yields higher quality maps than the later. Our experiments test via forward inference whether a proportion of visual features in *Clicktionary* maps are sufficient for recognizing an object, which is one way of answering your question of what features humans rely on for recognition. Indeed, we found that humans achieve significantly above-chance accuracy when at least 10% of the important features in *Clicktionary* maps are visible. This result is similar to what is reported in Figure 2 in the *ClickMe* paper.\n\nTo summarize, both the *ClickMe* dataset we used to harmonize DNNs and the *Clicktionary* dataset we used for our psychophysics depict visual features that are sufficient for object recognition.\n\n[1] Davenport J & Potter M. 2004. Scene consistency in object and background perception. Psychological science.\n", " > A much more interesting point would be to investigate what training procedure, architecture, or data enables a model to reproduce human saliency without resorting to training on this data. This would indicate which of the above most closely matches the conditions leading to the human visual system's choice of features for performing these tasks…. Given the same model architecture and training data, which training procedure (supervised, self-supervised, etc) leads to the best alignment with human saliency? Given the same training data and objective (e.g. supervised or self-supervised), which model architecture (ResNet, ViT, etc) leads to the best alignment with human saliency? Given the same architecture and training objective, which training data (ImageNet, ImageNet21k, etc) leads to the best alignment with human saliency?\n\nThe results you’re requesting are implicit in the performances of off-the-shelf models in Figures 3, 4, and 5 from the submitted manuscript. These models all use different augmentation strategies (e.g., adversarial training vs. the expansive augmentations of self-supervised models vs. the large-data training recipe of ViT), architectures, and training datasets. No model breaks the frontier described by the grey curves in Figures 3, 4, and 5 **except** for the harmonized models, which are significantly more aligned with humans and more accurate than their non-harmonized versions.\n\nThe space of model parameterizations and training strategies is infinitely large and extremely hard and slow to search through. Moreover, there’s no guarantee that any neural network architecture can be expected to do as well as the Neural Harmonizer that we introduced in our manuscript, or that the best-performing configuration would tell us anything about brains or cognition.", " (We initially mistakenly pasted our responses to reviewer cZRY here. Sorry!)\n\n>The authors propose a sound evaluation of the alignment between human and ANN saliency maps. In particular, the experiment they propose which incrementally reveals images according to human saliency maps appears to be a good way of comparing the features used by humans and ANN's in an apples-to-apples manner. Whether this experiments reveals \"how features are used\" rather than \"where these features are\" is less clear: it instead appears to be a better controlled version of the original comparison between saliency maps.\n\nSorry for the confusion. In the psychophysics experiment (results in Figure 5 and method diagram in SI Figure 1 included in the original submission), we asked humans and DNNs to recognize object images when only a proportion of their most important features were visible. The features used were selected and ranked according to **human** feature importance maps collected in the *Clicktionary* game, then were centered in each image over a phase-scrambled and masked version of the image. Rather than another saliency-to-saliency comparison, this experiment showed how humans vs. DNNs integrated features important to **humans** into object recognition decisions. Moreover, there was no “where” information at all in this experiment — all features were centered on the fovea. We have revised Section 4.2 to clarify.\n\n> Secondly, the authors make good use of this evaluation to show that improving ImageNet classification accuracy doesn't lead to better alignment with human saliency maps, underscoring the limitations of ImageNet as a benchmark. It would be interesting to see if other computer vision benchmarks, such as object detection or semantic segmentation are more predictive of human saliency.\n\nThis is a great future direction, and we have added it to the Discussion.\n\n> Finally, it is encouraging to see that co-training the network to reproduce saliency maps allows it to do so, without any cost to the ImageNet classification accuracy (or even with a slight improvement to it), however it is unclear what the scientific value of this result is. \n\nWe demonstrated that DNNs are systematically becoming **worse** models of human vision. We also introduced the Neural Harmonizer as a method for controlling this problem at scale. The scientific value here is identifying and fixing a fundamental flaw in DNNs, which has implications for theoretical and computational work in Neuroscience and Cognitive Science, and for industry in developing more reliable and predictable models of human visual behavior.\n\n> Aligning the training and testing objective usually improves test performance, hence improving the alignment with human saliency is hardly surprising. \n\nThere is no guarantee that DNN alignment with humans could be improved on independent test sets from two different human feature importance experiments (*ClickMe* and *Clicktionary*), each of which relied on different methods, or that harmonizing a model would also improve its alignment with human decision making on our novel psychophysics (Figure 5). There is nothing trivial about these results and there’s no reason to discount them as unsurprising.", " \n> In addition, what would the curve look like if the occlusion patterns were inverted, and one where to begin by starting to show peripheral regions of the image, and slowly showing the most important features last? Do the same patterns of results hold between humans and neural harmonizer trained networks? See for example the work of Deza & Konkle (ArXiv, 2020) and also Wang & Cottrell (JoV, 2017)\n\nThe *Clicktionary* maps we used to sample important object features in for the Figure 5 psychophysics are used in total — the X-axis depicts performance for 1% of the most important features to 100%.\n\nAre you asking for a comparison of object recognition performance between humans and DNNs on features which were not included in ClickMe maps? Do you have any advice on how to sample those features in a way that could be comparable to our psychophysics experiments?\n\nOne piece of evidence from the original *ClickMe* paper that may be relevant is that they compared human classification accuracy for objects masked to only reveal *ClickMe* features to objects masked to only reveal features that were salient according to the SALICON dataset. Participants were significantly more accurate at recognizing objects revealing *ClickMe* features vs. SALICON features.\n\n> There are no error bars for example, and authors could have definitely trained the other NN's with their Neural Harmonizer, to provide substantial evidence about how the Harmonizer provides better human-perceptual alignment.\n\nPlease see SI Fig. 6 (included in our original submission) for the performance of many different harmonized ResNet50s. We have also added error bars for human alignment and statistical tests to the main text. Thank you for this suggestion (in addition to all of the others!!), which reinforces and strengthens our findings.", " \n> Authors assume that feature importance maps from the two selected datasets represent where features which are important for the decisions are in a scene. However, I am not sure this aligns with locations people attend with their gaze. Authors should discuss this point in the paper. Eventually, an experiment involving saliency maps (using for example SALICON, a subset of imagenet with human visual saliency information) might be meaningful?\n\nThe main distinction to make is in whether human feature importance maps reflect bottom-up or top-down Saliency. SALICON reflects bottom-up saliency, and aligns with human eye-tracking data collected when participants are asked to look at images without any defined task. In the original *ClickMe* paper [1], they proposed that the *ClickMe* dataset instead reflects top-down, or task-driven saliency. They demonstrated the difference between bottom-up (SALICON) and top-down (*ClickMe*) saliency by asking individuals to categorize object images when only a proportion of the most important features were visible. In one case, features were revealed according to SALICON importance, and in the other case features were revealed according to *ClickMe* importance. Human participants were significantly more accurate at recognizing objects when features were revealed according to *ClickMe*, even when only ~10% of those features were visible. \n\nOur psychophysics experiments in Figure 5 support the finding that *ClickMe* captures top-down and task-driven saliency. DNNs that were harmonized with *ClickMe* feature importance were also significantly more aligned with human decision-making processes. It is always possible that an extremely controlled eye tracking study could produce data that are a more reliable indicator of human decision-making processes, and the Neural Harmonizer could certainly be used with that data, but there is no eye tracking dataset that is anywhere near large enough for co-training DNNs.\n\n> The authors refer to feature maps also as \"visual strategies\" often during the paper, however, I found this to be confusing since in the field this is more often used for visual scanpaths than for (static) saliency. I suggest use a different terminology.\n\nWe have added a sentence to the methods to clarify this. *ClickMe* and *Clicktionary* maps are the average of mouse scanpaths — participants paint the parts of the object they believe are important for classifying it. In that sense it is similar to your definition, albeit far less rich.\n\n> I am not sure wether presenting a partial image cropped is effective since, even when selecting a smaller area, people can see the rest of the image with peripheral vision. Trying to model this effect could have made the experiment more reliable.\n\nSee Figure SI 1 (included in the original submission) for the psychophysics method and more examples of how we revealed only a proportion of the most human-important features to machines and human participants. There is no diagnostic information in the periphery. Please let us know if we’ve misunderstood your comment.\n\n> Section 4.1: motivate the use of spearman's rank-correlation or provide references\n\nWe added a reference for this to the Results section where we introduce Spearman’s rank-correlation.", " > The rapid categorization paradigm has already been used to compare humans and DNNs decisions and it could be beneficial to provide those references (the provided references are from the neurosc. field)\n\nWe cited Eberardt et al., 2016, Linsley et al., 2018, and Serre T., 2007 in our original submission, which describe experiments comparing humans to models using rapid visual categorization. Are there any others you have in mind? We are happy to add more that we missed that fit the scope of our paper. \n\n> Author exclusively use saliency maps from Simonyan et al. to reveal feature importance. However, studies have found severe weaknesses of such metrics that can also be drastically attacked. Authors could provide more arguments on why they chose to rely specifically and exclusively on this method, or eventually use more.\n\nAs we discuss in our Response to all reviewers, saliency was chosen because it is fast to compute, and we found with it some models are nearly perfectly aligned with humans while others are not at all aligned with humans. We have added SI Figure 11 ([also see here](https://drive.internxt.com/s/file/1dd1d40e0a2b70243344/7bc64eb592e94dcb697779acb26e4549511fa4ba0bc4ace83c1ba73fea180f5b)) showing that our findings replicate when testing models with SmoothGrad [1] instead.\n\n> Related to the previous point, the proposed neural harmonizer method optimises neural networks to change their feature importance (w.r.t. the selected method of saliency). I rather have a different interpretation than those provided by the authors on the effect of this approach: this might lead the network to learn more effective activation that lead to human-like feature importance (maybe leveraging spatial biases of human annotators) while not changing the underlying decision process. \n\nCan you clarify what you mean by “more effective activation?” The average of *ClickMe* maps used for training yields a center bias, which explains 42% of human variance, which is significantly worse than 21 unharmonized DNNs and all of our harmonized models. Our psychophysics experiments in Figure 5 demonstrate that harmonizing models indeed changes their decision making, and how they integrate visual features into decisions, to be more like human observers.\n\n> The improvement in accuracy might be due to the additional loss and training data (in fact, multi-tasking is performed). \n\nThere’s no guarantee that co-training on human feature importance maps from *ClickMe* should preserve or improve accuracy. Our findings show that the two objectives are at least partially synergistic in large-scale training routines.\n\n> Why do authors provide results for only two networks (ResNet50 and VGG16) of the 85 presented in the first experiment, and why those two?\n\nSee point 1 in **Response to all reviewers** for our explanation and new modeling results ([Figure 3](HYPERLINK), [Figure 4](HYPERLINK), and [Figure 5](HYPERLINK)). We assure you we are not cherry picking results. Instead, the compute needed to harmonize each of the 85 models that we tested was more than we had available in our academic lab. We include significance tests in our revision showing that the pareto front represented by the harmonized models is significantly higher than the unharmonized models.", " > *Weak Results*: Why are there only 2 reported neural networks that have been trained with the neural harmonizer (there are 2 purple dots)? I would have expected that for the claim to be “the neural harmonizer successfully increases man-machine perceptual alignment”, that there would be nearly all blue CNN dots transcribed to purple, including (potentially) the yellow ones which are the Transformers. Without these extra data points, the results seem very weak, and almost suggests cherry picking.\n\nSee point 1 in **Response to all reviewers** for our explanation and new modeling results ([Figure 3](https://drive.internxt.com/s/file/53eb82c0084e2ec814bc/371fefa1acbf6aea724abed91895a4ba4eefafb469cc68c67cf2291b7df73740), [Figure 4](https://drive.internxt.com/s/file/9ff6afa4279f8049163f/c87fc2a992ea72ddc5e066c2f9f8c7c910ca7e6259cf23b80b597773b9baa904), and [Figure 5](https://drive.internxt.com/s/file/aa6ce7313067acf1b50e/acdc4983f07811e7859df6bf4f246a79e36e22ef06e07610e3bac6299b798ae5)). We assure you this is not cherry picking; rather, the compute needed to harmonize all 85 models that we tested was more than we had available in our academic lab.\n\n> That being said: How would the Transformer’s curve trained with a Neural Harmonizer look like?\n\nThis model is non-trivial to harmonize because of the large datasets used to train it. We have revised our discussion to discuss how harmonizing Visual Transformers and other models trained on ultra-large datasets used in industry groups (e.g., JIT-300M or JIT-3B) is a future direction of the work.\n\n> *Experimental Results may provide evidence for alternative explanation*: The occlusion results from Figure 5 may also suggest that the neural harmonizer has enforced a central image bias in CNNs :O ! (So a partial rather than full human-perceptual alignment).\n\nThis is an extremely insightful and smart suggestion. *ClickMe* does indeed have a center bias when all maps are averaged together ([click here to see the average map](https://drive.internxt.com/s/file/16c375747819dab9f369/2da19b5baaa28bf200852732d0f383c25eebe6040811930421bfd96320150c49))! A center bias is fundamental in any measure of saliency, such as eye-tracking, and hence it is important to understand what a saliency dataset offers above-and-beyond such a trivial bias. That said, this bias raises the unfortunate possibility that collecting *ClickMe* maps is a waste of time; all you need to do is co-train models on a centered gaussian to align them with humans.\n\nTo test this possibility, we measured the alignment between the center bias computed from all *ClickMe* maps and the *ClickMe* maps for each individual image. We found that the center bias explained 42% of human variance, which is a surprisingly high amount but also significantly lower than 21 unharmonized DNNs and all four of our harmonized models. See the cross in Figure 3 for the marker corresponding to the *ClickMe* center bias.\n\nInspection of individual *ClickMe* maps shows that they mostly focus on parts of foreground objects, such as the faces of animals or fronts and wheels of vehicles (SI Figure S3), thus it is likely that the surprising ability of a center bias to explain 42% of human variance in *ClickMe* maps is a function of where objects typically are positioned in ImageNet images rather than a center spatial bias per se as is discussed in the context of saliency and eye tracking.\n\nNotably, the largest-scale models (e.g., ConvNext, ViT, and CLIP) were **less** aligned with humans than this center bias, indicating that they have high inter-image variability in the features they find important for recognition and that these features are systematically out-of-alignment with humans. \n\nWe have added the citations you suggested and a discussion of this center bias in the results section of the main text.\n\n>It is expected that Transformers would not a priori have this [center] bias.\n\nCould you please clarify this comment? Why would any of the models we tested (Transformers or any of the CNNs) have an inductive bias to focus on the center of the image?\n\n>How would the Transformer’s curve trained with a Neural Harmonizer look like? \n\nWe have expanded our discussion to include Transformers and other ultra-large scales models, and issues involved with harmonizing them. In short, models which were trained with industry datasets like JIT-300M present a challenge for harmonization because of the computational resources they require. Furthermore, these datasets may need additional feature importance maps from humans (via *ClickMe* for example) in order to properly harmonize.", " Thank you to the reviewers for taking the time to read and review our paper. Your critiques are sharp and insightful and we found that all four reviewers converged on the following two issues which we have addressed over the rebuttal period:\n\n1. Why did we only include two harmonized DNNs in our manuscript?\n2. Why does the paper focus on gradient-based saliency for comparing humans and model feature maps and for training our Neural Harmonizer?\n\nWe have addressed these issues in the following ways:\n\n1. (**Xrpg**, **cZRY**, ) We focused on VGG16 and ResNet50 in our original version of the manuscript because they are featured in nearly all Neuro/Cog Science research that uses DNNs, and essentially every CNN architecture is derived from these two. We believed that if we were to show improvements in models that include/don’t include residual connections, then we were confident in the effectiveness of our Neural Harmonizer method.\n\n+ That said, we have taken to heart the Reviewers’ suggestion and over this review period we have harmonized two more CNNs, the MobileNet and EfficientNet_b0. Like the VGG16 and ResNet50 we discussed in our submission, both of these harmonized models improved over their unharmonized versions in top-1 accuracy and became significantly more aligned with human visual strategies for object recognition. Furthermore, following a suggestion from reviewer **Xrpg**, we found that the pareto front describing our harmonized models allowed for significantly better accuracy and alignment with humans than the pareto front describing non-harmonized models. See [Figure 3](https://drive.internxt.com/s/file/53eb82c0084e2ec814bc/371fefa1acbf6aea724abed91895a4ba4eefafb469cc68c67cf2291b7df73740), [Figure 4](https://drive.internxt.com/s/file/9ff6afa4279f8049163f/c87fc2a992ea72ddc5e066c2f9f8c7c910ca7e6259cf23b80b597773b9baa904), and [Figure 5](https://drive.internxt.com/s/file/aa6ce7313067acf1b50e/acdc4983f07811e7859df6bf4f246a79e36e22ef06e07610e3bac6299b798ae5) in the main text (or at each respective hyperlink) to find the additional results.\n\n2. ( **cZRY**) We focused on saliency in the paper for two reasons. First, we designed the neural harmonizer to scale with the size of state-of-the-art DNNs for object recognition. That means that we sought to minimize the additional compute needed to harmonize models. Saliency is the computationally cheapest model explanation to calculate. Second, we found that the saliency maps from some models (harmonized VGG-16) had a nearly perfect correlation with human feature maps, whereas other models (ConvNext) had extremely low correlations with human feature maps. Visual inspection (Figure 2 in the main text) of these maps reinforces this insight that existing DNNs mostly rely on features in different spatial locations than humans to make their object recognition decisions and that harmonization fixes this problem.\n\n+ As a check on whether or not the features revealed by saliency are idiosyncratic to that method, we recomputed human feature alignment on the *ClickMe* test dataset using SmoothGrad instead, which has been described as the most “reliable” feature visualization method [1]. See SI Figure 11 (or [here](https://drive.internxt.com/s/file/1dd1d40e0a2b70243344/7bc64eb592e94dcb697779acb26e4549511fa4ba0bc4ace83c1ba73fea180f5b)) for these results, which show the same trade-off and correction induced by the Neural Harmonizer that we describe for saliency in the main text.\n\nIn addition to the above results, over this review period, we have added citations and clarifications to our Related Work and Discussion (**Xrpg**, **cEc7**, **cZRY**), added an additional center bias control which validates that effectiveness of our Neural Harmonizer, and included error bars and statistical tests wherever possible (**Xrpg**). We will address each reviewer’s remaining comments directly.\n\nLastly, we want to re-emphasize that we have provided the first ever demonstration that the field of computer vision is systematically producing worse models for Human vision. This finding is enormously consequential for Neuroscience, Cognitive Science, and industry alike, each of which rely on neural network architectures to predict human behavior and visual representations. Our Neural Harmonizer is an efficient drop-in solution that can rectify this problem in large-scale neural network models. We thank the reviewers for their suggestions which have bolstered the evidence for our findings.\n\n[1] Colin J, Fel T, Cadene R, & Serre T. 2022. What I Cannot Predict, I Do Not Understand: A Human-Centered Evaluation Framework for Explainability Methods. ArXiv.\n", " This paper re-introduces a very important topic in the ML + CV community that has not been studied enough: are computer vision models aligned to human visual perception (and if they are not, why should we care?). The authors introduce the neural harmonizer as a training procedure that aligns the human-relevant features with a CNN to train from scratch a couple of new models from classical CNN architectures (ResNet + VGG) and they show that their models improve human perceptual alignment while also maintaining ImageNet Test Accuracy and performance. Furthermore, they empirically show that networks trained with the Neural Harmonizer are more robust to a peripheral occlusion task, and most importantly -- that their change in performance rate is similar to that of a human without any additional fine-tuning on the network. The paper’s main strengths is the paper’s theme as well as the very accessible way the paper has been written. Furthermore the paper’s experiments seem properly articulated and well-posed to support the main hypothesis and question that the authors introduce at the beginning of the paper. The psychophysics is pretty amazing.\n\nHowever, the paper still has some weaknesses that should be addressed/clarified:\n* **Weak Results:** Why are there only 2 reported neural networks that have been trained with the neural harmonizer (there are 2 purple dots)? I would have expected that for the claim to be “the neural harmonizer successfully increases man-machine perceptual alignment”, that there would be nearly all blue CNN dots transcribed to purple, including (potentially) the yellow ones which are the Transformers. Without these extra data points, the results seem very weak, and almost suggests cherry picking.\n* **Missing References:**\n * “Emergent Properties of Foveated Perceptual Systems”. Deza & Konkle. ArXiv, 2020.\n * “Central and peripheral vision for scene recognition: A neurocomputational modeling exploration” Wang & Cottrell. JoV, 2017.\n * “Joint rotational invariance and adversarial training of a dual-stream Transformer yields state of the art Brain-Score for Area V4”. Berrios & Deza. Brain-Score Workshop 2022.\n * “Texture-like representation of objects in human visual cortex”. Jagadeesh & Gardner. PNAS 2022.\n* **Experimental Results may provide evidence for alternative explanation**: The occlusion results from Figure 5 may also suggest that the neural harmonizer has enforced a central image bias in CNNs :O ! (So a partial rather than full human-perceptual alignment). It is expected that Transformers would not a priori have this bias. That being said: How would the Transformer’s curve trained with a Neural Harmonizer look like? In addition, what would the curve look like if the occlusion patterns were inverted, and one where to begin by starting to show peripheral regions of the image, and slowly showing the most important features last? Do the same patterns of results hold between humans and neural harmonizer trained networks? See for example the work of Deza & Konkle (ArXiv, 2020) and also Wang & Cottrell (JoV, 2017)\n See Weaknesses points (1) and (3). None, the paper actually does a great job in introducing current limitations of modern DL systems. The paper is overall well written. Providing additional experiments and/or a good rebuttal may improve my rating. I am also generally curious to know what other reviewers have thought about the maturity of this paper. \n\nI'm really on the fence with this paper. It's amazingly well written, addresses an important problem in modern ML + CV -- via the proper cog-sci/psychology insights, but is still missing more results that back-up their claim with stronger evidence. There are no error bars for example, and authors could have definitely trained the other NN's with their Neural Harmonizer, to provide substantial evidence about how the Harmonizer provides better human-perceptual alignment.", " The authors address the problem of evaluating the alignment of deep learning vision models with humans. To do so, they compare feature importance maps by humans, with saliency maps from DNNs. Additionally, they propose a training method (neural harmonizer) to improve such alignment. Finally authors present a psychophysic experiment using the rapid categorization paradigm to gather information of human decisions based on partial information of important features. Strength:\n- the topic is timely and relevant\n- the paper is clear and easy to read\n- the authors validate part of their claims with a human study\n- code is provided for reproducibility\n\nWeaknesses:\n- Structure of the paper is not optimal. The neural harmonizer should probably be described introduced in the method section.\n- The rapid categorization paradigm has already been used to compare humans and DNNs decisions and it could be beneficial to provide those references (the provided references are from the neurosc. field)\n- Author exclusively use saliency maps from Simonyan et al. to reveal feature importance. However, studies have found severe weaknesses of such metrics that can also be drastically attacked. Authors could provide more arguments on why they chose to rely specifically and exclusively on this method, or eventually use more.\n- Related to the previous point, the proposed neural harmonizer method optimises neural networks to change their feature importance (w.r.t. the selected method of saliency). I rather have a different interpretation than those provided by the authors on the effect of this approach: this might lead the network to learn more effective activation that lead to human-like feature importance (maybe leveraging spatial biases of human annotators) while not changing the underlying decision process. The improvement in accuracy might be due to the additional loss and training data (in fact, multi-tasking is performed). Which lead me to the following observation:\n- Why do authors provide results for only two networks (ResNet50 and VGG16) of the 85 presented in the first experiment, and why those two? Their explanation is given in page 6, they are \"selected because they are popular networks that sit on the boundary of the trade-off betweenDNN performance and alignment with humans\". This seems to be not fully true from figure 4. Additionally, it might be very useful to know the average performance on the other architectures (or at least a random sample of them, if training them all is prohibitive) in order to support the claim that the method improves alignment without decreasing the performance. Especially important are the performance on DenseNet121, mentioned by the authors as the very limit of the trade-off between alignment and accuracy.\n- Authors assume that feature importance maps from the two selected datasets represent where features which are important for the decisions are in a scene. However, I am not sure this aligns with locations people attend with their gaze. Authors should discuss this point in the paper. Eventually, an experiment involving saliency maps (using for example SALICON, a subset of imagenet with human visual saliency information) might be meaningful?\n\nMinor:\n- Page 4, row 2, \"was was\" (repetition)\n- The authors refer to feature maps also as \"visual strategies\" often during the paper, however, I found this to be confusing since in the field this is more often used for visual scanpaths than for (static) saliency. I suggest use a different terminology.\n- I am not sure wether presenting a partial image cropped is effective since, even when selecting a smaller area, people can see the rest of the image with peripheral vision. Trying to model this effect could have made the experiment more reliable.\n- Section 4.1: motivate the use of spearman's rank-correlation or provide references\n- In the paragraph \"The neural harmonizer aligns human and DNN visual strategies.\": authors mention \"All of the three neural harmonizer models...\", however they presented only two of them. I would be incline to change ma opinion if authors:\n- provide strong motivations on the choice of the one method for saliency, or present results for at least another different approach.\n- provide strong motivations on the choice of the two models to be improved with neural harmonizer, or provide average results for all initial 85 models\n- clarify why using feature importance map is sufficient to explain and measure alignment, in particular w.r.t. research in saliency and scanpath that rely directly on eye-tracking data The discussion of limitations is insufficient. The authors should point out that results are only provided for one explainability method, and only for two models. Additionally, they should point out how the notion of feature importance and what is actually captured by humans through the gaze might differ.", " The authors conduct an empirical evaluation of the alignment of human and artificial neural network (ANN) saliency maps, and propose a method for improving it. The authors use saliency maps collected from ImageNet by Linsley et al. and compare them to those estimated from a variety of ANN's. In a separate experiment, the authors obscure images to varying degrees according to the human saliency maps, and measure the resulting degradation in classification performance in humans and ANN's, again comparing the two. Finally, the authors propose a method for aligning the saliency maps of humans and ANN's by jointly training the network for the original classification objective, and a measure of alignment with human saliency. The resulting models' saliency maps are indeed better aligned with human ones. The authors propose a sound evaluation of the alignment between human and ANN saliency maps. In particular, the experiment they propose which incrementally reveals images according to human saliency maps appears to be a good way of comparing the features used by humans and ANN's in an apples-to-apples manner. Whether this experiments reveals \"how features are used\" rather than \"where these features are\" is less clear: it instead appears to be a better controlled version of the original comparison between saliency maps. \n\nSecondly, the authors make good use of this evaluation to show that improving ImageNet classification accuracy doesn't lead to better alignment with human saliency maps, underscoring the limitations of ImageNet as a benchmark. It would be interesting to see if other computer vision benchmarks, such as object detection or semantic segmentation are more predictive of human saliency.\n\nFinally, it is encouraging to see that co-training the network to reproduce saliency maps allows it to do so, without any cost to the ImageNet classification accuracy (or even with a slight improvement to it), however it is unclear what the scientific value of this result is. Aligning the training and testing objective usually improves test performance, hence improving the alignment with human saliency is hardly surprising. The fact that it improves ImageNet classification is more surprising, but is at odds with the first finding that models which improve classification accuracy do not improve the alignment with human saliency. \n\nA much more interesting point would be to investigate what training procedure, architecture, or data enables a model to reproduce human saliency **without resorting to training on this data**. This would indicate which of the above is most closely matches the conditions leading to the human visual system's choice of features for performing these tasks. As discussed above, the proposed neural harmonizer is of limited scientific interest, as it simply aligns training and testing for this particular metric (alignment with human saliency maps). \n\nAssuming this were removed from the paper, could the authors instead re-analyze their data to study which training procedure, architecture, or data enables a model to reproduce human saliency maps without resorting to training on this data? For example \n\n- Given the same model architecture and training data, which training procedure (supervised, self-supervised, etc) leads to the best alignment with human saliency?\n\n- Given the same training data and objective (e.g. supervised or self-supervised), which model architecture (ResNet, ViT, etc) leads to the best alignment with human saliency?\n\n- Given the same architecture and training objective, which training data (ImageNet, ImageNet21k, etc) leads to the best alignment with human saliency? There are no ethical or societal concerns associated with this work. ", " Summary: This paper focusses on evaluating the alignment between visual strategies of DNNs and human perception. Specifically, the ask how this alignment evolves as architectures become more complex. For a fair comparison the paper focusses on only the rapid, feed-forward component of human perception, and suggests evaluating alignment on visual strategies as defined by a two step process---identifying regions with important features and how these regions are used to make a classification decision. For the first part, the paper evaluates alignment between DNNs and humans on three datasets. These include ClickMe and Clicktionary datasets with ground truth annotations for human visual importance, and a third dataset collected by the authors using a psychophysics experiment involving rapid classification of images. The paper shows that identifying important features peaks as architectures become better at classification, but then start dipping as they get more complex. To address this, the neural harmonizer methodology is proposed. Finally, the paper tests how these features are used by exposing different models to an increasing percentage of human-identified important regions, showing similar trends as the previous experiments. Strengths:\n\n1. Extremely interesting problem. While accuracy on standardized datasets is a good diagnostic for progress, measuring if these improvements result in better alignment between biological and artificial intelligence is a fundamental goal for a multitude of reasons. This has also been very well motivated in the paper.\n\n2. The writing is clear and easy to follow. The work is placed well into the context of existing works, and is clear in elaborating how this work builds on top of this literature. \n\n3. Above all, the experimental design is very solid. Controls are sufficient, and claims are well supported with either experimental results or through existing literature. Psychophysics experiments are well designed, and good care has been taken to ensure as fair a comparison between humans and DNNs as possible.\n\n4. The neural harmonizer module is interesting as it increases alignment significantly.\n\n\nWeaknesses:\n\n1. The code and data are propriety and will NOT be released. The findings of this paper are interesting, but the most important contribution here seems to be an interesting benchmark for future researchers to focus on. Since the code and the data will not be released, it severely diminishes the utility for the research community. \n\nMinor Weakness:\n\nSome relevant recent literature is missing, and would be good to add to the paper:\n\nA. On minimal images: \n\n- Srivastava, S., Ben-Yosef, G. and Boix, X., 2019. Minimal images in deep neural networks: Fragile object recognition in natural images. arXiv preprint arXiv:1902.03227.\n\nB. On alignment in humans and machines in existing works:\n\n- Bomatter, P., Zhang, M., Karev, D., Madan, S., Tseng, C. and Kreiman, G., 2021. When pigs fly: Contextual reasoning in synthetic and natural scenes. In Proceedings of the IEEE/CVF International Conference on Computer Vision (pp. 255-264).\n 1. On the role of scene context: Human annotations highlighted lesser context areas (Page 5), but it is widely known that human visual recognition is strongly dependent on scene context. Does this suggest that what humans \"think\" of as visually important, may not essentially be the most important regions? Also may be suggested by work on minimal images, as it is counter-intuitive to humans that a few pixels can cause such large drops in accuracy. Would be good to see this discussed briefly in the limitations.\n\n\n2. A broader question is that the evaluation of alignment necessarily requires a gold standard of knowing what humans rely on the first place. How confident are we in the current measured ClickMe/Clicktionary style data? Also, how do the psychophysics data collected here improve upon these? A short discussion on this would be helpful. Yes." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 2, 3, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 4, 4, 4 ]

[ "Bv97-AJwM_w", "06-NbhnCi5z", "uRQ19eHwa7-", "zp7XLw964V-", "cx6ZxTW7CNd", "sj10B557NrL", "Ks1jBZ2ONQ4", "Ks1jBZ2ONQ4", "jSIEIZkAEOq", "7lM5hTjm2d0", "7lM5hTjm2d0", "jSIEIZkAEOq", "nips_2022_ZYKWi6Ylfg", "nips_2022_ZYKWi6Ylfg", "nips_2022_ZYKWi6Ylfg", "nips_2022_ZYKWi6Ylfg", "nips_2022_ZYKWi6Ylfg" ]

[ "TklI7RZvFh1", "DlZM2gIRrF5", "KxI25pvLPsZ", "p52BoPpNkr", "3YX9MZWuva3", "WWsekjFUV9x", "-kZbJy-ocq", "hD_IeBN5PYA", "-HfQZj4sDad", "8yB6yA38mhA", "xJDznhIyL_", "Q0f9WoCyQcR", "rtSO4vbbyxc", "DcxZ3g3FBiW", "ZC6iayMFdq5" ]

[ "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I appreciate the author's rebuttal and response to the questions. This helps confirm my good score.", " I thank the authors for their detailed response. My rating for that paper has been increased to a score of 6 (weak accept). ", " Thank you very much for your valuable comments, which are very helpful to further improve our manuscript. We will respond to the weaknesses in detail. Some figures and results of newly added experiments can be found in Page 6, Section Rebuttal in the newly submitted ‘Supplementary Material.pdf' file.\n\n### - Weaknesses\n\n> 1. the achieved improvement over SOTA is relatively small for the real-world datasets.\n\n* **Response**：\n\n In this paper, we used three real-world datasets (Camelyon16 Dataset, TCGA Lung Cancer Dataset and Clinical Cervical Dataset) to evaluate the performance of our framework. On the Camelyon16 Dataset, WENO improves the instance-level AUC significantly by **7~8 percentage points**; although the improvement for the bag-level AUC is relatively small (**1~2 percentage points)**. For the TCGA Lung Cancer Dataset and Clinical Cervical Dataset, we could not validate the instance-level metrics because there is no instance-level annotation. Our method still improves the bag-level AUC by **1~2 percentage points** on TCGA Lung Cancer Dataset, although the performance of existing methods is already very high and the room for improvement is very small. Our method also improves bag-level AUC by **1~2 percentage points** on Clinical Cervical Dataset.\n\n> 2. hyperparameter tuning has to be performed for the HPM module to determine the best threshold. This is discussed in the supplemental material. However, another hyperparameter, the number of epochs after which to bring the HPM module online is not discussed.\n\n* **Response**：\n\n We added a new robustness study on the starting epoch of the HPM strategy, and the results are shown in Page 6 Section 5 (Rebuttal) Figure 7 of the newly submitted ‘Supplementary Material.pdf’ file. We construct the WENO framework using ABMIL [1] as the teacher and experimented on a CIFAR-10-MIL dataset with a positive instance ratio of 0.2. In this experiment, we added the HPM strategy at three different time points (the 100th, 150th and 200th epoch) and the results show that their final instance-level AUCs are almost the same for both the teacher and the student networks. These results indicate that **HPM is not sensitive to the starting epoch.**\n\n\n\n [1] Ilse et al. \"Attention-based deep multiple instance learning.\" ICML, 2018.", " Thank you very much for your valuable comments, which are very helpful to clarify details and improve the quality of our paper. We will respond to all the weaknesses and questions in detail. Some figures and results of newly added experiments can be found in Page 6, Section 5 (Rebuttal) in the newly submitted ‘Supplementary Material.pdf' file.\n\n### - Weaknesses\n\n> 1. On page 2, lines 63-66, the authors mentioned that using soft labels as they did helps to alleviate the noisy pseudo-labels used in other methods. It is not clear how it is the case. From the description of the method, the pseudo-labels in this work change every SGD step since the network that builds them changes constantly. Therefore, they are noisier, especially at the beginning of the training. It is not clear why the authors claimed that their pseudo-labels alleviate the noise issue. In addition, there is no empirical evidence to support this claim.\n\n* **Response**：\n\n * **First, we would like to further explain what does “noisy pseudo labels” mean on Page 2, lines 63-66.** In weakly-supervised WSI analysis tasks, we only have the labels of slides (bags) and do not have the labels of patches (instances). In this setting, when we tackle the problem with instance-based methods, which first train an instance classifier and then aggregate the predictions of each instance in a bag to obtain the bag prediction, we need pseudo labels of the instances for model training. However, since the true labels of instances in positive bags are unknown, these methods typically train the instance classifier by selecting instances from positive bags and directly assigning them the hard positive pseudo labels (e.g., value 1). **This way of assigning pseudo labels leads to a large number of errors (which we denote as label noise) in the assigned positive pseudo labels**, thus limiting their performance. By \"alleviate the noisy pseudo-labels\", we mean that **our method can provide more accurate pseudo labels for training the student network**. There are two reasons contributing to the noisy-pseudo-label problem in instance-based methods: one is that the pseudo labels of these methods are usually produced by the instance classifier, which is also trained only with these pseudo labels. When the instance pseudo labels are wrong, the instance classifier will also give wrong predictions and thus falls into an error loop. Second, these methods adopt the hard-pseudo-label assignment strategy, i.e., directly assigning hard positive labels (e.g., value 1) to the selected positive instances. This also worsens the problem of incorrect pseudo labels.\n\n * **Second, we would like to further explain how we alleviate the above problems by using our *soft pseudo-labels*.**\n\n\t 1) The positive pseudo labels of instance classifier are distilled from the normalized attention scores of the teacher network. The teacher network is trained with correct bag labels, and the scores of each instance from the positive bags are delivered to the student network by normalized attention scores. In existing bag-based methods using attention mechanism, attention scores are widely used to produce instance predictions [1-3]. Thus, the student network gets part of its supervision from the teacher network, which helps reduce noise. As the training proceeds, **the pseudo labels generated by the teacher are actually more and more accurate rather than noisier.**\n\n\t 2) Normalized attention scores are a kind of soft labels. As mentioned in [4], soft labels contain more useful information compared to hard labels and are a very effective way of transferring knowledge between models. Using the normalized attention scores of the teacher network as the soft pseudo labels for the student network can avoid the effect of wrong hard pseudo labels. **We further added a comparison experiment on soft labels vs. hard labels** in the ablation study on Page 9, Section 5 (Ablation Study), Table 4 of the original manuscript, and the results are shown in the following Table 1. These results show that **using soft pseudo labels works better than using hard pseudo labels in our distillation framework**.\n\n\t Table 1: Ablation study on the Camelyon16 Dataset, where the second row indicates distillation using hard pseudo labels (true negative labels as well as pseudo labels that assign all instances in the positive bags to 1), and the third row indicates distillation using soft pseudo labels (true negative labels as well as normalized attention scores from the teacher network as positive pseudo labels).\n \n | Distillation | Soft Label | Shared Encoder | HPM | Instance-level AUC | Bag-level AUC |\n | :-: | :-: | :-: | :--: | :-: | :-: |\n |||||0.8480|0.8379|\n |√||||0.8715 | 0.8516 |\n |√|√||| 0.8787 | 0.8574 |\n |√|√|√ | | 0.9011 | 0.8583 |\n |√|√| √ | √ | **0.9271** | **0.8663** |", " ### - Weaknesses\n\n> 1. On page 2, lines 63-66, the authors mentioned that using soft labels as they did helps to alleviate the noisy pseudo-labels used in other methods. It is not clear how it is the case. From the description of the method, the pseudo-labels in this work change every SGD step since the network that builds them changes constantly. Therefore, they are noisier, especially at the beginning of the training. It is not clear why the authors claimed that their pseudo-labels alleviate the noise issue. In addition, there is no empirical evidence to support this claim.\n\n* **Response**：\n\n * **Second, we would like to further explain how we alleviate the above problems by using our *soft pseudo-labels*.**\n\n 3) Our student network is also able to learn from all true negative instances, and the student can also transfer the learned knowledge to the teacher through the shared feature extractors. In addition, the proposed Hard Positive Instance Mining (HPM) strategy can also force the teacher to find hard positive instances and give them more accurate pseudo labels. Thus, the pseudo labels generated by the teacher are becoming more accurate rather than noisier. \n \n * **Third, we would like to explain the** **empirical evidence provided in the original submission and new empirical evidence added in this rebuttal.** \n \n\t We demonstrate the quality of the pseudo labels in Page 9, Section 5 (Ablation Study), Figure 3 of the original manuscript. Panel (b) in Figure 3 represents the results of the instance-level classification directly using the normalized attention scores of the teacher network. **Note that this result is a direct indicator of the quality of the pseudo labels generated by the teacher.** As shown in the blue line (ABMIL+WENO without HPM) and the red line (ABMIL+WENO with HPM), the pseudo labels generated by ABMIL+WENO are indeed relatively noisy at the beginning of the training, but **the quality of the generated pseudo labels become more and more accurate as the training proceeds.**\n \n\t There are two main reasons for the increasing quality of WENO's pseudo labels: (1) the teacher (bag-level classifier) itself becomes more well-trained, and its attention scores can gradually distinguish positive/negative instances more accurately, i.e., the pseudo labels will become more accurate. As shown in the gray line in Figure 3 Panel (b), even raw ABMIL eventually achieves an instance-level classification AUC of 0.89. (2) We further adopt the distillation framework of teacher/student networks and adopt the method of sharing parameters so that the knowledge learned by the student can be transferred to the teacher, and we also propose the HPM strategy to force the teacher to learn the hard positive instances. Therefore, as shown in Figure 3 Panel (b), the quality of the final pseudo labels of ABMIL+WENO is much higher than that of raw ABMIL. The above Table 1 validates the role of each proposed modules.\n \n\t Finally, the soft pseudo labels given by the teacher network do change constantly, but **it does not mean that they become more inaccurate, and since we use soft labels, there is no 0-1 flipping like the hard labels.** As mentioned above, the soft pseudo labels are generally becoming more accurate as the iterations proceed. As shown in Page 9, Section 5 (Ablation Study), Figure 3 of the original manuscript, **the soft pseudo labels given by the teacher network tend to stabilize after the convergence of the teacher and the student network**. Taking the blue line (ABMIL+WENO without HPM) in Figure 3 panel (b) as an example, we **add the variance of the test instance-level AUC of the pseudo labels at each episode** (step size set to 50), as shown in the Table 2 below. It can be seen that the variance of the pseudo labels gradually becomes smaller as the training proceeds.\n \n\t Table 2: Variance of the Amplitude Change of the Instance Pseudo Labels at Each Episode (step size set to 50).\n \n\t | Epoch | 1-50 | 51-100 | 101-150 | 151-200 | 201-250 | 251-300 |\n\t | :-------------: | :-------: | :-------: | :-------: | :-------: | :-------: | :-------: |\n\t | ABMIL[1] + WENO | 3.804E-02 | 5.995E-06 | 9.418E-07 | 7.203E-07 | 2.247E-07 | 1.647E-07 |\n\n\t\n[1] Ilse et al. \"Attention-based deep multiple instance learning.\" ICML, 2018.\n\n[2] Li et al. \"Dual-stream multiple instance learning network for whole slide image classification with self-supervised contrastive learning.\" CVPR. 2021.\n\t\n[3] Zhang et al. \"DTFD-MIL: Double-Tier Feature Distillation Multiple Instance Learning for Histopathology Whole Slide Image Classification.\" CVPR. 2022.\n\t\n[4] Hinton et al. \"Distilling the knowledge in a neural network.\" arXiv preprint arXiv:1503.02531 2.7 (2015).", " > 2. On page 2, lines 70-72, the authors mentioned that sharing the feature extractor between student and teacher enhances knowledge distillation. It is not clear why it is the case.\n\n* **Response**：\n\n Sharing the feature extractor plays an important role in the knowledge distillation, so we provide detailed explanation and ablation study in the original manuscript. Concretely, we provide detailed explanations in Page 5, Section 3.2.1 (Framework Overview), lines 158-161 and Page 6, Section 3.2.3 (Student Network), lines 194-199 of the original manuscript. We also present the results of ablation experiments on the Camelyon16 Dataset in Page 9, Section 5 (Ablation Study), Table 4 of the original manuscript to show that sharing feature extractors performs better than using extractors independently.\n\n We would like to further explain why sharing the feature extractor enhances the knowledge distillation. As shown in Page 3, Figure 1 (a), (b) of the original manuscript, the traditional knowledge distillation methods usually have only single-way knowledge transfer, while the difference between this paper and previous methods is that there is double-way knowledge transfer between the teacher and the student, where the shared feature extractors play an important role. Our teacher and student branches are trained alternately. On this basis, since the feature extractors are shared, the optimization of the extractor when training the teacher can work directly on the student classifier, and the optimization of the extractor when training the student also works directly on the teacher classifier. Since the student classifier learns not only from the teacher's normalized attention scores, but also from the true negative instances, the student's instance-level classification ability can outperform the teacher's attention scores. Through shared feature extractors, the student network transfers this knowledge to the teacher network. On the other hand, the knowledge learned by the teacher network through bag classification and the HPM strategy can also be transferred to the student network, further enhancing the knowledge transfer and feedback.\n\n In the experimental results, as shown in the second and third rows of Page 9, Section 5, Table 4 of the original manuscript, without HPM, the performance of our framework with sharing extractors alone outperforms the baseline, which confirms the above argument.\n\n | Distillation | Shared Encoder | HPM | Instance-level AUC | Bag-level AUC |\n | :----------: | :------------: | :--: | :----------------: | :-----------: |\n | | | | 0.8480 | 0.8379 |\n | √ | | | 0.8787 | 0.8574 |\n | √ | √ | | 0.9011 | 0.8583 |\n | √ | √ | √ | **0.9271** | **0.8663** |\n \n\n> 3. In the entire paper, the pseudo-labels were described as the attention scores. It is not until eq.12 (page 6) that the authors describe the soft labels as being single scores that simulate probability. The text should be clear about this detail from the outset. In addition to fig.2, there should be an operation after attention scores come out from the teacher, before being used by the student’s CE loss.\n\n* **Response**：\n\n Sorry for not describing this detail clearly. The soft pseudo labels of the student network are obtained by normalizing the attention scores (to values between 0 and 1) of the teacher network. The norm function in eq. 12 (page 6) refers to the normalization function, which is formulated as follows:\n\n \\begin{equation}\n X_{\\text {norm }}=\\frac{X-X_{\\min }}{X_{\\max }-X_{\\min }}\n \\end{equation}\n\n where $X_{\\text {norm }}$ is the normalized data, $X$ is the original data, and $X_{\\max }$ and $X_{\\min }$ are the maximum and minimum values of the original data, respectively.\n \n We will revise the statement of ‘attention scores’ on line 11, 64, 156, 186, 320 of the original manuscript to ‘normalized attention scores’, and add the formulation of the normalization function in Section 3.1.2 and Section 3.2.3 in the final version.", " > 4. Hard positive instance mining (hpm) proposed in this paper is similar to hard mining in class-activation maps (CAMs). In the latter, strong activations are suppressed, thereby pushing the network to seek more positive regions. The same here, the authors drop high positive instances simulating suppression. Therefore, the proposed mining strategy is not really new; and literature discussion is necessary. See an example for CAMs ib Wei, Y., Feng, J., Liang, X., Cheng, M.-M., Zhao, Y., and Yan, S. (2017). Object region mining with adversarial erasing: A simple classification to semantic segmentation approach. CVPR 2017.\n\n* **Response**：\n\n We will add the mentioned literature discussion and discuss the differences in the final version.\n\n Similar to the mentioned reference, we also use the adversarial erasing strategy (which is very common, e.g., adversarial learning), but **the method of obtaining instance predictions is completely different from that of CAM**. CAM utilizes the network's own attention scores (which in our framework corresponds to the output of the Attention Module in the teacher network), while we use the predictions of the student (instance-level) classifier to perform hard positive instance mining instead of the teacher's own attention scores.\n\n On the other hand, we introduce the idea of hard positive instance mining into the field of whole slide image processing for the first time, and the results of ablation experiments in Page 9, Section 5, Table 4 of the original manuscript validate the efficiency of this strategy for whole slide image classification.\n\n | Distillation | Shared Encoder | HPM | Instance-level AUC | Bag-level AUC |\n | :----------: | :------------: | :--: | :----------------: | :-----------: |\n | | | | 0.8480 | 0.8379 |\n | √ | | | 0.8787 | 0.8574 |\n | √ | √ | | 0.9011 | 0.8583 |\n | √ | √ | √ | **0.9271** | **0.8663** |\n\n> 5. The main issue in this work is that it is unclear why there is an improvement? The authors are not using additional supervision. In fact, the pseudo labels are expected to be noisier and change constantly. It is unclear why training a student in parallel helps instance classification even though there are no instance labels. Authors are encouraged to provide further analysis to explain the observed improvement. If I had to guess, the main element that improves performance is in eq.12, in particular the zero-label of instances in negative bags. Authors explicitly provided instance labels but only for negative instances, giving their model a large advantage. Knowing what is not positive helps the model.\n\n* **Response**：\n\n * **1) For the performance improvement without using additional supervision:**\n\n The Multiple Instance Learning-based Whole Slide Image Classification itself is a weakly supervised learning problem with weak labels, and most existing studies investigated how to improve performance without using additional supervision by making better use of available information. Our method utilizes the same supervision as these studies, and we think that the performance improvement comes from the fact that our framework can exploit and mine the available information more efficiently. The most important reason is that we integrate a bag classifier and an instance classifier in a knowledge distillation framework to mutually improve the performance of both classifiers. In addition, we also share the feature extractors and propose the HPM strategy to enhance knowledge distillation to better exploit and mine the available information. As contrast, most existing bag-based methods are only able to utilize the supervised information at the bag-level, while we are able to utilize the normalized attention scores of the teacher network as the soft positive labels for the student network as well as all the negative instance labels.\n\n * **2) Response to “**Authors explicitly provided instance labels but only for negative instances, giving their model a large advantage**”.** \n\n In weakly supervised WSI classification, \"instance labels for negative instances\" is known information, which is available for all methods, but is utilized in different ways by different methods. Thus, the comparison with similar methods is fair. We only use this information more directly.\n\n ", " > 5. The main issue in this work is that it is unclear why there is an improvement? The authors are not using additional supervision. In fact, the pseudo labels are expected to be noisier and change constantly. It is unclear why training a student in parallel helps instance classification even though there are no instance labels. Authors are encouraged to provide further analysis to explain the observed improvement. If I had to guess, the main element that improves performance is in eq.12, in particular the zero-label of instances in negative bags. Authors explicitly provided instance labels but only for negative instances, giving their model a large advantage. Knowing what is not positive helps the model.\n\n* **Response**：\n\n * **3) From the perspective of information theory, our method avoids a large amount of information loss.**\n\n Intuitively, if grouping instances into bags is regarded as an operation on the instances, the instance labels have the maximum information entropy, and the bag operation reduces the information in the training data. The information entropy of a bag with instance labels is:\n $$\\begin{equation}\n H_{I}\\left(X_{i}\\right)=-K(P \\log P+(1-P) \\log (1-P))\n \\end{equation} $$\n The information entropy of a bag with only the bag label is:\n $$\\begin{equation}\n H_{B}\\left(X_{i}\\right)=-\\left(P^{K} \\log P^{K}+\\left(1-P^{K}\\right) \\log \\left(1-P^{K}\\right)\\right)\n \\end{equation} $$\n , where $K$ represents the bag length and $P$ represents the probability that each instance label is positive. We calculate and visualize the entropy difference between the instance labels and the bag label in Page 7 Section 5 (Rebuttal) Figure 8 of the newly submitted ‘Supplementary Material.pdf’ file. We can see the information loss increases when the bag-length K increases. As a bag usually contains thousands of instances, the bag-based approach will lose a lot of information and is not the best choice for instance-level classification. Even though instance labels from positive bags are not available, our WENO can directly train with all true negative instance labels from negative bags and the soft pseudo labels from the teacher network, thus avoiding information loss in negative bags.\n\n * **4) For pseudo labels which are “more noisier and constantly changing”:**\n\n In our method, although the pseudo labels generated by the teacher network are relatively noisy at the beginning, in fact, the pseudo labels become more and more accurate as the training proceeds. Please refer to **Response** of **Weakness 1** for more details about label noise.\n\n * **5) For the role of zero-labels of instances:**\n\n True negative instance labels do play an important role, but this is **only one aspect of our framework to achieve substantial improvement**. The strength of our framework comes from combining the bag classification framework and the instance classification framework in a knowledge distillation manner, i. e., the guidance of attention-based soft pseudo labels, the utilization of the information of all true negative instances, the information transfer and feedback of the student and teacher networks, and the use of the hard positive instance mining strategy. The results of the ablation experiments in the following table validate the effectiveness of each component.\n\n In addition, **using only true negative instances cannot perform the training**.\n\n | Distillation | Soft Label | Shared Encoder | HPM | Instance-level AUC | Bag-level AUC |\n | :----------: | :--------: | :------------: | :--: | :----------------: | :-----------: |\n | | | | | 0.8480 | 0.8379 |\n | √ | | | | 0.8715 | 0.8516 |\n | √ | √ | | | 0.8787 | 0.8574 |\n | √ | √ | √ | | 0.9011 | 0.8583 |\n | √ | √ | √ | √ | **0.9271** | **0.8663** |", " > 6. Finally, there is an important element missing in the experimental section: the classification accuracy per type of instance (positive/negative, ...). We do not know what pushed the AUC at instance-level to improve. Is it improving the positive instances or negative instances? My guess is the latter helps more since labels of negative instances are explicitly used.\n\n* **Response**：\n\n In pathological images, the problem of imbalance between the number of positive instances and negative instances typically exists. For example, the positive rate of patches in the Camelyon16 Dataset is only 4.3%, while that in the TCGA Dataset is over 80%. Therefore, we adopt the AUC metric to evaluate the performance of the model, which is a common evaluation metric for similar studies.\n\n In addition, we added additional metrics on CIFAR-10-MIL with a positive instance ratio of 0.2, which included True Positive Rate (TPR), True Negative Rate (TNR), False Positive Rate (FPR), False Negative Rate, Accuracy (with threshold=0.5) and AUC. The results are shown in the following Table. In the Table, the first row indicates the metrics of the pseudo labels when the instances in positive bags inherit the positive labels directly; the second row indicates the metrics of our framework with ABMIL as the teacher.\n\n It can be seen that despite the absence of true positive labels, WENO generates soft pseudo labels with an accuracy of 0.8826, while the method of directly inheriting bag labels has an accuracy of only 20%.\n\n | | TPR | TNR | FPR | FNR | Accuracy | AUC |\n | :-------------------: | :----: | :----: | :----: | :----: | :------: | :----: |\n | inheriting bag labels | 1.0000 | 0.0000 | 1.0000 | 0.0000 | 0.2000 | 0.5000 |\n | ABMIL + WENO | 0.4402 | 0.9932 | 0.0068 | 0.5598 | 0.8826 | 0.9308 |\n\n\n\n> 7. The code was not made available. Although the method is well described, there is a concern that the results in this paper would be difficult for a reader to reproduce.\n\n* **Response**：\n\n We have submitted a zip file of the source codes in the newly submitted supplementary files. And we promise to open source all the source codes on github to guarantee the reproducibility of the results.\n\n### - Questions:\n\n> Can you please clarify what is the 'norm' in Equation 6?\n\n* **Response**:\n\n The norm function in eq. 12 (page 6) refers to the normalization function, which is formulated as follows:\n $$\n \\begin{equation}\n X_{\\text {norm }}=\\frac{X-X_{\\min }}{X_{\\max }-X_{\\min }}\n \\end{equation}\n $$\n where $X_{\\text {norm }}$ is the normalized data, $X$ is the original data, and $X_{\\max }$ and $X_{\\min }$ are the maximum and minimum values of the original data, respectively.\n\n And we apologize for not describing this detail clearly. The soft pseudo labels of the student network are obtained by normalizing the attention scores (to values between 0 and 1) of the teacher network.\n\n We will revise the statement of ‘attention scores’ on line 11, 64, 156, 186, 320 of the original manuscript to ‘normalized attention scores’, and add the formulation of the normalization function in Section 3.1.2 and Section 3.2.3 in the final version.\n", " Thank you very much for the valuable comments, which are very helpful to further improve our manuscript. We will respond to the weaknesses, questions and limitations in detail. Some figures and results of newly added experiments can be found in Page 6, Section 5 (Rebuttal) in the newly submitted ‘Supplementary Material.pdf' file.\n\n### - Weaknesses\n\n> While the authors describe in detail the concept of HPM, the study and results are very weakly developed and presented. Thus I think that perhaps including this as part of the work is a bit premature and the remaining work to my eyes, stands on its own two feet.\n\n* **Response**：\n\n We appreciate your comments on the HPM strategy, and we agree that the HPM strategy deserves in-depth study. In the original manuscript, we have done the following three studies on the HPM strategy: **1)** In Page 9, Section 5, we present an ablation study (Table 4) to show the effectiveness of HPM; **2)** In Figure 3, we show how the HPM strategy influences the performance of the teacher and the student networks for instance classification; **3)** In Supplementary Material Page 5, Section 3, we conduct a robustness study on the threshold of the HPM strategy on the Camelyon16 Dataset, and the results are given in Table 3 of the Supplementary Material. To further study the HPM strategy, we perform **a new experiment about the robustness of HPM on its starting epoch**, and the results can be found in Page 6 Section 5 (Rebuttal) Figure 7 in the newly submitted ‘Supplementary Material.pdf’. Generally speaking, the HPM strategy is robust to the threshold and the starting epoch. We copy the main results of these studies here for your convenience.\n\n * **(1)** **Ablation Study of HPM Strategy on the Camelyon16 Dataset**\n\n \tAs shown in the third and fourth rows of the following Table (Page 9, Section 5, Table 4 in the original manuscript), **adding HPM can improve the AUC of both instance-level and bag-level classification**.\n \n | Distillation | Shared Encoder | HPM | Instance-level AUC | Bag-level AUC |\n | :----------: | :------------: | :--: | :----------------: | :-----------: |\n | | | | 0.8480 | 0.8379 |\n | √ | | | 0.8787 | 0.8574 |\n | √ | √ | | 0.9011 | 0.8583 |\n | √ | √ | √ | **0.9271** | **0.8663** |\n \n * **(2) About how the HPM strategy influences the performance of the teacher and the student networks**\n \n \tIn Page 9, Section 5, Figure 3 of the original manuscript, comparing the blue line (ABMIL+WENO without HPM) and the red line (ABMIL+WENO with HPM) in panel (b) and panel (c), we can see that the instance classification performance of both the teacher network and the student network **steadily improves after some vibration when HPM is added**.\n \n * **(3)** **Robustness Study of the Threshold of the HPM Strategy on the Camelyon16 Dataset**\n \n \tAs can be seen in the following table (Supplementary Material Page 5, Section 3, Table 3), the instance-level AUC with HPM strategy is significantly higher than that without HPM strategy at all thresholds; when the threshold is below 0.92, the bag-level AUC with HPM strategy is slightly lower than without HPM strategy, which may be caused by dropping too many positive instances. The instance-level AUC and bag-level AUC using HPM strategy are higher than the raw ABMIL at all thresholds. These results show that the **HPM strategy is robust to the Threshold used.**\n \n | Method| Threshold | Instance-level AUC | Bag-level AUC |\n | -------------------- | :-------: | :----------------: | :-----------: |\n | ABMIL [1]| - | 0.8480|0.8379|\n | ABMIL+WENO (w/o HPM) |1.0000| 0.8787|0.8574|\n | ABMIL+WENO (w/ HPM) |0.9800| 0.8884 | **0.8717** |\n | ABMIL+WENO (w/ HPM) |0.9600| 0.9196 | 0.8675 |\n | ABMIL+WENO (w/ HPM) |0.9400| **0.9271** | 0.8663 |\n | ABMIL+WENO (w/ HPM) |0.9200| 0.9256 | 0.8402 |\n | ABMIL+WENO (w/ HPM) |0.9000| 0.9204 | 0.8495 |\n | ABMIL+WENO (w/ HPM) |0.8800| 0.9042 | 0.8478 |\n \n * **(4)** **Robustness Study of the Starting Epoch of the HPM Strategy on the CIFAR-10-MIL Dataset**\n \n \tWe added a new robustness study on the starting epoch of the HPM strategy, and the results are shown in Page 6 Section 5 (Rebuttal) Figure 7 of the newly submitted ‘Supplementary Material.pdf’ file. We construct the WENO framework using ABMIL [1] as the teacher and experimented on a CIFAR-10-MIL dataset with a positive instance ratio of 0.2. In this experiment, we added the HPM strategy at three different time points (the 100th, 150th and 200th epoch) and the results show that their final instance-level AUCs are almost the same for both the teacher and the student networks. These results indicate that **HPM is not sensitive to the starting epoch.**\n\n[1] Ilse, Maximilian, Jakub Tomczak, and Max Welling. \"Attention-based deep multiple instance learning.\" International Conference on Machine Learning. PMLR, 2018.", " ### - Questions\n\n> This method appears to heighten the negative consequences of incorrectly labeled data (specifically true positives false labeled negative) because those instances labeled negative are going to adversely train the student network. Have you considered pairing this work with networks trained to catch this situation?\n\n* **Response**：\n\n Indeed, there are still some incorrectly labeled instances in the pseudo labels used for training the student network (an instance classifier) and we agree that pairing this work with networks trained to catch this situation is a very promising research direction. We will consider this combination in our future work to reduce the influence of the noisy pseudo labels produced by the teacher and further improve the performance of both networks. Thank you for your suggestion.\n\n Actually, in weakly supervised WSI classification, we always face the problem of noisy label in training an instance classifier because only the bag-level labels are available while the instance-level labels are not. In this paper, we tackle this problem by **reducing the noise of the pseudo labels by constructing a distillation framework**. We used a simple instance classifier as the student network, while other more advanced instance classifiers can also be used as the instance classifier in our framework. While we do not think that our method **heightens the negative consequences of incorrectly labeled data**, we agree that if an instance classifier that is more robust to incorrectly labeled instances in training data is used as the student network, the overall performance can potentially be further improved. ", " \n ### - Limitations\n\n> The major weakness of the paper is that the methods has not been used on well-benchmarked classification tasks. For example, does this strategy actually enhance methodologies for which MIL+RNN already deliver clinical grade results or is this method only going to improve results for which the dataset is small and/or the task is not clinically significant.\n\n* **Response**：\n\n Thank you for your comments. Actually, besides the two synthetic datasets, WENO was carefully validated on **three real-world clinical datasets**, including two widely used public benchmark datasets in the WSI field [2,3,4], the Camelyon16 Dataset and the TCGA Lung Cancer Dataset.\n\n **About clinically significant tasks**. To further demonstrate the potential of WENO to be applied to clinically significant problems, we experimented on **an inhouse cervical cancer dataset**. This task is to predict the lymph node metastatic status (positive or negative) of a patient from HE slides of the primary lesion. **Clinically**, this is a rarely studied but clinically significant task in WSI analysis field. Cervical cancer is the most common malignant tumor of the female reproductive system [5]. Accurate diagnosis of lymph node metastatic status is crucial to the selection of individualized treatment for patients with cervical cancer [6,7,8]. So far, there is still a lack of effective method to assess the lymph node metastatic status before surgical treatment. On the contrary, the HE slides of the primary lesion can be obtained by biopsy before surgical treatment. **Technically**, unlike the two former real-world datasets, this task is particularly challenging. Since there is no prior knowledge about what image features of the primary lesion indicate metastasis, even very experienced pathologists are unable to accurately distinguish between positive and negative instances of the HE slides of primary lesion. In this task, WENO achieves the best performance among all comparison methods, which indicates that WENO can be applied to the prediction of metastasis using primary lesion WSIs in clinical practice.\n\n **Performance comparison to MIL+RNN.** Comparison to MIL+RNN was only done on the TCGA dataset in the original manuscript and we **added comparison on the other two real-world datasets**. As can be seen, using WENO outperformed **MIL+RNN**[9] on all three clinical datasets. The results are presented in the following tables.\n\n - **Results on the Camelyon16 Dataset:**\n \n |Methods|Instance-level AUC|Bag-level AUC|\n |------------------|:------------------:|:-------------:|\n |MIL-RNN [9]|0.8245|0.8162|\n |ABMIL [1] + WENO|0.9271|**0.8663**|\n |DSMIL [2] + WENO|**0.9377**|0.8495|\n\n - **Results on the TCGA Lung Cancer Dataset:**\n \n |Methods|Bag-level AUC|\n |-----------------|:-------------:|\n |MIL-RNN [9]|0.9107|\n |ABMIL[1] + WENO|0.9663|\n |DSMIL[2] + WENO|**0.9727**|\n \n - **Results on the Cervical Cancer Dataset:**\n\t\n |Methods|Bag-level AUC|\n |-----------------|:-------------:|\n |MIL-RNN [9]|0.7563|\n |ABMIL[1] + WENO|0.8056|\n |DSMIL[2] + WENO|**0.8222**|\n\n **Potential of being used on large datasets.** Finally, WENO was not validated on the large clinical datasets mentioned in the MIL+RNN paper [9], because most of the data in that study are not publicly available [9] (mentioned in Section Data availability). However, given the excellent performance demonstrated on the three clinical datasets and the fact that WENO does not increase the complexity of existing algorithms much, WENO could be used on large clinical datasets.\n\n\n[1] Ilse et al. \"Attention-based deep multiple instance learning.\" ICML. 2018.\n\n[2] Li et al. \"Dual-stream multiple instance learning network for whole slide image classification with self-supervised contrastive learning.\" CVPR. 2021.\n\n[3] Shao et al. \"Transmil: Transformer based correlated multiple instance learning for whole slide image classification.\" NeurIPS 34 (2021): 2136-2147.\n\n[4] Zhang et al. \"DTFD-MIL: Double-Tier Feature Distillation Multiple Instance Learning for Histopathology Whole Slide Image Classification.\" CVPR. 2022.\n\n[5] COHEN et al. Cervical cancer [J]. Lancet, 2019,393(10167):169-182.\n\n[6] CANFELL et al. Mortality impact of achieving WHO cervical cancer elimination targets: a comparative modelling analysis in 78 low-income and lower-middle-income countries [J]. Lancet, 2020,395(10224):591-603.\n\n[7] ZIGRAS et al. Early Cervical Cancer: Current Dilemmas of Staging and Surgery [J]. Curr Oncol Rep, 2017,19(8):51.\n\t\n[8] LEE et al. 2018 FIGO Staging System for Uterine Cervical Cancer: Enter Cross-sectional Imaging [J]. Radiology, 2019,292(1):15-24.\n\t\n[9] Campanella et al. \"Clinical-grade computational pathology using weakly supervised deep learning on whole slide images.\" Nature Medicine 25.8 (2019): 1301-1309.", " The authors utilization whole slide image (WSI) classification as a classic instance and bag classification problem as most tasks based on whole slide images have slide-level (bag) classification labels and small patches which compose the slides (instances) for the the instance labels are unknown. This formulation is necessary because WSI contain too much data to be process on a single GPU. Multiple instances learning paired with an aggregator function, like RNN, has been proven to deliver clinical level results, most classically for \"tumor/not tumor\" tasks. The authors suggest that these method are limited in tasks where instance level classifications are dichotomized as challenging and not challenging and that certain bags with few levels of challenging instances can be false negatives. All of this is a set up for their model which benefits from work in the field of knowledge distillation. Knowledge distillation is a pairing of two models labeled student and teacher, where the teacher network is a MIL-type model using bags of instances with attention and the the student is an instance level classifier that uses all instances in negative bags as negatives and instances with \"positive attention\" from the teacher network labeled as positives (authors call them soft pseudo labels). The authors also employ a \"Hard Positive Instance Mining\" HPM strategy whereby the instances where are predicted to be positive with high probability are excluded from the teacher training to make teacher task more challenging. The authors then implemented the strategy using synthetic datasets with CIFAR-10 and CRC-100K datasets with instance labels. Camelyon16 was used as a real cancer dataset with both instance and bag level label. Finally, the model was trained and tested on real-world datasets without known instance level classifications, TCGA NSCLC dataset and and in house cervical cancer dataset. Using both ABMIL and DSMIL, adding knowledge distillation improved overall bag level classification performance as measured by AUC. This work is very strong because the authors have properly formulated the many challenges of whole slide image classification and incorporated emerging methods from the field of knowledge distillation/transfer learning to improve upon existing state of the art methodologies in WSI classifications. From my own work, I have observed that attention maps derived from MIL training provide what appears to be very useful information but that information, as far as I know, has not been effectively harnessed in a practical way. By formulating the problem with interactions between student and teacher networks, the bag level classifier can provide soft labels for the classification of tiles while the classification results from the student network can be harnessed to \"stress test\" the bag level classifier. \n\nWhile the authors describe in detail the concept of HPM, the study and results are very weakly developed and presented. Thus I think that perhaps including this as part of the work is a bit premature and the remaining work to my eyes, stands on its own two feet. This method appears to heighten the negative consequences of incorrectly labeled data (specifically true positives false labeled negative) because those instances labeled negative are going to adversely train the student network. Have you considered pairing this work with networks trained to catch this situation? The major weakness of the paper is that the methods has not been used on well-benchmarked classification tasks. For example, does this strategy actually enhance methodologies for which MIL+RNN already deliver clinical grade results or is this method only going to improve results for which the dataset is small and/or the task is not clinically significant. ", " This work presents a method to improve instance classification in whole slide images (WSI) using only class labels of WSI. To this end, the authors consider a knowledge distillation method where a teacher and a student model learn from each other alternatively. The teacher model is a bag (WSI) classifier while the student model is an instance classifier. The knowledge transfer between the two models is instance score attention which indicates the contribution of the instance to the bag prediction. Experimental validation was performed over 2 synthetic datasets and 3 real-world datasets for histology data, and the proposed method outperforms several SOTA methods. Strengths:\n+ The paper is clearly written and organized. Their problem statement and the proposed approach are clearly described. \n+ The paper discusses an important application that is improving the instance classification in WSI data.\n+ The empirical results show the benefit of the method, and some ablation studies are provided.\n\nWeaknesses:\n - On page 2, lines 63-66, the authors mentioned that using soft labels as they did helps to alleviate the noisy pseudo-labels used in other methods. It is not clear how it is the case. From the description of the method, the pseudo-labels in this work change every SGD step since the network that builds them changes constantly. Therefore, they are noisier, especially at the beginning of the training. It is not clear why the authors claimed that their pseudo-labels alleviate the noise issue. In addition, there is no empirical evidence to support this claim.\n - On page 2, lines 70-72, the authors mentioned that sharing the feature extractor between student and teacher enhances knowledge distillation. It is not clear why it is the case.\n - In the entire paper, the pseudo-labels were described as the attention scores. It is not until eq.12 (page 6) that the authors describe the soft labels as being single scores that simulate probability. The text should be clear about this detail from the outset. In addition to fig.2, there should be an operation after attention scores come out from the teacher, before being used by the student’s CE loss.\n - Hard positive instance mining (hpm) proposed in this paper is similar to hard mining in class-activation maps (CAMs). In the latter, strong activations are suppressed, thereby pushing the network to seek more positive regions. The same here, the authors drop high positive instances simulating suppression. Therefore, the proposed mining strategy is not really new; and literature discussion is necessary. See an example for CAMs ib Wei, Y., Feng, J., Liang, X., Cheng, M.-M., Zhao, Y., and Yan, S. (2017). Object region mining with adversarial erasing: A simple classification to semantic segmentation approach. CVPR 2017.\n- The main issue in this work is that it is unclear why there is an improvement? The authors are not using additional supervision. In fact, the pseudo labels are expected to be noisier and change constantly. It is unclear why training a student in parallel helps instance classification even though there are no instance labels. Authors are encouraged to provide further analysis to explain the observed improvement. If I had to guess, the main element that improves performance is in eq.12, in particular the zero-label of instances in negative bags. Authors explicitly provided instance labels but only for negative instances, giving their model a large advantage. Knowing what is not positive helps the model. \n- Finally, there is an important element missing in the experimental section: the classification accuracy per type of instance (positive/negative, ...). We do not know what pushed the AUC at instance-level to improve. Is it improving the positive instances or negative instances? My guess is the latter helps more since labels of negative instances are explicitly used.\n- The code was not made available. Although the method is well described, there is a concern that the results in this paper would be difficult for a reader to reproduce. Can you please clarify what is the 'norm' in Equation 6? Please refer to the weaknesses described in Strengths And Weaknesses.", " This paper presents a novel method to train a teacher-student attention-MIL model with weak supervision in a way that the student can be used to improve the teacher. Dubbed WENO, the method shares an encoder between the teacher and student model and while the teacher's bag-level attention scores are used to train the student (distillation), the student's instance model is used to select hard examples for the teacher's bag. This is designed to avoid a common pitfall of MIL models where the teacher tends to use only easy-to-classify positive instances from the bag and becomes weak at classifying hard examples. The method can be added to existing attention-based MIL methods. The method is evaluated on 2 synthetic and 3 real-world datasets of WSI histology images, and is using 2 SOTA MIL methods (ABMIL and DSMIL). The method is shown to outperform SOTA by a significant margin on datasets where the prevalence of the positive class is low, and by a small margin for real-world datasets. An ablation study shows that that each key part of the method (distillation, shared-encoder and hard-example-selector) all participate in improving the baseline.\n strengths:\n- the method combines for the first time multi-instance-learning (MIL) with weakly-supervised knowledge distillation.\n- the method addresses the issue with attention-based MIL methods where the teacher's performance stops improving after a while and even decreases because it focuses more and more on a few easy-to-classify examples. The proposed HPM (hard-positive-mining) module to alleviate this issue is novel and uses the student's predictions after a set number of epochs to select hard examples for the teacher's bag.\n- the method improves upon SOTA for 3 public datasets of WSI histology. It comes ever-closer (within 3%) to fully-supervised models trained with instance-level labels (expensive to obtain).\n- the ablation study is useful and convincing.\n- the method is not specific to WSI histology images and can be applied to any MIL setting\n- the method does not affect inference complexity, only training is affected. This is a key factor in most real-world applications.\n- the paper is very well written and clarity is excellent\n\nweaknesses:\n- the achieved improvement over SOTA is relatively small for the real-world datasets.\n- hyperparameter tuning has to be performed for the HPM module to determine the best threshold. This is discussed in the supplemental material. However, another hyperparameter, the number of epochs after which to bring the HPM module online is not discussed.\n no questions. Beyond the author-stated limitation related to hyperparameter tuning, i see no further limitations of the approach.\n" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 6, 8 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 5 ]

[ "ZC6iayMFdq5", "DcxZ3g3FBiW", "ZC6iayMFdq5", "DcxZ3g3FBiW", "DcxZ3g3FBiW", "DcxZ3g3FBiW", "DcxZ3g3FBiW", "DcxZ3g3FBiW", "DcxZ3g3FBiW", "rtSO4vbbyxc", "rtSO4vbbyxc", "rtSO4vbbyxc", "nips_2022_JoZyVgp1hm", "nips_2022_JoZyVgp1hm", "nips_2022_JoZyVgp1hm" ]

[ "g9G-IPHsTFF", "6Pd6oIOxq-", "x7_2T8TXlok", "x_vmhjBRqV", "zuzO1L_m7wUb", "l2-87TFn_8e", "YnAItZpbkwo", "xSGZwbU3-5P", "iHXjiv6FtAZ", "GBrDV2W8Z7I", "0Tqg1P8cRs-", "ROnG7qN0ULW", "2Rf56lZiEO0", "0NHxqESH6V", "4w2qIgZpLj", "iuRXfVwv_Zc", "BU5XvfmQQX2", "vZrgtsuh1a5", "_h5Xbwpc4YF", "dDL5xaHq2-", "AAMBrrWylV", "C3nDCp6rh3f", "pEKZ66_EFlPb", "Bt7axM9JIm5", "qnslfO5jaqT", "Ab7FzA6XZxW", "8RRVz1PrNu", "TZ3eL1hbs-w", "_zxhSuQu4gC", "FZpvQzsMmf7", "S4oqMeOCT4W", "uZLiuIuUB5b", "qSsVwbKEll8", "dIl6RSum847", "gZdIcwVT92u", "2wvC8H1xGM4", "VzC-5h6nqw", "-NI2iGvNM0f", "rbYXADWj15", "FLOg7pb4sNi", "qbu6a4HoiuC", "dO5thVImDnUV", "SwQnIIf5TlB", "P4C1KC6tB4D", "2ZPfigWFNi", "RMaIirYX2fS" ]

[ "author", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Below we update the result of [1,2] of fine-tuning for $15$ epochs.\n___\n\n|Method|training-free? |\tFPR95 ($\\downarrow$)\t| AUORC ($\\uparrow$)|\n|:-:|:-:|:-:|:-:|\n| [1] |\tx |\t56.36|\t86.91|\n| [2] |\tx\t| 52.78\t| 87.83|\n|RankFeat |✔\t|**36.80** | **92.15** |\n\nGiven the huge time cost of fine-tuning for $15$ epochs, the results of [1,2] are still not comparable against our $\\texttt{RankFeat}$ . With this evaluation, we believe that we can claim that our method has an advantage on ImageNet-1k even against training-needed approaches.\n\n>[1] Csi: Novelty detection via contrastive learning on distributionally shifted instances. NeurIPS 2020\n>\n>[2] Learning and Evaluating Representations for Deep One-class Classification. ICLR 2021\n>\n\n___\n\nFinally, we would like to thank $\\color{blue}{Reviewer\\ dq6u\\ (R2)}$ for the review and replies. \n\nThough we do not change $\\color{blue}{R2}$'s mind in the end, we appreciate his/her efforts and time spent on this paper.", " We thank $\\color{blue}{Reviewer\\ dq6u\\ (R2) }$ for the instant reply and detailed comments. Below we address the concern in detail.\n\n___\n\n>The setup described above is very unfair to those methods\n>\n>Where is the results for PANDA or Mean-Shift on your table?\n>\n\nThe experiment settings (batch size and training epochs) are based on our computational resources. We have tried our best to put the baselines in the best setting to run the experiment. We cannot train PANDA or Mean-Shift for now but we will try to update the result of [1,2] of fine-tuning for 15 epochs by Tuesday night.\n\n> If authors want to compare to CSI on ImageNet-like dataset, why not use the ImageNet-30 dataset ? (CSI results for this already on their paper)\n\nThe aim of this additional ImageNet-1k experiment is to respond to $\\color{blue}{R2}$ 's concern in the previous reply \"Finally, to claim that author's methods has an advantage on ImageNet-1k, authors should provide results of the other methods I mentioned above on the same benchmark, which authors doesn't do.\" So we considered ImageNet-1k instead of ImageNet-30. \n\n>In the same way owners of the medical dataset are providing a model pre-trained with labels on that dataset, they can provide a model pre-trained in an SSL-manner. In fact, providing a SSL model that is trained without any labels is much more secure\n\nYes, we agree. But the point we want to make here is that they might not provide any training data for security. Then these OOD approaches that need training data could not work. \n\n>The fact that there is publicly available pre-trained ImageNet models doesn't mean those models were free to train\n\n***Yes, but these models are indeed free to practitioners who use *post hoc* OOD detection methods.***\n\nAlso, the advantage of ***(3) Post hoc methods do not change any parameters and will not affect the standard ID classification accuracy*** can not be neglected. We would like $\\color{blue}{R2}$ to refute this point if possible.\n\nWe would also like to hear what $\\color{blue}{R2}$ thinks about our additional experiment in ***3. Post hoc method can get performance improvements when extra training or data is allowed*** in the previous reply.\n\n\n___\n\nThanks again for $\\color{blue}{R2}$' time and reply. Considering the limited time left, we sincerely hope $\\color{blue}{R2}$ could directly respond to the crucial points listed above.\n", " - The setup described above is **very unfair** to those methods, and I don't think it should be reported. Please consult respective papers for fair setup\n- If authors want to compare to CSI on ImageNet-like dataset, why not use the ImageNet-30 dataset ? (CSI results for this already on their paper)\n- Advantages for post-hoc method that the authors describe revolve around having access to pre-trained models\n - The fact that there is publicly available pre-trained ImageNet models doesn't mean those models were free to train\n - Simply, for a new domain (e.g. medical... etc) there is no pre-trained models, and presented method has no computational advantage\n- Where is the results for PANDA or Mean-Shift on your table ?\n- > Suppose that we are doing OOD detection for medical imaging where the training data is private and not available\n - In the same way owners of the medical dataset are providing a model pre-trained with labels on that dataset, they can provide a model pre-trained in an SSL-manner. In fact, providing a SSL model that is trained without any labels is much more secure\n", " Thanks for the instant reply!\n___\n\nFor [1,2], we fine-tune the pre-trained BiT ResNetv2-101 (the same architecture and model we used in Table 2 of the paper) using the loss in [1,2] on ImageNet-1k for $3$ epochs. The batch size is $1024$ and the learning rate is $0.001$. We set the learning rate to a small value because the model is already pre-trained. The evaluation OOD datasets also follow Table 2 of the paper and we report the average results across the four datasets. The data augmentation techniques of CSI [1] for contrastive learning include Inception crop, horizontal flip, color jitter, and grayscale transform.\n\nIn the original papers [1,2], they train the models on CIFAR from scratch. However, on ImageNet obviously we cannot finish training the models from scratch before the rebuttal deadline. So we choose to only fine-tune the models for $3$ epochs. \n\nAs for the convergence, to be honest, we think it converges but we are not 100\\% sure since we only have losses of $3$ epochs. We estimate that the maximum training epoch we can afford is $15$ epochs (this could be done by Tuesday morning approximately if we resume training from now). \n___\n\nWe are willing to continue training the model till $15$ epochs if $\\color{blue}{R2}$ thinks it is needed. Nonetheless, given the extra time cost of fine-tuning for $3$ epochs, [1,2] cannot achieve competitive performance against our approach, which can show our *post hoc* method's advantage.\n ", " Before getting to other points, can you please provide full details on the table on point 4. Did you actually train [1]&[2] till convergence on ImageNet-1k to get those numbers ? what architecture was used ? training and evaluation details and logs...etc ? please provide full details on those experiments for each presented method in that table...", " ___\n\n**4. Comparison against [1,2,3] on ImageNet-1k.**\n\nWe would like to clarify that [1,2,3] are all not *post hoc* because [1,2] use extra unsupervised training and [3] uses few-shot fine-tuning (all leverage training data). Nonetheless, we are willing to compare these baselines on the ImageNet-1k benchmark. \n\n|Method| training-free? |FPR95 ($\\downarrow$)|AUORC ($\\uparrow$)|\n|:-:|:-:|:-:|:-:|\n| [1]| x| 63.17| 81.75|\n| [2]| x| 61.89| 82.23|\n| [3] MSP| x | 57.19 | 85.61 |\n| [3] Mahalanobis| x | 65.49 | 83.77|\n| RankFeat| $&#10004;$ | **36.80** | **92.15** |\n\nAs indicated above, [3] indeed improves the ordinary MSP and Mahalanobis score by fine-tuning, but all the results are not comparable against our $\\texttt{RankFeat}$. With this evaluation, we believe that we can claim that our method has an advantage on ImageNet-1k.\n\n\n>[1] Csi: Novelty detection via contrastive learning on distributionally shifted instances. NeurIPS 2020\n>\n>[2] Learning and Evaluating Representations for Deep One-class Classification. ICLR 2021\n>\n>[3] Exploring the Limits of Out-of-Distribution Detection. NeurIPS 2021\n>\n>[4] Energy-based Out-of-distribution Detection. NeurIPS 2020\n\n___\n\n\nThanks again and it is more than welcome to have further discussions!\n", " We thank $\\color{blue}{Reviewer\\ dq6u\\ (R2)}$ for the detailed response and the enthusiasm for discussion! Below we address the concerns in detail. \n\n___\n\n**1. Advantages of post hoc methods over training-needed methods.**\n\nWe do not agree that the concept of *post hoc* OOD methods makes little sense. Specifically, we think that post hoc methods have the following advantages over training-needed methods:\n\n***(1) Post hoc methods can be directly applied to any pre-trained model.*** $\\color{blue}{R2}$ may argue that the fine-tuning or training of training-needed methods is light-weighted. But as we discussed before, when the model is transferred to ImageNet-1k or even larger datasets, then fine-tuning can be a big concern. In particular, some methods like CSI [1] need to train a model from scratch, which would pose a larger computational burden.\n\n***(2) Easy use due to widely available pre-trained models.*** The standard pre-trained models are widely available nowadays on different deep learning platforms. It is much more convenient to load a pre-trained\nmodel instead of training or fine-tuning one. \n\n***(3) Post hoc methods do not change any parameters and will not affect the standard ID classification accuracy.*** Last but not least, *post hoc* methods do not change parameters of a given model. That being said, the model can be also used for the standard classification of ID datasets. So one model could be applied in two closely-related tasks: (1) distinguishing ID and OOD samples and (2) classifying ID samples. However, for training-needed methods, the model can only be used for anomaly detection. \n\n***If $\\color{blue}{R2}$ cannot deny all the advantages discussed above, we insist that the *post hoc* OOD approaches have the meaning of being there.***\n\nFinally, if $\\color{blue}{R2}$ thinks it is necessary, we are willing to add one sub-section in the related work or in the supplementary material to introduce the training-needed methods and discuss the difference from *post hoc* approaches in detail.\n\n**2. Knowledge might not be available in real-life applications**\n\nIn real-life applications, there are scenarios where the training data are not available. Suppose that we are doing OOD detection for medical imaging where the training data is private and not available. In this case, we may only have access to the given pre-trained models. Then training-needed methods cannot work. Can $\\color{blue}{R2}$ refute this example?\n\n**3. Post hoc method can get performance improvements when extra training or data is allowed**\n\nLet us stop discussing the meaning of *post hoc* OOD detection for a while and think of the problem setting from another perspective. $✨✨✨$ *Supposing that extra training or data is allowed for *post hoc* methods, what would happen?*\n\nWe take our $\\texttt{RankFeat}$ as an example and we can have one simple variant that leverages training and extra data: **RankFeat (training)**: we apply our RankFeat in the training process by perturbing the high-level feature as $\\mathbf{X}'=\\mathbf{X}-\\mathbf{s_{1}}\\mathbf{u_{1}}\\mathbf{v_{1}}$. Then the residual feature $\\mathbf{X}'$ is fed to the pooling and FC layer for classification. This can improve the representation power of the residual feature matrix apart from the rank-1 subspace so that the OOD detection ability can be improved.\n\nFor one-class CIFAR10 and CIFAR100, We fin-tune the trained CIFAR models using **RankFeat (training)** and report the average AUROC ($\\uparrow$) below:\n\n|Method | CIFAR10 | CIFAR100|\n|:-:|:-:|:-:|\n|RankFeat (post hoc)| 88.58 | 82.43 |\n|RankFeat (training)| **95.76 (+7.18)** | **93.19 (+10.76)** |\n\nAs can be seen, when we are able to leverage extra training, the performance will get significant improvements. A similar phenomenon has also been observed in [4]. We also believe that it is possible to design more sophisticated mechanisms to make better use of the training data, but we would like to strive to use the most simple *post hoc* setting.\n\n___", " Thanks for the reply,\n\n> For post hoc methods like ours, we do not need any knowledge from any dataset and the method can be applied in a sample-wise manner. However, the training-needed methods do need information from both the training and validation set of the ID dataset.\n\nOOD detection task is primarily defined based on the ID dataset. An OOD detection method without any knowledge from any dataset (even the ID) is a concept that makes little sense.\n\nThis is manifested much more clearly as we delve into the details of the proposed method, it requires a model pre-trained in a fully supervised manner on the ID dataset!! So the authors make two very contradicting claims:\n- Their work is post-hoc in the sense that it does not need any knowledge from any dataset\n- They require a model pre-trained in a fully supervised manner on the ID dataset\n\n> PANDA [3] needs to extract pre-trained features of both the training and validation set for OOD detection (features of 60000 images). Even if one does not perform any fine-tuning\n\nWhat is the difference between fully supervised training on the ID dataset and requiring those features for evaluation ? More memory, but totally the same input requirements! so author's work make the exact same assumptions about available data, as PANDA, but with much worse results\n\nMoreover, other methods like CSI [1] (btw this one is fully unsupervised, i.e. it has lesser input requirements and significantly outperforms this work) uses clustering to get negligible performance drop while requiring a very small fraction of training data. This clustering trick makes ImageNet case trivial\n\nThis work [2] is fully unsupervised, and doesn't require any info about training data during inference, so it should qualify as post-hoc according to your criterion, it also achieves significantly better results than yours\n\nAlso this work [3] has an MSP baseline that should also qualify as post-hoc according to your criterion, it also achieves significantly better results.\n\nFinally, to claim that author's methods has an advantage on ImageNet-1k, authors should provide results of the other methods I mentioned above on the same benchmark, which authors doesn't do.\n\n[1] Csi: Novelty detection via contrastive learning on distributionally shifted instances. NeurIPS 2020\n\n[2] LEARNING AND EVALUATING REPRESENTATIONS FOR DEEP ONE-CLASS CLASSIFICATION. ICLR 2021\n\n[3] Exploring the Limits of Out-of-Distribution Detection, Neurips 2021", " We thank $\\color{blue}{Reviewer\\ dq6u\\ (R2)}$ for the detailed reply. Below we answer the questions in a point-by-point manner. \n___\n\n**1. The key to post hoc methods is no prior knowledge given from any dataset**\n\nYes, for a fair comparison, we do limit our main comparison to *post hoc* methods, as also done in previous works [1,2]. ***The comparison fairness we have been talking about mainly depends on how much knowledge is given for OOD detection.*** Other factors like fine-tuning epochs or fine-tuning time consumption do not really matter. For *post hoc* methods like ours, we do not need any knowledge from any dataset and the method can be applied in a sample-wise manner. However, the training-needed methods do need information from both the training and validation set of the ID dataset.\n\nFor example, PANDA [3] needs to extract pre-trained features of both the training and validation set for OOD detection (features of $60,000$ images). Even if one does not perform any fine-tuning, the pre-trained features are always needed for computing the OOD score, which is still not fair to *post hoc* methods. The performance might suffer from a large degradation when the dataset size gets smaller. Also, fine-tuning on the CIFAR benchmark is fast, but what if PANDA is transferred on the ImageNet benchmark? The fine-tuning time might be a big concern then.\n\n***Based on the difference in the prior knowledge given, we do not agree that the training-need methods have neglectable differences from *post hoc* methods.***\n\nFinally, we note that we do not neglect the entire training-needed OOD literature: we also compare with MOS [4], a training-needed method on the ImageNet-1k benchmark. If $\\color{blue}{R2}$ thinks it is necessary, we are willing to add one paragraph in the related work section to introduce all the discussed training-needed OOD detection methods in detail and to clarify their difference from *post hoc* approaches (of course this should be done after we are allowed for an additional content page). \n\n**2. Misunderstanding of Figure 3 in PANDA [3]**\n\nWe would also like to point out one misunderstanding about PANDA. The AUORC of Figure 3 in PANDA [3] refers to the performance of a single class (Class 17) of CIFAR100 instead of the whole CIFAR100 dataset. This can never indicate that the average performance of PANDA is better than our method even when it is not fine-tuned at all. \n\n**3. The main focus of the experiments is the ImageNet-1k benchmark**\n\nWe would like to emphasize that the main focus of our experiments is the ImageNet-1k benchmark. The aim of conducting experiments on CIFAR is to show that our method can be applied to datasets of smaller resolutions and fewer images. The results indicate that our method indeed outperforms other *post hoc* baselines. ***We think the comparison against post hoc methods is sufficient on CIFAR.***\n\nNonetheless, we agree that on CIFAR our method is not as advantageous as on ImageNet because of the much lower resolution. This has a direct influence on our method because the feature matrix gets smaller. \n\n**4. A large portion of the time consumption comes from the model itself.** \n\nWe would like to clarify one misunderstanding about the time consumption: ***a large portion of the time cost comes from the model itself***. This is because our backbone is BiT ResNetv2-101, which is a relatively large model. The inference of the model is slow in itself. Here we report the inference time of *post hoc* methods for a single image below: \n\n|Method | Time Consumption (ms)|\n|:-:|:-:|\n|MSP|7.92|\n|Energy|8.34 (+0.42)|\n|ReAct|8.79 (+0.87)|\n|**RankFeat (#20 iter)**| 9.22 (+1.30) |\n\nFor the most simple baseline MSP, the time cost is basically the inference time of the model. So actually our method only incurs **1ms** more time cost compared to the original inference time.\n\n**5. Experiment on Species**\n\nAs requested by $\\color{blue}{R2}$, we also did an evaluation on Species, and the experimental results show the superior performance of our method on another large-scale benchmark. This applicability and advantage have not been observed in previous *post hoc* methods. We sincerely hope that $\\color{blue}{R2}$ could consider this merit.\n\n>[1] ReAct: Out-of-distribution Detection With Rectified Activations. NeurIPS 2021\n>\n>[2] On the Importance of Gradients for Detecting Distributional Shifts in the Wild. NeurIPS 2021\n>\n>[3] PANDA: Adapting Pretrained Features for Anomaly Detection and Segmentation. CVPR 2021\n>\n>[4] MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space. CVPR 2021\n\n___\n\nA final word: from $\\color{blue}{R2}$'s replies, we believe that he/she is very very knowledgeable about the literature on anomaly detection and the related benchmarks. $&#x1F44D;$ But the main focus of *post hoc* OOD detection is different. We hope that $\\color{blue}{R2}$ can take this point into consideration. \n\nThanks again and it is more than welcome to post any further comments.", " First, I am very grateful for all the effort by the authors in their feedback and rebuttal, thanks!\n\nSecond, I can now much better see the main problem with the authors evaluation\n\n- Authors claim the existence of a specific category of OOD algorithms, which they call post-hoc algorithms\n- Authors restrict all their evaluation comparisons to that specific category of algorithms (effectively neglecting most prior work on OOD detection)\n- Authors claim SotA performance (based on the proposed segmentation of OOD literature)\n\nI totally fail to understand the usefulness of that claimed segmentation of OOD detection work. Like some of the other OOD work they require a model pre-trained in a fully supervised manner on the ID dataset, authors claim that the fact that other works (e.g. [1]) benefits from a light fine-tuning on the target dataset is enough for the authors to totally disregard them from comparison (btw as seen in Figure 3 in [1], it still performs much better than this work, even without any fine-tuning).\n\n\nTo get an idea about the huge gap in OOD detection performance:\n- This work achieves AUC of 88 in CIFAR10, while the current SotA is 97.5 [2]\n- This work achieves AUC of 82 in CIFAR100, while the current SotA is 96.5 [2]\n- This work achieves AUC of 78 in CIFAR10 vs CIFAR100, while the current SotA is 98.5 [3]\n\n\nBased on the huge performance difference, and no noticeable difference between the requirements of those methods, I don't think this work provides a real contribution to this problem.\n\nOne last point worth mentioning, that is not discussed regarding fair comparisons to prior works, this work incurs a substantial computational overhead of ~ 10 ms per image during inference, none of the above literature requires such overhead, which is substantial given the negligible inference time of used models on modern GPUs\n\n[1] Panda: Adapting pretrained features for anomaly detection and segmentation, CVPR 2021\n\n[2] Mean-Shifted Contrastive Loss for Anomaly Detection, arXiv 2022\n\n[3] Exploring the Limits of Out-of-Distribution Detection, Neurips 2021", " We thank $\\color{green}{Reviewer\\ Ft9S\\ (R3)}$ for raising the score and we are delighted that you are satisfied with the empirical observation.\n\n___\n\nWe have rephrased the intuition a bit to make it more clear by saying that a larger explained variance ratio corresponds to higher informativeness, but we understand that the PCA-based informativeness explanation might not convince everyone. It is an important direction that is worth further research in the future.\n___\n\nFinally, we would like to express our thanks to $\\color{green}{R3}$ for his/her careful/detailed review and constructive suggestions throughout the rebuttal phase. \n\n", " 1.(a) The results look good to me.\n1.(b) Your intuition sounds circular to me, and unfortunately neither convincing nor comprehensive to me, but I am satisfied with empirical observations.\n\nI will increase the rate to 6. ", " We thank $\\color{green}{Reviewer\\ Ft9S\\ (R3)}$ for the constructive suggestions and encouraging feedback. Below we address the concerns in detail.\n\n___\n\n**1(a). Average $\\mathbf{s_{1}}$ on other OOD datasets**\n\nThe average $\\mathbf{s_{1}}$ on other datasets is reported in the two tables below.\n\n|ID: CIFAR10| OOD: MNIST| OOD: SVHN| OOD: LSUN|\n|:-:|:-:|:-:|:-:|\n|55.32| **94.69**| **86.47**| **79.71**|\n\n|ID: MNIST| OOD: CIFAR10| OOD: SVHN| OOD: LSUN|\n|:-:|:-:|:-:|:-:|\n| 34.74 | **79.12** | **81.25**| **75.83**|\n\nAs indicated above, the average $\\mathbf{s_{1}}$ on other OOD datasets also tends to be larger than that of ID.\n\n**1(b). Giving an intuition on assumption**\n\nThanks for the good advice on improving the understanding. Beyond the empirical performance and visualization results, the intuition behind why OoD involves a larger first singular value is based on Sec. E of the revised supplementary material: ***(a)*** PCA-based explained variance and ***(b)*** Our empirical conjecture that well-trained network weights caused and amplified the difference.\n\nIn the revised introduction, after we introduce the difference of ID/OOD on the first singular value (line35), we immediately say \"The intuition behind is that the OOD feature corresponds to a larger PCA explained variance ratio and the well-trained network weights might cause and amplify the difference (see Sec. E of the supplementary for the detailed illustration)\", which might give a hint to the readers on the intuition. Unfortunately, in the current stage, we cannot find stronger evidence than this explanation apart from empirical performance and visualization results. In future work, we will find more convincing evidence to support our intuition.\n\n**3. Formal theoretical analysis in the paper**\n\nThanks for the advice on making the paper more formal. \n\nFor the theoretical part *'Removing the rank-1 matrix with a larger $\\mathbf{s_{1}}$ would reduce the upper bound of RankFeat more'*, we have reformulated this part into a ***proposition-proof format*** in the revised paper. We first give a proposition about the upper bound and the impact of $\\mathbf{s_{1}}$, then we prove the proposition step by step.\n\nFor the theoretical part *'Removing the rank-1 matrix is likely to make the statistics of OOD features closer to random matrices'*, we have revised this part by giving a ***formal theorem of Manchenko-Pastur Law***. Then we discuss how to use it to evaluate the statistical distance of ID/OOD feature to random matrices.\n\n**4. Consistent Sample-wise notation**\n\nThanks for the detailed comment. We have revised all the notations to the sample-wise form including the theoretical analysis section.\n___\n\nThanks again and please let us know if you have any further questions.", " 1. How about other OOD datasets? Please compare extensively not just for CIFAR10/MNIST; there are other OOD datasets you need to check. \\\n'more informative' does not mean anything to me. This is not insightful for future readers. \\\nThe main problem of this paper is that it provides no insightful understanding on why the OoD involves larger $s_1$ singular value. I know this is an assumption, and it is empirically verified for some datasets partially. This was a concern of one of the other reviewers. \\\nA good intuition on why this assumption holds will be good to readers. \n\n2. I haven't really checked the supplementary, but I believe in you. I suggest the authors to fully make sure everyhitng clear.\n\n3. What I asked to formalize is **NOT** Manchenko-Pastur Law. What I asked is to formalize your own claims in theorem-proof format; namely, formalize the claims 'Removing the rank-1 matrix with a larger $s_1$ would reduce the upper bound of RankFeat\nmore' and 'Removing the rank-1 matrix is likely to make the statistics of OOD features closer to random\nmatrices'. \\\nStating the formal theorem of Manchenko-Pastur Law is good to me but stating its proof is not necessary.\n\n4. Some notations are still in the batch in the theory section. And they do not seem correct; logits are not in the batch while inputs are in the batch. At least please make sure everything is correct and clear whether the authors use batch-wise or sample-wise notation.\n", " Thanks for the advice and for raising the score!\n\n___\n\nWe have revised line6 and line34 by adding some glue sentences to make the information flow better.\n\nFinally, we sincerely thank $\\color{brown}{Reviewer\\ SMeo}$ for his/her patience and so many lightning-fast replies of the detailed discussion. We greatly appreciate your appreciation of the idea of our paper and your efforts in improving the paper!\n\n___", " The connection between sentences is a little stiff.......To revise and make it smooth......", " Thanks for the great advice and positive feedback! \n\n___\n\nWe totally agree with you that it is also an assumption and ***we have explicitly emphasized this point in the Abstract and Introduction of the revised paper (line6 and line34)***. \n___ ", " If you is willing to add a sentence to claim that ''based on this observation, we ${\\bf assume}$ that....'' in abstract or some importance positions, I will increase your score to 6.", " It is an assumption, which may hold for suitable backbone and most benchmarks.\n\nBut it is Not a fact for all cases!", " I don't care whether you can provide a theory.\n\nI just care whether you can explain your perspective reasonably.\n\nIn ReAcT, as you claimed, they ${\\bf assume}$ that the OOD feature has abnormally larger activations than the ID feature.\n\nBut in your paper, you have not said that the first eigenvector of OOD is larger (or smaller) than that of ID is an ${\\bf assumption}$ .\n\nYou claim it as a fact or an observation. So if the observation is not right, your work will be problemtic. \n\nI can accept the example that you say \" Based on the observation, we ${\\bf assume}$ that.........'' and \"Our experiments also show that the assumptions hold in most benchmarks.\"\n\nIn addition, can you ensure your observation still hold for any backbones?\n\n", " Thanks for the follow-up!\n\n___\n\nTo single out one piece of result, $\\texttt{ReAct}$ [2] assumes that the OOD feature has abnormally larger activations than the ID feature. In your opinion, this should be a problematic idea because this abnormality is not proved theoretically but supported by empirical evidence.\n\n>[2] ReAct: Out-of-distribution Detection With Rectified Activations. NeurIPS 2021\n\n___", " Sorry. I don't agree with you.\n\nI also read paper [1]-[5]. \n\nThey are based on empirical results.\n\nBut they are not based on a problematic idea.", " Thanks for maintaining the score!\n\n___\n\nWe sincerely respect your decision but we would like to keep our opinion that ***in science it is very often the case that we draw conclusions on conjectures as long as there is strong empirical evidence supporting them.***\n\nSpecifically, our observation is supported by ***(1)*** *empirical results on several benchmarks*, ***(2)*** *visualization of singular value distributions*, and ***(3)*** *PCA-based informativeness explanations*. We believe that these are sufficient to support our opinion.\n\nIn the literature on OOD detection, most OOD methods are based on intuitive observation and lack strong theoretical guarantees [1,2,3]. However, this does not affect the fact that these state-of-the-art approaches achieve good empirical results and are widely used.\nIn a more general sense, many deep learning methods are intuitive but are ubiquitous [4,5].\n\n>[1] Energy-based Out-of-distribution Detection. NeurIPS 2020\n>\n>[2] ReAct: Out-of-distribution Detection With Rectified Activations. NeurIPS 2021\n>\n>[3] On the Importance of Gradients for Detecting Distributional Shifts in the Wild. NeurIPS 2021\n>\n>[4] Deep Residual Learning for Image Recognition. CVPR 2016\n>\n>[5] Densely Connected Convolutional Networks. ICCV 2017\n\n\n___", " Thank your for your efforts.\n\nTo be honest, I like the idea of the paper very much.\n\nHowever, your idea is based on a problematic observation, which results in that your method may be not useful in practical case.\n\nI am sorry. I will not change my score, unless you can make me believe that your idea is correct in most practical cases, but not just in several benchmarks.\n\n\n\n", " Thanks for your inspiration for future work! \n\n___\n\nGiven a pre-trained model and ID data, if we have statistics of the singular values distributions of the ID feature, it might be possible to cherry-pick OOD samples and collect an OOD dataset that might violate our observation (*the assumption of this is the prior knowledge of statistics of ID feature matrices and the cherry-picking process of OOD samples*). However, in practice for the existing OOD datasets that we have tested, we can empirically observe that the first singular value of OOD data always tends to be larger. \n\nUnfortunately, we cannot prove that it is always true in theory because the deep networks are highly non-linear and the training data can be very large-scale. The impact of a training (optimization) process on the model weights and on the feature statistics cannot be tractably analyzed in equations. We just searched the relevant literature again and we could not find any theoretical reference that did similar proofs. ***So we believe that finding a strong theoretical guarantee of (*post hoc*) OOD methods is still an open problem. It is a good and important research direction for our future work and even for the community.***\n\n___\n\nThanks again and it is more than welcome to post any further comments!", " After a pre-trained model is given for ID, can we construct an OOD data to ensure that \n\nthe first singular value of the OOD feature always tends to be much smaller than that of ID feature ?\n\nOr we can only construct OOD data whose first singular value is larger than ID?\n\nIf the second case is correct, could you prove it?", " Thanks for your detailed explanation! Now we fully understand your question.\n\n___\n\nIn your described case 1 and case 2, the conclusion seems to be always contradictory. If case 1 holds then case 2 does not hold and vice versa. **However, one important thing that is missed here is that the models in case 1 and case 2 are totally different: the model is always pre-trained on the ID data.** So in case 1 the model is pre-trained on the insider circle, and the model in case 2 is pre-trained on the outsider circle. Since the two models are trained on different circles, case 1 and case 2 are not contradictory, and they can both hold.\nActually, as we explained and empirically showed in Sec. E of the revised supplementary material (Figure 5), *it is the well-trained model weights that caused and amplified the first singular value difference of the ID and OOD features.* \n\n___\n\nHope that we understand your question correctly and that the above explanation is sufficient to eliminate your doubt. If not, please let us know and we will add more figures and data to explain this better. 😀", " Thank you for your reply.\n\n I still cannot understand why the first singular value of the OOD feature always tends to be much larger than that of ID feature.\n\nBecause as I know the OOD is diverse and we cannot guarantee whether the OOD data 's first singular value is larger or smaller than that of ID.\n\nCould you conduct experiments for this case that \n\n1. double circles: the insider circle is ID and the outside circle is OOD. At this case, the first singular value of the OOD feature always tends to be much larger than that of ID feature?\n\n2. double circles: the outsider circle is ID and the inside circle is OOD. At this case, the first singular value of the OOD feature always tends to be much larger than that of ID feature?\n\nIf 1 is correct, then 2 is not correct; if 2 is correct, then 1 is not correct. So your claim that the first singular value of the OOD feature always tends to be much larger than that of ID feature may be not correct.\n\nCould you explain above cases?\n\nIf you answer above cases, I will add your scores to 7; otherwise, I will decrease your score. \n\nYou may wander that why I am so care about this question? Because the question is the core discovery of your paper.\n\n", " We thank $\\color{brown}{Reviewer\\ SMeo}$ for the follow-up and the insightful comments. Below we address the concerns in detail.\n___\n\n**1. Why does the feature matrix tend to be less informative for the unseen OOD data?**\n\n\nFor the unseen OOD data, the distribution is different from that of ID data. The feature matrix of OOD data might embed less information because the model weights never encounter the OOD distribution and are unaware of the OOD data. *This is reflected in the larger PCA explained variance ratio of OOD feature*.\n\nWe totally understand the reviewer's concern that this is an intuitive explanation. However, we would like to note that most *post hoc* methods also have similar intuitions:\n\n- $\\texttt{MSP}$ assumes that the OOD data correspond to a less determined prediction score.\n- $\\texttt{Energy}$ assumes that the energy of the OOD logit is different from that of ID.\n- $\\texttt{ReAct}$ assumes that the OOD feature has a larger abnormal value. \n- $\\texttt{GradNorm}$ assumes that the gradient of OOD data has a larger vector norm.\n\nAll of those methods intuitively assume the behavior of OOD and ID data is different in certain aspects. Our $\\texttt{RankFeat}$ has a similar intuition with $\\texttt{ReAct}$.\n\n\n**1. Near-OOD experiment of CIFAR10 versus CIFAR100**\n\nThanks for the advice on the near-OOD evaluation. We agree that the near-OOD case where the ID and OOD are similar is indeed challenging to all *post hoc* methods because no prior knowledge is given. \n\nWe have added a standard near-OOD experiment of CIFAR10 versus CIFAR100 in Sec. B.4 of the revised supplementary material, which is the same near-OOD benchmark as in [1]. Here we attach the result for the reviewer's convenience.\n\n|Method | ID: CIFAR10 & OOD: CIFAR100 |\tID: CIFAR100 & OOD: CIFAR10|\n|:-:|:-:|:-:|\n|MSP |82.07/**78.27** |\t86.86/70.54|\n|ODIN |\t76.96/77.79 |\t86.15/72.13|\n|Energy|\t76.45/77.82 |\t86.20/71.99|\n|ReAct|\t79.48/71.80 |\t88.41/69.86|\n|GradNorm|\t84.45/52.17 |\t92.78/52.19|\n|RankFeat|\t**75.10**/78.02 |\t**82.63**/**74.35**|\n\nThe above Table reports the average FPR95 ($\\downarrow$) / AUROC ($\\uparrow$). As can be observed, our $\\texttt{RankFeat}$ still has an advantage over other baselines in most metrics. ***This demonstrates that in the near-OOD detection case, the novel observation holds and our method still works***.\n\n>[1] A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection. ICML Workshop 2021\n___\n\nThanks again and it is more than welcome to post any further comments!\n", " Why does the feature matrix tend to be less informative for the unseen OOD data?\n\nConsider the near OOD detection (A Simple Fix to Mahalanobis Distance for Improving Near-OOD Detection), the ID and OOD data may have overlap or be similar.\n\nIn the near OOD detection case, could you guarantee this?\n\nI hope more experiments on the near OOD can be conducted to prove this.\n\n", " We thank $\\color{green}{Reviewer\\ Ft9S}\\ (R3)$ for the instant reply and thoughtful comments. We respond to the questions point by point as follows.\n\n___\n\n**1. OOD Still Involves a Larger $\\mathbf{s_{1}}$ on CIFAR10 and MNIST**\n\nThanks for the insightful advice! We can still observe a clear gap in $\\mathbf{s_{1}}$ of OOD and ID data on CIFAR10 and MNIST. Some statistics are reported below:\n- For CIFAR10 as ID and MNIST as OOD, the mean $\\mathbf{s_{1}}$ of ID is 55.32, and the mean $\\mathbf{s_{1}}$ of OOD is **94.69**.\n- For MNIST as ID and CIFAR10 as OOD, the mean $\\mathbf{s_{1}}$ of ID is 34.74, and the mean $\\mathbf{s_{1}}$ of OOD is **79.12**.\n\n***We think that the observation holds in general because intuitively models trained on the ID training set naturally tend to be more informative for the similar ID validation set***. Nonetheless, we may agree that the performance improvements on smaller datasets might not be as significant as those on ImageNet due to the low resolution and fewer classes.\n\n\n**2. Models Are Trained From Scratch on CIFAR10 versus CIFAR100 and One-class CIFAR**\n\nThanks for the detailed comment. We agree that if we use CIFAR100 as OOD, fine-tuning an ImageNet pre-trained model is not fair. However, we would like to clarify that ***for the newly added experiment in the rebuttal phase (CIFAR10 versus CIFAR100, and one-class CIFAR), the CIFAR models are all trained from scratch***. We only fine-tune the model in the experiment of Sec. B.3. For Sec. B.3 where the OOD benchmark does not have overlapping categories with ImageNet, fine-tuning a pre-trained model is still fair and we do so for better classification accuracy. On the other hand, for other CIFAR experiments (Sec. B.4 and Sec. B.5) where CIFAR10 or CIFAR100 is used as OOD, we train the models from scratch for a fair comparison. We have explicitly added this explanation in the revised Sec. B.4 of the supplementary material.\n\n**3. Formal Theorem and Proof of Manchenko-Pastur Law**\n\nThanks for the suggestion on making the paper more self-contained! In Sec. F of the revised supplementary material, we have added \na more formal and rigorous theorem of Manchenko-Pastur Law as well as a brief proof.\n\n**4. Notations Are Reduced to Sample-Wise**\n\nThanks for the good advice on easing the understanding and improving the readability! Now we realized that we even do not need to introduce the batch dimension since our method is applied sample-wisely. In the revised method section, the notations have been corrected to a single sample instead of batched samples.\n\n___\n\nThanks again and it is more than welcome to post any comments!", " We thank $\\color{brown}{Reviewer\\ SMeo}\\ (R4)$ for the instant reply and constructive suggestions. Below we address the concerns in detail.\n\n___\n\n**1. Revision of Theoretical Part**\n\nRegarding the revision of the theoretical part of Sec. 3, we try to make it more clear that the aim of our bound is to give insights. Specifically, we did:\n\n- We avoid deterministic tone when analyzing the impact of our upper bound. Instead, we use milder phrases like *'is likely to'* and *'would'*. The exemplary usages can be found at line109, line132, and line142 of the revised paper.\n- After we introduce our bound analysis, we immediately emphasize that ***“Notice that our bound analysis strives to improve the understanding of OOD methods from new perspectives instead of giving a strict guarantee of the score”*** at line134 of the revised paper. Then we present one use case of using bound analysis to explain the shrinkage and skewness of score distributions.\n\nWe hope that these revisions can give the impression that our bound could give insights to a better understanding of our method.\n\n\n**2. Why OOD Feature Has a Larger $\\mathbf{s_{1}}$**\n\nThanks for the insightful advice! This behavior can be explained intuitively. \n\n***Since the model is well-trained on the training set of ID data, the feature matrix is likely to be more informative when the model is fed with a similar validation set of ID data. On the contrary, the feature matrix tends to be less informative for the unseen OOD data***.\n\nThe informativeness is directly reflected by the Eigen spectrum of Fig. 2 of the supplementary material: *an isolated larger dominant eigenvalue usually implies that the matrix is less informative*. This can be better understood by considering applying PCA to the feature matrix. Suppose that we are using PCA to reduce the dimension of ID and OOD features to 1. The amount of retained information can be measured by explained variance (%). The metric is defined as $\\sum_{i=0}^{k}\\mathbf{s_{i}}^2/\\sum_{j=0}^{n}\\mathbf{s_{j}}^2$ where $k$ denotes the projected dimension and $n$ denotes the total dimension. It measures the portion of variance that the projected data could account for. We compute the average explained variance of all datasets and present the result below:\n\n|Dataset |\tImageNet-1k |\tiNaturalist | SUN | Places | Textures|\n|:--|:-:|:-:|:-:|:-:|:-:|\n|Explained Variance (%) |\t28.57 |\t38.74 |\t35.79 |\t35.17 |\t42.21|\n\nAs can be seen above, all the OOD datasets have a larger explained variance ratio than the ID dataset. *That being said, to retain the same amount of information, we need fewer dimensions for the projection of OOD features. This indicates that the information of the OOD feature is easier to be captured and the OOD feature matrix is thus less informative*. \n\nFor a detailed explanation and analysis, please refer to Sec. E of the revised supplementary material. \n___\n\nThanks again and it is more than welcome to post any comments!", " I sincerely appreciate the detailed replies of the authors.\n\nBut I still have some major concerns unaddressed, and also minor ones. Particularly, after reading the review of Reviewer dq6u on the experiment fairness, it gives me some doubt. Please address the following issues if possible.\n\nMajor ones:\n\n1. **The core claim that OOD involves larger $s_1$ singular values is still questionable.** \n * (a) Currently, in Fig. 2 in supplementary, you provided variation of OOD but not of IND.\n * (b) I'd like to specifically question the following. Consider a ResNet18 trained on MNIST (IND) from scratch under the standard supervised scheme. Would CIFAR10/LSUN/SVHN as OOD involve larger $s_1$ singular values?\n * (c) Also, in the same manner, consider ResNet18 trained on CIFAR10 from scratch, and take MNIST/LSUN/SVHN as OOD. Would it involve the same trend? For this, the authors do not have to upload additional figures or tables; **verbally confirming this would be sufficient for me**.\n\n2. **The experiment on CIFAR10 is not fair.** \n * (a) Most of OOD detection methods (including the ones mentioned by Reviewer dq6u) train on CIFAR10 from scratch. **For fair comparison, the authors must use a model trained on CIFAR10 only.** If a model is pre-trained on ImageNet and fine-tunned on CIFAR10, then CIFAR100 is not OOD since the model already saw the classes of CIFAR100 during one of the training stages. \n * (b) Regarding this, are the models reported in Sec. B pre-trained on ImageNet-1K? (In the Table 3 caption of supplementary, it says that the model is trained on CIFAR100. But in the text (line 27), it says that the model is pretrained on ImageNet-1K. This is confusing.)\n * (c) Also, to be honest, there are many CIFAR10 trained supervised models on GitHub. I assume the authors can directly apply their proposed method to this already trained models.\n\nMinor ones:\n\n3. The presentation of theory in Sec. 3 is still not rigorous.\n * (a) Your high-level explanation is good and sufficient. My concern is not this but its rigor and self-containment. To fully understand the theory, I had to look into [40,49]. Also, to clearly see the assumptions of the theoretical implications, I had to *mine* them myself. \n * (b) It would be really great if the authors can provide formal, clear assumptions and implications using rigorous notation in the supplementary, maybe in Theorem-Proof format. \n\nOptional ones:\n\n4. Notation. Now I clearly understand the exact algorithm applied in this paper. But I am still wondering if the authors have to consider 'batch' of samples rather than a single sample. \n\nTo increase the rate to higer than borderline accept, please address the issues 1 and 2 above. To increase it even more, please address the issue 3 and possibly 4.\n\nI see that the method is very effective at large-scale train dataset (ImageNet). At this stage, however, I cannot really give more than borderline accepct since I still cannot confirm the generality of the major claim (larger $s_1$ over OOD); the major claim is evidneced only with ImageNet IND, a generic object dataset, but IND can be diverse and something different such as MNIST or CIFAR10 (low-resolution and a small number of classes).\n\nI won't degrade my rate although the authors do not reply to any of the above issues.", " Dear Authors,\n\nI have read your response.\n\nTo response 4, I am interesting in how you revise your theoretical part. I except your revision.\n\nCould you give a detailed explainations to response why the first singular value of the OOD feature always tends to be much larger than that of ID feature?\n\nIf you answer these two issues, I will increase your score to 7.\n\nBest Regards,", " We sincerely thank all the reviewers for their careful reviews and constructive suggestions, which indeed helps to shape the paper better. &#x1F600; &#x1F600; &#x1F600; \n\n___\n\n\nWe appreciate the reviewers' common sentiment that our work is \n**well-motivated** ($\\color{red}{R1}$, $\\color{brown}{R4}$), **novel** ($\\color{red}{R1}$, $\\color{green}{R3}$), **simple and intuitive** ($\\color{red}{R1}$, $\\color{brown}{R4}$), **written clearly and organized well** ($\\color{red}{R1}$, $\\color{brown}{R4}$), and has **rich experiments that show strong performance improvements and good application diversity** ($\\color{green}{R3}$, $\\color{brown}{R4}$). We are also glad that $\\color{blue}{R2}$ thinks our method is **interesting**, and $\\color{red}{R1}$ finds that our work has **a good alignment of theoretical effect and empirical results**. \n\nThe paper has been significantly revised to address the reviewers' concerns and to absorb the reviewers' suggestions. The changes have been highlighted in $\\color{red}{red}$ in both the main paper and the supplementary material. We have summarized the changes as follows:\n\n**1. More visualization of Fig. 1(a) ($\\color{red}{R1}$, $\\color{green}{R3}$, $\\color{brown}{R4}$)**\n\nWe have added the top-5 singular value distributions of every dataset to Sec. D.1 of the revised supplementary material. The novel observation consistently holds: *the dominant singular value of OOD features always tends to be significantly larger than that of ID features on every OOD dataset* The caption of Fig. 1 is also updated with specific dataset information.\n\n**2. Explanation of how fusion helps to improve performance ($\\color{red}{R1}$)**\n\nWe discussed how the fusion improves the score to the revised method section (line95)\n\n**3. Explanation of how RankFeat makes the score distributions squeezed and skewed ($\\color{red}{R1}$)**\n\nWe add the related explanation and discussion to line134 of the revised theoretical analysis section.\n\n**4. More evaluation on other benchmarks ($\\color{blue}{R2}$, $\\color{brown}{R4}$)**\n\nThe additional experiments of ***comparison against MOS and KL Matching***, ***of Species benchmark***, ***of CIFAR10 versus CIFAR100***, and ***of one-class CIFAR10 and CIFAR100*** have been added to the Sec. B of the supplementary material. We might move the experiments of Species and of comparison against MOS and KL Matching to the main paper when we are allowed for an additional content page. \n\n**5. Clarification that our method is post hoc ($\\color{blue}{R2}$)**\n\nIn the revised Sec B.3 of the supplementary material, we have clarified that our method is *post hoc*, and the implementation details are reported to describe how we obtain CIFAR models.\n\n**6. Notation issues and how SVD is applied ($\\color{green}{R3}$)**\n\nWe have corrected the notation issues throughout the paper and have explained how SVD is applied detailedly in the revised method section. The pseudo-code is also attached to Sec. A of the supplementary material.\n\n**7. PCA-based explanation of why OOD has a larger dominant singular value ($\\color{green}{R3}$)**\n\nThe PCA-based explanation has been added to Sec. E of the revised supplementary material. We also briefly discussed this point in the revised introduction to show the intuition behind our observation.\n\n**8. Formal Theorem and Proof ($\\color{green}{R3}$)**\n\nIn the revised paper, we reformulate the theoretical analysis into a more formal proposition-proof format. Also, we have added the formal and rigorous theorem of MP law as well as the proof to Sec. F of the revised supplementary.\n\n**9. Explanation of why we use Energy score ($\\color{brown}{R4}$)**\n\nWe explained why we use Energy score as the base function at line120 of the revised theoretical analysis section. \n\n**10. Milder Theoretical Analysis and Clarification about Assumption ($\\color{brown}{R4}$)**\n\nWe have revised Sec. 3 of the paper to give the impression that our bound analysis strives to give insights instead of giving strong score guarantee. Also, we have explicitly emphasized our assumption in the revised Abstract and Introduction.\n\n___\n\n*For brevity, we refer to reviewers $\\color{red}{kEL5}$ as $\\color{red}{R1}$, $\\color{blue}{dq6u}$ as $\\color{blue}{R2}$, $\\color{green}{Ft9S}$ as $\\color{green}{R3}$, and $\\color{brown}{SMeo}$ as $\\color{brown}{R4}$ respectively.", " We thank $\\color{brown}{Reviewer\\ SMeo\\ (R4)}$ for the encouraging feedback and the constructive suggestions! The response to the concerns are as follows:\n\n___\n\n**1. Detailed Explanation of Fig. 1(b)**\n\nThanks for the careful review! For Fig. 1(b), the x-axis is the sample index and the y-axis denotes the index of the predicted class in the range from $1$ to $1,000$ (ImageNet-1k has $1,000$ categories). The orange points represent the original class prediction, while the blue points are the class prediction when our $\\texttt{RankFeat}$ is applied. For OOD data, the orange and blue points hardly overlap, which indicates that our RankFeat largely perturbs the decision. By contrast, many decisions of ID data stay consistent, which is reflected by the heavily-overlapped straight lines. *The phenomenon could imply that the OOD decisions are more dependent on the rank-1 feature matrix*.\n\n**2. More Experiments of Fig. 1(a)**\n\nThanks for the constructive suggestion. ***The experiment in Fig. 1 is based on SUN, but the observation holds for every OOD dataset***. In Sec. D.1 of the revised supplementary material, we have added the top-5 singular value distribution of all the OOD datasets. The observation is consistent on every OOD dataset: the first singular value of the OOD feature always tends to be much larger than that of ID feature.\n\n**3. Why We Use Energy Score**\n\nThanks for the insightful advice! We choose Energy score because it is both empirically and theoretically sound. Empirically, it achieves better performance than other basic score functions like MSP, ODIN, and Mahalanobis distance (see Table 2 of the paper). Theoretically, it aligns with the probability density of the input: the energies of samples are associated with the likelihood of occurrence of data. We have added the reason to line120 (Eq. (9)) of the revised paper. \n\nThis can be explained from our upper bound analysis. The basis of the theory is the tight bound $\\max(\\mathbf{y}') < \\log \\sum \\exp(\\mathbf{y}') < \\max(\\mathbf{y}') + \\log(Q)$, which is brought by the Log-Sum-Exp trick. *This is an inherent property of Energy score. If we use other score functions, the inequality and subsequent bound analysis might not hold*. \n\n**4. Bound Analysis is to Give Insight**\n\nThanks for the thoughtful comment! ***We would like to clarify that our upper bound analysis strives to give insights into the working mechanism of RankFeat instead of giving a strict guarantee of the score***. Considering the diversity of model architectures and data distributions, it might be unlikely to give a strong and generic theoretical guarantee. *Our bound analysis strives to improve the understanding of OOD methods from new perspectives*. We have shown several use cases of our bound analysis:\n- The impact of removing the rank-1 matrix can be analyzed concretely by studying the upper bound (see line129).\n- Relying on our bound analysis, we can build a theoretical connection between our RankFeat and ReAct (see line157).\n- The bound analysis can be used to explain the shrinkage and skew of score distributions in Fig. 2 (see line134). \n\n**5. Performance of Removing $\\mathbf{s_{i}}\\mathbf{u_{i}}\\mathbf{v_{i}}^{T}$ for $i>1$**\n\nThanks for the insightful question. We did one experiment of removing $\\mathbf{s_{i}}\\mathbf{u_{i}}\\mathbf{v_{i}}^{T}$ for $i=2$ and $i=3$ , and present the results in the format of FPR95 ($\\downarrow$) / AUROC ($\\uparrow$) below:\n\n|Method|iNaturalist|SUN|Places|Textures|\n|-|:-:|:-:|:-:|:-:|\n|Energy|64.91/88.48|65.33/85.32|73.02/81.37|80.87/75.79|71.03/82.74|\n|Removing $\\mathbf{s_{2}}\\mathbf{u_{2}}\\mathbf{v_{2}}^{T}$|62.12/89.28|65.84/85.23|73.33/80.88|80.41/76.45|70.42/82.96|\n|Removing $\\mathbf{s_{3}}\\mathbf{u_{3}}\\mathbf{v_{3}}^{T}$|63.51/88.99|65.05/85.47|72.64/81.37|79.47/76.92|70.17/83.19|\n\nAs can be seen above, the performance only gets marginal improvements over Energy score. *It meets our expectation as the other singular values of ID and OOD features are not that different*.\n\n___\n\nThanks again and it is more than welcome to post any further comments.", " ___\n\n**6. Divergence to Random Matrices Measures Informativeness of Rank-1 Feature**\n\nThanks for the thoughtful comment! Actually, the divergence criterion to random matrices is a measure of the informativeness of the rank-1 feature. When the rank-1 matrix is removed, the residual OOD feature matrices are much closer to random matrices in statistics than the residual ID feature. ***This indicates that the rank-1 feature of the OOD feature might convey more information, which can partly explain the working mechanism***.\n\n___\n\nThanks again and it is more than welcome to post any further comments.", " We thank $\\color{green}{ Reviewer\\ Ft9S\\ (R3)} $ for the careful review and the positive feedback! Below we address comments in detail:\n\n___\n\n**1. RankFeat (SVD) is applied to each individual feature within the mini-batch.**\n\n*We would like to clarify that the SVD is applied on each individual sample matrix in the mini-batch*. Given a mini-batch of ID/OOD data $\\mathbf{X}{\\in}\\mathbb{R}^{B{\\times}C{\\times}HW}$ where $B$ denotes the batch size of the mini-batch, our RankFeat first performs SVD on each individual sample/matrix of shape $C{\\times}HW$ within the mini-batch. The decomposition is defined as $\\mathbf{U}\\mathbf{S}\\mathbf{V}^{T}=\\mathbf{X}$ where $\\mathbf{U}{\\in}\\mathbb{R}^{B{\\times}C{\\times}C}$ and $\\mathbf{V}{\\in}\\mathbb{R}^{B{\\times}HW{\\times}HW}$ are batched left and right singular vector matrices, respectively. The $B$ at line71 denotes the batch size, and the $\\mathbf{X}$ at line107 can be either mini-batch matrices or a single feature map. *All the theoretical and empirical results hold for both a single sample and batched samples*. \n\nWe have explained the notations and how SVD is applied more detailedly in the revised method section of the paper. Moreover, we also present the Pytorch-like pseudo code in Sec. A of the revised supplementary material. For the convenience of the reviewer, we also attach the code here:\n\n```python\nfeat = model.features(inputs)\nB, C, H, W = feat.size()\nfeat = feat.view(B, C, H * W)\nu,s,vt = torch.linalg.svd(feat)\nfeat = feat - s[:,0:1].unsqueeze(2)*u[:,:,0:1].bmm(vt[:,0:1,:])\nfeat = feat.view(B,C,H,W)\nlogits = model.classifier(feat)\nscore = torch.logsumexp(logits, dim=1)\n```\n\n**2. Dataset in Fig. 1(a) and More Visualization**\n\n***The dataset of Fig. 1(a) is based on SUN, but the observation consistently holds for every OOD dataset***. In Sec. D.1 of the revised supplementary material, we have added the top-5 singular value distributions of all the OOD datasets. the first singular value of OOD feature tends to be much larger than that of ID feature on every OOD dataset. The caption of Fig. 1 of the paper is also updated with the specific dataset. \n\n**3. Small $\\mathbf{x}$ or Capital $\\mathbf{X}$ in Eq. (4)**\n\nThanks for pointing out this issue. In the last version of the paper, We want to emphasize that our RankFeat is applied on the *intermediate feature matrices* so we use the capital $\\mathbf{X}$. Now we realized that it might be inappropriate and would cause misunderstandings. We have changed the notations to $\\mathbf{x}$ in the revised paper where $\\mathbf{x}$ denotes the input data. \n\n**4. Logit $\\mathbf{y}'$ in Eq. (4)**\n\nThe $\\mathbf{y}'$ is a mini-batch (set) of logits in the shape of $B{\\times}Q$ where $B$ denotes the batch size and $Q$ denotes the number of classes. The summation is performed on the class dimension as $\\sum_{i=1}^{Q} \\exp(\\mathbf{y}'_{i})$.\n\n**5. Why OOD Feature Has a Larger $\\mathbf{s_{1}}$**\n\nThanks for the insightful comment! We can explain this behavior intuitively. Since the model is well-trained on the training set of ID data, the feature matrix is likely to be more informative when the model is fed with a similar validation set of ID data. On the contrary, the feature matrix tends to be less informative for the unseen OOD data. \n\nThe informativeness is reflected by the Eigen spectrum: an isolated larger dominant eigenvalue usually implies that the matrix is less informative. This can also be understood by considering applying PCA to the feature matrix. Suppose that we are using PCA to reduce the dimension of ID and OOD feature to $1$. The amount of retained information can be measured by explained variance (\\%). The metric is defined as $\\sum_{i=0}^{k}\\mathbf{s_{i}}^2/\\sum_{j=0}^{n}\\mathbf{s_{j}}^2$ where $k$ denotes the projected dimension and $n$ denotes the total dimension. It measures the portion of variance that the projected data could account for. We compute the average explained variance of all datasets and present the result below: \n\n|Dataset|ImageNet-1k|iNaturalist|SUN|Places|Textures|\n|-|:-:|:-:|:-:|:-:|:-:|\n|Explained Variance (\\%)| 28.57 | 38.74 | 35.79 | 35.17 | 42.21|\n\nAs can be seen above, all the OOD datasets have a larger explained variance ratio than the ID dataset. ***That being said, to retain the same amount of information, we need fewer dimensions for the projection of OOD features. This indicates that the information of the OOD feature is easier to be captured and the OOD feature matrix is thus less informative.*** We have added this PCA-based explanation to Sec. E of the revised supplementary material. Despite this explanation, we agree that this problem is still worth further research in future work. \n\n___\n\n", " ___\n\n**5. Experiment of CIFAR10 versus CIFAR100**\n\nThanks for the interesting advice! We evaluate the *post hoc* methods in the setting of CIFAR10 versus CIFAR100, *i.e.,* CIFAR10 as the ID set with CIFAR100 as the OOD set and vice versa. The Table below presents the results in the format of FPR95 ($\\downarrow$) / AUROC ($\\uparrow$). \n\n|Method (on ResNet-56)|ID: CIFAR10 \\& OOD: CIFAR100|ID: CIFAR100 \\& OOD: CIFAR10|\n|-|:-:|:-:|\n|MSP | 82.07/**78.27** | 86.86/70.54 |\n|ODIN| 76.96/77.79 | 86.15/72.13 | \n|Energy| 76.45/77.82 | 86.20/71.99 |\n|ReAct| 79.48/71.80 | 88.41/69.86 |\n|GradNorm| 84.45/52.17 | 92.78/52.19 |\n|**RankFeat**| **75.10**/78.02 | **82.63**/**74.35** |\n\n\nOur $\\texttt{RankFeat}$ slightly outperforms other baselines. Interestingly, all the *post hoc* approaches have similar performance; none of them has an FPR95 score lower than $70\\\\%$. This might indicate that the patterns learned on CIFAR10 and CIFAR100 are quite similar, which is too challenging for *post hoc* methods to distinguish. *We conjecture that in this case *post hoc* methods might not work well, and additional training might be needed to better tell apart CIFAR10 and CIFAR100 samples*. This experiment has been added to Sec. B.4 of the revised supplementary material.\n\n**6. Experiment on One-class CIFAR10 and CIFAR100**\n\nThanks for the constructive suggestion. We also conduct two experiments on one-class CIFAR10 and one-class CIFAR100. For CIFAR100, we follow [4] and select $20$ super-classes. The Table below presents the average AUROC ($\\uparrow$).\n\n|Method (on ResNet-56)|CIFAR10|CIFAR100|\n|-|:-:|:-:|\n|MSP | 56.87 | 66.19 |\n|Energy | 77.76 | 73.42 |\n|ReAct | 85.82 | 79.58 |\n|**RankFeat** | **88.58** | **82.43** |\n\nOur RankFeat outperforms other baselines on the average result and on most sub-sets. For the detailed performance of each class on CIFAR10, please defer to the revised Sec. B.4 of the supplementary material.\n\n**7. Experiment on Species**\n\nThanks for the constructive suggestion! Species [2] is actually a good OOD benchmark since it is dedicated for ImageNet-1k and ImageNet-21k as ID sets. Here we select four sub-sets of Species (Protozoa, Microorganisms, Plants, and Mollusks) and report the average results on ImageNet-1k below. The best three results are highlighted with $\\color{red}{red}$, $\\color{blue}{blue}$, and $\\color{cyan}{cyan}.$\n\n|Method|Average FPR95 ($\\downarrow$)| Average AUROC ($\\uparrow$)|\n|-|:-:|:-:|\n|MSP | 73.79 | 81.44 |\n|ODIN | 70.96 | 84.14 |\n|Energy | 70.88 |84.03 |\n|ReAct | 67.02 | $\\color{cyan}{85.06}$ |\n| **RankFeat (Block 4)**| $\\color{blue}{58.12}$ |74.19 |\n| **RankFeat (Block 3)**| $\\color{cyan}{59.02}$ |$\\color{blue}{87.58}$ |\n| **RankFeat (Block 3+4)**| $\\color{red}{51.11}$|$\\color{red}{88.37}$ |\n\nOur $\\texttt{RankFeat}$ achieves the best performance, outperforming other methods by **15.91\\%** in the average FPR95 and by **3.31\\%** in the average AUROC. We have added this experiment and the detailed results on each sub-set to Sec B.2 of the revised supplementary material. \n\n**8. Comparison against ReAct on CIFAR**\n\nWe agree that on the CIFAR benchmark the performance gap of RankFeat over ReAct is not that significant in terms of AUROC compared to that on the ImageNet-1k benchmark. *However, our method outperforms RankFeat in FPR95 by **10\\%** on RepVGG and by **20\\%** on ResNet, which is substantially significant and cannot be neglected*. Actually, as pointed out by $\\color{red}{ Reviewer\\ kEL5\\ (R1)} $ and explained in the revised paper (line134), our method naturally performs better in terms of FPR95 than AUROC due to shrinkage and skew of the distributions. \n\n>[1] Mos: Towards scaling out-of-distribution detection for large semantic space. CVPR 2021 \n>\n>[2] Scaling Out-of-Distribution Detection for Real-World Settings. ICML 2022\n>\n>[3] Panda: Adapting pretrained features for anomaly detection and segmentation. CVPR 2021\n>\n>[4] Csi: Novelty detection via contrastive learning on distributionally shifted instances. NeurIPS 2020\n>\n>[5] Energy-based Out-of-distribution Detection. NeurIPS 2020\n>\n>[6] A baseline for detecting misclassified and out-of-distribution examples in neural networks. ICLR 2017\n>\n>[7] ReAct: Out-of-distribution Detection With Rectified Activations. NeurIPS 2021\n\n___\n\nThanks again and it is more than welcome to post any further comments.", " We thank $\\color{blue}{Reviewer\\ dq6u\\ (R2)} $ for the constructive suggestions and insightful comments! In the following, we respond to the concerns in detail.\n\n____\n\n**1. Misunderstanding about Fine-tuning on CIFAR**\n\nWe would like to clarify that the aim of the fine-tuning process on CIFAR is to obtain a well-trained classifier. Since there are no widely used public models pre-trained on CIFAR, we load models pre-trained on ImageNet-1k and fine-tune them on CIFAR, which is a standard routine to get CIFAR models. We report the implementation details in order to ensure a fair comparison and to facilitate reproducibility. ***Our method is indeed post hoc and is not involved in any training process***. We have updated the paragraph to clarify this point better in the revised supplementary material.\n\n**2. Our Method is Post-hoc and Evaluation is Conducted against Post-hoc Approaches**\n\nOur method as well as the baselines are all *post hoc* methods. Here '*post hoc*' means that the method does not need any extra training procedure and can be directly applied to a pre-trained model for inference. The extra training process like in [1,3,4] would leverage the prior knowledge of the training or validation set, which is somehow unfair to post hoc methods. *Therefore, approaches that need an extra training process are not considered in the evaluation of the original paper*. \n\n**3. Comparison with training-needed methods in MOS [1]**\n\nFor the baselines described in the benchmark [1], we compare most methods except for MOS [1] and KL Matching [2]. This is because MOS is not post hoc and needs extra training procedures before being applied to the classifier. For the same reason, PANDA [3] and CSI [4] need an extra training process and are not considered for comparison. As for KL Matching [2], it requires the labeled validation dataset and requires computing $k$ distributions for each class where $k$ denotes the class number. This is a bit unfair to post hoc baselines because these methods usually do not need any labeled validation set. Nonetheless, we note our proposed RankFeat still holds an advantage even against these approaches. The Table below presents the comparison on the ImageNet-1k benchmark:\n\n|Methods |Post hoc? |Free of Val. Set?|Average FPR95 ($\\downarrow$)|Average AUROC ($\\uparrow$)|\n|-----------|:-----------:|:-----------------:|:-----------------------------------:|:---------------------------------:|\n|RankFeat| $&#10004;$ | $&#10004;$ | **36.80** | **92.15** |\n|KL Matching [2] | $&#10004;$ | x | 54.30 | 80.82|\n|MOS [1] | x | $&#10004;$ | 39.97 | 90.11| \n\nOur RankFeat achieves the best performance without any extra training or validation set. We have added this comparison to Sec. B.1 of the revised supplementary material.\n\n**4. ImageNet-1k cannot be Simply Categorized As a Far-OOD Benchmark**\n\nWe do not agree that the ImageNet-1k benchmark can be categorized as a Far-OOD benchmark. The ImageNet-1k is more challenging than traditional CIFAR benchmarks in terms of complexity and diversity. The ImageNet-1k validation set consists of $50,000$ high-resolution images in $1,000$ classes, while CIFAR validation set only has $10,000$ low-resolution ($32\\times32$) images in $10$ or $100$ classes, not to mention the more realistic and complex image contents of ImageNet-1k. As for the four OOD datasets (iNaturalist, SUN, Places, and Textures), three of them (iNaturalist, SUN, and Places) have similar scene and object images with ImageNet-1k, which makes it hard to distinguish the ID and OOD samples. ***All of these indicate that the ImageNet-1k benchmark is not a Far-OOD benchmark***. \n\n|Energy Score| CIFAR10 | ImageNet-1k |\n|-----------|:-----------:|:-----------------:|\n|Average FPR95 ($\\downarrow$)| **35.60** | 58.41 |\n|Average AUROC ($\\uparrow$) | **93.57** | 86.17 |\n\n|MSP Score| CIFAR10 | ImageNet-1k |\n|-----------|:-----------:|:-----------------:|\n|Average FPR95 ($\\downarrow$)| **56.71** | 66.95 |\n|Average AUROC ($\\uparrow$) | **91.17** | 81.99 |\n\nOne evidence to support this opinion is that many OOD methods that achieve good performance on the CIFAR benchmark have a large performance degradation on the ImageNet-1k benchmark. For example, as shown in ReAct [7], the performance of Energy score [5] and MSP score [6] on ImageNet-1k is inferior to that on CIFAR (see the Table above). \n____", " ___\n\n**5. How RankFeat Helps the Distribution Get Squeezed and Biased**\n\nThanks for the insightful comment! As revealed in Fig. 2 of the paper, the score distributions of ID and OOD data are indeed more squeezed and biased (skewed). In particular, the OOD distribution becomes more skewed than the ID data. \n\nThis can be understood from the analysis of our upper bound $\\texttt{RankFeat}(\\mathbf{x}) <\\frac{1}{HW} \\Big(\\sum_{i=1}^{N} \\mathbf{s_i}- \\mathbf{s_{1}}\\Big)||\\mathbf{W}||_ \\infty + ||\\mathbf{b}||_ \\infty + \\log(Q)$. The subtraction of $\\mathbf{s_{1}}||\\mathbf{W}||_ \\infty $ would largely reduce the numerical range of both ID and OOD scores, which could squeeze the score distributions. Since the dominant singular value $\\mathbf{s_{1}}$ contributes the most to the score, removing $\\mathbf{s_{1}}||\\mathbf{W}||_ \\infty$ is likely to make many samples have similar scores. This would concentrate samples in a small region and further skew the distribution. Consider that the OOD feature tends to have a much larger $\\mathbf{s_{1}}$. This would have a greater impact on the OOD data and skew the OOD score distribution more. We have added the related discussion in the theoretical analysis of the revised paper. \n\n___\n\nThanks again and it is more than welcome to post any further comments.\n", " We thank $\\color{red}{ Reviewer\\ kEL5\\ (R1)} $ for the encouraging feedback and the constructive comments! In the following, we respond to the concerns point by point.\n\n_____\n\n**1. Bound and Sum of Singular Values**\n\nThanks for the careful review and insightful comment. We agree that when $\\mathbf{s_{1}}$ gets smaller, the upper bound will be larger. However, this does not mean that the bound will loosen; the tightness of our bound is only determined by $||\\mathbf{u_{i}}||_ \\infty$, $||\\mathbf{v_{i}}||_ \\infty$, and the triangular inequality of the vector norm sum. Throughout all the experiments, we do not encounter a case where the first singular value $\\mathbf{s_{1}}$ is greater than the sum of other ones.\n\n**2. Dataset used for Fig. 1**\n\n***The experiment in Fig. 1 is based on SUN, but the observation holds for every OOD dataset***. In Sec. D.1 of the revised supplementary material, we have added the top-5 singular value distributions of all the OOD datasets. The observation is consistent on every OOD dataset: the first singular value of OOD feature always tends to be much larger than that of ID feature. The caption of Fig. 1 in the paper is also updated with the specific dataset.\n\n**3. Convergence of SVD and PI**\n\nThanks for the insightful comment. For the SVD, the convergence does not depend on the singular value and can be guaranteed. For the Power Iteration (PI), as pointed out by $\\color{red}{ Reviewer\\ kEL5} $, the convergence speed is indeed determined by the adjacent singular value ratio. Since our method only computes the dominant singular value, the convergence speed is thus limited by $(\\mathbf{s_{1}}/\\mathbf{s_{2}})^{n}$ where $n$ denotes iteration times. The larger the ratio is, the faster the convergence speed would be. In the extreme case when the first two eigenvalues are exactly identical ($\\mathbf{s_{1}}=\\mathbf{s_{2}}$), the PI would fail to converge.\n\n\nWe can measure the convergence speed by computing the statistics of the singular value ratio. The Table below presents the evaluation results of $(\\mathbf{s_{1}}/\\mathbf{s_{2}})$ on each dataset:\n\n| Dataset | ImageNet-1k | iNaturalist | SUN | Places | Textures |\n| - | :-: | :-: | :-: |:-: |:-: |\n| Max | 4.09 |5.07 | 4.11 | 4.19 | 7.33 |\n| Min | 1.06 | 1.18 | 1.12 | 1.10 | 1.05 | \n| Mean | 1.54 | 2.08 | 1.87 | 1.78 | 2.44 | \n\nEven the minimum of the ratio is still larger than $1$. Supposing that we iterate $20$ times, the minimum convergence speed $1.05^{20}\\approx2.65$ is still reasonable. This is also reflected in Table 6 of the paper: the performance gap between PI and SVD is within $0.1\\\\%$ from 20 iterations on. ***This demonstrates that the PI can approximate the SVD well for any feature matrix in practice***. Throughout all the experiments, we do not encounter any non-convergence or instability issue of PI.\n\n**4. Results without Fusion and How the Fusion Helps**\n\nThanks for the constructive suggestion. Actually, the performance of each individual block without fusion is reported in both Table 2 and Table 3 of the paper. Here we attach the results of Table 2 for the convenience of explanation. The values are reported in FPR95 ($\\downarrow$) / AUROC ($\\uparrow$).\n\n| Dataset | iNaturalist | SUN | Places | Textures | Average|\n| -- | :----: | :----: | :----: | :----: | :----: |\n| Block 4 | 46.54/81.49 |**27.88**/92.18 | **38.26**/88.34 | 46.06/89.33 | 39.69/87.84 |\n| Block 3 | 49.61/91.42 |39.91/92.01 | 51.82/88.32 | 41.84/91.44 | 45.80/90.80 | \n| Block 3+4 | **41.31**/**91.91** |29.27/**94.07** | 39.34/**90.93** | **37.29**/**91.70** | **36.80**/**92.15** | \n\nAs can be observed above, Block 4 feature slightly outperforms Block 3 feature on SUN and Places, while Block 3 feature has an advantage on iNaturalist and Textures. This might stem from the fact that the intermediate features at different layers would focus on different semantic information. The decision cues for OOD detection are very likely to be different for Block 3 and Block 4 features. ***The fusion could leverage the distinguishable information of both features and achieves a good compromise for better performance***. We have added this explanation in the revised method section of the paper.\n\n_____\n\n\n", " The paper proposes a method to predict if a sample of in distribution or out of distiribution. The authors decomposes the features via SVD and remove the largest eigenvalue and its rank-1 matrix from the features. They show the theoretical effect of their method in the bound of their log probabilities. They surpassed the baseline methods in FPR and AUROC by 7-18%, and did an ablation study for the effect of higher ranks and other feature layers. Strengths:\nThe method is simple and intuitive, the results also align with intuitions and achieve high improvement over the current baselines. The authors supported and motivated their ideas well. for example, Figure 1 and 2 are good motivations and pictured well. The paper is written clearly and organized. \nThe ablation study for removing rank-1 vs including only rank-1 and rank-k (swiping k) cases is very helpful to answer initial questions on the reader's mind. \n\nWeaknesses:\nAlthough the complexity of power iterations is reasonable, they may converge very slowly if the eigenvalues have close values. -In the bound (equation 13), it looks like if s1 gets closer to the other eigenvalues, the bound seems to loosen more if the sum of other eigenvalues are smaller than the s1. Is it a case not encountered in the problems?\n\n- What is the dataset you used for the Figure 1?\n\n- Did you observe any problems with the convergence of SVD decomposition?\n\n- How are your results without the fusion of 3rd and 4th block? How does the fusion help?\n\n- The algorithm does better in terms of FPR compared with AUROC, this might suggest that the distribution gets squeezed and biased. How do you explain this? The authors did not foresee any negative impacts of their work.", " The authors present a new OOD detection method `RankFeat`, which removes the largest singular value and the associated singular\nvectors from high-level features extracted from a classifier pre-trained on a labeled dataset (e.g. ImageNet-1k) The presented method is interesting, but the evaluation is extremely limited and fails to position the performance of the proposed method in relation to all the OOD literature\n- The paper mainly evaluates on the dataset first proposed on [1]\n - This dataset is very new, few works use it for evaluation\n - This dataset is only a far-OOD dataset, i.e. an easy dataset where OOD samples are far from ID samples\n - I won't be convinced until a more through evaluation is done that includes near-OOD datasets, specifically\n - The standard one class vs the rest [2] is done in at least CIFAR10, and CIFAR100 (prefereably also ImageNet-30), as can be seen in e.g. [3]\n - The whole CIFAR10 vs CIFAR100 (and vice-versa)\n - It would be very interesting to show also evaluations that try to expose usefulness of pre-trained models for OOD \n - The Species dataset, proposed in [4]\n - One class SVHN, porposed in [5]\n- The paper compares only to a handful of other methods, many SotA methods in literature are ignored\n - Paper must compare to other works that tries to adapt pre-trained classifiers, e.g. PANDA [6]\n - Paper must compare to completely unsupervised methods, e.g. CSI [3]\n - Paper should explore the situation where ID dataset is polluted\n- How can the method be described as post-hoc, when authors needed to fine-tune the model for 100 epochs on CIFAR before evaluation on CIFAR ?\n- I find this strange, but why the authors doesn't compare to the method described in [1] (the original paper of the evaluation dataset) ?\n- CIFAR results in the appendix aren't convincing in superiority compared to ReAct\n\n\n[1] Mos: Towards scaling out-of-distribution detection for large semantic space. CVPR 2021\n\n[2] Systematic construction of anomaly detection benchmarks from real data. In KDD 2013\n\n[3] Csi: Novelty detection via contrastive learning on distributionally shifted instances. NeurIPS 2020\n\n[4] Scaling Out-of-Distribution Detection for Real-World Settings. ICML 2022\n\n[5] No Shifted Augmentations (NSA): compact distributions for robust self-supervised Anomaly Detection. arXiv 2022\n\n[6] Panda: Adapting pretrained features for anomaly detection and segmentation. CVPR 2021 All suggestions are in the weaknesses section N/A", " The paper claims that OOD and IND involve different largest singular value of feature map matrix. Based on its foundational claim, the authors propose a simple OOD detection score devised by subtracting the corresponding rank-1 matrix from (the feature maps) of a given (pretrained) network. [Strengths]\n\nGood performance. It reduces FPR95 quite significantly for large-scale OOD testing environments.\n\nNovel observation. To my best knowledge, this is the first paper to study OOD samples using the singular value of a feature (map) matrix. Particularly, according to the authors' claims, IND and OOD show different behaviors in terms of the largest singular value of feature map matrix.\n\nApplication Diversity. The proposed method can be applied to both ResNet and ViT based architectures.\n\n[Weaknesses]\n\n1. The paper does not provide precise notations for the proposed method in both main paper and supplementary. Particularly, it is very important to which matrix SVD is applied, but the paper is not clear on this point. (Namely, is it applied to a mini-batch of feature maps, the feature maps of whole train set, or a the reshaped feature map of a single sample? The singular value will be completely different depending on whether the shape of X is [B, CHW] or [C, HW].) Moreover, some notations (which are critical for understanding and implementing the method) are also not clear.\n\n2. Its foundational claim (the largest singular value is larger in OOD than in IND) is not extensively validated. This is validated in only one experiment given in Figure 1(a). I am wondering if this claim would still hold even if different datasets are used for IND and OOD.\n\n3. (minor) The paper does not give a convincing explanation of its foundational claim; namely, why OOD involves a larger singular value s_1 than IND? I saw the supplementary part for this, but the explanation is not so convincing.\n\n4. (minor) Some of the given theory is not rigorous. Particularly, the convergence criterion to a random matrix given in the second part of the theory is not clear.\n\n 1. Could you specify the datasets used for ID and OOD for Figure 1 in its caption if possible? \n2. (Critical) What is B in the line 71? Is it batch size or the number of all samples? Does it include OOD samples? \n3. (Critical) Shouldn't the capital X in Eq. (4) be small x? Can RankFeat be computed for a single test sample x? What is y'? I know it is logit, but is it a set of logits of multiple samples or the logit of a single sample? How is it summed? What is the index of the sum in Eq. (4)?\n4. (Critical) Overall, I don't precisely understand on which matrix exactly SVD is applied. Is it applied to the feature maps of training (or validation) set? Or is it applied to the feature map of a single sample? Is SVD computed only once and are u_1 v_1 s_1 fixed during whole inference? Or do you have to re-compute u_1 v_1 s_1 every time you make inference on a different test sample? This is very critical for accepting the paper. In fact, X with shape [B, C, HW] is not a matrix (2d tensor) but a 3d tensor. Do the authors use torch.svd on the matrix shaped by [B, C, HW]? \n5. Doex X in line 107 have to be a batch of feature maps? Or the theory would still hold even if X is the feature map of a single sample?\n\n\n The limitations are given in the above 'weaknesses' and 'questions'. Please address all my questions and the second and fourth points of the weaknesses. In particular, please focus on clarifying your method, exactly which matrix SVD is applied to, and when SVD is applied.\n\nI am quite positive with the paper except for the notation issue and the second point of the 'weaknesses'. I personally think scalar quantities should not be bold-faced; it is quite confusing. ", " This paper aims to address OOD detection issue by proposing a novel method called RankFeat.\n\nBy observing the OOD feature matrix tends to have a significantly larger dominant singular value, the author believes that by removing the rank-1 feature, the over-confidence of OOD samples is mitigated, and consequently the ID and OOD data can be better distinguished.\n\nBased on the above idea, the propose RankFeat, which aims to removing the rank-1 matrix from the high-level feature.\n\nTheory has shown that it seems RankFeat achieves smaller energy score than ReAct.\n\nAdditionally, experiments have shown this method achieve a large improvement.\n\nLastly, ablation studies are conducted. Strengths:\n1. This method is easy and the idea is clear.\n2. The writing is good and organisation is also good.\n3. Experiments are rich. \n\nThe basic idea of this paper does give researchers a novel perspective to understand OOD detection. I also like this idea.\n\nWeakness:\n1. I still can not understand figure 1(b). Could you provide more detailed introduction?\n2. I am interesting in more datasets to conduct experiments in figure 1(a). \n3. According to Eq. 9, your method is based on an assumption that the energy-based score is effective. Do you have checked other score function to implement your idea? or do you have argued that energy-based score is the optimal for your method?\n4. The theory is not right The basic reason is that you cannot guarantee the bound in Eq 17 is the tightest bound, so you cannot use it to compare with your method's bound Eq 14. For example, a<1, b<2 cannot conclude that a<b. Here you have the same mistake.\n5. The theory is weak. Eq 14 has shown that RankFeat achieves small energy score . However, you omit a basic issue that why a small energy score is good for OOD detection. You should use theory to explain it; otherwise, I think your paper has some unmentioned assumptions. The basic idea of this paper does give researchers a novel perspective to understand OOD detection. I also like this idea. But I have many issues raised.\n\nIssues:\n(Major)1. In the real world applications, the OOD datasets can be changeable and diverse. Could you guarantee the observation in Figure 1(a) still holds? I would very, very much doubt this observation. I think you should conduct much more experiments to support the basic view. In fact, if you can give theory (allowed assumptions) or abundant experiments to support the basic view, I think this paper can be accepted by NeurIPS; otherwise, I may not accept it.\n\n(Major) 2. Experiments should be conducted to show why energy-based score is optimal for your method in Eq. 9.\n\n(Minor) 3. In line 222, I find you remove features from 1 to n. How about only removing features n?\n\n(Major) 4. The theory is over-claimed. Please revise it according to weakness 4 and 5.\n\nI think this paper can be accepted if the authors can address all my issues.\n\n\n\n In the real world applications, the OOD datasets can be changeable and diverse. Could you guarantee the observation in Figure 1(a) still holds? I would very, very much doubt this observation. I think you should conduct much more experiments to support the basic view. In fact, if you can give theory (allowed assumptions) or abundant experiments to support the basic view, I think this paper can be accepted by NeurIPS; otherwise, I may not accept it." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 3, 6, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 5, 4 ]

[ "x7_2T8TXlok", "x7_2T8TXlok", "x_vmhjBRqV", "zuzO1L_m7wUb", "l2-87TFn_8e", "xSGZwbU3-5P", "xSGZwbU3-5P", "iHXjiv6FtAZ", "GBrDV2W8Z7I", "FLOg7pb4sNi", "ROnG7qN0ULW", "2Rf56lZiEO0", "0NHxqESH6V", "S4oqMeOCT4W", "iuRXfVwv_Zc", "BU5XvfmQQX2", "vZrgtsuh1a5", "_h5Xbwpc4YF", "dDL5xaHq2-", "AAMBrrWylV", "C3nDCp6rh3f", "pEKZ66_EFlPb", "Bt7axM9JIm5", "qnslfO5jaqT", "Ab7FzA6XZxW", "8RRVz1PrNu", "TZ3eL1hbs-w", "_zxhSuQu4gC", "FZpvQzsMmf7", "uZLiuIuUB5b", "qSsVwbKEll8", "dIl6RSum847", "VzC-5h6nqw", "2wvC8H1xGM4", "nips_2022_-deKNiSOXLG", "RMaIirYX2fS", "2ZPfigWFNi", "2ZPfigWFNi", "P4C1KC6tB4D", "P4C1KC6tB4D", "SwQnIIf5TlB", "SwQnIIf5TlB", "nips_2022_-deKNiSOXLG", "nips_2022_-deKNiSOXLG", "nips_2022_-deKNiSOXLG", "nips_2022_-deKNiSOXLG" ]

[ "qy01B6EbJ1V", "tqWVUHJhWM", "RlVXa6NpH-6X", "n1zf1Kfr88", "_uJ7vRdgg4-", "NAuycHTh4zU", "pL0iwZ6BM4O", "srsd11UZNdU", "VtMtcdQVmi0", "xpFs33qT7gJ", "U3H8haJHnHP", "muwJMxw-2GN" ]

[ "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I really appreciate the time you've taken to engage with all my questions and comments. I found your answers helpful for my understanding. I also reviewed some of the changes you've made to the manuscript and I agree with you that your changes to Figure 3 really help. As such, I've revised my score upwards.", " Thank you again for your detailed inquiries and thoughtful comments. We appreciate your evident and highly non-trivial reviewing efforts.\n\n1. *“I don't agree that figure 2 provides an easily understandable minimal example.”* \n\nWe would like to begin with an additional clarification. Since our work lies at the intersection of several disciplines, our paper is written in a way that is intended to be read by multiple audiences, and our choices regarding structure, wording, notation, and illustrations reflect this. In particular, our choice of graphical examples was designed to aid readers who are not necessarily fluent in invariant learning. For these readers, our reasoning was that graphs should:\n\n(i) convey the basic structure around our user model,\n\n(ii) gradually progress from simple to complex, and\n\n(iii) first focus on where and how spuriousness can arise (e.g., user behavior), and only then on how invariance can be achieved (regularization and additional structure), these being in line with our focus in Sec. 3 and Sec. 4, respectively.\n\nIn these three senses - and at least in our minds - Fig. 2 is “minimal”. Our belief was that Fig. 2 would help readers (who are not accustomed to examining graphs for possible handles on invariance) think about spuriousness in a way that sets the ground for the behavioral model and Fig. 3 in Sec. 3. However, as Fig. 2 is more confusing than helpful, **we gladly remove it altogether**.\n \n2. *“if we had $\\bar{x}$, it seems like using it alongside x and r to predict would be correct.”* \n\nIn line with your views - we would first like to clarify the math behind the model, and then discuss possible misunderstandings regarding the illustration in Fig. 3.\n \n**The role of $\\bar{x}$ in prediction:** \nBegin by considering - irrespective of Fig. 3 - a user choosing via Eq. (1). Fix e, and consider a distribution $D^e_{X,\\bar{X},R}$. What would describe the generating mechanism of y? Eq. (1) states that y (which is a deterministic function of $\\tilde{v}$) depends on x,r, and e - not $\\bar{x}$. In other words - if we sample only $x,r \\sim D^e_{XR}$, then this provides sufficient information for determining $y=\\tilde{v}(x,r|e)$; had we then sampled $\\bar{x} \\sim D^e_{\\bar{X}|x,r}$, this would not have any effect on y, nor would such an instance of $\\bar{x}$ contain any additional information regarding the jointly-sampled y beyond that in x,r. \nConsider now a system that aims to learn $y$ for such a user. The system observes samples $(x,\\bar{x},r,y)$, and so it may seem appealing to learn a mapping $\\hat{y}=f(x,\\bar{x},r,y)$. However, $y$ does *not* depend on $\\bar{x}$. Hence, relying on $\\bar{x}$ in $f$ would *not* be optimal, since learning may (wrongly) use correlations between $\\bar{x}$ and $y$. Furthermore, assuming (incorrectly) that conditioning on $x,\\bar{x},r$ blocks all paths from $e$ to $y$ would (wrongly) imply that `naively’ training $f$ using e.g. standard ERM should suffice for learning a robust predictor. But in effect, it would not.\n\n**Graphically illustrating dual perspectives:** \nNow, return to Fig. 3 (left). Importantly, the diagram is *not a causal graph*. To see this, note that (i) in line with the above, a graph depicting the DGP of y would *not* include an $\\bar{x}$ variable, and (ii) the $\\bar{x}$ variable in the diagram is *integrated over* - an operation which is not depicted by causal graphs.\nWhat the diagram does convey is a *model of user beliefs* (in which $\\bar{x}$ does play an active part), as is common in choice modeling (and would likely be evident to a reader from this field). What we believe may have caused confusion is the attempt to connect this model to the pursuing causal graph - which is obtained via integration and choice - *in the same diagram*, and in a way that simultaneously presents the perspectives of both the system (which observes instances of $\\bar{x}$) and the user (which integrates over its possible values and w.r.t. personal beliefs). \nGiven your helpful feedback, **we have now decomposed Fig. 3 (left) into two distinct components: a model of user beliefs, and the resulting DGP.** We have also revised the caption to provide more detail on differences and connections, and will continue to revise the text in a way that better conveys these subtle points. We have also made it clearer that Fig. 3 is intended to show only how spuriousness can arise, and not how to treat it (which, as you note, requires additional structure), and use it to set the stage for Sec. 4 on invariant learning. \nWe are hopeful that our reasoning regarding the role of $\\bar{x}$ in prediction is now made clear (at least in terms of how spuriousness can be inadvertently missed), and is better conveyed in both writing and illustrations.\n\n\n3. “Writing y→x,r when y was used to denote the decision is indeed confusing.” \n\nWe agree, and thank you for pointing this out. We will make sure to decouple y from v when needed in the revised version of the paper.\n\n", " Dear authors,\n\nThanks for taking the time to write a detailed response and answer all of my questions. I want to start by clarifying something you mentioned in your reply: you didn't see why I would doubt the soundness of your approach. I want to clarify that, as I wrote in my detailed comments, in the submitted manuscript, there was enough confusing notation that I felt there was a gap between what was written in plain English and what appears in the graphs or the math. \n\nYour answers gave me some clarity but I'd like to still drill down into some points.\n\n1. Re: answer to: ``(2) Can you clarify the motivating figure 2 model?\"\n\nYes, I understand that it's the presence of $\\bar{x}$ that creates spuriousness: as you write in section 3.3, a classifier that uses only $x$ and $r$ could use $e$ information contained in $x$ and $r$ to compensate for not knowing $\\bar{x}$. However, I don't agree that figure 2 provides an easily understandable minimal example. Figure 2 causes confusion: it suggests that the environment truly causes the decision $y$, in which case the CF invariance to $e$ in definition 1 doesn't really make sense. Since Figure 2 is used to explain the problem formulation, I think it makes sense to go straight to something like Figure 3 left, which is makes the source of spuriousness *much* clearer.\n\n2. Re: answer to (3) \"If $\\bar{x}$ is actually observed, why isn't learning a flexible predictor from $x, \\bar{x}$ and $r$ the optimal thing to do?\"\n\nI don't really follow your intuitions. To clarify my thinking here, put simply, in figure 3 (left), $x, \\bar{x}$ and $r$ block all paths from $e$ to $y$. Thus, if we had $\\bar{x}$, it seems like using it alongside $x$ and $r$ to predict would be correct. You write in S3.3 that \"the reliance of users on 𝑥̄ for producing 𝑦 [...] means that, effectively, such an edge exists.\" I don't understand how to reconcile this with your point in the reply that \"This means that the generation of $y$ does not depend on $\\bar{x}$ as input.\" \n\nCould you provide some more intuitions or clarity for how to understand your answer, especially in terms of Figure 3 left?\n\n3. Re: answer to \"4) Can you better justify how, in the anti-causal model, the user's decision y could causally precede the perception of value?”\n\nYes, I understand that perceived value could cause $x$ and $r$. However, writing $y \\rightarrow x,r$ when $y$ was used to denote the decision is indeed confusing -- it conflates the decision with the true value. Your reply helps and some rewriting of this section will help. To substantiate my original comment around soundness, this notation is one example that had me feeling that there was a technical gap.\n\n4. Re: Proposition 2\n\nThanks for your explanation. I appreciate the time you put into adding extra empirical studies to the implications of the result.", " Thank you for your detailed review. We appreciate your careful attention to detail, and will be sure to revise the paper in a way that makes these details readily available to readers who are interested. \nIn your review, you express concern for the “soundness” of our approach. We fail to see why - nor do we see any comment in the review that points to a concrete source of unsoundness. To the best of our understanding:\n* Q1 and Q6 regard *clarification*. In our response we both clarify and provide additional details.\n* Q2, Q3, and Q4 reflect what we believe are *misunderstandings* by the reviewer.\n* Q5 presents what you perceive as a limitation. We respectfully disagree, and present an alternative viewpoint.\n\nHaving addressed these issues - and given our clarification in the general thread above as to what we consider to be our main focus and contributions - we are hopeful that you would be willing to favorably reconsider your evaluation.\n\n**Detailed response:**\n\n(1) *”Can you clarify whether in definition 1? Does the invariance have to hold for every possible unit (i.e., this is truly counterfactual and would be impossible to verify without assumptions on the full SCM)? If so, why bother since the graph can't identify such a criteria anyway?”* \n\nTechnically, and in its most general form, the result from Veitch et. al. (2021) on which Prop. 1 is based requires unit-level invariance. As Veitch et. al. show, population-level invariance (which regularization promotes) can be implied from unit-level invariance under further fine-grained assumptions on the graph, and in particular, using variables which are not affected by e (denoted $x^{\\perp}_e$, see proof in Appendix A). In our work, we make this assumption explicit where necessary (e.g., Sec. 5.3; see Fig. 6), but intentionally abstract away from it when it is not. For example, Sec. 3 focuses on the decision-making aspects of modeling; hence, Fig. 3 does not explicitly show an $x^{\\perp}_e$ variable because it is not essential to understanding the relation between user beliefs and the system’s modeling choice. At the same time, there is nothing preventing a modeler from including such a variable - the example holds just as well with it. \n\nHowever, we agree with your point on the importance of understanding the connection between structure and Prop. 1, and will clarify the importance of being precise about relational assumptions when modeling in concrete tasks.\n\nIn regards to whether population-level invariance is helpful: as Veitch et al. comment, population-level invariance is a necessary (though not sufficient) condition which, under observational data, is likely “the closest proxy for counterfactual invariance we can hope for” (see section “Gap to Counterfactual Invariance” in their paper). Veitch et al. support this claim with experiments; we believe we do so as well, especially in our new experiment on mixed populations (see general response above). Whether this claim holds more broadly (or not) will hopefully be determined as further evidence amounts, and as more useful ways of achieving user-level invariance are discovered, by future works in this young but growing line of research (e.g., see the recent work in https://arxiv.org/abs/2207.09768).\n", " (2) *”Can you clarify the motivating figure 2 model, and explain why the $e{\\rightarrow}y$ link is being considered \"spurious\" or non-causal here? As explained in more detail above, invariant causal learning assumes that the environment has no causal effect on the target y because if it did, environment-invariance isn't intuitively a sensible ask to begin with.”* \n\nIn our example (which Fig. 2 illustrates), it is $\\bar{x}$ that becomes spurious - not $e$. To see this, note that data is generated by a user model in which $\\bar{x}$ is only indirectly related to $y$ (through integration). We apologize if this was unclear.\n\nIndeed, in some cases we present e as directly affecting $y$; however, this should *not* be taken to mean that we assume that all causal paths to $y$ originate in $e$. Fig. 2 is intended to depict the minimal structure necessary to convey our modeling ideas, and so presents a simplified generative process; the framework itself does not prevent $x$ or $r$ depending on some other variable that is unrelated to $e$, so that some elements of $x,r$ are invariant. This is made explicit in Sec 5.2 (see Fig. 6) and in Appendix A (see Fig. 7).\n\n(3) *”Can you clarify that my understanding of S3.3 was right, and clarify why learning a flexible predictor from $\\bar{x}$, $x$ and $r$ (if $\\bar{x}$ was observed) isn't the optimal thing to do, since we could just learning the (invariant) causal mechanisms directly?”* \n\nTo the best of our understanding, we believe your intuition here is wrong. To see this, recall the important distinction that while the system observes $\\bar{x}$, the user - whose decisions determine $y$ - does *not* (lines 131; 196). The decision rule (Eq. (1)) accounts for (user-side) uncertainty regarding $\\bar{x}$ by summing over possible assignments to $\\bar{x}$, and so the true mechanism which generates $y$ relies on distributional information regarding $\\bar{x}$ - *not* on specific instantiations. This means that the generation of $y$ does not depend on $\\bar{x}$ as input.\n\nHowever, if the system learns functions of the form $f(x,\\bar{x},r)$ from inputs of the form $(x,\\bar{x},r,y)$, then learning will likely utilize variation in $\\bar{x}$ to explain y, if they correlate (nothing in the objective discourages this). This would mean that the learned $f(x,\\bar{x},r,y)$ will vary with $\\bar{x}$ - whereas the true generating process of $y$ does not - and in a way that fits the training environments; hence, such a model is unlikely to generalize well to new environments.\n\nA subtle point is that if the system has access to data which includes instances of $\\bar{x}$, then it also has access to the (empirical) distribution of $\\bar{x}$. This means that, at least in principle, the system can utilize this distributional information in learning. However, nothing in the learning objective encourages learning in this particular way. \n", " (4) *”Can you better justify how, in the anti-causal model, the user's decision y could causally precede the perception of value?”* \n\nThe user’s decision y does not precede the perception of value. Please refer to line 275, where we describe anti-causal users as “believing that an item’s *value* causes its description”. This is not to be confused with the user’s decision, which is a function of her perceived value. An anti-causal edge x<-v appears if the user *believes* the information x presented to her by the system depends on the item’s value (the notation x<-y, which “folds” v->y into y (line 206), may indeed be confusing in this regard; we will clarify this). One scenario in which this can occur is when a user believes that the system can accurately estimate v - perhaps even better than the user herself can - and sets x and/or r accordingly. As an example, consider a restaurant recommendation service which reveals information about restaurants that matches (predicted) user tastes: e.g., a tempting menu item (for a restaurant that is predicted to match her tastes), or an overcrowded seating area and a long line (for a restaurant which does not).\n\nNote that a descriptive model of anti-causal user *decisions* requires being precise about the role and form of perceived values; these can be distinct from those described for the causal user in Eq. (1).\n\n(5) *”Can you articulate what CI tests you're envisioning to distinguishing between anti-causal and causal user models (presumably, testing to see if y is a collider for x and r)?”* \n\nPlease see our detailed response to all reviewers on this subject in the general thread above.\n\n(6) *”Can you generally clarify proposition 2, perhaps with an example?”* \n\nOn a high-level, Prop. 2 begins by stating that it is possible for two users of the same type but of different sub-types - namely skeptics vs. believers - to generate very similar observational data (the proposition itself portrays an extreme case where they can be identical, but the overall message is that observational data may conceal important variation in causal user perceptions). Next, consider that if we were to train a predictive model by minimizing the loss on data generated by one of these users, then we would expect this model to also have low loss for data generated by the other user (note that since both users are of the same type, Prop. 1 states that they require the same regularization, and so their objectives match). Hence, it would seem beneficial to pool both datasets together - since this would provide more data from the “same” distribution - and train a single predictive model. Indeed, if our goal was to optimize in-distribution performance, then this reasoning would be correct; however, the key statement of Prop. 2 is that for out-of-distribution performance, *it would be better to train different models*, one for each user, and independently. The conclusion carries over to populations of same-type users that consist of two sub-populations of different sub-types.\n\nFormally, in our proof we construct a data generating process that is entailed by the graph in Figure 6. We show that under certain settings for this DGP, if we sum out all variables other than $x,r,y$ (in our construction this means summing out a confounder $c$ and the environment variable $e$), we may arrive at the same joint distribution over $x,r,y$ for two users where one is a believer ($r{\\rightarrow}x_{sp}$, for some features $x_{sp}$) and one is skeptic ($r{\\leftarrow}x_{sp}$). But whereas for the believer, the optimal CI predictor takes both $r$ and $x_{ac}$ into account, this model is not CI for the skeptic user and hence they do not share optimal robust models. \n\nThe proof is constructive and one may easily construct numerical examples, one such example is constructed for the simulation in section 5.3. Notice that in Table 1, when $\\lambda=0$, the performance is the same for all user subclasses, regardless of the subgroup we trained on. Implying that the non-robust models learned via ERM are the same for both users. It is only when we learn a robust model (i.e., $\\lambda > 0$) that we observe the benefits of learning a different model for each subclass.\n", " Thank you for your reviewing efforts; although our paper is likely not in your main area of expertise, we nonetheless hope it served as an interesting and pleasant read. \n\n(1) *No comparisons with other exciting works (e.g., those in Sec. 2):* \nWhile the papers surveyed in Sec. 2 relate to causal inference in the general setting of recommendation, their focus is quite different than ours: [29] focus on inference, and in particular aim to correct for exposure bias; [56] present a method for “deconfounding” possible confounders; [7] seek to find a policy that maximizes ITE, rather than predicting; [58] propose to leverage item popularity as a confounder; [55] study causes for bias amplification; etc. Hence, we do not see how they can be applied to our setting.\n\n(2) *It seems the prior knowledge regarding users' causal beliefs needs to be known ahead for modeling. How can such information be obtained in real-world tasks?* \nPlease see our detailed response to all reviewers on this subject in the thread above.", " Thank you for your encouraging review, please see our response to your questions below.\n\n(1) *How do the MMD and the CORAL regularization methods satisfy the respective necessary conditional independence requirements needed for preventing spurious correlations?* \nConsider two environments, $e_1$ and $e_2$. For marginal MMD, note that the penalty constitutes a metric between the distributions of representations in each environment, $D^{e_1}(\\phi(x,r))$ and $D^{e_2}(\\phi(x,r))$. MMD encourages these distributions to be similar; hence, when the penalty is low, we can expect to have $P(\\phi(x,r) \\mid E=e) \\approx P(\\phi(x,r))$ for $e \\in {e_1, e_2}$, i.e., that the probability of observing a certain representation is independent of the environment from which it was sampled. This means that for a predictive model that operates on these representations, the desired independence (approximately) holds. \nFor conditional MMD, stratifying over y and then using the same reasoning gives the necessary conditional independence. \nAs for CORAL, while it is not a proper metric between distributions, it does match certain properties of the distributional (i.e. covariance matrices), and is hence used in practice as a proxy for distribution matching (and often works better than MMD).\n\n\n(2) *Not completely mathematically clear why the conditional independencies described in lines 216-217 are satisfied:* \nThe conditional independencies in lines 216-217 merely exemplify how different beliefs can lead to different factorizations, irrespective of the (possibly different) conditional independencies needed for robust learning.\n", " We thank all reviewers for their efforts and valuable comments, which we will implement in our next revision of the paper, hopefully in the coming week. In this thread we discuss two themes that came up in more than one review. All other points are addressed in individual responses below.\n\n(1) **Focus and contribution:** \nOur key goal in the paper is to show how accounting for users’ causal perception can benefit robust learning. In accordance, our primary focus is on *modeling*, and we were happy to learn that all reviewers are appreciative of our efforts in this regard. To this end, we rely on recent advances in invariant learning, and we believe our result in Prop. 2 is a humble contribution to this growing literature. However, we use the framework of counterfactual invariance mostly as the best currently-available testbed for exploring our ideas regarding causal user modeling. As we state in the paper, we view our main contribution as being *conceptual* - our paper is about *making an intriguing and non-trivial connection between three distinct fields*. As to the connection to counterfactually-invariant learning, we believe our framework is flexible enough to remain relevant and applicable in future iterations of this young domain, as it evolves.\n\n(2) **What we mean by “graph knowledge”:** \nAll reviewers requested, in one way or another, that we further elaborate on possible means to infer user graphs. Since our work considers the question “how can knowledge regarding users’ causal beliefs be useful?”, naturally we place emphasis mostly on what to do with such knowledge - rather than how to obtain it. Nonetheless, as per your request, we will gladly provide more details about graph inference in our next revision of the paper. \n\nAt the same time, **we would like to make an important clarification in this regard**. While there exist disciplined ways to infer graphs or orient certain edges - either from observational data (i.e., from the extensive literature on causal graph discovery) or through experimentation (i.e., using the established practice of A/B invariance testing) - an important point we wish to make is that our approach does not require, per se, precise and verified graph knowledge on each individual user. Rather, we envision our framework as applicable in cases where there is *good prior knowledge* regarding users’ causal beliefs, possibly even at the population level. For example, our beers experiment is designed to capture a setting where users are likely to be casual; our fashion experiment targets a setting where users are likely to be anti-causal. \n\nThe use of domain knowledge to determine the learning objective (e.g., how to regularize) is common practice in machine learning. For example, practitioners apply L1 regularization when they *believe* the true underlying model is likely to be sparse - not because some formal verification test guarantees this (and not for a lack of theory on sparse learning, on which there is plenty). Likewise, and relevant to our case, when there is good reason to believe that most users are of one “causal” type or another, we view our results as providing guidance as to how to devise the learning objective: Prop. 1 suggests what regularization to apply, Prop. 2 suggests treating different sub-populations independently. \n\nTo further ground this perspective, **we have added to the paper an additional experiment** on mixed populations. Focusing on believers vs. skeptics, we demonstrate how even a rough guess of how to partition the population (and learning “as if” each noisy sub-population was actually pure) still provides significant improvement in predictive outcomes. Our current revision includes these results and key setup details (Sec. 5.4), and we will continue to update with more details in the coming week. \n\nOverall, we hope our refined perspective and new results help shed a different light on how our framework can be interpreted.\n", " This paper studies the problem of predicting item relevance to users, in a way that is robust to changes in the data distribution. It is a particular case of tackling the bigger challenge of out of distribution generalization - here different environments are represented by different users' beliefs. The paper gives a strategy for trustworthy relevance prediction which does not require full information of the underlying causal graph. It only requires one to know whether the graph is causal or anti-causal, and for each of these scenarios an appropriate regularization scheme is chosen. Strengths:\n\n1. The paper is very well-written and the motivation and setup are very clear. I enjoyed reading this work. \n2. The learning algorithm proposed requires minimal knowledge of the causal graph (i.e. whether it corresponds to (a) causal and (b) anti-causal with two possible subclasses - believer or skeptic; this latter sub-distinction is very nice and quite realistic for modeling user behavior). \n3. The connection to economics and user behavior psychology by modeling the response y via an expected utility function is interesting. \n4. This model also accounts for the case in which some intrinsic information about the product (encoded in x) is missing. \n5. The algorithm is clear and the experiments are thorough, accounting for all possible scenarios. \n\n\nWeaknesses:\n\n1. While I intuitively understand it, it is still unclear to me how the MMD and the CORAL regularization methods satisfy the respective necessary conditional independence requirements needed for preventing spurious correlations. Similarly, it is not completely mathematically clear to me why the conditional independencies described in lines 216-217 are satisfied. \n2. Inferring the type of causal and non-causal graph is still non-trivial. The authors do mention some approaches for this in lines 294-295, i.e. A/B testing or conditional independence testing from observational data, but the paper could significantly benefit from a more developed discussion of possible ways to infer the graph in practice. \n\n My only question is the same as Point number 1 in weaknesses. The authors have mentioned limitations of their method both in the discussion section as well as in the description of their experimental results. ", " This paper proposes a learning framework that is robust to environment changes to predict the relevance of items to users. The key idea is to model users as reasoning about decisions through a causal graph and show how minimal information regarding the graph can be used to contend with distributional changes. The proposed framework is novel and the paper is fairly well written, and experimental results support the paper's statement that adopting users' causal beliefs results in better prediction performances.\n\nHowever, there are no comparisons with other exciting works. According to section 2 related works, there exist, several models that adopt causal inference techniques for recommendation tasks, the paper would be more sound if the prediction performances are compared against those works. It seems the prior knowledge regarding users' causal beliefs (causal or anti-causal) needs to be known ahead for modeling. How can such information be obtained in real-world tasks? N/A", " The paper considers a recommendation setting where we observe the attributes of users, of items, and aspects of the recommendation itself such as a relevance, an explanation of the relevance, etc. The task is to use this information to predict the user's decision, whether or not they will interact with the item of interest. The decision could be binary, a rating, or something else.\n\nThe problem is to produce a predictor of user decisions that is invariant to changes in the distribution of the observed features (attributes, recommendation aspects, etc.). We expect such invariant predictors to achieve bounded risk when deployed to unseen distributions of data. This paper closely follows work on counterfactual (CF) invariance, a criteria based on counterfactual distributions that captures desirable behavior in predictors. The criteria can be *approximately* satisfied by regularizing predictors (where the regularization crucially depends on the causal model of the features and label).\n\nTo extend the ideas of invariance to user decision predictions, the paper makes a key insight: the decision is affected by the causal model by which a user reasons about features to make a decision. Thus, a key idea in the paper is to parameterize such causal models of user reasoning. After formalizing a notion of CF invariance in the user decisions setting, the paper uses the idea of boundedly rational agents to instantiate a causal model of user decision making. In such a model, they articulate how paths in the graph can encourage predictors to exploit non-causal (i.e., spurious) information that doesn't remain stable across distributions. Then, the paper draws upon results from the work on CF invariance to propose regularizers to discourage predictors from using such non-causal information. Since the regularization scheme depends on the causal model, the paper distinguishes two different causal models of users that lead to different regularizers. They empirically study CF invariant perdictors of user decisions with recommendation data and simulated outcomes, finding evidence of robustness to distribution changes and substantiating that indeed, it is important to match regularizers appropriately with causal models. Strengths:\n1. The paper takes a new approach to robust recommendations, making the novel connection that for invariant decision prediction, modeling the user decision making process is what is relevant. In this vein, using ideas from boundedly rational agents, the paper instantiates some causal models of users and articulates what paths in these models incentivize predictors to use spurious information. These connections are non-trivial to develop and can inspire extensions and new veins of work in the recommendation setting.\n2. The empirical studies that involve recommender data with simulated outcomes can be considered another contribution in this paper. Such experimental evaluation could also provide new tasks and baselines for those looking to work on the problem of invariant recommendations.\n3. The writing is generally clear and the authors do a good job or motivating technical ideas with examples and intuitions. The authors seem to have to covered related work well too.\n\nWeaknesses:\n1. In applying and extending ideas about CF invariance, there are some technical gaps and ambiguities throughout the paper that leave me doubting the soundness of some ideas. I'll enumerate:\n+ the notion of CF invariance has always been a bit poorly formalized. Consider definition 1. Does the invariance have to hold for every possible unit (i.e., this is truly counterfactual and would be impossible to verify without assumptions on the full SCM)? Or, does $f_u(\\cdot)$ have to be invariant for all values of x and r, i.e., $P(f_u(x(e), r(e) | X=x, R=r; \\theta) = P(f_u(x(e'), r(e') | X=x, R=r; \\theta) \\forall x, r$? Or, do you want it to hold on average across interventions to $e$, i.e., $P(f_u(x(e), r(e); \\theta) = P(f_u(x(e'), r(e'); \\theta)$? Definition 1 isn't well defined enough to make these distinctions clear. Note that causal graphs alone could only identify versions 2 or 3 of this invariance.\n+ In the same vein, if definition 1 is intended to be truly counterfactual (i.e., must be satisfied for every possible unit specified by the SCM), since the causal graph can never identify it anyway, why bother? Why not just pick a population-level (i.e., interventional as in version 2 or 3 above) version of invariance to satisfy?\n+ The motivating causal model in figure 2 is a bit strange because in this model, the decision truly is causally affected by the environment. In this case, a predictor that satisfies CF invariance in Definition 1 would not capture the causal process of user decision making, which is often the underpinning of invariant causal learning. In fact, much of the work on invariant causal learning begins by assuming that the environment has no causal effect on the target $y$ because if it did, environment-invariance isn't intuitively a sensible ask to begin with. However, in this paper, the $e \\rightarrow y$ motivation persists and is described as the main pathway by which predictors exploit spurious information. It's not non-causally spurious information in this case, though, so the motivation is quite confusing.\n+ The notation in S3.1 and figure 2 tend to obfuscate the fact that what we want is for some of the *information* in $x$ and $r$ to be discarded. That is, we want to partition the information in those variables into a part that a desirable predictor $f_u(\\cdot)$ can use and a part that $f_u(\\cdot)$ should't use. For example, the work by Veitch et al. makes this information decomposition explicit, thereby allowing us to reason about what graphical relationships the \"nice\" part of $x, r$ have to other variables. By being more coarse-grained and only encoding $x$ and $r$, however, it's not easy to reason about what parts of the variables an invariant predictor ought to use, and what relationships the parts have to other variables in the graph.\n+ In S3.2 on \"rational users\", the authors say that a rational user model is akin to assuming a causal graph in which there is no direct arrow from $e$ to $y$, which handicaps the ability to avoid spurious pathways. This statement is confusing. A causal model with no arrow from $e$ to $y$ seems like the best case scenario because any flexible predictor from $x$ and $r$ to $y$ would be able to capture the causal mechanisms by which $y$ is produced. Perhaps a fairer assessment here is that although rational users constitute a best case scenario, this is not a likely model of users.\n+ In S3.3, it seems like if we had the function $v_u(x, \\bar{x}, r)$ (which doesn't depend on the environment), then I could construct an invariant predictor. But, since $\\bar{x}$ is latent, a predictor is incentivized to reconstruct $\\bar{x}$ information using the observed variables $x$ and $r$. However, since $e$ leaves its imprint on $x$ and $r$ and also affects $\\bar{x}$, a predictor might just memorize $e$-relevant information instead. However, the authors say that using $\\bar{x}$ if it *was* observed would be bad because it could lead to overfitting -- this doesn't match my intuition because I'd have thought that observing $\\bar{x}$ is a best-case scenario because then, all paths from $e$ to $y$ are blocked and any flexible predictor could capture the causal mechanisms governing $y$ from $x, \\bar{x}$ and $r$.\n+ In S4.1, the story of the anti-causal user doesn't make sense to me because $v_u(x, \\bar{x}, r)$ sounds like reflects the user's perception of value -- how could the user's decision $y$ possibly causally precede the perception of value? Put differently, the notation may be using $v_u$ to conflate true and perceived value.\n+ In Prop 1, $y$ and $e$ being confounded is not $e \\rightarrow y$. The authors should clarify what they mean here.\n\n2. The paper relegates an important limitation to just 1 sentence. In S4.1, after articulating how the choice of anti-causal versus causal matters for regularization, the authors state that ``this can be done using focused interventions (e.g., A/B testing), or for observational data, using simple conditional independence tests.'' Conducting A/B tests to determine a causal arrow direction for each user is impractical. It's important to spend more time, then, discussing the orientation of edges using CI tests and addressing all the limitations therein. Presumably the idea is to test for v-structures between $x$ and $r$, and $y$? This needs to be explained more directly since in general, causal structure learning won't orient all edges.\n\n3. In a similar vein to above, the empirical studies focus on one or the other causal model (anti-causal vs causal), without addressing the challenge the authors themselves motivated, that typically, a training distribution consists of a mixture of these two causal model modalities. I would love to see this issue tackled more.\n\n3. Section 4.2 could do with a figure that helps to illustrate the proposition and the reasoning about v-structures. This section is hard to follow especially because we don't have the notation to talk about the parts of information that a CF invariant predictor uses. That being said, this proposition seems to provide a novel insight beyond the existing work of CF invariance, so perhaps it would have been more interesting in this paper to dwell on the differences between skeptics and believers than between anti-causal and causal users. I described the main technical gaps I perceived above. I'll reiterate the points as clear questions for the authors here:\n\n1. Can you clarify whether in definition 1? Does the invariance have to hold for every possible unit (i.e., this is truly counterfactual and would be impossible to verify without assumptions on the full SCM)? If so, why bother since the graph can't identify such a criteria anyway?\n\n2. Can you clarify the motivating figure 2 model, and explain why the $e \\rightarrow y$ link is being considered \"spurious\" or non-causal here? As explained in more detail above, invariant causal learning assumes that the environment has no causal effect on the target $y$ because if it did, environment-invariance isn't intuitively a sensible ask to begin with.\n\n3. Can you clarify that my understanding of S3.3 was right, and clarify why learning a flexible predictor from $\\bar{x}, x$ and $r$ (if $\\bar{x}$ was observed) isn't the optimal thing to do, since we could just learning the (invariant) causal mechanisms directly?\n\n4. Can you better justify how, in the anti-causal model, the user's decision $y$ could causally precede the perception of value? \n\n5. Can you articulate what CI tests you're envisioning to distinguishing between anti-causal and causal user models (presumably, testing to see if $y$ is a collider for $x$ and $r$)? \n\n6. Can you generally clarify proposition 2, perhaps with an example? As discussed in the weaknesses above, I'd encourage the authors to spend more time discussing the challenges underpinning distinguishing between anti-causal and causal models. Moreover, both in exposition and empirically, it would be good to see more about how to practically deal with the issue of users in the data coming from a mix of these models." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 6, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 1, 4 ]

[ "tqWVUHJhWM", "RlVXa6NpH-6X", "muwJMxw-2GN", "muwJMxw-2GN", "muwJMxw-2GN", "muwJMxw-2GN", "U3H8haJHnHP", "xpFs33qT7gJ", "nips_2022_ikXoMuy_H4", "nips_2022_ikXoMuy_H4", "nips_2022_ikXoMuy_H4", "nips_2022_ikXoMuy_H4" ]

[ "65U49Rg-skb", "LyJ9tM3v9T", "H90ET4ijme_", "8EyMGgOKRi", "9UbIqPxb4rl", "NP6bahx8IpS", "h74mGOJDfIN", "sNR5TsJ7W2d", "ke830KfrIZz", "TtOEfVfcggF", "gmoLHX33KOy", "PsMZvgXftyI", "0X9_fcsILKT", "9cSoH2JHrGH", "2RsnTS5eUBr", "s6dwonP-qQJ", "x5Ths3AKScc", "Je7SdHDvcSi" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We greatly appreciate your precious feedback on our research. Experiments of adding back features before downsampling have been included in the revision (Appendix D).", " Hi authors,\n\nthanks for the quick response regarding the experiments results request. The table resolved my concern and I suggest add this results and analysis in the revised version. This concludes that adding the non-downsampled feature already helps by 0.4 (naively) and 0.7 (one transform layer). And this particular form authors proposed further benefits from bottleneck-like architecture. ", " Thank you very much for the constructive feedback. We would like to add the following response to address your concerns.\n\nFirst, we give the entire pipeline of the \"downsample-then-upsample\" architecture.\n\n```\nx' = DWConv_1(x) # downsample, with LN\nV = Linear(x')\nout = nn.PixelShuffle(DWConv_2(V)) # upsample, with LN\n```\n\nAssume the channel dimension of x is $C$ and the reduction ration of downsampling is $R$. Then, the rationale behind the impulse-like graph created when applying the upsampling module can be explained as follows:\n\n(1) DWConv_1 with output channel $C$ is applied to downsample the input feature map x. After DWConv_1, medium- and high-frequency information is reduced (downsampling can be seen as denoise to some extent).\n\n(2) DWConv_2 with output channel $C \\times R^2$ is adopted to reconstruct the lost medium- and high-frequency information, which means the \"downsample\" and \"upsample\" modules are trained adversarially in the optimizing process.\n\n(3) \"V\" is the input of upsample operation, which brings extra information from the self-attention branch.\n\n(4) Therefore, the upsample operation's ability to reconstruct lost information is determined by \"V\" and $R$. In ResTv2, values of $R$ are set as [8, 4, 2, 1] respectively in the four stages, which means the reconstructing ability is high in the first two stages and becomes weak in the last two stages. This may explain why only 3 polylines (the first two stages have 3 blocks) are impulse-like.\n", " The authors did a great job of dealing with most of my concerns. I am satisfied with the new experiments and agree with the authors' clarifications. One thing I pointed out is not yet clear: what is the rationale behind such an impulse-like graph (in the frequency domain) created when applying the upsampling module in Q4? It would be nice to discuss why this happened in the final paper revision. Finally, aside from this, I am happy to update my score and vote for acceptance of the paper.", " Thank you very much for the constructive feedback. We would like to add the following response to address your concerns.\n\n1. The results of ResTv2’s variants (keeping the downsample operation) under the ablation study settings are listed as follows. \n\n| Method | Params | FLOPs | Throughput | Top-1 (%) |\n|-----------|--------|-------|------------|-------------|\n| ResTv2-T | 30.43M | 4.10G | 826 | 80.3 |\n| w/o_up | 30.20M | 4.08G | 935 (+109) | 79.0 (-1.3) |\n| x_w/o_up | 30.20M | 4.08G | 929 (+103) | 79.4 (-0.9) |\n| lx_w/o_up | 32.35M | 4.40G | 904 (+78) | 79.7 (-0.6) |\n\nHere, \"*w/o_up\" means eliminating the upsample operation. \"x_w/o_up\" means adding back the original feature before downsample (i.e., x). \"lx_w/o_up\" means adding the linearly projected x.\n\nWe can see, EMSAv2 has a better speed-accuracy trade-off.\n\n2. Novelty and Motivation of ResTv2: \n\n(1) In ResTv2, the same downsample operation is shared by both the self-attention and convolution branches, which can significantly reduce the computational costs in ResTv1. \n\n(2) As introduced in ResTv1, EMSA can only capture global information without the upsample operation. Therefore, to address this issue, adding the upsample operation on \"V\" in the newly proposed ResTv2 builds a convolutional hourglass architecture to effectively capture local information, which is complementary to global information captured by the self-attention branch.\n\nAssume the input feature is x. Here, we give the entire pipeline of the \"downsample-then-upsample\" design.\n```\nx' = downsample(x)\nV = linear(x')\nout = self.up (V)\n```\n\nThe pytorch implementation of self.up (i.e., Pixel-shuffle in Fig 2(b)):\n```\nself.up = nn.Sequential(\n nn.Conv2d(dim, sr_ratio * sr_ratio * dim, kernel_size=3, stride=1, padding=1, groups=dim),\n nn.PixelShuffle(upscale_factor=sr_ratio))\n```\n", " Hi Authors,\n\nthanks for presenting the results for A3, however, the target setting I thought about is keep the downsample operation, but add back the original one (feature before downsample) instead of the (downsampled-upsampled feature), in this case, wound not increase flops. Also, the flops/inference throughput presented in A3 is from downsampling operation, which is contribution from V1 paper, not this paper. ", " Dear Reviewer 21zc:\n\nWe thank you for the precious review time and valuable comments. We have provided corresponding responses and results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest Wishes!", " Dear Reviewer TbMq:\n\nWe thank you for the precious review time and valuable comments. We have provided corresponding responses and results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest Wishes!", " Dear Reviewer cW5j:\n\nWe thank you for the precious review time and valuable comments. We have provided corresponding responses and results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest Wishes!", " We have carefully answered the questions proposed by all three reviewers, many of which provided significantly valuable feedback helping us improve the paper, for example, to show the generalization of our method on ViT methods without downsample operations, such as Swin Transformer. In addition, we add the codes corresponding to Fig.3 in the Supplementary Material (file name: \"fig_3.py\"), as well as the experimental results for ViTs without downsampling strategies in Appendix C. ", " Thank you very much for the insightful and constructive comments. \nAppendix is available with the main submission file, and Codes are available in the Supplementary Materials, which contain more content and details to help understand this manuscript.\n\n**Q1**: Does the upsample operation designed only work well for the specific efficient Transformer model with the downsample operation?\n\n**A1**: (1) The \"downsample-then-upsample\" design builds a convolutional hourglass architecture [1] to effectively capture local information. Therefore, it works well for different efficient Transformer models with the downsample operation, such as the ResT series and PVT family.\n\n(2) The downsample operation is shared by the convolution and self-attention branches and significantly reduce computational costs. Without the downsample operation, the upsample operation can be simplified into a DWConv (i.e., reduction sr_ration=1). \n\nHere we give the PyTorch implementation and experimental results, respectively.\n```\nself.up = nn.Conv2d(dim, dim, kernel_size=3, stride=1, padding=1, groups=dim)\n```\nWe set spatial reduction sr_ratio for ResTv2-T as 1 (i.e., without the downsample operation. We call this \"variant of ResTv3-T\").\nFor Swin Transformer [2], we only add the upsample operation for the even blocks (starting from 0, i.e., in W-MSA) since the odd blocks start with a shift window (i.e., SW-MSA), which impairs the feature maps' spatial continuity.\n\n| Method | Params | FLOPs | Throughput | Top-1 (%) |\n|-----------------|--------|-------|------------|-------------|\n| ResTv2-T | 30.43M | 4.10G | 826 | 82.3 |\n| ResTv3-T_w/o_up | 30.25M | 6.51G | 648 | 80.2 |\n| ResTv3-T | 30.42M | 6.52G | 591 (-57) | 80.7 (+0.5) |\n| Swin-T | 28.33M | 4.49G | 755 | 81.3 | \n| + up | 28.35M | 4.50G | 713 (-42) | 81.9 (+0.6) |\n| Swin-S | 49.61M | 8.75G | 437 | 83.2 | \n| + up | 49.66M | 8.76G | 399 (-38) | 83.7 (+0.5) |\n\nWe can see in the above table that the upsample operation still works well for ViTs without downsample operations.\n\n**Q2**: For Eq.2, is the Norm operation also eliminated along with the Conv? If so, the paper does not mention it, which is somewhat confusing.\n\n**A2**: Yes, Norm operation is also eliminated. In ResTv1, the Norm operation is adopted to restore the diversity of MSA, which is impaired by the multi-head interaction module (MHIM). Since MHIM is eliminated in ResTv2, Norm operation in Eq. 2 is no longer needed.\n\n**Q3**: I think a more detailed description of Fig.3 is needed for a better understanding, e.g., the meaning of coordinates and curves.\n\n**A3**: Codes of Fig. 3 are available in the Supplementary Materials (fig_3.py). Here, we give some explanations. \n Take Figure 3(a) as an example to illustrate the relative log amplitudes of Fourier transformed feature maps:\n\n- 11 different colored polylines represent 11 blocks in ResTv2-T, and the bottom one is the first block.\n- We only use half-diagonal components of shift Fourier results. Therefore, for each polyline, $0.0\\pi$, $0.5\\pi$, and $1.0\\pi$ can also represent low-, medium-, and high-frequency, respectively. \n\nCompared with Figures 3(a) and 3(b), in earlier blocks, the average value of the upsampling branch is higher than the self-attention branch, particularly in $0.5\\pi$ and $1.0\\pi$, which means the upsample branch can capture more medium- frequency and high-frequency information. Compared with Figures 3(b) and 3(c), almost all value of the combined branch is higher than the self-attention branch, particularly in earlier blocks, demonstrating the upsample module's effectiveness.\n\nGenerally speaking, the receptive field of convolution is enlarged by stacking more layers. But self-attention has a global receptive field, which means self-attention mainly focuses on semantic information (low-frequency). In earlier blocks, the receptive field of the upsample branch is short, which mainly captures medium- frequency and high-frequency information (corner, texture, etc.). The upsample branch will capture more low-frequency information as the receptive field becomes higher in deep blocks.\n\n**Reference**\n\n[1] Newell, Alejandro, Kaiyu Yang, and Jia Deng. \"Stacked hourglass networks for human pose estimation.\" ECCV, 2016.\n\n[2] Liu, Ze, et al. \"Swin transformer: Hierarchical vision transformer using shifted windows.\" ICCV, 2021 (best paper).\n", " **Q4**: Illustration of Figure 3.\n\n**A4**: Codes of Fig. 3 are available in the Supplementary Materials (fig_3.py). Here, we give some explanations. \n Take Figure 3(a) as an example:\n\n- 11 different colored polylines represent 11 blocks in ResTv2-T, and the bottom one is the first block.\n- We only use half-diagonal components of shift Fourier results. Therefore, for each polyline, $0.0\\pi$, $0.5\\pi$, and $1.0\\pi$ can also represent low-, medium-, and high-frequency, respectively. \n\nCompared with Figures 3(a) and 3(b), in earlier blocks, the average value of the upsampling branch is higher than the self-attention branch, particularly in $0.5\\pi$ and $1.0\\pi$, which means the upsample branch can capture more medium- frequency and high-frequency information. Compared with Figures 3(b) and 3(c), almost all value of the combined branch is higher than the self-attention branch, particularly in earlier blocks, demonstrating the upsample module's effectiveness.\n\nGenerally speaking, the receptive field of convolution is enlarged by stacking more layers. But self-attention has a global receptive field, which means self-attention mainly focuses on semantic information (low-frequency). In earlier blocks, the receptive field of the upsample branch is short, which mainly captures medium- frequency and high-frequency information (corner, texture, etc.). The upsample branch will capture more low-frequency information as the receptive field becomes higher in deep blocks.\n\n**Q5**: Illustration of Figure 4.\n\n**A5**: Linear CKA measures the similarity of two tensors (higher value means higher similarity). In Fig. 4, 11 points in each polyline represent 11 blocks, and 0 is the first block. Here, \"up\", \"attn\", and \"com\" are short for upsample, self-attention branch, and combined branches(i.e., EMSAv2), respectively. \nTake the red polyline (\"up_attn\") as an example. It measures the similarity between upsample branch and the self-attention branch. In block 0, cka<0.2 means feature maps in the upsample and self-attention branches are quite different. In block 10, cka>0.9, which implies feature maps in these two branches has higher similarity.\n\n**Q6**: The details of Pixel-shuffle are not clearly presented. \n\n**A6**: Thank you. Pixel-shuffle will be clearly presented in the revised version. Here, we give some explanations. Assume sr_ratio is the reduction rate in downsample operations. Then, the PyTorch implementation of Pixel-shuffle is provided as:\n```\nself.up = nn.Sequential(\n nn.Conv2d(dim, sr_ratio * sr_ratio * dim, kernel_size=3, stride=1, padding=1, groups=dim),\n nn.PixelShuffle(upscale_factor=sr_ratio))\n```\n\n**Q7**: What is the meaning of the computational density? \n\n**A7**: Computational density can be measured in TFLOPS on specific environments (such as cuDNN, GPU type, etc.) \nFor example, VGG-16 has 8.4× FLOPs as EfficientNet-B3 but runs 1.8× faster on 1080Ti, which means the computational density of the former is 15× of the latter [5].\n\n**Q8**: Is the LN after DwConv in EMSAv1 removed in EMSAv2?\n\n**A8**: No. LN after DwConv is not removed. To simplify, we do not show LN in Fig. 2.\n\n**Q9**: How does the upsampling change the latency? Please specify the latency or throughput in Table 2 (b).\n\n**A9**: Results are listed in the following table, which will be included in the revision.\n\n| Upsample | Params | Throughput | Top-1 (%) |\n|---------------|--------|------------|---------------|\n| w/o | 30.26M | 919 | 79.04 |\n| nearest | 30.26M | 878 (-41) | 79.16 (+0.12) |\n| bilinear | 30.26M | 870 (-49) | 79.28 (+0.24) | \n| pixel-shuffle | 30.43M | 826 (-93) | 80.33 (+1.29) | \n\n**Q10**: The difference in the results between the target of K and V in Table 2 (a) is slight, so it should be verified from multiple runs.\n\n**10**: Top-1 accuracy under 100 epochs and 300 epochs are shown in the following table.\n\n| Targets | 100 epochs | 300 epochs |\n|---------|------------|------------|\n| K | 80.03 | 79.98 |\n| V | 80.33 | 82.34 |\n\nWe can see, upsampling V works better.\n\n**Q11**: Table 2 (c) should contain the results with the models having a similar number of parameters of the baselines.\n\n**A11**: Block numbers in different stages are listed as follows:\n\nConvNet: 1->2->6->2;\n\nConvNetv2: 2->3->6->2; \n\nConvNetv3: 2->3->6->3.\n\nResults of the modified Table 2 (c) are shown as follows:\n\n| Upsample | Params | FLOPS | Throughput | Top-1 (%) |\n|-----------|--------|-------|------------|-----------|\n| EMSA | 30.26M | 4.08G | 919 | 79.04 |\n| ConvNet | 26.11M | 3.56G | 1078 | 77.18 |\n| ConvNetv2 | 26.67M | 4.09G | 854 | 77.91 |\n| ConvNetv3 | 32.58M | 4.54G | 712 | 78.23 |\n| EMSAv2 | 30.43M | 4.10G | 826 | 80.33 |\n\n It can be easily seen that EMSAv2 has a better speed-accuracy trade-off.\n\n**Reference**\n\n[5] Ding, Xiaohan, et al. \"Repvgg: Making vgg-style convnets great again.\" CVPR 2021.", " Thank you very much for the insightful and constructive comments. \nAppendix is available with the main submission file, and Codes are available in the Supplementary Materials, which contain more content and details to help understand this manuscript.\n\n### Part1: ###\n\n**Q1**: Novelty is incremental. The major change over the baseline ResTv1 is the pixel-shuffle only.\n\n**A1**: The proposed ResTv2 is with adequately significant novelty which can be summarized as follows:\n\n(1) We are the first to adopt upsample operations to reconstruct the lost information caused by downsample operations. The \"downsample-then-upsample\" design builds a convolutional hourglass architecture [1] to effectively capture local information. Besides, the downsample operation can significantly reduce the computational cost of MSAs. In other words, our method also provides an efficient way to combine ConvNets and ViTs. Although experiments are primarily conducted on ResTv2, we also demonstrate that \"downsample-then-upsample\" design can be applied to many ViTs with/without downsample strategies (e.g., PVT [2], Swin [3]). \n The results are listed below to demonstrate the effectiveness of our design on PVT and Swin Transformer on ImageNet-1k under 300 epochs settings. \n\n| Method | Params | FLOPs | Throughput | Top-1 (%) |\n|--------|--------|-------|------------|-------------|\n| PVT-T | 13.27M | 1.94G | 1038 | 75.1 |\n| + up | 13.95M | 1.95G | 947 (-91) | 76.9(+1.8) |\n| PVT-S | 24.49M | 3.82G | 781 | 79.8 |\n| + up | 24.79M | 3.84G | 696 (-85) | 81.3(+1.5) |\n| Swin-T | 28.33M | 4.49G | 755 | 81.3 | \n| + up | 28.35M | 4.50G | 713 (-42) | 81.9 (+0.6) |\n| Swin-S | 49.61M | 8.75G | 437 | 83.2 | \n| + up | 49.66M | 8.76G | 399 (-38) | 83.7 (+0.5) |\n\nNote that we only add upsample operations for the even blocks (starting from 0, i.e., in W-MSA) in Swin Transformer because the odd blocks start with a shift window (i.e., SW-MSA), which impairs the feature maps' spatial continuity.\n\n(2) We comprehensively explore different ways to efficiently apply backbones such as ResTv2 into dense prediction tasks. We point out the gap between the theoretical FLOPs and the actual speed, which has challenged the common reviews that window attention is more suitable for higher resolution inputs [3]. We also highlight that the actual speed is more critical in designing a model. These findings can provide guidance on how efficiently to adopt backbones with downsample strategies (e.g., PVT) to downstream tasks.\n\nTherefore, this paper is adequately significant and novel, particularly according to Michael's viewpoint [4]: \"Taking an existing network and replacing one thing is better science than concocting a whole new network just to make it look more complex.\"\n\n**Q2**: Why the upsampling module should be involved? \n\n**A2**: The \"downsample-then-upsample\" design constructs a convolution branch to capture local information, which is complementary to global information captured by the self-attention branch. \nBesides, the convolution and self-attention branches share the same downsample operation, which significantly reduce computational costs. That is, EMSAv2 provides an efficient way to combine ConvNets and ViTs. Finally, assume the output of the self-attention branch has size $N \\times C$, where $N$ is the spatial dimension (i.e., $H \\times W$) and $C$ is the channel dimension, and the output of V has size $N'\\times C$. Since V is obtained by the downsample operation and linear projection, i.e., $N'<N$. Therefore, we upsample $V$ to make the convolution and self-attention branches have the same size.\n\n**Q3**: What can we learn from the architectural modifications from ResTv1 to RestV2 such as the block number at the first stage is halved.\n\n**A3**: In Table 6 in Appendix A, we add the upsample operation to ResTv1-Lite (with the same number of blocks in the first stage as ResTv1-Lite). Results have shown that the upsampling can bring 0.93 Top-1 accuracy gain (75.04 vs. 74.11). In addition, since the resolution of the first stage is high (1/4 of the input image), halving the block number can significantly reduce computational cost. In Table 7 in Appendix B, we estimate the role of the Multi-head Interaction Module (short for MHIM) and find that when the channel dimension of each head (in EMSAv2) is large (e.g., 96), the accuracy improvement by MHIM is limited. Therefore, we eliminate MHIM as default.\n\n**Reference**\n\n[1] Newell, Alejandro, Kaiyu Yang, and Jia Deng. \"Stacked hourglass networks for human pose estimation.\" ECCV, 2016.\n\n[2] Wang, Wenhai, et al. \"Pyramid vision transformer: A versatile backbone for dense prediction without convolutions.\" ICCV 2021.\n\n[3] Liu, Ze, et al. \"Swin transformer: Hierarchical vision transformer using shifted windows.\" ICCV, 2021 (best paper).\n\n[4] Michael J. Black. \"Novelty in Science: A guide for reviewers\", https://perceiving-systems.blog/en/post/novelty-in-science\n", " ### Part2: ###\n\n**Q3**: Performance of adding back non-downsampled linear/conv projected V?\n\n**A3**: Here, we set downsample sr_ratio for ResTv2-T as 1 (i.e., without downsample operation). Then, the performance of adding back non-downsampled linear/Conv projected V (ResTv3-T) on ImageNet-1k under the ablation settings is shown as below.\n\n| Method | Params | FLOPs | Throughput | Top-1 (%) |\n|-----------------|--------|-------|------------|-------------|\n| ResTv2-T | 30.43M | 4.10G | 826 | 80.3 |\n| ResTv3-T_w/o_up | 30.25M | 6.51G | 648 (-178) | 80.2 (-0.1) |\n| ResTv3-T | 30.42M | 6.52G | 591 (-235) | 80.7 (+0.4) |\n\nWe can see that adding back non-downsampled linear/Conv projected V (i.e., ResTv3-T) can improve the Top-1 accuracy of ResTv3-T_w/o_up by +0.5 (80.7 vs. 80.2). However, without the downsample operation (i.e., ResTv3-T), the inference throughput of ResTv2-T will be greatly reduced (826 vs. 591). \n\n**Q4**: If applying the proposed upsample to other work that downsample K/V for saving computation (e.g PVT), can we see performance improvements as well?\n\n**A4**: Yes, absolutely. We can apply the upsample strategy to improve the performance of PVT. \nAs shown in Figure 1, the upsample operation can improve the Top-1 accuracy of PVT-T and ResT-Lite by +2.1 and +0.9, respectively, under 100 epochs settings. Here we also list the results on ImageNet-1k under 300 epochs settings in the table below, in which we can see that the upsample operation can significantly improve the performance of PVT (>1.5 gain on Top-1 accuracy). \n\n| Method | Params | FLOPs | Throughput | Top-1 (%) |\n|---------|--------|-------|------------|------------|\n| PVT-T | 13.27M | 1.94G | 1038 | 75.1 |\n| + up | 13.95M | 1.95G | 947 (-91) | 76.9(+1.8) |\n| PVT-S | 24.49M | 3.82G | 781 | 79.8 |\n| + up | 24.79M | 3.84G | 696 (-85) | 81.3(+1.5) |\n", " Thank you very much for the insightful and constructive comments. \nAppendix is available with the main submission file, and Codes are available in the Supplementary Materials, which contain more content and details to help better understand this manuscript. \n\n### Part 1: ###\n\n**Q1**: Novelty is too limited. Current presentation is more like a patch fix to ResT.\n\n**A1**: The proposed ResTv2 is with adequately significant novelty which can be summarized as follows:\n\n(1) We are the first to adopt upsample operations to reconstruct the lost information caused by downsample operations. The \"downsample-then-upsample\" design builds a convolutional hourglass architecture [1] to effectively capture local information. Besides, the downsample operation can significantly reduce the computational cost of MSAs. In other words, our method also provides an efficient way to combine ConvNets and ViTs. Although experiments are primarily conducted on ResTv2, we also demonstrate that \"downsample-then-upsample\" design can be applied to many ViTs with/without downsample strategies (e.g., PVT [2], Swin [3]). \n The results are listed below to demonstrate the effectiveness of our design on PVT and Swin Transformer, on ImageNet-1k under 300 epochs settings. \n\n| Method | Params | FLOPs | Throughput | Top-1 (%) |\n|--------|--------|-------|------------|-------------|\n| PVT-T | 13.27M | 1.94G | 1038 | 75.1 |\n| + up | 13.95M | 1.95G | 947 (-91) | 76.9(+1.8) |\n| PVT-S | 24.49M | 3.82G | 781 | 79.8 |\n| + up | 24.79M | 3.84G | 696 (-85) | 81.3(+1.5) |\n| Swin-T | 28.33M | 4.49G | 755 | 81.3 | \n| + up | 28.35M | 4.50G | 713 (-42) | 81.9 (+0.6) |\n| Swin-S | 49.61M | 8.75G | 437 | 83.2 | \n| + up | 49.66M | 8.76G | 399 (-38) | 83.7 (+0.5) |\n\nNote that we only add upsample operations for the even blocks (starting from 0, i.e., in W-MSA) in Swin Transformer because the odd blocks start with a shift window (i.e., SW-MSA), which impairs the feature maps' spatial continuity.\n\n(2) We comprehensively explore different ways to efficiently apply backbones such as ResTv2 into dense prediction tasks. We point out the gap between the theoretical FLOPs and the actual speed, which has challenged the common reviews that window attention is more suitable for higher resolution inputs [3]. We also highlight that the actual speed is more critical in designing a model. These findings can provide guidance on how efficiently to adopt backbones with downsample strategies (e.g., PVT) to downstream tasks.\n\nTherefore, this paper is adequately significant and novel, particularly according to Michael's viewpoint [4]: \"Taking an existing network and replacing one thing is better science than concocting a whole new network just to make it look more complex.\"\n\n**Q2**: We already have the residual path that adds the original X, difference here is that this method adds conv/linear transformed, downsampled-then-upsampled X back.\n\n**A2**: \n(1) Motivation: \nThe residual path is adopted to solve the degradation problem, while the \"downsample-then-upsample\" design aims to reduce the computational cost of MSA and still retain high model capacity. In fact, the \"downsample-then-upsample\" design is a convolutional hourglass architecture [1] adapted to capture the local information complementary to long-distance dependency. For example, this design can improve the Top-1 accuracy of ResTv2-T by +1.3 (shown in Table 2(c)).\n\n(2) Degradation Problem in ResTv2: \nIn fact, we design two strategies to remedy the degradation problem in ResTv2.\n(a) A \"residual path\" between the input and output is applied in EMSAv2 and FFN, similar to ViT and ResNet. \n(b) Far more warm-up epochs are adopted to stabilize the optimization process ( We use 50 epochs in ResTv2, while in ResTv1, there are only 5 epochs).\n\n**Reference**\n\n[1] Newell, Alejandro, Kaiyu Yang, and Jia Deng. \"Stacked hourglass networks for human pose estimation.\" ECCV, 2016.\n\n[2] Wang, Wenhai, et al. \"Pyramid vision transformer: A versatile backbone for dense prediction without convolutions.\" ICCV 2021.\n\n[3] Liu, Ze, et al. \"Swin transformer: Hierarchical vision transformer using shifted windows.\" ICCV, 2021 (best paper).\n\n[4] Michael J. Black. \"Novelty in Science: A guide for reviewers\", https://perceiving-systems.blog/en/post/novelty-in-science\n\n\n\n", " The paper modifies the original attention block in ResT paper by 1. Rewind conv+IN based multi-head attention in ResT to original multi-head attention form (no conv, IN) in ViT. 2. Add upsampling operation to the downsampled V. Image classification performance is validated on ImageNet. Besides, the paper conducted ablation studies on how different window-based attention (Win, Cwin, Hwin, Global) affect AP, FLOPs, Throughput when transfer to object detection task. \n Strengths:\n\tThe paper presents results across a range of different vision tasks, including ImageNet classification, object detection and segmentation on COCO, semantic segmentation on ADE20k and achieves competitive results. \n\tBesides, FLOPs and parameters, Throughput is also benchmarked to make give one more practical aspect of model performance. \n\nWeaknesses:\n\tNovelty is too limited. At core, what the paper proposed is to upsample k/v, where k/v are downsampled for saving computations. Current presentation is more like a patch fix to ResT. If the generalization abilities of the proposed upsampling operation beyond ResT is validated, as there exist many other ViT variants saving computations by downsampling (e.g. PVT), the proposed method can be much strengthened. \n 1.\tThe target is to recover the lost information in the K/V downsampling process by using the proposed upsampling operation. We already have the residual path that adds the original X (no information loss from resolution change), difference here is that this method adds conv/linear transformed, downsampled-then-upsampled X back. Curious to see the performance if we just add back non-downsampled linear/conv projected V instead of the downsampled-then-upsampled one?\n2.\tIf applying the proposed upsampling to other work that downsample K/V for saving computation (e.g PVT), can we see performance improvements as well? \n\n\n---post-rebuttal---\nThe authors' response has partially resolved my concerns, specific they have presented the upsampling operation can generalize to other ViT variants, I changed my rating towards accept. The paper proposes specific change to ResT, the change might benefit other methods, but not validated in the work. ", " This paper proposes a vision transformer network based on the previously proposed ResT-V1 architecture by involving a new element that performs upsampling (of a token sequence). The upsampling module is actually attached to the projected output of value to recover the dimensionality of the original sequence length. The authors additionally refine the baseline ResT-V1 network 1) removing the multi-head interaction components; and 2) reconfiguring the network stage due to the appearance of the upsampling module. The modifications seem to work well but the key design choice still remain. The authors provide experimental results on ImageNet and some downstream tasks to justify the effectiveness of the proposed network architecture. ### Strengths\n- The paper is easy to follow\n- The exploration of using pixel-shuffle as the upsampling model for recovering the original signal is a nice idea, and interpreting it as the convolutional hourglass architecture also seems to make sense.\n\n\n### Weaknesses\n- Novelty is incremental. The major change over the baseline ResTv1 is the pixel-shuffle only, and the rest of the modifications are not new and cannot be one of the contributions. \n- Any intuitions or insights of why the architecture should be designed like this are missing: why the upsampling module should be involved? What can we learn from the architectural modifications from ResTv1 to RestV2 such as the block number at the first stage is halved.\n- Experimental justifications in Sections 3.4 and 4.3 do not seem to be enough backups for the explanation of the proposed architectural design. For example, Figure 3 tells us the upsampling module seemingly reduces the difference in the log amplitude between particular frequencies and the center frequency. However, this does not indicate the upsampling module is necessarily used. Furthermore, one may naturally ask the questions: 1) why do some specific frequencies only benefit from information recovery?; 2) If the upsampling module really helps information flow, shouldn't the entire frequency have the same effect?; 3) why the output-side layers do not benefit from it? Furthermore, Figure 4 is not clearly illustrated.\n\n- The details of Pixel-shuffle are not clearly presented. Is it the pixel-shuffle operation used in the super-resolution field? Then, why the dimensionality remains the same after upsampling in Figure 2. (b)?\n\n - What is the meaning of the computational density? at line 109 in p3. \n\n- Is the LN after DwConv in EMSAv1 removed in EMSAv2? \n\n- How does the upsampling change the latency? Please specify the latency or throughput in Table 2 (b)\n\n- The difference in the results between the target of K and V in Table 2 (a) is slight, so it should be verified with the results from multiple runs.\n\n- Table 2 (c) should contain the results with the models having a similar number of parameters of the baselines; can the authors provide the models have similar parameters with EMSA and EMSAv2? The authors did not provide the limitations and potential negative societal impact of their work.", " This paper proposes an improved vision Transformer architecture based on the ResTv1. To address the issue that the downsample operation in ResTv1 will impair the long-distance modeling ability, an upsample operation is employed to reconstruct the lost information. Besides, authors apply the proposed ResTv2 to different downstream tasks. Extensive results demonstrate the effectiveness and efficiency of this Transformer backbone. Strengths: \n1) The proposed architecture is simple but seems effective for different downstream tasks. \n2) It is interesting that the authors find the gap between the theoretical FLOPs and the actual speed, and they consider the actual speed when designing the model. \n3) The experiments and theoretical analysis are sufficient.\n\nWeaknesses:\n1) The main contribution of this paper is to introduce the upsample operation into the ResTv1 to compensate for the lost information from the downsample. Though this simple design can provide the performance benefit, the generalizability of this design seems narrow, does it only work well for the specific efficient Transformer model with the downsample operation? \n2) For Equ.2, is the Norm operation also eliminated along with the Conv? If so, the paper does not mention it, which is somewhat confusing. 3) I think a more detailed description of Fig.3 is needed for a better understanding, e.g., the meaning of coordinates and curves.\n Please explain the aforementioned three weakness issues (especially the 1-st issue about the generalizability) Yes, the authors address the efficiency to some extent. They point out the gap between the theoretical FLOPs and the actual speed, and consider the actual running speed more when designing the model." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 5, 5 ]

[ "LyJ9tM3v9T", "9UbIqPxb4rl", "8EyMGgOKRi", "PsMZvgXftyI", "NP6bahx8IpS", "9cSoH2JHrGH", "Je7SdHDvcSi", "x5Ths3AKScc", "s6dwonP-qQJ", "nips_2022_2OdAggzzF3z", "Je7SdHDvcSi", "0X9_fcsILKT", "x5Ths3AKScc", "2RsnTS5eUBr", "s6dwonP-qQJ", "nips_2022_2OdAggzzF3z", "nips_2022_2OdAggzzF3z", "nips_2022_2OdAggzzF3z" ]

[ "jr60FKOwGVA", "InyFbVFRmk_", "NsZgZtoix_X", "i_fUcMMJ88W", "mFW8XR5rkwY", "O6O1VZCOiK0", "rjfwV1JMxnk", "Md62xw4p3E", "zOT-2mWo2BB", "OSIEbY6x1t8", "t8qCd-4y-jB", "cQdxBRoF8Wt", "x_lFXdfZO8D", "GGfluge0qr1", "u--QtGS6fj8", "K64diYZ_nc", "fjGiTIVQaUZ", "9H7u7Ao6YHl", "RZDpTqILqg2", "t4udpnSokX1", "nXagM6Tranu", "11DSJ-byK6HS", "GiQ3pdsNLT", "5CiMN0te7q7", "HSd2tQ4dOfT", "i2ugl_WXwd", "5hDancDCbik", "ruh3uzjqvq", "zaEXyqR4Q8O", "mEwnaTfLnB6", "Hqf-Rag8dwp", "g2JM5VrgrmJ", "JVjRr7I3iYWY", "UoHDYjF4b0d", "RaEzfU5voe69", "DEy2VYA5XBW", "bgmp3f1yhT", "OxfD1FdWerb", "V3ybhIP9d-p", "2gxLjDEV13C", "WNlitlmLZn", "fv4Rt-Xf8-I" ]

[ "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for the response. Unfortunately we did not update Section 3.3 according to the new experiments which is why the description there suggests that the whole private training dataset is used. In the new results above, $D_{P1}$ is \\# GMM, $D_{P2}$ is \\# train so that $D_P \\neq D_{P1} \\cup D_{P2}$. Similarly $D_N$ corresponds to \\# test. We will update Section 3.3 to make this point clear. ", " Thanks for the thorough response.\n\nI'm satisfied with the author's justification for introducing a trusted arbitrator, especially since it has precedent in the model stealing literature.\n\nI'm still unsure about the issue of revealing the private dataset $D_P$ (used to train the encoder) to the arbitrator. The method as described in the paper seems to require that representations are produced for all instances in $D_{P}$ using the stolen encoder (see [previous comment](https://openreview.net/forum?id=CCBJf9xJo2X&noteId=i_fUcMMJ88W)). If this is not the case, then some refactoring may be needed to avoid confusion.\n\nI will consider revising my score during the reviewer-AC discussion period.", " Thanks - this is a convincing explanation. I'd personally like to see a remark in the paper explaining why the formulation differs from Maini et al. (2021). Although I realize space is limited.", " Thanks for the response - it's great to see experiments varying the amount of private data revealed to the arbitrator. However, I don't see how this experiment is compatible with the description of the method given in Section 3.3 of the paper.\n\nOn line 174, it is stated that the \"victim's encoder $f_v$ is trained using the whole private training dataset $D_P$\". On lines 183-184 the arbitrator is said to train a density estimator based on the representations of $D_{P2}$ from the stolen encoder $f_s$. Then in line 186, the arbitrator is said to generate representations of $D_{P1}$ and $D_N$ using the stolen encoder $f_s$. \n\nThus it seems $D_P = D_{P1} \\cup D_{P2}$ (the data used to train the victim's encoder) and $D_N$ (the test set) are all passed through the stolen encoder $f_s$.", " We would like to thank the reviewer for the questions and comments. The paper has definitely improved as a result. We would like to check one last time if there are any pending questions that we have not adequately addressed.", " We thank the reviewer for the discussion and appreciate the positive feedback. If there is anything more we could further improve, please let us know.", " We updated Table 6 and Section D in Appendix. We show that, for example, for $150$ components for GMM on CIFAR10, the training time is 962.07 seconds, which is around $23$X longer than for $20$ components. Moreover, GMM overfits the training set for $150$ components since the p-values for encoders $f_s$ stolen with SVHN and STL10 queries are relatively high (> 0.05), while the p-value for the victim encoder $f_v$ is relatively low ($8.42e-10$).", " I would like to thank the authors for addressing my concerns during the short rebuttal period. I will keep my rating as \"Borderline accept\".", " We thank the reviewer for the discussion and appreciate the positive feedback.", " Hello authors,\n\nThanks for the detailed reubuttal. Yes, most of my issues have been addressed, and I am now adjusting my scores to reflect that. Best of luck!", " We thank the reviewer for the response and further comments, we really appreciate the positive feedback.\n\nThese are our new modifications:\n1. We removed Appendix A (since it was the same content as in the new Section 5.4).\n2. We resolved the inconsistencies and revised the paper. \n3. We added the correct statement regarding the number of components for GMMs to the main paper in Section 5.2 and referenced the Appendix: *\"We observe that the larger the number of components for GMMs, the better the defense is. We describe our approach to the selection of components for GMMs in Appendix D.\"* (Now it is Appendix D instead of E since we removed Appendix A on the limitations of our work).\n\nWe will add the runtime for training GMMs and elaborate on the case of overfitting.", " I thank the authors for their thorough response to my concerns, and for clarifying the misunderstandings. I especially appreciate the explicit acknowledgement of limitations, and the updated results.\n\nHere are some follow-up comments:\n- Is Appendix A needed? It seems to me that it has the same content as Section 5.4.\n- Appendix E states *We observe that the smaller number of components for GMMs, the better the defense is*. Shouldn't this statement be flipped? It seems that increasing components makes the defense better.\n- The updated results on CIFAR10 with 20 components look better, please update the statements on L306 and L652 accordingly. \n- The new results however raise the importance of Appendix E and the discussion on the number of components. This appendix should ideally be summarized in the paper, and at worst referenced when discussing the main results. It would also be beneficial to substantiate the drawbacks of increasing components by (i) measuring training runtime (ii) demosntrating the case of overfitting that is stated. \n\nI am positive about the paper and believe it is a worthy contribution to the literature, thus I raise my score. The authors solve a relevant problem in a sound way (and are the first to do so), and have in my opinion adequately responded to all major concerns of reviewers. Nonetheless, I am looking forward to reading responses of other reviewers and find it necessary that they acknowledge that their concerns were appropriately covered, or continue the discussion otherwise.", " We would like to follow up to check whether the reviewer's concerns have been addressed.\n\nBased on the reviewer's suggestions we have:\n1. motivated better the additional scores and clarified their correspondence to fidelity;\n2. updated and added results to Table 1;\n3. provided evaluation for MSE and SoftNN loss functions;\n4. tried other density estimation models such as normalizing flows but found them inadequate for our task;\n5. added the section on limitations to the (revised) main paper with the suggested modifications;\n6. proposed an adaptive attack against our defense based on random obfuscations.", " We would like to follow up to check whether the reviewer's concerns have been addressed.\n\nBased on the reviewer's suggestions we have:\n1. elaborated on our defense method where we compare the representations from a single SSL encoder via GMMs;\n2. showed that the higher quality of the extracted encoder, the higher confidence of our defense;\n3. provided the empirical analysis to show that selecting the standard confidence threshold of 0.05 works as expected for our defense;\n4. explained the robustness of dataset inference to obfuscations;\n5. defined the mutual information and cosine similarity scores as metrics to measure the quality of stolen SSL encoders;\n6. addressed the comments on terminology as well as the placement of Theorem 1 in the (revised) main paper;", " We would like to follow up to check whether the reviewer's concerns have been addressed.\n\nBased on the reviewer's suggestions we have:\n1. combined the linear evaluation on downstream tasks and our metrics into a single table and ran additional experiments to present differences between the metrics;\n2. elaborated on adding noise or dropout as a form of attack on our defense;\n3. explained more the performance difference between stolen encoder $f_s$ and an independent one $f_i$;\n4. defined clearly the dataset inference as \"the process of identifying whether a suspected model copy has private knowledge from the original model’s dataset, as a defense against model stealing\";\n5. updated Figure 1 to simplify its flow/structure;\n6. addressed minor comments.", " We would like to follow up to check whether the reviewer's concerns have been addressed.\n\nBased on the reviewer's suggestions we have:\n1. showed that the dataset inference for encoders is compatible with the direct query access;\n2. ran a new experiment to present the minimum number of queries required for our dataset inference, and in general, the dependence between the number of queries vs the confidence of our test;\n3. added new results that show the impact of fine-tuning on stolen encoders;\n4. elaborated more on the suitability of GMMs for our task;\n5. cited suggested related work;\n6. added a section on limitations to the revised paper;\n7. updated Figure 1. ", " We thank the reviewers for their comments and feedback. We answer all the questions below in-line and provide a revised version of our paper (both the main and the appendix), where the new or updated parts are marked in blue.", " Next, we also present our new results from Table 10. For example, we observe that when stealing with SVHN queries from the CIFAR10 victim encoder, we cannot identify the stolen encoder as extracted from the victim based on the victim's performance on downstream tasks. On the other hand, our metrics show evidence of stealing after around 30K queries. Additionally, our metrics correctly show a negligible similarity between the victim and independent encoders. We also note that the cosine similarity score has an almost linear dependence on the number of queries that the adversary used to extract the victim encoder, which is helpful to adequately measure the quality of this stolen encoder.\n\n| \\# of Queries | Dataset | CIFAR10 | STL10 | SVHN | $S(\\cdot,f_v)$ | $C(\\cdot,f_v)$ | p-value |\n|----------------|----------|---------|-------|------|----------------|----------------|----------|\n| Victim Encoder | N/A | 87.4 | 73.4 | 49.5 | 1 | 1 | 1.37e-16 |\n| 500 | SVHN | 22.3 | 20.8 | 20.1 | 0.00 | 0.07 | 5.69e-1 |\n| 1K | SVHN | 26.5 | 23.4 | 29.9 | 0.06 | 0.11 | 9.02e-1 |\n| 2K | SVHN | 40.0 | 35.2 | 46.7 | 0.12 | 0.13 | 7.83e-1 |\n| 3K | SVHN | 44.4 | 39.8 | 56.3 | 0.18 | 0.21 | 8.04e-1 |\n| 4K | SVHN | 47.4 | 42.5 | 60.8 | 0.22 | 0.19 | 6.30e-1 |\n| 5K | SVHN | 49.5 | 43.8 | 60.9 | 0.29 | 0.28 | 4.28e-1 |\n| 10K | SVHN | 55.6 | 46.6 | 58.9 | 0.38 | 0.36 | 6.42e-1 |\n| 20K | SVHN | 57.7 | 48.7 | 60.4 | 0.43 | 0.39 | 9.81e-2 |\n| 30K | SVHN | 58.0 | 49.2 | 57.0 | 0.57 | 0.45 | 6.73e-2 |\n| 40K | SVHN | 61.4 | 51.1 | 55.0 | 0.69 | 0.49 | 4.83e-2 |\n| 50K | SVHN | 61.2 | 51.7 | 54.8 | 0.76 | 0.50 | 3.97e-2 |\n| 50K | CIFAR10 | 84.8 | 70.7 | 52.4 | 0.84 | 0.95 | 8.73e-7 |\n| 50K | STL10 | 86.8 | 73.0 | 49.8 | 0.89 | 0.92 | 1.04e-2 |\n| Independent | SVHN | 57.5 | 50.6 | 80.5 | 0.12 | 0.0001 | 2.96e-1 |\n| Independent | CIFAR100 | 73.8 | 61.7 | 67.7 | 0.63 | 0.001 | 3.67e-1 |\n| Independent | STL10 | 79.4 | 73.1 | 55.8 | 0.34 | 0.001 | 5.21e-1 |", " Next, we also present our new results from Table 10. For example, we observe that when stealing with SVHN queries from the CIFAR10 victim encoder, we cannot identify the stolen encoder as extracted from the victim based on the victim's performance on downstream tasks. On the other hand, our metrics show evidence of stealing after around 30K queries. Additionally, our metrics correctly demonstrate a negligible similarity between the victim and independent encoders. \n\n| \\# of Queries | Dataset | CIFAR10 | STL10 | SVHN | $S(\\cdot,f_v)$ | $C(\\cdot,f_v)$ | p-value |\n|----------------|----------|---------|-------|------|----------------|----------------|----------|\n| Victim Encoder | N/A | 87.4 | 73.4 | 49.5 | 1 | 1 | 1.37e-16 |\n| 500 | SVHN | 22.3 | 20.8 | 20.1 | 0.00 | 0.07 | 5.69e-1 |\n| 1K | SVHN | 26.5 | 23.4 | 29.9 | 0.06 | 0.11 | 9.02e-1 |\n| 2K | SVHN | 40.0 | 35.2 | 46.7 | 0.12 | 0.13 | 7.83e-1 |\n| 3K | SVHN | 44.4 | 39.8 | 56.3 | 0.18 | 0.21 | 8.04e-1 |\n| 4K | SVHN | 47.4 | 42.5 | 60.8 | 0.22 | 0.19 | 6.30e-1 |\n| 5K | SVHN | 49.5 | 43.8 | 60.9 | 0.29 | 0.28 | 4.28e-1 |\n| 10K | SVHN | 55.6 | 46.6 | 58.9 | 0.38 | 0.36 | 6.42e-1 |\n| 20K | SVHN | 57.7 | 48.7 | 60.4 | 0.43 | 0.39 | 9.81e-2 |\n| 30K | SVHN | 58.0 | 49.2 | 57.0 | 0.57 | 0.45 | 6.73e-2 |\n| 40K | SVHN | 61.4 | 51.1 | 55.0 | 0.69 | 0.49 | 4.83e-2 |\n| 50K | SVHN | 61.2 | 51.7 | 54.8 | 0.76 | 0.50 | 3.97e-2 |\n| 50K | CIFAR10 | 84.8 | 70.7 | 52.4 | 0.84 | 0.95 | 8.73e-7 |\n| 50K | STL10 | 86.8 | 73.0 | 49.8 | 0.89 | 0.92 | 1.04e-2 |\n| Independent | SVHN | 57.5 | 50.6 | 80.5 | 0.12 | 0.0001 | 2.96e-1 |\n| Independent | CIFAR100 | 73.8 | 61.7 | 67.7 | 0.63 | 0.001 | 3.67e-1 |\n| Independent | STL10 | 79.4 | 73.1 | 55.8 | 0.34 | 0.001 | 5.21e-1 |", " We thank the reviewer for the valuable, detailed, and positive feedback. Our responses are in-line below:\n\n>**The motivation for the additional contribution (two scores) is somewhat unclear. Can the authors make a stronger point for why linear evaluation on several tasks (as in Table 3 in [14]) is insufficient/unnecessary; what is the reason for not including such evaluation alongside proposed metrics?**\n\nOur motivation is to improve the assessment of the quality of stolen encoders by providing complementary evaluation metrics, in addition to downstream accuracy. Relying on downstream accuracy is often insufficient in our setting, because an independently trained encoder can have high downstream accuracy without being stolen from the victim encoder. An example of this phenomenon is shown in the results below (from Table 9): independently trained encoders have high downstream accuracy, but low cosine similarity.\n\n| Number of Queries | Dataset for Stealing |Downstream CIFAR10 | Downstream STL10 | Downstream SVHN | Cosine Similarity |\n|-------------|----------------|----------------|------|------|-----------------|\n|500 | CIFAR10 |24.5 |23.3 |19.3 |0.24 |\n|5K | CIFAR10 |53.3 |45.2 |58.1 |0.4 |\n|7K | CIFAR10 |57.9 |50.9 |69.2 |0.46 |\n|8K | CIFAR10 |59.6 |52 |72.6 |0.47 |\n|9K | CIFAR10 |59.9 |50.8 |71.5 |0.49 |\n|10K | CIFAR10 |59.1 |51.3 |72.3 |0.52 |\n|20K | CIFAR10 |60.6 |51.5 |73.4 |0.58 |\n|30K | CIFAR10 |60.7 |52.1 |74.1 |0.63 |\n|50K | CIFAR10 |59.8 |51.6 |75.1 |0.69 |\n|50K | STL10 |60.6 |51.5 |76.8 |0.89 |\n|50K | SVHN |55.6 |48.7 |82.2 |0.91 |\n|*Independent*| CIFAR10 |87.4 |73.4 |49.5 |0.009 |\n|*Independent*| CIFAR100 |73.8 |61.7 |67.7 |0.007 |", " >**In a similar vein, both scores (MI and cosine) to me seem analogous to fidelity, and not accuracy as claimed in the paper. Can the authors elaborate on this claim further? Making this part more cohesive with the rest of the paper would make the contribution stronger.**\n\nWe agree that mutual information and cosine similarity scores are more similar to the fidelity score from supervised learning instead of accuracy. We indicated this in the abstract: *“As part of our evaluation, we also propose to measure the fidelity of stolen encoders without involving downstream tasks and to quantify the effectiveness of the theft detection; instead, we leverage mutual information and distance measurements.”* We corrected the statement at the beginning of Section 4 in the revised version of the paper.\n\n>**Some results seem to be missing in Table 1, e.g. ImageNet as D_S for first two choices of D_P. While the conclusions certainly hold in almost all cases, the test does not pass for CIFAR10 as D_P and SVHN as D_S, making it more necessary to provide a complete and convincing evaluation.**\n\nWe ran additional experiments to steal from SVHN and CIFAR10 victim encoders using ImageNet queries. The results for running dataset inference on these stolen models are as follows:\n| Victim’s Dataset | Stealing Dataset | p-value | $\\Delta \\mu$ (effect size) |\n|---------|---------------|--------------------|--------------|\n| CIFAR10 | ImageNet | 6.34e-3 |3.47 |\n| SVHN | ImageNet | 5.32e-8 | 5.52 |\n\nWe updated Table 1 to include the required results (e.g., ImageNet as D_S for the first two choices of D_P). We also improved the GMM model (increased the number of components from 10 to 20) and obtained higher confidence (p-value below 0.05) that the encoder was indeed stolen for the pointed out case with CIFAR10 as $D_P$ and SVHN as $D_S$ (the victim model trained on CIFAR10 and stealing with the SVHN dataset).\n\n| | Dataset | Obfuscation | p-value | $\\Delta \\mu$ (effect size) |\n|--------|----------|-------------|----------|----------|\n| Victim | CIFAR10 | | 4.52e-17 | 10.73 |\n| Stolen | SVHN | | 3.97e-2 | 3.04 |\n| Stolen | CIFAR10 | | 8.73e-7 | 5.09 |\n| Stolen | STL10 | | 1.04e-2 | 3.42 |\n| Stolen | CIFAR10 | shuffle | 1.72e-6 | 4.98 |\n| Stolen | CIFAR10 | pad | 3.34e-6 | 4.84 |\n| Stolen | CIFAR10 | transform | 6.81e-7 | 5.11 |\n| Independent | CIFAR100 | | 3.67e-1 | -0.37 |\n| Independent | SVHN | | 2.96e-1 | 0.98 |\n", " >**Further, 4.3 claims that the paper focuses on both MSE and InfoNCE stealing losses, but 5.1 seems to be imply only InfoNCE is used in the evaluation. Can the authors comment on this mismatch? The evaluation would be stronger if MSE and SoftNN were added.**\n\nWe focused on the InfoNCE loss for stealing since, in most cases, it gave the best performance of the stolen encoders. For completeness, we report the results of our ownership resolution for different loss functions used for stealing (as in Table 2 in [14]). We steal the CIFAR10 encoder using 9000 queries from the CIFAR10 test data with the MSE, InfoNCE and SoftNN loss functions. As the table below shows, we are able to achieve low p-values for all of the loss functions. \n\n| Loss | Accuracy (%) on CIFAR10 | p-value | $\\Delta \\mu$ (effect size) |\n|---------|---------------|--------------------|--------------|\n| *Victim* | 86.9 | 1.37e-16 | 9.34 |\n| MSE | 79.8 | 7.82e-11 | 8.39 |\n| InfoNCE | 77.6 | 3.56e-6 | 4.64 |\n| SoftNN | 77.8 | 5.64e-4 | 3.98 |\n\n>**(Nit) It would be interesting to see if different density estimation methods would be able to further boost the performance, did the authors experiment with this?**\n\nWe chose GMMs because other density estimation models such as normalizing flows are overparameterized and would require more training data. In essence, we do not need to model the density of the representations very accurately: our only requirement is for the method to distinguish between the densities of the representations.\n", " >**Regarding limitations, it would be good to more explicitly acknowledge the strength of results compared to the supervised case and reflect on statements given in [14].**\n\nIndeed, the results from the Supervised Learning (SL) show that the detection of the stolen model is possible with fewer queries than in the SSL setting and the significance level in SL is set to 1% while it is 5% for SSL. Previous work [1, 2] have shown that self-supervised encoders trained using heavy augmentations and contrastive learning generalize better than their supervised counterparts, which makes it harder for the dataset inference to differentiate between train and test representations in SSL than in SL setting.\n\nThe dataset inference is harder to apply in the SSL setting than in the supervised setting [14]. The preliminary work [14] assumed access to the projection head, which usually is not accessible for public APIs that return only representations instead of their projections. The method based on the loss values from [14] considers the data points separately. We directly use representations instead of their projections and extend the method to model the distributions of train vs test representations holistically. We found that using GMMs allowed us to differentiate between the representations from train vs test sets, which was not possible by utilizing the loss values of projected representations. We added Section 5.4 on Limitations in the main paper.\n\n*References:*\n\n[1] [Concept Generalization in Visual Representation Learning](https://openaccess.thecvf.com/content/ICCV2021/html/Sariyildiz_Concept_Generalization_in_Visual_Representation_Learning_ICCV_2021_paper.html). Mert Bulent Sariyildiz, Yannis Kalantidis, Diane Larlus, Karteek Alahari. ICCV 2021.\n\n[2] [Contrasting Contrastive Self-Supervised Representation Learning Pipelines.](https://openaccess.thecvf.com/content/ICCV2021/html/Kotar_Contrasting_Contrastive_Self-Supervised_Representation_Learning_Pipelines_ICCV_2021_paper.html) Klemen Kotar, Gabriel Ilharco, Ludwig Schmidt, Kiana Ehsani, Roozbeh Mottaghi. ICCV 2021.\n\n[14] [On the difficulty of defending self-supervised learning against model extraction.](https://proceedings.mlr.press/v162/dziedzic22a.html) Adam Dziedzic, Nikita Dhawan, Muhammad Ahmad Kaleem, Jonas Guan, Nicolas Papernot. ICML 2022.\n\n>**I find it necessary to consider the prospect of adaptive adversaries.**\n\nWe introduce the possible adaptive attacks against our method as obfuscations (shuffle, pad, transform). We show that our method can still help detect model stealing even when the adversary obfuscates their representations. One other obfuscation method could pad the representations with noise values instead of zeros. Then, we should expect that the more noise (e.g., higher standard deviation for the Gaussian noise) we add, the worse the performance of our defense. However, this would also lower the downstream accuracy of the stolen model, which gives the trade-off between the strength of the adaptive attack and the utility of the stolen encoder. Additionally, the shuffle and pad obfuscations can hinder the performance of the cosine similarity score in assessing the quality of stolen encoders but the mutual information score is a more robust metric in these cases. \n\nWe ran additional experiments for random obfuscation. We add Gaussian noise $N(0, 0.1)$ to the random dimensions of representations. Below, we present the mutual information scores (denoted as S) and p-values for the CIFAR10 victim encoder stolen using the STL10 dataset. In the first (header) row *Corrupt %* represents the percent of representation dimensions being obfuscated. 0 means no obfuscation, and 100 means all dimensions are corrupted. \n\n| Corrupt % | 0 | 20 | 40 | 60 | 80 | 100 |\n|-----------|---------|---------|---------|---------|---------|---------|\n| S | 0.89 | 0.81 | 0.77 | 0.76 | 0.71 | 0.69 |\n| p-value | 1.04e-2 | 3.76e-2 | 4.91e-2 | 8.00e-2 | 1.03e-1 | 4.73e-1 |\n", " We appreciate the constructive feedback. We thank the reviewer for the detailed analysis of our paper and provide a case-by-case response to the comments below. \n\n>**The defender is required to reveal private training/test data to a trusted arbitrator. This is not required in the original formulation for classifiers (Maini et al., 2021), where the defender is able to run dataset inference themselves given query access to the stolen model.**\n\nWe strictly improve upon the original dataset inference, where the private data points are directly revealed to the potential adversary. Our method is compatible with direct query access, thus the defender can also send the private training data points to the potentially stolen encoder and obtain the corresponding representations to calculate the relevant log-likelihoods needed to train a density estimator for dataset inference. However, the adversary might capture our private data points as a result of this querying and claim that they also trained their encoder on these points. The arbitrator, as the 3rd trusted party, eschews this problem. While the presence of a trusted arbitrator is indeed an additional requirement in our method, this arrangement has been made primarily to allow for an increased level of transparency between the defender and a potential adversary in the process of dataset inference. We note that it is still possible for the defender to run dataset inference themselves.\n", " >**In order to run dataset inference, the defender’s private train/test data sets must be passed through the adversary’s encoder (in their entirety).**\n\nIn our method, we do not require to pass the datasets in their entirety through the adversary’s encoder. Our method does require a significantly larger number of private samples compared to the original formulation of dataset inference. However, this is primarily because of the fundamental difference between the supervised and self-supervised settings and the size of the output representations where getting a signal that is statistically significant requires a larger number of queries. \nWe run additional experiments, where we compute the p-values for ownership resolution with different numbers of private data points used and show that the signal becomes weaker as the number of utilized data points decreases. \n\nIn the Table below (Table 17 in the Appendix), we detect if a given encoder was stolen using a different number of queries. $D_P$ is the victim's private data, $D_S$ is the data used for stealing. *# GMM* is the number of data points used to train the GMM, *# train* is the number of private data points and # test is the number of test data points that are used to compare (in terms of the representations) using GMM. *# total* is the total number of data points used for our dataset inference method. We observe that for the ImageNet victim stolen with SVHN queries, our method requires at least 30K queries for GMMs and 10K for both private training and test data points. For the SVHN victim stolen with SVHN queries, our method requires at least 5K queries for GMMs and 1K for both private training and test data points. \n\n\n| $D_P$ | $D_S$ | \\# GMM | \\# train | \\# test | \\# total | p-value | $\\Delta \\mu$ (effect size) |\n|----------|-------|--------|----------|---------|----------|----------|--------------|\n| ImageNet | SVHN | 100K | 50K | 50K | 200K | 3.33e-4 | 14.79 |\n| ImageNet | SVHN | 50K | 50K | 50K | 150K | 1.11e-3 | 10.76 |\n| ImageNet | SVHN | 50K | 25K | 25K | 100K | 8.99e-3 | 9.68 |\n| ImageNet | SVHN | 50K | 10K | 10K | 70K | 3.42e-2 | 8.26 |\n| ImageNet | SVHN | 50K | 5K | 5K | 60K | 7.81e-2 | 6.32 |\n| ImageNet | SVHN | 40K | 10K | 10K | 60K | 2.81e-2 | 8.63 |\n| ImageNet | SVHN | 40K | 5K | 5K | 50K | 9.72e-2 | 6.01 |\n| ImageNet | SVHN | 30K | 10K | 10K | 50K | 4.52e-2 | 8.47 |\n| ImageNet | SVHN | 30K | 5K | 5K | 40K | 1.23e-1 | 5.89 |\n| ImageNet | SVHN | 20K | 10K | 10K | 40K | 6.52e-2 | 7.81 |\n| ImageNet | SVHN | 10K | 10K | 10K | 30K | 4.52e-1 | 3.59 |\n| SVHN | SVHN | 50K | 10K | 10K | 70K | 8.23e-68 | 10.69 |\n| SVHN | SVHN | 50K | 1K | 1K | 52K | 7.63e-32 | 7.53 |\n| SVHN | SVHN | 10K | 10K | 10K | 30K | 9.80e-10 | 4.05 |\n| SVHN | SVHN | 10K | 1K | 1K | 12K | 2.36e-6 | 3.41 |\n| SVHN | SVHN | 5K | 1K | 1K | 7K | 7.33e-4 | 2.28 |\n| SVHN | SVHN | 1K | 1K | 1K | 3K | 4.56e-1 | 1.26 |", " >**One way around this would be to compel the adversary to share their model with the trusted arbitrator. However this may not be possible from a legal perspective.**\n\nThis is indeed how we envision an application of dataset inference in the practical setting. As the defender shares both a model and their private data with an arbitrator, we work under the assumption that it is not unreasonable for the arbitrator to also request the adversary’s model. This assumption has precedent in this field; for example, proof-of-learning, which the reviewer aptly points out as another related work, requires a third-party verifier with access to model weights acting as arbitrator (\"the verifier would be a legal entity resolving ownership disputes\" [1]).\n\nAnother alternative is to use protocols from cryptography such as homomorphic encryption and secure multi-party computation for private inference (inference on encrypted data), which would avoid the need for the victim to reveal the private data points [2,3].\n\n>**Is it possible to make this approach more practical given the issues raised above?**\n\nTo summarize the responses above, we believe two changes can address the issues raised: \n\n1. The defender can reveal a smaller subset of their training data at the expense of lower confidence in the outcome of dataset inference.\n2. Concerns around the direct querying of the adversary’s model with private training data from the defender can be addressed using cryptographic primitives such as homomorphic encryption and/or a secure multiparty computation approach for private inference [2,3].\n\n**References:**\n\n[1] [Proof-of-learning: Definitions and practice.](https://arxiv.org/abs/2103.05633) Hengrui Jia, Mohammad Yaghini, Christopher A. Choquette-Choo, Natalie Dullerud, Anvith Thudi, Varun Chandrasekaran, Nicolas Papernot. IEEE Symposium on Security and Privacy (S&P), 2021.\n\n[2] [MP2ML: A Mixed-Protocol Machine Learning Framework for Private Inference.](https://encrypto.de/papers/BCDSY20.pdf) Boemer, Fabian and Cammarota, Rosario and Demmler, Daniel and Schneider, Thomas and Yalame, Hossein. 2020.\n\n[3] [Delphi: A Cryptographic Inference Service for Neural Networks.](https://www.usenix.org/conference/usenixsecurity20/presentation/mishra) Pratyush Mishra and Ryan Lehmkuhl and Akshayaram Srinivasan and Wenting Zheng and Raluca Ada Popa. USENIX, 2020.\n", " >**Can this approach handle more subtle forms of stealing? E.g., where an encoder is initialized by model extraction, then refined on independent training data.**\n\nWe thank the reviewer for this suggestion. We ran additional experiments to evaluate this setting and observed that our approach is able to identify fine-tuned models as stolen. We use a stolen encoder from the SVHN victim model (stolen with SVHN data) and then retrain it with standard contrastive learning using 5 epochs on the following number of samples (5K, 10K, 25K, 50K) from CIFAR10. We then check how our dataset inference performs on the fine-tuned encoders. As expected, the p-values increase with more samples for fine-tuning, while the values of the effect size decrease. \n\n| # of samples | p-value | $\\Delta \\mu$ (effect size) |\n|---------|---------------|--------|\n| 5K | 3.24e-16 | 7.03\n| 10K | 1.82e-16 | 7.14 |\n| 20K | 6.91e-14 | 6.09 |\n| 50K | 5.28e-12 | 5.53 |\n\nWe also check how the number of epochs over which the fine-tuning is done influences our defense. We use the same stolen encoder as in the previous experiment and keep 50K as the number of data points used for fine-tuning. We also observe that with more epochs, p-values increase while the values of the effect size decrease. \n\n| # of epochs | p-value | $\\Delta \\mu$ (effect size) |\n|---------|---------------|--------|\n| 5 | 5.28e-12 |5.53 |\n| 10 | 8.73e-6 |4.62 |\n| 25 | 6.81e-1 |1.34 |\n| 50 | 1.73e-1 |0.92 |\n| 100 | 8.53e-1 | -0.53 |\n\nWe note that in the original work on dataset inference for supervised models [31], the fine-tuning was done directly on the victim model (which was directly accessed by an adversary) instead of on a stolen model. Additionally, the extra computation required by the adversary for fine-tuning diminishes the benefit of stealing the encoder.\n\n>**It would be good to elaborate on what makes GMMs suited for this task. As I understand, GMMs are not universal approximators when the number of components is fixed. In practice, how would one choose the number of components?**\n\nWe chose GMMs because other density estimation models like normalizing flows are overparameterized and would require more training data. In essence, we do not need to model the density of the representations very accurately: our only requirement is for the method to distinguish between the densities of the representations.\n\nGiven an appropriate number of components, the use of GMMs is justified by the Central Limit Theorem. They enjoy theoretical properties of being consistent and asymptotically normal estimators. The efficiency of training a GMM trades off its simplicity relative to other more complex parametric density estimation methods.\n\nA Gaussian mixture model is a universal approximator of densities, in the sense that any smooth density can be approximated with any specific nonzero amount of error by a Gaussian mixture model with enough components [1]. In our method, we do not fix the number of components but find the number of components so that we are able to (1) correctly mark the victim model as the original model trained on the given private training set and (2) obtain a non-conclusive answer (indicating that we cannot state that the model was stolen) for an independent model. Then, a GMM with this number of components is used to assess the potentially stolen SSL encoder.\n\nThere are several proposed methods in the literature to choose the number of components for a GMM, based on validation, mutual information, or AIC and BIC scores [2] (more details can be found [here](https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.109.8192&rep=rep1&type=pdf)). However, we observe that our setting allows us to efficiently find an appropriate number of components.\n\n**References:**\n\n[1] [Deep Learning (book)](https://www.deeplearningbook.org/). Ian Goodfellow, Yoshua Bengio, and Aaron Courville. 2016.\n\n[2] [The estimating optimal number of Gaussian mixtures based on incremental k-means for speaker identification](https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.109.8192&rep=rep1&type=pdf). Younjeong Lee, Ki Yong Lee, Joohun Lee. International Journal of Information Technology, 2006.\n\n[31] [Dataset Inference: Ownership Resolution in Machine Learning](https://openreview.net/forum?id=hvdKKV2yt7T). Pratyush Maini, Mohammad Yaghini, Nicolas Papernot. ICLR 2021.\n", " >**Another related work that ought to be cited is by (Jia et al., 2021). They discuss an alternative reactive defense for model stealing called proof-of-learning.**\n\nWe added this paragraph in Section 2 on Related Work: *“Proof-of-Learning (Jia et al., 2021) is a reactive defense that involves the defender claiming ownership of a model by showing incremental updates of the model training. It is a complementary method to dataset inference, which instead identifies a stolen model. PoL could be applied directly to SSL encoders, however, it requires an expensive verification process, where the verifier needs to perform model updates and the prover needs to save intermediate weights of the model, which is more expensive than dataset inference with GMMs.”* Please, see the revised paper.\n\nWe note that our defense and Proof-of-Learning are not alternatives of each other, but rather complementary: our defense helps identify an adversary's model as stolen from the owner's, whereas Proof-of-Learning helps verify that a model is trained by the owner.\n\n>**Limitations are discussed in appendices; however, a summary should be included in the main paper.**\n\nWe added Section 5.4 as a summary of Limitations to the main paper: *“If the t-test run as part of dataset inference is inconclusive for an extracted encoder, we cannot state whether the encoder was stolen. Similarly, for an independent encoder, there is the possibility of it being incorrectly classified as stolen. Previous work [26,38] has shown that self-supervised encoders trained using heavy augmentations and contrastive learning generalize better than their supervised counterparts, which makes it harder for the dataset inference to differentiate between train and test representations in SSL than in the SL setting [14]. The loss values of projected individual representations are insufficient for dataset inference [14]. We build on top of this observation to enable dataset inference for encoders and use GMMs to distinguish between train and test representations.”*\n\n>**I wonder if Figure 1 could be simplified, as it seems many of the quantities do not need to be computed to run the test against a single potentially stolen encoder.**\n\nWe simplified Figure 1 in the revised paper, where we present only the ownership resolution for a single potentially stolen SSL encoder. The full overview of our method (also slightly simplified), where we show each stage of the dataset inference, was moved to section J in the Appendix as Figure 7.", " Thank you for your detailed, helpful, and insightful feedback. We address individual points below.\n\n>**Lines 203-205. As a baseline, the authors should include experiments for scenarios where downstream tasks (single, or 2-3 combined) are trained using the \"feature extractors\". It's true that \"a single downstream task cannot adequately reflect...\", but it would be nice to have some estimates (performance numbers) to know for sure how much this difference really is.**\n\nWe have already included these numbers in the Appendix H and Tables 7, 8, and 9. We have also modified Table 9 and combined it with results from Tables 1, 2, and 3, to incorporate the performance on downstream tasks and our new metrics, namely the mutual information score, cosine similarity, and the p-values. Table 9 is for the victim encoder pre-trained on the SVHN dataset. We also added a corresponding Table 10 for the victim encoder that is pre-trained on the CIFAR10 dataset. Please, see our revised paper and the appendix in the supplementary materials.\n\nWe present below our new results from Table 9. We observe that an encoder of high quality is extracted after around 7K queries according to the downstream tasks and our metrics show evidence of stealing after around 9K queries. Thus, the linear evaluation on downstream tasks and our metrics indicate model stealing after a similar number of queries used by an adversary. We also note that the cosine similarity score has an almost linear dependence on the number of queries that the adversary used to extract the victim encoder, which is helpful to adequately measure the quality of this stolen encoder.\n\n| \\# of Queries | Dataset | CIFAR10 | STL10 | SVHN | $S(\\cdot,f_v)$ | $C(\\cdot,f_v)$ | p-value |\n|----------------|----------|---------|-------|------|----------------|----------------|----------|\n| Victim Encoder | N/A \t| 57.5\t| 50.6 | 80.5 | 1 \t| 1 \t| 9.69e-227 |\n| 500 \t| CIFAR10\t| 24.5\t| 23.3 | 19.3 | 0.00 \t| 0.24 \t| 6.89e-1 |\n| 5K \t| CIFAR10\t| 53.3\t| 45.2 | 58.1 | 0.11 \t| 0.40 \t| 3.51e-1 |\n| 7K \t| CIFAR10\t| 57.9\t| 50.9 | 69.2 | 0.14 \t| 0.46 \t| 4.72e-1 |\n| 8K \t| CIFAR10\t| 59.6\t| 52.0 | 72.6 | 0.53 \t| 0.47 \t| 9.87e-2 |\n| 9K \t| CIFAR10\t| 59.9\t| 50.8 | 71.5 | 0.57 \t| 0.49 \t| 6.23e-2 |\n| 10K \t| CIFAR10\t| 59.1\t| 51.3 | 72.3 | 0.69 \t| 0.52 \t| 5.82e-3 |\n| 20K \t| CIFAR10\t| 60.6\t| 51.5 | 73.4 | 0.92 \t| 0.58 \t| 2.31e-7 |\n| 30K \t| CIFAR10\t| 60.7\t| 52.1 | 74.1 | 0.93 \t| 0.63 \t| 2.11e-10 |\n| 50K \t| CIFAR10\t| 59.8\t| 51.6 | 75.1 | 0.94 \t| 0.69 \t| 1.19e-17 |\n| 50K \t| STL10 | 60.6\t| 51.5 | 76.8 | 0.95 \t| 0.89 \t| 1.65e-11 |\n| 50K \t| SVHN\t| 55,6\t| 48.7 | 82.2 | 0.96 \t| 0.91 \t| 1.05e-75 |\n| Independent\t| CIFAR10\t| 87.4\t| 73.4 | 49.5 | 0.90 \t| 0.009 \t| 3.56e-1 |\n| Independent\t| CIFAR100 | 73.8\t| 61.7 | 67.7 | 0.90 \t| 0.007 \t| 2.13e-1 |\n| Independent\t| STL10\t| 79.4\t| 73.1 | 55.8 | 0.84 \t| 0.015 \t| 4.62e-1 |\n", " >**Lines 322-322: How about adding noise in intermediate layers (or inputs/outputs), or dropout?**\n\nGiven the structure of neural networks, where intermediate layers affect subsequent ones and the errors accumulate, these types of noise additions would lead to a functionally different adversary model. While this would likely avoid the model being detected as stolen, it would also negatively affect the utility of the model for the adversary. As part of our defense setup, we assume that the encoder provided by the adversary to the arbitrator is the same as the encoder it uses normally. Otherwise, the adversary could provide an unrelated model to the arbitrator from where detecting whether a model is stolen would not be possible. \n\nThere have been defenses based on a similar idea of random perturbation of intermediate layers in the area of adversarial examples [1]. However, such “noisy” networks have a drop in their performance and there are methods to recover obfuscated outputs, such as EOT (Expectation Over Transformation) [2]. In our case, the defender could query the noisy encoder many times with the same input and take the averaged representation so that the effect of added noise is minimized. \n\n**References:**\n\n[1] [Towards Robust Neural Networks via Random Self-ensemble.](https://openaccess.thecvf.com/content_ECCV_2018/html/Xuanqing_Liu_Towards_Robust_Neural_ECCV_2018_paper.html)\nXuanqing Liu, Minhao Cheng, Huan Zhang, Cho-Jui Hsieh. ECCV 2018. \n\n[2] [Synthesizing Robust Adversarial Examples.](https://proceedings.mlr.press/v80/athalye18b.html) Anish Athalye, Logan Engstrom, Andrew Ilyas, Kevin Kwok. ICML 2018.\n\n\n>**Table 2: Performance difference between $f_s$ for some cases does not seem to be too far from $f_i$.**\n\nWe discussed the details of scores and their performance tradeoffs in the main paper in Section 5.3. In general, we see that for the mutual information scores, the differences between $f_s$ and $f_i$ are not very large, which is likely because the mutual information score is based on an approximation. Even though the differences are small, they are sufficient to distinguish between the stolen and independent encoders in most cases. In contrast, the cosine similarity score has large differences between $f_s$ and $f_i$ when no obfuscations are applied but is not robust under obfuscations where the score for $f_s$ becomes almost equivalent to $f_i$. \n\n>**Line 34: Isn't *dataset inference* the threat model? Like membership inference or property inference?**\n\nDataset inference is not a threat model. The original paper on dataset inference describes it as “the process of identifying whether a suspected model copy has private knowledge from the original model’s dataset, as a defense against model stealing” in the abstract and we use the same formulation in our work. \n\n>**Figure 1 is too complicated - either increase the size (and de-clutter) or simplify the flow/structure.**\n\nWe simplified Figure 1 in the revised paper, where we present only the ownership resolution for a single potentially stolen SSL encoder. The full overview of our method (also slightly simplified), where we show each stage of the dataset inference, was moved to the new section J in the Appendix as Figure 7.\n\n>**Minor Comments.**\n\nThe overfill issues for Tables 2 and 3 and the comment on line 342 have also been fixed. Regarding the comment for line 347, we would like to clarify that we consider our method as a *reactive* defense, which works after a model has been stolen; however for consistency with [15,30] we refer to it as a defense.\n\n**References:**\n\n[15] [Increasing the cost of model extraction with calibrated proof of work](https://openreview.net/forum?id=EAy7C1cgE1L). Adam Dziedzic, Muhammad Ahmad Kaleem, Yu Shen Lu, and Nicolas Papernot. ICLR 2022.\n\n[30] [EncoderMI: Membership Inference against Pre-trained Encoders in Contrastive Learning](https://dl.acm.org/doi/10.1145/3460120.3484749). Hongbin Liu, Jinyuan Jia, Wenjie Qu, Neil Zhenqiang Gong. CCS 2021.\n", " We appreciate the positive, encouraging, and constructive feedback. We thank the reviewer for the detailed analysis of our paper and below provide a case-by-case response to the comments.", " We do not compare representations from different SSL encoders in our dataset inference method. Instead, we compare the representations from a single SSL encoder via GMMs. To elaborate on our defense method, we create a separate GMM for each potentially stolen SSL encoder. Then, we pass the private train and test data samples through the SSL encoder to obtain the respective representations that are further passed through the GMM and compared in terms of their likelihood (current Figure 7 in the revised paper, previously it was Figure 1, which shows this process in detail). Additionally, the obfuscation methods demonstrate that even when the adversary modifies its representations, the fact that we compare the train and test representations only from a single SSL encoder, it enables us to detect the model theft. Thus, a similar distribution in the feature space between the victim and stolen SSL encoders is not required for our method to work.", " In general, we show that the higher quality of the extracted encoder, the higher confidence of our defense in resolving the encoder as being stolen. Indeed, as shown empirically in Table 3. Specifically, our method marks an encoder as stolen if, for the standard significance level (confidence threshold) of 0.05, the SVHN encoder is queried with 10K queries, while the ImageNet encoder with 40K queries (we updated Table 3, please see the revised paper).", " The verifier can select the significance level (confidence threshold) according to their tests on the victim encoder (being stolen) and independent SSL encoders. Our empirical analysis shows that selecting the standard confidence threshold of 0.05 works as expected for our defense. The range of p-values might vary substantially, however, the main point is that the differences between them are sufficient to distinguish between stolen vs independent SSL encoders.", " Our defense compares representations for train and test sets obtained from a single given SSL encoder (we do not compare representations made by different SSL encoders, as explained in the answer to [Q1](https://openreview.net/forum?id=CCBJf9xJo2X&noteId=g2JM5VrgrmJ)). The shuffling changes the order of elements in the representation vectors only between the victim and stolen encoders, however, the order of elements in the representation vectors remains the same for each answered query from a given SSL encoder. Then, GMMs are still able to either differentiate between the distributions of train and test representations or mark them as similar for a given SSL encoder. If we shuffled representations from a given SSL encoder for each query differently, then these representations would not be useful for legitimate users on their downstream tasks.", " The mutual information and cosine similarity scores are primarily used to measure the quality of stolen SSL encoders and not to assess the performance of defense methods.", " We modified the writing to make this clearer. We use the same terminology as in the previous paper on this topic [14], where the term “encoder” is used in the context of self-supervised learning and denotes a pre-trained model using self-supervised methods such as contrastive learning. We used “SSL encoder” in the answers to avoid any ambiguity.\n\n**References:**\n\n[14] [On the difficulty of defending self-supervised learning against model extraction.](https://proceedings.mlr.press/v162/dziedzic22a.html) Adam Dziedzic, Nikita Dhawan, Muhammad Ahmad Kaleem, Jonas Guan, and Nicolas Papernot. ICML, 2022.\n", " Thank you for the suggestion. We moved Theorem 1 to the main part of the paper and have kept the proof in the Appendix (I.1). Please, see the revised paper.", " This paper investigates dataset inference for encoders. Dataset inference is a defense against model stealing, which allows the defender to identify whether a suspected stolen model has private knowledge from the original model’s training data. Originally formulated for classifiers, the authors adapt dataset inference to encoders by testing for differences in encoder representations on the defender’s training data vs. held-out data. Specifically, they fit a GMM to estimate the distribution of the suspected stolen encoder’s representations on training data. They then use the GMM to evaluate the likelihood of the encoder’s representations: if the encoder is stolen then the likelihood of the training data is expected to be higher than the likelihood of the held-out data. Experiments in the vision domain demonstrate that the method successfully identifiers stolen encoders with high confidence. The confidence is shown to improve when the stolen encoder’s representations are closer to the original, as measured by mutual information and cosine similarity. *Quality*\n\nThe idea of comparing encoding representations on private training data vs held-out data makes sense. However some aspects of the approach are not practical:\n- The defender is required to reveal private training/test data to a trusted arbitrator. This is not required in the original formulation for classifiers (Maini et al., 2021), where the defender is able to run dataset inference themselves given query access to the stolen model.\n- In order to run dataset inference, the defender’s private train/test data sets must be passed through the adversary’s encoder (in their entirety). This is problematic if it is necessary to query the adversary’s encoder via a public API under their control. The adversary could simply steal the defender’s private data. One way around this would be to compel the adversary to share their model with the trusted arbitrator. However this may not be possible from a legal perspective. Note that this is not an issue for the original formulation by Maini et al. (2021), where it is only necessary to pass a small fraction of the private training set through the adversary’s model.\n \n*Originality and Significance*\n\nWhile dataset inference is not a new idea, it has only been applied to classifiers to date. Extensions to other models with more complex outputs, such as encoders, are well-motivated. There is some prior work on membership inference for encoders (Liu et al., 2021), which ought to be discussed in the paper. Given the close connection between membership inference and dataset inference, Liu et al.’s approach could be an alternative to the approach proposed in this paper. Another related work that ought to be cited is by (Jia et al., 2021). They discuss an alternative reactive defense for model stealing called proof-of-learning. \n\n*Clarity*\n\nThe paper is clear overall. I wonder if Figure 1 could be simplified, as it seems many of the quantities do not need to be computed to run the test against a single potentially stolen encoder.\n\n- Maini, Pratyush, Mohammad Yaghini, and Nicolas Papernot. \"Dataset Inference: Ownership Resolution in Machine Learning.\" International Conference on Learning Representations. 2020.\n- Liu, Hongbin, et al. \"EncoderMI: Membership inference against pre-trained encoders in contrastive learning.\" Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security. 2021.\n- Jia, Hengrui, et al. \"Proof-of-learning: Definitions and practice.\" 2021 IEEE Symposium on Security and Privacy (SP). IEEE, 2021. Is it possible to make this approach more practical given the issues raised above?\n\nCan this approach handle more subtle forms of stealing? E.g., where an encoder is initialized by model extraction, then refined on independent training data. Such cases are apparently handled in the original formulation of data inference by Maini et al. (2020).\n\nIt would be good to elaborate on what makes GMMs suited for this task. As I understand, GMMs are not universal approximators when the number of components is fixed. In practice, how would one choose the number of components? Could other density estimators be used? Limitations are discussed in appendices, however a summary should be included in the main paper.", " The authors propose a detection method for dataset inference for the unsupervised setting of models. Unlike prior work on models meant for classification, the authors in this work focus on models trained to generate feature representations (SSL). The detection technique relies on log-likelihood statistics using density estimation models, along with measures of distributions like MI. The proposed method has promising results, taking a step in the direction of making dataset inference broader and more useful in the real world. # Strengths\n\n- The paper is well written and sets up the threat model, as well as the proposed method(s) and the rationale behind them, quite well.\n- Empirical evaluation is thorough, with datasets ranging from CIFAR to ImageNet. \n\n# Weaknesses\n\n- Lines 203-205. As a baseline, the authors should include experiments for scenarios where downstream tasks (single, or 2-3 combined) are trained using the \"feature extractors\". It's true that \"a single downstream task cannot adequately reflect...\", but it would be nice to have some estimates (performance numbers) to know for sure how much this difference really is.\n- Lines 322-322: How about adding noise in intermediate layers (or inputs/outputs), or dropout?\n- Table 2: Performance difference between $f_s$ for some cases does not seem to be too far from $f_i$ # Minor comments\n\n- Line 34: Isn't 'dataset inference' the threat model? Like membership inference or property inference?\n- Figure 1 is too complicated- either increase the size (and de-clutter) or simplify the flow/structure.\n- Line 342: \"implies\" -> \"suggests\"\n- Line 347: \"defense\" -> \"detection\". At the point in time where the method is launched, the adversary has reportedly already stolen the model, and thus it is merely the question of detecting (or confirming) whether that is true, not preventing the adversary from stealing the victim's model.\n- Tables 2,3 seem to have overfill issues. Addressed in Section 6", " This paper generalizes the dataset inference defend originally proposed for supervised learning to self-supervised learning. Focusing on the model stealing black-box attack, the authors utilize GMM to capture the density discrepancy between training and testing datasets of an adversary model. Furthermore, the authors propose new evaluation metrics based on mutual information and cosine similarity, and demonstrate the effectiveness and robustness through extensive experiments. Overall, it is an interesting paper. - Strengths:\n - The motivation is clearly explained in the introduction to demonstrate that adaptation of data inference defend for SSL models is non-trivial.\n - Extensive experiments are provided to show the effectiveness of the proposed defending towards model stealing attack.\n - The code is provided in the supplementary. I appreciate the authors to do that.\n\n- Weakness:\n\n - The proposed method heavily relies on the assumption that the stolen model shares similar distribution in the feature space on the private training dataset with the victim model. If so, I'm curious whether the proposed method can only work when the stolen model is well-trained, which is to some extent proved by Table 3 (e.g., in the bottom part, when the number of queries is 5K, the p-values is 1.23e-1 > 0.05).\n - I think a common problem for density estimation related algorithms to work in reality is the generality of the confidence threshold. In your case, this is the p-value threshold which has been set as 0.05 according to line 193. Although it works in your experiments, we can see in Table 3, the range of p-values might vary a lot under different datasets.\n - I wonder how the robustness of dataset inference to obfuscations comes, especially for shuffle, which will totally disrupt the high-dimensional space and GMM. Could you provide further explanation about this property?\n\n - It would be stronger to show the effectiveness of the proposed mutual information score and cosine similarity score as evaluation metrics for defending if they are applicable for different defending methods instead of only the proposed data inference defending, like the watermark defense mentioned in line 95-103.\n\n - Writing:\n - In Section 2 (e.g., line 95-103), it seems that the terminology \"encoder\" has been viewed the same with \"self-supervision pre-trained encoder\" by default, which is not the case.\n - It would be better to put the theorem in the main paper with the proof remained in the appendix, like Theorem 1.1 in line 266. - See the Weakness part. - See the Weakness part.", " The paper proposes a new defense against model stealing of self-supervised models, using the recently proposed dataset inference framework. Similar to original dataset inference for supervised models, the proposed defense detects stealing based on a hypothesis that stolen models exhibit different behavior on private and test data. In this case, this is quantified by using auxilliary density estimation models and observing the log likelihood of data from the two sources. Further, the paper proposes two metrics to measure the quality of stealing: mutual information score and cosine similarity score. The paper is a solid contribution to an active field and is a good follow-up to [14] which posit that dataset inference is significantly harder in the case of SSL. While the results still are less convincing than in the supervised case, the work clearly demonstrates that successfully adapting dataset inference to SSL is possible if more tailored approaches are used. The paper is very well written and structured. \n\nI believe the work has no fundamental weaknesses. However, I have several relatively minor concerns (raised below in Questions), which I hope the authors can sufficiently address in their response; I am willing to reassess the work after the discussion. - The motivation for the additional contribution (two scores) is somewhat unclear. Can the authors make a stronger point for why linear evaluation on several tasks (as in Table 3 in [14]) is insufficient/unnecessary; what is the reason for not including such evaluation alongside proposed metrics? In a similar vein, both scores (MI and cosine) to me seem analogous to fidelity, and not accuracy as claimed in the paper. Can the authors elaborate on this claim further? Making this part more cohesive with the rest of the paper would make the contribution stronger.\n- Some results seem to be missing in Table 1, e.g. ImageNet as $D_S$ for first two choices of $D_P$. While the conclusions certainly hold in almost all cases, the test does not pass for CIFAR10 as $D_P$ and SVHN as $D_S$, making it more necessary to provide a complete and convincing evaluation.\n- Further, 4.3 claims that the paper focuses on both MSE and InfoNCE stealing losses, but 5.1 seems to be imply only InfoNCE is used in the evaluation. Can the authors comment on this mismatch? The evaluation would be stronger if MSE and SoftNN were added.\n- (Nit) It would be interesting to see if different density estimation methods would be able to further boost the performance, did the authors experiment with this? I find the discussion of societal impact sufficient. Regarding limitations, it would be good to more explicitly acknowledge the strength of results compared to the supervised case and reflect on statements given in [14]. More importantly, to avoid the cat-and-mouse nature of attack/defense work in the field (similar to adversarial examples literature until recently), I find it necessary to consider the prospect of adaptive adversaries, i.e. the robustness of the defense against attackers aware of the proposed defense. I acknowledge that designing an adaptive attacker is often a highly non-trivial contribution in itself; a short explicit discussion would still benefit the paper. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 5, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 4, 4, 4 ]

[ "i_fUcMMJ88W", "mFW8XR5rkwY", "5CiMN0te7q7", "HSd2tQ4dOfT", "V3ybhIP9d-p", "Md62xw4p3E", "t8qCd-4y-jB", "WNlitlmLZn", "OSIEbY6x1t8", "u--QtGS6fj8", "cQdxBRoF8Wt", "x_lFXdfZO8D", "fv4Rt-Xf8-I", "WNlitlmLZn", "2gxLjDEV13C", "V3ybhIP9d-p", "nips_2022_CCBJf9xJo2X", "t4udpnSokX1", "zaEXyqR4Q8O", "fv4Rt-Xf8-I", "fv4Rt-Xf8-I", "fv4Rt-Xf8-I", "fv4Rt-Xf8-I", "V3ybhIP9d-p", "V3ybhIP9d-p", "V3ybhIP9d-p", "V3ybhIP9d-p", "V3ybhIP9d-p", "2gxLjDEV13C", "2gxLjDEV13C", "WNlitlmLZn", "WNlitlmLZn", "WNlitlmLZn", "WNlitlmLZn", "WNlitlmLZn", "WNlitlmLZn", "WNlitlmLZn", "WNlitlmLZn", "nips_2022_CCBJf9xJo2X", "nips_2022_CCBJf9xJo2X", "nips_2022_CCBJf9xJo2X", "nips_2022_CCBJf9xJo2X" ]

[ "5-KPKKRU10L", "BDi8itl42Z", "AqOB92l_oiW", "hyQkA4s68hQ", "z4FcS-MgkDL", "MTVEquc-lFp", "5pooTuQXfCl", "f6uTpc-N9z", "UhI-_IA2rLl4", "cc-8ItjQbvd", "RfasM-yXnCF", "d5RzeBawjY", "zisilOKt83M" ]

[ "author", "author", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear reviewers,\n\nThank you again for providing feedback and questions on our paper. We will incorporate the discussion so far into our paper, and welcome any additional comments!\n\nIn the meantime, we were actually able to update and verify our findings on the higher-resolution TinyImageNet 64x64, which was one of the key lingering concerns. Using the same model backbone (ConvNet with 4 convolutional layers, Instance Norm, and ReLU activations) and a distillation budget of 1 image per class, we can obtain 16.0% (± 0.7) retraining accuracy, significantly outperforming the prior method MTT/TM [15] at 8.8% (± 0.3) accuracy. We’re very excited about this result, and will deepen the exploration and add full results on this benchmark in the next revision.", " Thank you for all the additional feedback and insightful questions.\n\n**Q: I/C Comparison**\n\nThanks for the question. The full 100 I/C vanilla BPTT can get 71.8 and the 10 I/C can get 70.1, without extra augmentation and downsampling.\n\n**Q: plot of memory budget and bases ratios**\n\nThanks. Note that the bases are also part of the learnable parameters in our model. Increasing the number of bases (learnable) will increase the expressive power in representing images across classes. We agree that it would be very interesting to explore the transformer type of attention and parameterizations. Thank you for the feedback!\n\n**Q: momentum term**\n\nWe did tune the learning rate, and there is a fluctuation in the gradients. We will inspect more. Thank you for the suggestions on forward-only Adam and the second momentum term. They are all great points. We’ll keep exploring this and add them to the paper.\n\n**Q: buffer size in Continual Learning**\n\nInitially, we were just putting the accuracies of every 4 tasks and the last 4 tasks for better viewing, regarding the question of whether the shrinking buffer sizes will affect the performance on late tasks, but realizing it might be easiest to put all the numbers from all 20 tasks.\n\n**Q: related work**\n\nThank you for bringing up the paper. We are aware of this paper and think it could be a great combination to incorporate the TBPTT into our model as the training framework. We will also discuss this work in our paper.\n", " Thanks for the detailed answers. Since there is little time left for the author-reviewer discussion, I will increase my score to 7 (accept). But, I hope the authors can address all my remaining questions and add the new experiments to the appendix.\n\nQ: I/C Comparison\n- Thanks for the visualization. Have you ever trained a model on the 99 recalled images per class? I want to know more about how it compares with the vanilla BPTT baseline with 100 images per class.\n\nQ: plot of memory budget and bases ratios\n- From your interpretation, it seems that the number of bases dominates the expressive power of the distilled data. However, the fixed bases seem to have very limited expressive power compared to a set of learnable parameters. It would be interesting to see what will happen if you further parameterize the bases similar to the attention layer in Transformer. There is no need to run any experiments, and I hope the authors can explore more in future work.\n\nQ: momentum term\n- Thanks for the results. It seems that backpropagating through the momentum term really helps the performance. As for Adam, if you use it in a forward-only manner, why will it cause unstableness? Have you tuned the learning rate (I guess it needs at least 10x smaller)? However, if you mean the instability when backpropagating through Adam, you might want to add a small epsilon term to the second momentum term. Besides, it would be interesting to see the performance of forward-only Adam.\n\nQ: buffer size in Continual Learning\n- I'm confused about what you mean by every 4 tasks and the last 4 tasks. Could you clarify a bit?\n\nQ: related work\n- Here is a recent paper [1] that uses 1-step TBPTT, which seems to have good training and memory efficiency. Their distilled images also seem real and natural. What is your thought on that? Do you think replacing the BPTT component with their method can yield a better result?\n\n[1] Zhou, Yongchao, Ehsan Nezhadarya, and Jimmy Ba. \"Dataset Distillation using Neural Feature Regression.\"\n", " Thank you for the follow-up questions! We have made the corresponding updates in the main paper and appendix. Let us know if you have other questions. We are happy to elaborate and discuss.\n\n**Q. Visualization**\n\nWe have updated the appendix in section D “More visualization comparisons”. Two settings are added as suggested. In the first setting, we compare the visualizations of synthetic images on dataset CIFAR100 from four classes: apple, aquarium fish, bed, and bottle. The vanilla BPTT baseline has 100 images per class and the memory addressing algorithm (ours) has 10 images per class budget with 43 bases, leading to 99 recalled images per class. In the second setting, we show the recalled images under 2, 10, and 50 I/C budgets, with 8, 43, and 215 bases respectively. As we are comparing with the vanilla BPTT, we also used bases with the original resolution to be fair. We’ll add all the suggested visualization and analysis to the final version as well.\n\n**Q: visualization vs. performance**\n\nThanks for the questions. Intuitively, BPTT emphasizes only the end position of parameters in the space. This potentially means that there are no strong constraints on gradient trajectory — the loss can be minimized as long as it reaches the correct final position. The _single-step gradient matching_ method imitates the gradient trajectories from the real datasets (which is a very sensible choice) and indicates that it tries to replicate the whole searching process from the optimizer (e.g., in [3]). Note that, during the search process, there can be gradient steps that only try to escape from some local regions, potentially leading to short-range behaviors and local information to distill. The recent work MTT/TM[1] also discussed the problem and nicely dealt with it and uses multi-step gradient matching to directly match the start and end positions of fragments in teacher trajectories. Another observation is from Deep Gradient Leakage [2]: through using the single-step gradients, it’s possible to approximately recover the whole image in a batch, while the goal of dataset distillation is to extract only the useful parts. This also indicates that there is extra information besides the core parts which are solely useful for optimization.\n\nNote that we think both BPTT and gradient matching methods are great frameworks and have strong potential in Dataset Distillation. It would be nice to see the efforts on either side to push the algorithms forward and generate stronger distilled data or broaden the field to other tasks or applications.\n\n**Q: Abbreviation**\n\nThanks, we agree and have updated the draft in both the caption and the paragraph. We will explain more details about table 2 and update the notations in both captions and paragraphs, once have more space.\n", " **Q: plot of memory budget and bases ratios**\n\nYes, table 3 counts the number of bases and addressing mats, and table 4 counts the total number of dimensions to store the bases and addressing mats. Regarding the U-shape behavior, it’s a great observation. Our interpretation is that, when the storage budgets are high, the algorithm would need more bases to be expressive enough to generate data that capture more detail-level information in the dataset that is useful for optimization, leading to higher ratios. \n\nIn general, there can be several factors to consider when working with a new dataset: (1) the complexity of the dataset — intuitively, when the dataset is simple, there might not be a strong need for too many bases, for example, the models can work well on MNIST without having too many bases; (2) the sharing among classes — when there is a strong sharing among classes (through observation of the dataset), the number of bases can be reduced; (3) expressiveness vs variations trade-off — with more bases, the set of reusable components are more powerful, with more coefficient matrices, the more variations of composing the principal components can be captured in the distilled data. Based on the practical usage, it might be worth considering which part needs more capacity depending on the datasets or tasks.\n\nThis is a great question. Thanks for diving into the details of our algorithm!\n\n**Q: momentum term**\n\nFor sure, below are the performance of no-momentum, forward-momentum only, and full momentum. No-momentum uses BPTT without momentum terms. Forward-only momentum uses the momentum term only in the forward BPTT, but blocks the gradients on the momentum term in the backward pass (except for the gradients on the current time step weights). Full momentum is our full model. All the experiments are performed on CIFAR10 with 200 inner optimization steps.\n\n| Accuracy | 1 I/C | 10 I/C |\n|-----------------------|------------|------------|\n| no-momentum | 40.5 (0.8) | 51.0 (0.5) |\n| forward-only momentum | 45.6 (0.7) | 57.4 (0.3) |\n| full momentum | 49.1 (0.6) | 62.4 (0.4) |\n\n\nWe did try Adam and found that it leads to unstableness when being used as the inner loop optimizer. Specifically, the gradients on the distilled data are not stable, leading to difficulties in the learning process. \n\n**buffer size in Continual Learning**\n\nSorry for the confusion, we instead provide the accuracies of all tasks under a random seed. The reported accuracies are the retained performance after observing the full task sequence.\n\nMNIST Rotation\n\nPerformance (accuracies) of all tasks (1-20): \n\n82.28, 81.37, 82.44, 84.11, 81.66, 80.59, 82.32, 81.48, 83.41, 81.12, 80.78, 82.5, 80.67, 81.83, 79.17, 84.03, 78.13, 80.18, 75.36, 76.65\n\nCIFAR100\n\nPerformance (accuracies) of all tasks (1-20): \n\n62.2, 63.0, 61.2, 55.8, 76.6, 53.6, 68.2, 55.6, 57.2, 69.6, 69.6, 62.8, 71.0, 60.2, 63.2, 56.0, 53.4, 63.0, 62.4, 53.0\n\n**Misc**\n\nYes, we agree. the visualizations are included in the appendix.\n\n**Beyond performance**\n\nThank you. We appreciate that the reviewer also agrees with the contributions beyond the performance.\n\n[1] George Cazenavette, Tongzhou Wang, Antonio Torralba, Alexei A Efros, and Jun-Yan Zhu. Dataset distillation by matching training trajectories. CVPR’2022\n\n[2] Deep Leakage from Gradients Ligeng Zhu, Zhijian Liu, Song Han, NeurIPS’2019\n\n[3] Dataset Condensation via Efficient Synthetic-Data Parameterization, ICML'2022", " Thanks for the response. I appreciate this paper's idea of the new parameterization of the distilled data, and I still have the following questions.\n\nQ: I/C Comparison\n- I would like to know more about the generated images' quality. For example, I want to see the performance with 100 coefficients compared to the baseline methods that distill 100 images. I know that it is not fair in terms of storage. It is a good way to tell whether the images have better quality or the performance improvement is mainly due to the new parameterization that allows you to generate more images.\n\nQ: visualization vs. performance \n- Why do you think \"contour\" is more critical for the BPTT type of algorithm? In other words, why does gradient matching learn high frequency and local information, and why does BPTT capture the contours? Besides, could you provide more synthetic image visualizations when you increase the I/C budget for several classes which you think are representative? I want to understand the order of each class's \"principle component\" and whether there is a trend that the synthetic images become more diverse and diverse in what sense.\n\nQ: Abbreviation\n- Why not do it in the current version? I feel like it hurts the reading experience.\n\nQ: plot of memory budget and bases ratios\n- Does Table 3 mean K/r and Table 4 mean K_d/(r_K*d_y)? From Table 3, it seems that there is a U-shape behavior where we want a high ratio with a low or high memory budget and a relatively low ratio when we have a medium budget. What is your interpretation of this observation? And, what is the best practice or intuition to choose the proper ratio when considering a new dataset with a certain memory budget? What can we do besides performing a hyperparameter sweep on the validation set?\n\nQ: momentum term\n- Could you provide any quantitative results to see the effect of each hypothesis? If (1) turns out to be more critical, then does it mean the main reason why we want to use more BPTT steps is to find a better-optimized parameter? Then, would an algorithm that converges faster (e.g., Adam) give us better performance?\n\nQ: buffer size in Continual Learning\n- I'm confused about what you mean by every 4 tasks and the last 4 tasks. Could you clarify a bit?\n\nMisc\n- It will be great also to include a visualization of BPTT, even if it looks similar. Otherwise, the readers will not know that information.\n\nBeyond performance\n- I agree with the contributions to the dataset distillation community.", " We would like to thank the reviewer for the detailed and valuable comments. A new revision is submitted with an updated draft. We address the specific questions below.\n\n**Q. small datasets and more diverse models**\n\nThanks for the suggestions. We are running experiments with larger images. Note that BPTT takes longer times on higher resolution data. We will include our findings (whether positive or negative) with thorough explorations in the final version, along with the computational cost of these experiments. Current still very early results show that our algorithm can achieve 9.8% on 1 I/C TinyImageNet (compared to 8.8% using trajectory matching [15]).\n\n\nWe have verified our algorithm on larger models and cross-architecture performance:\n\n1 I/C:\n\n| | AlexNet | ResNet12 | ConvNet |\n|----------|------------|------------|------------|\n| AlexNet | 58.53(0.5) | 53.63(0.6) | 57.32(0.6) |\n| ResNet12 | 53.21(0.8) | 58.49(0.5) | 57.01(0.3) |\n| ConvNet | 50.50(1.3) | 55.86(0.6) | 66.4(0.4) |\n\n10 I/C:\n\n| | AlexNet | ResNet12 | ConvNet |\n|----------|-----------|-----------|-----------|\n| AlexNet | 65.6(0.5) | 60.2(0.6) | 63.7(0.6) |\n| ResNet12 | 62.3(0.9) | 67.8(0.3) | 65.2(0.6) |\n| ConvNet | 63.8(0.8) | 67.5(0.4) | 71.2(0.4) |\n\n**Q. writing update**\n\nWe have cleared the typos and updated a new draft in the revision. Thank you for the very detailed comments!!\n\n**Q. line 15 optimization algorithm**\n\nWe follow previous works and use SGD with momentum 0.5 and learning rate 0.01 as the optimizer.\n\n**Q. Generative models**\n\nThanks for the suggestion. We will add the discussion to the paper.\n\n**Q. Small number of steps in BPTT and memory constraints**\n\nNote that one critical reason hinging the previous work is the lack of momentum terms. For the memory constraint, the GPU memory of our BPTT is constant in time. To solve the memory problem, we manually coded the BPTT back-propagation process, instead of relying on the computation graph and autograd in Pytorch. Our manual implementation leads to constant memory (does not linear grow with time), but needs 1.3x time comparing to autograd with full computation graphs (the models need to commute between CPU and GPU).\n\n**Q. trade-off between time and space**\n\nSince the current dataset distillation works are not lossless compression, the decompression results vary across settings, leading to difficulties in the trade-off discussion (compared to lossless compression where the target is always the original data).\n\nThe main bottleneck is now still how to distill information more effectively in to the data. For example, with a better distillation algorithm, more informative content can be distilled in one image per class and the benefits come for free - the model can be re-trained using the same amount of distilled data and achieve higher performance. In our algorithm, since we use bases-coefficients decomposition, more coefficients can lead to higher re-training time. But this can be solved using larger batch sizes. \n\n**Q. full recovering rate**\n\nThanks for the suggestion. Note that in the current Dataset Distillation works [10,13,14,15], achieving full recovering rate is still an open problem (e.g., DM[14] sacrifices accuracies for training speed and has pushed it to 95% relative recovering rate on CIFAR10, but still hasn't achieved 100%. We will discuss it in our main paper.\n\n**Q. notation**\n\nWe will update the notation in the text and equations in the final version.\n\n**Q. lossless compression**\n\nThanks for the interesting suggestion. The lossless compression can be applied to both distilled data from previous methods and our memory representations. The major difference between lossless compression and the line of dataset distillation works is information prioritization - whether the compressed data affects the downstream decision making process. Comparing to applying a standard compression, it would be interesting instead to consider differentiating through a standard compression algorithm for dataset distillation and learning the bits that affect the downstream optimization process. We leave it as the future work.\n\n**Q. limitations**\n\nSee **Beyond performance** and **BPTT limitations** in [this response](https://openreview.net/forum?id=RYZyj_wwgfa&noteId=UhI-_IA2rLl4).\n", " We would like to thank the reviewer for the detailed and valuable comments. We address the specific questions below. \n\n**Q: momentum term**\n\n(Also explained in other responses)\n\nSince we are using the BPTT process, the end positions of the inner optimization are critical and decide what information can be backpropagated through the optimization process. In our experiments, we find that the momentum term can help on:\n\n(1) Producing the optimized parameters that better summarize the distilled datasets (with the smoothing effects). For example, when we perform the forward pass using momentum, but block the gradients on the momentum term in the backward pass (except for the gradients on the current time step weights), the performance is still higher than the no-momentum version, indicating that the end position (when obtained with momentum terms) produces more informative gradients for training.\n\n(2) Momentum term is the summation of decayed forward gradients on multiple time steps (alg. line 11). The gradients on the outer loop loss (alg. line 15) can be backpropagated via the momentum through multiple previous time steps, potentially mitigating the gradient vanishing issue. The rationale for using momentum for BPTT (in the different context of hyperparameter tuning) is also discussed in [1].\n\nHow the backpropagation on momentum is performed: we refer the reviewer to paper [2] alg. 2 for details. The BPTT forward process is unfolded in alg. box lines 11-12. The back-propagation process on BPTT is a standard chain-rule derivation that intuitively uses the momentum term as a “bridge” to propagate gradients directly to previous steps. We will also add explicit details to the main paper.\n\n**Q: alg. 1 line 12**\n\nWe explicitly write out the update rule in line 12 to highlight the details of momentum usage. It can be also wrapped as an opt operation.\n\n**Q: larger images**\n\nThanks for the suggestion. We are running experiments with larger images. Note that BPTT takes longer times on higher resolution data. We will include our findings (whether positive or negative) with thorough explorations in the final version, along with the computational cost of these experiments. Current still very early results show that our method can achieve 9.8% on 1 I/C TinyImageNet (compared to 8.8% using trajectory matching [15]). Besides larger images, we also validated the results with more model architectures in response to reviewer 3HqT.\n\n**Q: algorithm's time and the solution of memory constraints**\n\nWe show the training time v.s. achieved accuracy in the following table. We will add more discussions on the training time.\n\n| mins | 46 | 120 | 600 |\n|------------|------|------|------|\n| accuracy | 0.40 | 0.43 | 0.48 |\n\n| mins | 285 | 720 | 2350 |\n|------------|------|------|------|\n| accuracy | 0.57 | 0.61 | 0.65 |\n\nThe GPU memory of our BPTT is constant in time. To solve the memory problem, we manually write the BPTT back-propagation process, instead of relying on the computation graph and autograd in Pytorch. Our manual implementation leads to constant GPU memory (does not linearly grow with time), but needs 1.3x time compared to autograd with full computation graphs (the models need to commute between CPU and GPU).\n\n**Q: line 110**\n\nWe have updated the draft.\n\n**Q: separate learning of M and A**\n\nThanks for the interesting suggestion! Separate training of memories and attentions can indeed lead to benefits with Sigmoid or Softmax attentions in feature learning. The lottery ticket situation can probably happen with sigmoid attentions and with large enough redundancies. Note that our model uses the linear matrix and does not constrain the values to [0,1]. Also, due to it is a compression problem, there is not much redundancy in the representation or budget. Better training of memories and matrices (with various regularities or attention forms) itself is indeed a quite interesting direction. We leave it for future works.\n\n**Q: similarities in figure 2**\n\nThe cat and dog similarity in figure 2 is still higher than most other pairs, such as cat and automobile. The eventual similarity is determined by the effectiveness in model optimization, e.g. the model might decide a medium-level similarity leads to better performance.\n\n**Q: continual learning in one pass (epoch)**\n\nYes, our model can distill the datasets and achieve good performance in a single epoch. We use memory buffer and multi-replay to increase the sample size and optimization steps. But even without the Reservoir memory buffer to store more real data samples, our performance is still pretty good (e.g., 77.6% on RotationMNIST, compared to the current 80.32%).\n\n**Limitation**\n\nSee **BPTT limitation** and **Beyond performance** in [this response](https://openreview.net/forum?id=RYZyj_wwgfa&noteId=UhI-_IA2rLl4).\n\n[1] Gradient-based Hyperparameter Optimization through Reversible Learning. ICML 2015\n\n[2] Forward and Reverse Gradient-Based Hyperparameter Optimization. ICML 2017\n", " **Q: momentum term**\n\nSince we are using the BPTT process, the end positions of the inner optimization are critical and decide what information can be backpropagated through the optimization process. In our experiments, we find that the momentum term can help on:\n\n(1) Producing the optimized parameters that better summarize the distilled datasets (with the smoothing effects). For example, when we perform the forward pass using momentum, but block the gradients on the momentum term in the backward pass (except for the gradients on the current time step weights), the performance is still higher than the no-momentum version, indicating that the end position (when obtained with momentum terms) produces more informative gradients for training.\n\n(2) Momentum term is the summation of decayed forward gradients on multiple time steps (algorithm line 11). The gradients on the outer loop loss (algorithm line 15) can be backpropagated via the momentum through multiple previous time steps, potentially mitigating the gradient vanishing issue. The rationale for using momentum for BPTT (in the different context of hyperparameter tuning) is also discussed in [2].\n\n**Q: buffer size in Continual Learning**\n\nHaving more buffer size to store real data for distillation can indeed lead to higher performance on early tasks. This is quite common in continual learning with the Reservoir sampling strategy (e.g., in [3]). But our algorithm's performance drop is relatively small. For example, on MNIST-Rotation and CIFAR100, we show the accuracies of every 4 tasks and the last 4 tasks:\n\nMNIST Rotation\n\nevery 4: 81.37, 80.59, 81.12, 81.83, 80.18\n\nlast 4: 78.13, 80.18, 75.36, 76.65\n\nCIFAR100\n\nevery 4: 62.2, 76.6, 57.2, 71.0, 53.4\n\nlast 4: 53.4, 63.0, 62.4, 53.0\n\n**Misc:**\n\nUsing soft labels as queries during testing is a very interesting idea. This is essentially interpolating between classes with different weights. Another possible variation could be interpolating the coefficients (addressing outputs) within each class or label as augmentations. Note that, currently, the coefficients are un-normalized, leading to potentially different scales at each dimension. We leave this for future works and thank the reviewer for this suggestion.\n\nVisualization of BPTT (no memory representation): very similar to the appendix ones. We found the BPTT in general produces images that emphasize quite a lot on the contours of objects and tend to capture less on specific textures.\n\n\n**Q: BPTT limitation**\n\nAs mentioned in section 6, BPTT is relatively slow as it requires solving the inner optimization process. However, note that our proposed representation can be flexibly applied to other distillation frameworks, this major contribution is orthogonal to previous works.\n\nThere is a large bulk of works on tackling or approximating the inner process of BPTT, ranging from implicit differentiation to approximation methods (e.g., truncation, real-time approximate learning). We believe providing observation on the full unapproximated BPTT has shown the potential of this algorithm and the bi-level optimization procedures, and can lead to more explorations in this direction.\n\n***Beyond performance**\n\nBesides the benchmarks with fixed settings, our algorithm introduces several important properties:\n\n(1) Flexible budgets. We can handle various target budgets, such as difficult-to-balance ones (e.g., 150 images over 100 classes), or float budgets (e.g., 3.5 I/C). This advantage of our algorithm is critical in the broader and practical usage of dataset distillations.\n\n(2) Not linearly grow with the number of classes. This benefit can be critical in future works which target datasets with large number of classes. For example, in ImageNet21k, it is almost unavoidable to adopt other representations, since even 1 I/C will lead to 21,000 images in the standard way of parameterizing the distilled data.\n\n(3) Addressable memories open the directions to other tasks and data modalities. A key advantage of our algorithm is that it allows continuous queries as “labels” to address the memories and obtain distilled images. This in general makes it possible for the distillation of image datasets where queries are from other modalities, such as audios, language, or even image themselves (image-image pairs in datasets).\n\n**References**\n\n[1] Dataset Condensation via Efficient Synthetic-Data Parameterization, ICML 2022\n\n[2] Forward and Reverse Gradient-Based Hyperparameter Optimization. ICML 2017\n\n[3] On Tiny Episodic Memories in Continual Learning, Arxiv 2019", " We would like to thank the reviewer for the detailed and valuable comments. A new revision is submitted with the updated draft. We address the specific questions below.\n\n**Q: I/C Comparison**\n\nWe updated the revision in the caption on I/C (we also emphasized it in the main figure and equation 4). Note that the parameterization and forms of data are also a fundamental question for Dataset Distillation. An effective parameterization can facilitate the understanding of what critical information affects the training of models. I/C is actually _measuring and reflecting this perspective and property of algorithms_. A recent work [1] from ICML’22 also discusses the parameterization of dataset distillation. We will add further clarifications and potentially use pixels per class following [1] for better clarity.\n\nThe number of generated images does not necessarily correspond to the performance. Having more coefficients under the same budget does not always lead to a strong advantage over a smaller number of coefficients. For example, CIFAR10 and SVHN with 307 coefficients underperform fewer coefficients (115, 76, 51, or 19) in figure 4. We think it is the decomposition on representation that leads to good performance — the parameterization is an effective way to capture the principal components and the variations in datasets.\n\n**Q: visualization vs performance**\n\nIndeed there are some empirical observations in each work on how the appearance of images might correlates with performance. However, we believe that there are still no formal connections built (e.g., through extensive experiments, human studies or theories) between what kind of appearances of images can necessarily lead to a strong performance. The visualization more potentially shows the property of the algorithm class. For example, with single-step gradient matching methods, the distilled data can potentially contain more high frequency and local information from the data. For BPTT which emphasizes the endpoint position of parameters, the contours of objects and how contours might vary (even in small scales) seem to be more critical.\n\n**Q: Abbreviation**\n\nWe will update this in the final version.\n\n**Q: Figure 3**\n\nWe have updated the figure in the revision.\n\n**Q: training time vs accuracy, memory requirement**\n\nWe show the performance progresses along with time. The following tables are under CIFAR10 1 I/C budget, without memory representation (table 1) and with memory representation (table 2). Our algorithm can achieve high performance relatively fast. \n\nTable 1:\n\n| mins | 46 | 120 | 600 |\n|------------|------|------|------|\n| accuracy | 0.40 | 0.43 | 0.48 |\n\nTable 2:\n\n| mins | 285 | 720 | 2350 |\n|------------|------|------|------|\n| accuracy | 0.57 | 0.61 | 0.65 |\n\nTo solve the memory problem, we manually write and code the BPTT back-propagation process, instead of relying on the computation graph and autograd in Pytorch. Our manual implementation leads to constant GPU memory (does not linearly grow with time) but needs 1.3x time compared to autograd with full computation graphs (the models need to commute between CPU and GPU).\n\nCompared to the single-step gradient matching algorithm, BPTT is slower. The multi-step trajectory matching [15] can also distill in shorter time, but requires pretraining of a model database. We discuss more details of BPTT in **BPTT limitation**.\n\n**Q: plot of memory budget and bases ratios**\n\nFollowing the reviewer's suggestion, we compute the ratios of the number of bases (#basis) and number of mats (\\#mats) under different budgets (number of images per class), shown in table 3. Besides the suggested one, we also computed the ratios of the total number of dimensions, shown in table 4. We will include this analysis in the paper.\n\nTable 3:\n\n| \\#basis/\\#mats | 1 | 10 | 50 |\n|--------------|------|------|------|\n| MNIST | 0.55 | 0.14 | 1.92 |\n| FashionMNIST | 0.55 | 0.63 | 0.45 |\n| SVHN | 0.26 | 0.16 | 0.49 |\n| CIFAR10 | 0.26 | 0.16 | 0.49 |\n| CIFAR100 | 8.0 | 0.55 | - |\n\nTable 4:\n\n| \\#basis-dim/\\#mat-dim | 1 | 10 | 50 |\n|---------------------|------|------|------|\n| MNIST | 0.68 | 0.09 | 0.15 |\n| FashionMNIST | 0.68 | 0.19 | 0.07 |\n| SVHN | 1.01 | 0.19 | 0.15 |\n| CIFAR10 | 1.01 | 0.19 | 0.15 |\n| CIFAR100 | 0.48 | 0.03 | - |\n\n**Q: trade-off between the number of bases and addressing matrices**\n\nThe trade-off is shown in figure 4. In our experiments, we first compute all possible value pairs for (number of bases, number of addressing matrices), select the middle ones with a reasonable amount of matrices, and choose the one with the highest performance on the validation set. Note that the performance is in general quite similar among different \\#bases-\\#matrices as long as it is not close to the edge cases (too few bases to capture principal components or too few coefficients to capture variations).\n", " This paper formulates the dataset distillation as a memory addressing process where the synthetic datasets can be generated through an addressing matrix based on a learned memory representation. The proposed method improves the compression rate of distilled data by considering the class similarity and improving the BPTT framework. The proposed method is evaluated on five image classification datasets and applied to continual learning and few-shot learning. This paper is well-motivated and focuses on a significant problem (the parameterization of the distilled data) in dataset distillation. The proposed method is novel, and the results are encouraging.\n- Originality: The proposed method proposes a new way to parameterize the distilled data and opens up a new application for few-shot learning.\n- Quality: This paper is technically sound, and most of the arguments are well supported. The evaluation is not perfectly fair, and additional study is needed to understand the method better.\n- Clarity: This paper is easy to follow and mostly well-written, with minor flaws.\n- Significance: The proposed method achieves state-of-the-art performance when a fixed memory budget is given. The addressable memory parameterization can also be applied to other dataset distillation methods. This paper also shows that dataset distillation can benefit continual learning and few-shot learning. Table 1\n- The comparison to previous methods is not perfectly fair, and \"I/C\" is misleading. Due to the parameterization, the proposed method can generate more synthetic data than previous methods. Therefore, the proposed method is expected to achieve higher accuracy than previous methods. Thus, the number of addressing matrices (or the exact number of synthesis examples) needs to be shown somewhere in the table. I want to see whether more distilled data can fully explain the improvement or if the distilled images also get better quality. Appendix Figures 4 and 5 show that the recalled images lack diversity. I am surprised that the method achieves such a good performance.\n\nTable 2\n- It may be better to clarify the abbreviation (i.e., ds, Aug) in the caption.\n\nFigure 3\n- You mention that unrolling the trajectories long enough (e.g., 200 steps) can improve performance (Line 202). Could you show a complete picture in Figure 3 up to 200 steps? Due to the long unroll of the BPTT, I would also like to see a plot of test accuracy versus training time and the memory requirement of the proposed method. How does it compare to other baseline methods?\n\nFigure 4\n- I am curious about the trade-off between the number of bases and addressing matrices given a fixed memory budget. What is the general rule to scale these two numbers? I want some plot where the x-axis is the memory budge, and the y-axis is the ratio between these two numbers.\n\nResults 2\n- I can see that long unrolls will be very important, but it is unclear why momentum can be so significant? What's the insight behind that?\n\nLine 301\n- \"the buffer size keeps shrinking when more compressed representation of tasks is stored\": does it imply that the later distilled data tend to have a low quality?\n\nMisc\n- What would happen if you use a soft label for query (as a data augmentation) during test time? Will the performance get improved?\n- It will be interesting to see the visualization of the interpolation between two different classes. Does the \"half dog half ship\" image make sense?\n- I want to see some visualization of the images generated by BPTT. How does it compare to the previous method? Due to the long unroll of the BPTT, the training efficiency and memory requirement can be the biggest concern when scaling this approach to complex datasets or larger models.", " Based on the observation that classes can share concepts and representations, the authors propose a new Dataset Distillation method that trains a learnable memory shared across classes. The objective is to learn basic concepts that can be shared and then, through a function A, learn to combine these concepts to generate examples given a class y_i. To learn the method, the authors use a bi-level optimization process. The inner loop verified the generalization properties of the current memory, and the outer loop updated the memory and attention function. Additional to the method, the authors propose a modification in the momentum factor during the inner loop that helps improve performance. This method achieves good results in various Dataset Distillation benchmarks and good results in Continual Learning scenarios. Strengths:\n- S.1 The observation that concepts are shared across tasks is very intuitive. This observation, as the authors note, helps compress data so that it does not grow linearly as the number of classes increases, and may also lead to finding better concepts for classes that the model has not considered before.not seen.\n- S.2 The paper is well written, placing much emphasis on the different contributions that the authors propose. The different concepts and notations used are well explained.\n- S.3 Using the bi-level optimization strategy helps generate weights that can support the problem of continuous labels.\n- S.4 The results show that the proposed method achieves outstanding results. The experiments that were carried out demonstrate the contributions proposed by the authors.\n\nWeaknesses:\n- W.1 The reason for adding the momentum update is not clear. Nor how it is done. Is there any intuition behind this contribution?\n- W.2 Is there a reason why line 12 of Algorithm 1 does not use the opt function? It is used in equation 3, but not in the algorithm, which can cause confusion.\n- W.3 It is known that benchmarks of the dataset distillation problem are standard and normally use only small images. However, many of the previous methods have problems when the size of the images increases. It would be interesting to confirm the performance of this method on larger images. Alternatively, add it to the limitations.\n- W.4 There is no comparison of the algorithm's time or the number of iterations. Adding more iterations to the inner loop must come at a high cost.\n- W.5 Typo: Line 110, the abbreviation BPTT is used before defining Q.1 In several works, the attention masks are learned independently of the model/memory weights, so that interference between the learning processes is avoided. Does it make sense to learn M and A separately? In some ways, this experiment seems helpful to ensure that the memory acquires basic concepts, and not that function A selects useful random vectors that can achieve a goal, like finding the lottery ticket from a memory.\n\nQ.1.2 Perhaps the previous question is related to what happens in Fig. 2. For some classes, there is an intuitive and testable relationship of similarity. However, this similarity is not seen in other intuitively similar classes (cats and dogs). Is there any explanation for what is happening?\n\nQ.3 One of the problems with using long paths in the inner loop is the amount of memory used to store the entire associated computation graph. Although there are techniques to mitigate this, it is not mentioned. Can this proposal be explained in more detail? Has this problem been encountered?\n\nQ.4 It is unclear how the method is used in the Continual Learning environment. A single-pass context is mentioned. However, how can the proposed method be learned in just one data pass? Did the simple-pass apply only to the test adaptation? Or is the model capable of learning to compress information in a single epoch? The authors mention a limitation that is very relevant and I share", " The paper proposes to compress the critical information of a large dataset into compact addressable memories. This method achieves better results than the previous dataset distillation/condensation methods. Strengths.\n1. The results are much better than previous methods.\n2. The method is based on a reasonable assumption that there are redundancies in the previous condensed dataset. The method achieves a higher compression rate by reducing redundancies.\n3. The paper is well organized and developed.\n\nWeaknesses.\n1. The experiments are only on small datasets. The size of the dataset $N$ and the dimension of input $d$ are small. The authors should report results on large datasets. Specifically, in [15], Tiny ImageNet and ImageNet subsets are used in the experiments.\n2. The experiments on large models instead of small models are needed. Does the method depend on a specific neural architecture? The authors may investigate other neural networks.\n3. Other missing experiments are mentioned in the questions below.\n4. The writing is fair. Several typos and errors are listed below.\n\n* Line 45. significanly -> significantly\n* Line 50. lead to -> leads to\n* Line 63. There has been -> There have been\n* Line 64. criterions -> criteria\n* Line 66. It emphasize on -> It emphasizes\n* Line 70. gaussian processes -> Gaussian processes\n* Line 79. dillema -> dilemma\n* Lines 92, 100, 151. e.g. -> e.g.,\n* Line 99. the number of synthetic data sample -> the number of synthetic data samples\n* Line 115. seprately -> separately\n* Line 121. outperforms -> outperform\n* Line 146. defines -> define\n* Line 170. having to enumerating -> having to enumerate\n* Equation 3. J(\\phi) -> min J(\\phi)\n* Line 179. discuss in detail about the learning framework -> discuss in detail the learning framework\n* Line 212. there are strong evidence -> there is strong evidence\n* Line 213. there are information re-using -> there is information re-using\n* Line 223. with shape 28 × 28 -> with a shape of 28 × 28\n* Line 228. are color image 228 dataset -> are color image 228 datasets\n* Line 263. distinct to each other -> distinct from each other\n* Line 292. 200 sample -> 200 samples\n* Line 308. pervious -> previous 1. Algorithm 1. Lines 8 - 13 are the detailed optimization algorithm for $\\theta$. In line 15, there is the optimization algorithm for $\\phi$. What are the details of this optimization algorithm?\n2. There is also a research direction that generative models are used to condense a dataset. This direction is closely related to this work and should be discussed in the paper.\n3. In previous data distillation works, the number of inner-loop optimization steps is small. The major reason is that the memory consumption and execution time are quite large with a large trajectory. Could the authors discuss how they address this issue?\n4. There is a trade-off between time and space. If we prefer a higher compression rate, we have to pay the cost of extra computation (e.g., the computation for decompression). Could the authors discuss this trade-off and make a comparison with previous work?\n5. Instead of reporting the performance given a specified compression rate, it is also important that what is the compression rate if we can fully recover the original performance. Namely, what is the size of the smallest dataset that can be trained to achieve the full dataset performance?\n6. The authors use the notation $M=${$b_0, ..., b_{K-1}$}. It can be simplified as $M \\in R^{K \\times d}$.\n7. Is it possible to compress the condensed dataset directly? For instance, the previous methods can generate a condensed dataset. Could we apply several lossless compression on them? It is better for the authors to discuss it. As a derived method of the dataset distillation framework, the proposed method inherits the limitations of the original method on the large models and large datasets. The authors also mention it in the last section." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 5 ]

[ "nips_2022_RYZyj_wwgfa", "AqOB92l_oiW", "RfasM-yXnCF", "MTVEquc-lFp", "MTVEquc-lFp", "UhI-_IA2rLl4", "zisilOKt83M", "d5RzeBawjY", "cc-8ItjQbvd", "RfasM-yXnCF", "nips_2022_RYZyj_wwgfa", "nips_2022_RYZyj_wwgfa", "nips_2022_RYZyj_wwgfa" ]

[ "L-vR9uzQxmL", "zW6IE1ik1X-", "4mw_8Y4b2F8", "q7aUlZGF5kD", "-V0XxKzGkJ8", "yrZE10XmleEt", "CjJAsWuYtvw", "fKVq1-YA9Z1", "5bDANs0tFFZ", "S1DsTBBFHv6", "pMw2lbuyEb_", "RMOPfLSKojI6", "kbpn40SChz82", "02KvufBCPM4", "DzreTeINLPh", "LBD4iquI7Ir", "GC8PjZrarz6", "NEQ8I_5NU-4" ]

[ "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " A few dozen point clouds is insufficient for our model to learn a strong generalized prior. The remaining time in the discussion phase did not allow us to report results on 10 or 20 instances per category. In the final version, we will analyze both training stages for varying instance counts per category. \n\nWe highlight that our method generalizes to unseen, real-world distributions given *only Acronym, a synthetic dataset*. There are a number of existing datasets that include even larger instance counts than Acronym. ShapeNetSem (a superset of Acronym) has 270 categories and 12,000 mesh instances. The ABC dataset has over 1 million meshes. ModelNet includes 151,128 mesh instances. Our method produces state-of-the-art results on unseen classes using 2,995 labeled meshes and 3,408 unlabeled point clouds. Specifically, using only this synthetic training data, we demonstrate results on the YCB dataset (see Fig. 7 of the revised submission) which is a real-world point cloud dataset acquired with RGBD cameras. Our mesh reconstructions of the measured data, e.g., recovering the \"handle\" of a pitcher, may serve as input to complex robotic grasping tasks. Importantly, existing methods fail for this task (see Fig. 7 of the revised submission). Even on synthetic, unseen data, existing methods fail (see Fig. 5).\n\nAddressing the second question, we can incorporate test-time refinement by using our self-supervised loss to refine the model to a given input point cloud. We provide more specific details in Sec. 1.3 of our supplement. \n", " Thanks for the authors of the reponse to my questions. I endorse the experimental results provided by the authors, which demonstrate the effectiveness of this method. For me, it would make the paper better if the underlying theoretical proofs were provided for the self-supervised loss and convergence to the signed distance function.", " Thank you for your detailed response. \n\nMy questions have been sufficiently answered by the authors, and the new results confirm the claims made in the paper. I think that having first set of results (_Ours (Stage 1), 20 Classes_; _Supervised Only, 20 Classes_; _Supervised Only, 76 Classes_) in the main paper would be a useful addition, the rest can go to supplementary. \n\nI have also read the other reviews and the authors' reponses to them.\n\nI stand with my original rating and strongly recommend accepting the paper.", " Thank you for the detailed response. \n\nRegarding the question about seen and unseen categories being similar, I am satisfied with the description about the CD histogram improving overall. Please make sure to include this discussion. I appreciate the additional results with normalized point clouds, and think they are a valuable addition. I do not have further follow up question.", " Hi, \n\nThanks for providing the detailed ablation results on data split, different training setting, and etc. Although the rebuttal has addressed most of my questions, my major concern is still on the significance of the major technical contribution, requirements of massive multi-category labeled training data, and its generalization to real-world data. To be more specific, the author might be able to give a little bit more clarification that how many labeled instances per category would be enough, like would 10/20 instances per category be still a reasonable setting? I do see that the generalization to real-world data is actually in a reasonable quality, but would the proposed framework can be combined with further test-time mesh refinement? \n\nThanks!", " Dear Reviewer GFH2 ,\n\nFollowing your questions, we provided additional experiments to illustrate both the potential and limitations of our meta-learning approach. We also empirically showed the sign prediction accuracy of our self-supervised formulation. In light of this, we would like to know whether you believe we have addressed your concerns, and if so we hope that you would be willing to increase your score.\n\nThank you for your time,\n\nThe Authors", " Dear Reviewer 84Fy ,\n\nFollowing your questions, we provided additional baseline experiments to illustrate the effectiveness of our approach. In light of this, we would like to know whether you believe we have addressed your concerns, and if so we hope that you would be willing to increase your score.\n\nThank you for your time,\n\nThe Authors", " Dear Reviewer 8obm,\n\nFollowing your questions, we provided additional explanations and YCB visualizations to illustrate the effectiveness of our approach in real-world settings. In light of this, we would like to know whether you believe we have addressed your concerns, and if so we hope that you would be willing to increase your score.\n\nThank you for your time,\n\nThe Authors", " Dear Reviewer 39TN,\n\nFollowing your questions, we addressed the role of the self-supervised loss in our meta-learning approach, convergence proofs, and we provided additional intuition and experiments to illustrate the effectiveness of our approach. To this end, we experimentally validate the sign prediction accuracy of our self-supervised loss. In light of this, we would like to know whether you believe we have addressed your concerns, and if so we hope that you would be willing to increase your score.\n\nThank you for your time,\n\nThe Authors ", " > Response to Question 1 \n\nWe employ the self-supervised loss in the first stage to emulate second stage training. In our second stage, we introduce unlabeled data which mandates unsupervised training objectives. We find that this emulation in the first stage is essential to consuming real unlabeled data in the second stage.\n\nTo better illustrate this, we point to the following experiment:\nWe train two different models for a prior on six classes with a total of 600 meshes: the first model is trained with the proposed method while second model is only trained with the supervised loss. As suggested by the reviewer, for the second model we introduce existing strategies against overfitting. We use dropout (20%) and add small amounts of Gaussian noise perturbations to the point clouds.\n\nThen, we use both priors to train our second stage in exactly the same fashion. Our method performs better when reconstructing unseen classes. This validates that emulating the desired training process improves generalization. We provide quantitative results on *unseen* classes (mean/median CD * 10-4):\n\n| | Ours | Supervised-only Prior (Augmentation + Dropout) |\n| -------- | -------- | -------- |\n| After training stage 1| 0.972 / 0.657 | 1.027 / 0.697|\n|After training stage 2| 0.420 / 0.316 | 0.851 / 0.568|\n\nWe highlight that after training stage 1, both methods perform approximately on par on unseen classes but not after stage 2, validating the effectiveness of the two stage approach.\n\n> Response to Question 2 (and weaknesses)\n\nTheorem 1 from NeuralPull provides a proof that, **if** their choice of loss converges, then it will converge to a *signed* distance function. It provides no guarantees on convergence, nor mathematical intuition for training behaviour given varying object geometries, finite sampled point clouds, and MLP initialization. Indeed *both our approach and NeuralPull are reliant on SAL’s geometric initialization* to avoid noisy non-converging solutions.\n\nAnalytically, the difference between our formulation and NeuralPull's is that they approximate the normal of points on the latent surface $\\textbf{p}$ as $\\textbf{N} = \\nabla f(\\textbf{q})/|\\nabla f(\\textbf{q})|_2$, where $\\textbf{q}$ is a query point, proportional to the gradient of the MLP-learned SDF. Note that this only becomes true for the unknown target SDF. In contrast, we estimate the normal of $\\textbf{p}$ as a signed unit vector to a query point $\\textbf{q}$. Specifically, both methods predict points $p^\\prime_i$ on the surface as:\n\nNeuralPull: $p^\\prime_i = q_i - f(q_i) \\times \\frac{\\nabla f(q_i)}{||\\nabla f(q_i)||_2}$\n\nOurs: $p^\\prime_i = q_i - |f(q_i)| \\times \\frac{(q_i - p_i)}{||(q_i - p_i)||_2}$\n\nBoth methods approximate the normal of $\\textbf{p}$. However, during training, the surface is represented by a finite set of random sampled locations. Thus, for a given query point $q$, NeuralPull is not guaranteed to find a surface point $p$ such that $\\nabla f(q)$ is the direction vector between $p$ and $q$, and is susceptible to accumulated errors from this procedure. As such, our formulation is an alternative of NeuralPull's formulation that accounts for non-continuous sampling, improving convergence behavior without disputing the proof of Theorem 1.\n\nEq. (8) of our main text provides an intuitive explanation of why our method penalizes incorrect sign predictions. Empirically, we further illustrate the effectiveness of our approach with the following two experiments below:\n\nFirst, we run NeuralPull and our self-supervised loss as stand-alone methods. We train on five point clouds from the QueenBed class, and run inference on 130,000 points near the surface of each point cloud. While both methods produced low $\\ell_2$ losses, our method produced significantly higher sign prediction accuracy, which explains why our reconstruction results have sharper edges and details, while NeuralPull's appear often smoothed out (Fig. 8 in Appendix of revised manuscript).\n\nConfusion matrix for NeuralPull:\n| 650,000 points | Pred Pos | Pred Neg |\n| -------- | -------- | -------- |\n| 449,650 Pos| 437,779 (0.974) | 11,871 (0.026)|\n| 200,350 Neg| 37,986 (0.190) | 162,363 (0.810)|\n\nOur self-supervised method:\n| 650,000 points | Pred Pos | Pred Neg |\n| -------- | -------- | -------- |\n| 449,650 Pos| 449,245 (0.999) | 405 (0.001)|\n| 200,350 Neg| 2,765(0.014) | 197,585 (0.986)|\n\nSecond, we swap out our self-supervised loss for NeuralPull's loss to train our full model. We provide training details, curves, and results in the Appendix (Fig. 9, Tab.4) of our revised submission.\n\nLastly, SAL provides rigorous theoretical foundations on the amount of information in unlabeled point clouds, namely that you can *provably* fit an SDF to these point clouds alone. While these proofs cannot be directly extended to our mixed-loss meta-learning setup, we will add further reference and discussion of them in the final text.", " > “This paper gives me an illusion of as long as you can keep randomly splitting your labeled multi-category dataset and train with two different losses(GT-supervised and Self-supervised), you can get a well-generalized model with good pretraining weights”\n> \nThe specific dataset split and unsupervised loss is essential for the proposed approach to work. We illustrate this with the following experiments that provide further intuition. In the first experiment, we show that the diversity in data is important for the model to learn a generalized prior. Randomly splitting is an effective strategy if the given dataset is balanced in terms of geometry. In the second experiment, we show that not any two (supervised/unsupervised) losses work but the choice of the unsupervised loss is essential for the convergence of the proposed method.\n\n#### Training Data in First Stage:\nWe train two models on our meta-learning first stage. The first trains on the following six diverse shape classes: 'Bench', 'QueenBed', 'EndTable', 'FloorLamp', 'Monitor', 'PottedPlant'. The second trains on six classes that are semantically and geometrically similar: ‘EndTable’, 'AccentTable', 'CoffeeTable', 'DiningTable', 'RoundTable', 'Table'. Then we evaluate on 166 unseen classes. The first model outperforms the second, validating that the diversity in the training set is more important than the raw number of classes. Although even with less diverse data, our meta-learning approach can still produce generalized priors.\n\nWe provide quantitative results (mean/median CD * 10-4) here and training curves in *Fig. 11 of our revised submission*.\n\n| | Six Diverse Classes | Six Similar Classes |\n| -------- | -------- | -------- |\n| CD| 0.972 / 0.657 | 1.321 / 0.934|\n\n#### Effect of Unsupervised Loss:\nTo illustrate the importance of our unsupervised loss, we point to Sec. A.2 in our revised paper and Fig. 6 of our supplemental material. Using NeuralPull's loss instead of our unsupervised loss, training seems to converge to local minima. We attribute this to inaccurate sign predictions, which build up as we increase the number of meshes. This conflicts with the supervised loss which produces accurate sign predictions. Thus, the model is unable to converge at a meaningful signed distance function. We provide training curves in *Fig. 9 of our revised submission* and a qualitative example in *Fig. 10*. Quantitative evaluation (mean/median CD * 10-4) is listed below:\n\n| | Ours (stage 1) | Ours w/ NeuralPull loss (stage 1) |\n| -------- | -------- | -------- |\n| CD| 0.972 / 0.657 | 359.6 / 361.0|\n\n> “current work...doesn't generalize to real-world partial scans, which is the major and crucial application scenerios for semi-supervised learning/Meta-learning” \n\nWhile we demonstrate robust reconstruction of real-world complete point cloud scans from YCB (Fig. 6 and 7), we are not able to directly apply our method to partial scans. Our self-supervised loss for training on unlabeled data relies on nearest neighbors on the point cloud as proxies for ground truth distance values, which missing regions in partial scans lack. We agree that this is an important direction of future work and will discuss this in the next revision of the text.\n\n> “What if in stage 1, we simply first train on all the labeled data directly with GT/SSL loss, what will be the results on the next stage of semi-supervised training?”\n\n*Directly with GT loss:* Our “no split” experiment is not followed by semi-supervised training. A prior that is trained only on the supervised loss performs worse on the second stage, because there is no emulation of the model to train on unlabeled data. We validate this further as follows:\n\nWe train two separate models for a prior. Both train on six classes with a total of 600 meshes. The first model is trained exactly using our method as explained in our manuscript. The second model is trained only with a supervised loss, using dropout (20%) and small amounts of Gaussian noise augmentation to the point clouds to prevent overfitting.\n\nThen, we use both priors to train our second stage in exactly the same fashion. With our prior, our model performs significantly better when reconstructing unseen classes. We provide quantitative results on 166 *unseen* classes (average/median CD * 10-4) here:\n\n| | Ours | Supervised Prior (Augmentation + Dropout) |\n| -------- | -------- | -------- |\n| After training stage 1| 0.972 / 0.657 | 1.027 / 0.697|\n|After training stage 2| 0.420 / 0.316 | 0.851 / 0.568|\n\nWe highlight that after training stage 1, both methods perform on par on unseen classes. However, our prior that emulates semi-supervised training is able to excel in the second stage.\n\n*Directly with SSL loss:* We report in supplemental Sec.5 that using SSL alone cannot produce a well-trained prior and cannot be used to train the second stage.", " > “one of the baselines for Section 4.1 should be ConvOccNet with the same decoder as you use.\"\n\nThe \"No split\" setting is indeed exactly ConvOccNet with our decoder (encoder of ConvOccNet + our decoder), and we have clarified this in the revised manuscript. We validate the effectiveness of the proposed decoder quantitatively in Tab. 2 as an ablation experiment.\n\n> “The method is technically given access to 76 more classes...while supervised methods only get 20. It would be better to try supervised training on more diverse classes...to better emulate a supervised training approach that is trying to generalize to other shape classes.”\n\nWe address this question in two parts.\n\n#### Comparison to supervision with more classes:\nWe report three results below: training our meta-learning approach with 20 classes, and training only with the supervised loss on 20 and 76 classes. We test all methods on 166 unseen classes. With our meta-learning approach, our model achieves lower CD even when compared to training 76 classes using only the supervised loss.\n\n| | Ours (Stage 1), 20 Classes | Supervised Only, 20 Classes | Supervised Only, 76 Classes |\n| -------- | -------- | -------- |------|\n| CD| 0.407 / 0.250 | 1.164 / 1.367 | 0.908 / 0.866 |\n\n#### Training proposed method with more classes in the first stage:\nAs 20 classes appear to be 'enough' for the model to learn a generic shape prior, to better understand *what* exactly in the training data leads to better generalization, we ran the following experiment:\n\nWe train two models on our meta-learning first stage. The first trains on the following six diverse shape classes: 'Bench', 'QueenBed', 'EndTable', 'FloorLamp', 'Monitor', 'PottedPlant'. The second trains on six classes that are semantically and geometrically similar: ‘EndTable’, 'AccentTable', 'CoffeeTable', 'DiningTable', 'RoundTable', 'Table'. Then we evaluate on 166 unseen classes. The first model achieves a lower CD than the second, validating that the diversity in the training set is more important than the raw number of classes.\n\n| | Six Diverse Classes | Six Similar Classes |\n| -------- | -------- | -------- |\n| CD| 0.972 / 0.657 | 1.321 / 0.934|\n\n> “It would be interesting to have a baseline that does the same setup as your approach (Phase 1 and 2) but change the self-supervised loss to be the same as Neural Pull”\n\nWe swap out our self-supervised loss for NeuralPull's loss to train our full model. We only train six classes on stage 1 due to time constraints. With NeuralPull's loss, training seems to converge to local minima. We attribute this to inaccurate sign predictions, which build up as we increase the number of meshes. We provide training curves in *Fig. 9 of our revised submission* and a sample of reconstruction results in Fig. 10. For a more detailed discussion of sign predictions, see *Tab. 3 of our revised submission*. Quantitative results (mean/median CD * 10-4) are reported below:\n\n| | Ours (stage 1) | Ours w/ NeuralPull loss (stage 1) |\n| -------- | -------- | -------- |\n| CD| 0.972 / 0.657 | 359.6 / 361.0|\n\n> \"For unsupervised methods (Section 4.2), it would be good to compare to IGR...PHASE+FF [* 1] or DiGS [* 2]\"\n\nWe were unable to complete this experiment due to time constraints. In our final version, we will compare to these methods.\n\n> “No quantitative comparison to single network per shape methods...e.g. IGR, SIREN...such quantitative results...would serve as a good upper bound for seeing how close your method can generalize.”\n\nWe have conducted an additional experiment to compare our method to a single-object method, SIREN, and will include additional results in the final version. These methods can outperform ours on single objects (lower CD) because they have more complex or specific training objectives and loss functions. However, we note, that single object methods fail for multiple objects, as shown in Fig. 5 and 6 in our supplemental material. We run SIREN on the author provided sample point cloud, \"Thai Statue,\" and also use our model to run inference on the same file. \n\n| | Ours | SIREN |\n| -------- | -------- | -------- |\n| CD of Thai Statue| 0.124 | 0.064|\n\n> “Why does adding the semi-supervised training decrease the Chamfer distance on seen classes so much (0.503 to 0.351)? Shouldn't the network have been trained enough to memorise/overfit those shapes/shape classes?”\n\nOur goal is generalization, so we employed early stopping to prevent our first stage from overfitting on the labeled set. After training for double the number of iterations, our first stage is able to achieve improved results on seen classes (CD of 0.351), but performs worse in generalization. This means for the \"seen shape\" evaluation, semi-supervised training plays a role of extending training. ", " > \"If the dataset contains categories that are distinct, but very similar according to their shape, this may potentially affect to what extent claims can be made about generalization\"\n\nWe agree that some categories in the train and test sets have similar shape, and that is easier to reconstruct these \"unseen\" but similar categories. However, Fig. 3 in the main text reports the **log-scale** per-category histogram of reconstruction quality, and we observe improvements to the entire distribution of Chamfer Distance scores over 100+ categories as compared to existing methods. Qualitatively, in Fig. 5 of the main text and supplementary Figs. 2 and 3, even \"outlier\" objects such as the thin-structure flamingo, helicopter, and flat-faced scissors are accurately reconstructed despite the fact they do not structurally resemble any category of the train set.\n\n> “It would be very helpful to see multiple instances of real world generalization capability, especially of different types of objects. The data is not re-scaled to match the distribution of the original training data. While this makes sense to showcase generalization ability, not doing this pre-processing and showing the results removes a valuable evaluation of the model.”\n\nWhile leaving the data un-scaled highlights the generalizability of the method, we agree that pre-processing input point clouds is beneficial. We document results in *Fig. 7 of the revised submission*. After re-centering and normalization, we find our reconstructions further improve and all margins compared to baseline methods are preserved or increased.\n\n> “Lack of provided context for real world applicability. There is a multitude of ways in which 3D point clouds can be obtained for which we would like to get a detailed and high quality mesh estimate. However, the characteristics, such as the amount and kinds of noise, or number of points of the point clouds depend on the method they were obtained (e.g. multiple depth sensor readings vs. multi-view stereo). It would be very useful if the paper included some text about how the tasks designed and used for evaluation (e.g. 5K points with a specific kind of Gaussian noise) in the paper are a good proxy for the real world utility of models like GenSDF.”\n\nWe include results on the YCB dataset which is a real-world point cloud dataset acquired from multi-view RGBD captures. The fused multi-view point clouds in this dataset resemble input measurements for a robotic part-picking or manipulation task. We demonstrate robust mesh reconstructions of the measured data, e.g., recovering the \"handle\" of a pitcher in *Fig. 7 in the revised manuscript*, which may serve as input to complex robotic grasping tasks. In the next version, we will add further discussion of the tasks our work may support and what level of noise in the point cloud it is susceptible to. \n\nTo illustrate how our model can adapt to noise that drastically exceeds measurement noise in YCB, we gradually add Gaussian noise with mean zero and variance $\\sigma^2$ to the input point cloud and evaluate the CD (* 10-4).\n\n| $\\sigma^2$ | 0.0 | 0.01 | 0.05 | 0.1 | 0.15 | 0.2 |\n| -------- | -------- | -------- |------|------|------|------|\n| CD| 0.870 |0.911 | 3.122 | 5.208|7.429|7.391|\n\nQualitatively, from $\\sigma^2 > 0.1$, the reconstructed object degrades severely. Future work could investigate specifically learning noise-robust geometric priors for mesh reconstruction from low-quality point clouds.", " We thank all reviewers for their thoughtful feedback and we are happy to see the positive reception. We address each reviewer's questions individually below. Additionally, *we have added an Appendix in the revised submission of the main manuscript with additional experimental results such as training curves and figures that we could not attach in the comments*. All changes compared to the previous submission are highlighted in blue color. We reference those results in some of our responses to the individual reviewers.", " This work proposes GenSDF, a method for object surface estimation, parameterized by SDF, from 3D point cloud inputs. The main distinctions of GenSDF to prior work is its ability for high quality generalization to novel classes not seen during training, and the ability to take advantage of \"unlabeled\" point cloud data (without know SDFs) as supervision during training. GenSDF achieves this by two well designed training phases, first a meta learning procedure to train a general shape prior, by sampling labelled and unlabeled subsets of the labelled training set, and a second semi-supervised step where the fully labelled training set is used in addition to an additional entirely unlabeled set. GenSDF also proposes a well designed loss for using unlabeled point clouds as supervision for an SDF prediction model.\n\nEvaluation is performed on Acronym (a subset of ShapeNet), split into 20 labeled training classes, 70 unlabeled classes for semi-supervised training, and 166 classes for testing. GenSDF significantly outperforms SDF-supervised and unsupervised . GenSDF can also directly generalize to point clouds from scans of the YCB dataset. Ablation studies directly demonstrate the benefit of the proposed two-stage training procedure. ## Originality\n### Strengths\nDirect generalization to unseen categories in the domain of surface estimation from point clouds has not been investigated before, and is an important application (see Significance). This method proposes a novel and well designed two stage training procedure, along with a loss function for using unlabeled data samples. The model's design is supported by high quality ablation studies and significantly higher performance than baselines in terms of chamfer distance.\n\n## Quality\n### Strengths\n1. _Simple, elegant and effective implementation_: The high level idea of learning a general shape prior that can be used for semi supervised training with unlabeled data makes sense, and paper addresses this using a simple but effective approach of repeatedly partitioning the training set into labeled and unlabeled classes. Further, in order to train models on point clouds only, where only the distance to the nearest point in the point set is available, it's necessary to use a loss that is a proxy for SDFs. The proposed loss is a straightforward and improved proxy between nearest point unsigned distance and SDF values relative to prior methods, and includes an additional term to encourage precision closer to the 0-level set.\n2. _High performance relative to baselines_: The performance of GenSDF vs. the closest baseline in terms of chamfer distance is 0.351 vs 1.348 for seen and 0.407 vs 2.333 for unseen. This further highlights the poor generalization ability of prior methods.\n\n### Weaknesses\n1. _Evaluation to unseen classes_: The Acronym dataset is based on ShapeNetSem. While ShapeNetSem does contain 270 different categories, a lot of these are distinct but semantically similar. For example, Chair, OfficeChair, Stool, SideChair, Barstool, AccentChair are all similar chair-like objects that are distinct categories in ShapeNetSem, and Table, RoundTable, EndTable, DiningTable, CoffeeTable, AccentTable are also all similar table-like objects that are distinct categories in ShapeNetSem. If the dataset contains categories that are distinct, but very similar according to their shape, this may potentially affect to what extent claims can be made about generalization.\n2. _Further evaluation on YCB_: The paper shows two qualitative examples on YCB. It would be very helpful to see multiple instances of real world generalization capability, especially of different types of objects. The data is not re-scaled to match the distribution of the original training data. While this makes sense to showcase generalization ability, not doing this pre-processing and showing the results removes a valuable evaluation of the model.\n\n## Clarity\nThe paper is very well written and easy to follow. The visualizations of the reconstructions and the diagrams are high quality. The tables are clearly formatted.\n\n## Significance\n### Strengths\nIt is useful to develop object surface estimation methods that generalize, so that they can be used in cases where lots of ground truth meshes (necessary to derive SDF for supervision) are not available.\n\n### Weaknesses\nLack of provided context for real world applicability. There is a multitude of ways in which 3D point clouds can be obtained for which we would like to get a detailed and high quality mesh estimate. However, the characteristics, such as the amount and kinds of noise, or number of points of the point clouds depend on the method they were obtained (e.g. multiple depth sensor readings vs. multi-view stereo). It would be very useful if the paper included some text about how the tasks designed and used for evaluation (e.g. 5K points with a specific kind of Gaussian noise) in the paper are a good proxy for the real world utility of models like GenSDF.\n 1. It is clear that GenSDF is better at generalization to unseen categories than prior methods. However, the shape similarity of what are supposed to be different categories in ShapeNetSem affects these claims to some extent. Can the authors please comment on how the fact that there are semantically very similar categories that may end up being split in the seen and unseen sets affects the claims that can be made about generalization ability?\n2. Regarding the point under weaknesses in significance, can the authors please provide a bit more context about how they design the evaluation task relative to potential real world applications of GenSDF? Including this in the introduction of the paper would help the reader understand the significance of what the model can do. The authors have discussed some limitations of their work throughout the draft. The paper itself doesn't have high potential for negative societal impact.", " The paper considers the task of learning to reconstruct shapes (via the SDF) from \"unlabelled\" point clouds (no mesh and no normals) using a single network that must generalize for unseen shapes (and shape classes). The network is allowed to train on both labelled data (meshes) and unlabelled data (unoriented point clouds). The proposed method trains with a standard supervised loss on labelled data, and a self supervised loss that builds upon Neural Pull [19] (but corrects it to properly penalization incorrect signs) for unlabelled data. They further train the supervised loss with the self-supervised loss on psudo-unlabelled data, claiming it greatly helps generalize, with ablations studies demonstrating this. Strengths\n- A data driven approach to shape reconstruction with a strong focus on generalization\n- Specifically allows to learn to generalize from a large corpus of unlabelled shapes.\n- Fixes an important weakness in the NeuralPull training objective\n- Proposes introducing unsupervised training into the the initial supervised training step that shows significant improvement in generalization\n- Shows large improvement over baseline methods for both unsupervised and supervised methods, without further test time refinement\n\nWeaknesses\n- The baselines for this task could be better. \n\t- Section 4.4 says that \"No split\" is essentially ConvOccNet but has lower CD due to a different choice of decoder, but the difference from this choice as decoder is really large. As a result one of the baselines for Section 4.1 should be ConvOccNet with the same decoder as you use.\n\t- The method is technically given access to 76 more classes via unsupervised training for it to learn to generalize on (since the other methods do not have an unsupervised learning method), while supervised methods only get 20. It would be better to try supervised training on more diverse classes (but a few in each class such that the overall number of supervised meshes to train on is the same) to better emulate a supervised training approach that is trying to generalize to other shape classes. \n\t- It would be interesting to have a baseline that does the same setup as your approach (Phase 1 and 2) but change the self-supervised loss to be the same as Neural Pull, which would show how important your change is.\n\t- For unsupervised methods (Section 4.2), it would be good to compare to IGR without normals (the autodecoder setting), which has a better unsupervised loss (Eikonal term) than SAL and doesn't have the defect that NeuralPull does. For an even stronger baseline, PHASE+FF [* 1] or DiGS [* 2] would be even better (again with the autodecoder setting).\n- No quantitative comparison to single network per shape methods (which you call Single-object methods in the supp material), e.g. IGR, SIREN. Although, as you argue in the supp material, this is a different setting, such quantitative results (which you have given a qualitative result for) would serve as a good upper bound for seeing how close your method can generalize.\n\n[* 1] https://arxiv.org/abs/2106.07689\n[* 2] https://arxiv.org/abs/2106.10811 Why does adding the semi-supervised training decrease the Chamfer distance on seen classes so much (0.503 to 0.351)? Shouldn't the network have been trained enough to memorise/overfit those shapes/shape classes? What do you believe the semi-supervised training is adding here (we don't need object level generalisation to perform well on seen shapes)? A short discussion of limitations is given in the conclusion. No negative societal impacts are discussed, but I agree that there are no direct negative impacts.", " Given multiple-category labeled (with GT SDF) and unlabeled point cloud data, this paper introduces a simple yet effective meta-learning inspired pretraining stage before the conventional semi-supervised stage in order to train a generalizable SDF function model. Their strategy frequently randomly splits the labeled data into a self-supervsied and GT-supervised group with different categories, which creates diversity of different tasks and encourage a shared embedding network for better model initialization, and better leverage labeled multi-category data as guidance, assisted by self-supervision loss on unlabeled data.\n\n **Strengths**\\\n[originality]\nIt is novel to apply episodic scheme on randomly split hybrid training for SDF learning as pretraining;\nThey further introduce a self-supervised loss regularization item[Section 3.2], which is well considered for the target task;\n\n[quality & clarity] \nThe paper is written with a smooth logic flow, and clear explanation on the methods and experiments, with a lot of high-quality visualization and comparison, like Figure 5 in main paper, and figures in the supps. \n\n[significance]\nThis simple yet effective training paradigm is helpful and inspiring for a lot of 3D learning tasks, the achieved results[Figure 3, Table 1] are \nmuch better than compared baselines.\n\n**Weakness**\n1. This paper gives me an illusion of as long as you can keep randomly splitting your labeled multi-category dataset\nand train with two different losses(GT-supervised and Self-supervised), you can get a well-generalized model with good pretraining weights;\nI am surprised at this conclusion, in which the author might want to give more details like training curves, failure cases, to really show the full potential and limitation of this proposed framework, while also explain better on the intuition behind;\n\n2. No ablation study on the discussed 'Self-supervised Loss Component' in line 163-182, we want experiments to support the authors' argument on this alternative formulation to avoid incorrect sign predictions; \n\n3. As mentioned by the author in the supp., it seems current work only supports complete point cloud, it doesn't generalize to real-world partial scans, which is the major and crucial application scenerios for semi-supervised learning/Meta-learning to demonstrate its effectiveness. Even though current work is not designed for partial scans, the author should at least show some qualitative results. 1. What if in stage 1, we simply first train on all the labeled data directly with GT/SSL loss, what will be the results on the next stage of semi-supervised training? The no split in Table 2 seem to be the desired one, but I am not sure whether it is followed by semi-supervised training, and have the exactly same training setting except for the splitting;\n\n2. How to decide the split ratio between labeled and unlabeled dataset, would smaller number of labeled data (like only 5 classes instead of 20/1) lead to big degrade to the methods? How is the split frequency being decided, will it be a big influence factor to the pretraining performance?\n\n3. A recent paper 'Shape As Points: A Differentiable Poisson Solver' can also reconstruct surface from complete point cloud by learning a general geometry equation solver, is it possible to also compare with this paper? Although quantitative results would be better, comparison in text is valid if the experiments become too complex. The main limitations are two-fold as mentioned by the authors:\n1. It requires multi-category data with ground truth for training;\n2. It does not consider partial scans, and may fail on partial and noisy data;", " The main contribution of this paper is to improve the generalization capabilities of implicit representations learning. This paper introduce an episodic training scheme where we split data into subsets with disjoint classes to learn a generalized shape representation at the first stage. The second stage allows the model to ingest large amounts of unlabeled data to diversify the shape model learned in the first stage. Strengths：\n\n(1) This paper proposes a training scheme that can learn implicit representations from both labeled and unlabeled point cloud data, and the method produces effective experimental results.\n\n(2) Enhancing the implicit representation learning capability of the network using both labeled and unlabeled point cloud data simultaneously is a meaningful research problem, and from the experimental results, the paper also proposes a framework that can combine both kinds of data effectively.\n\nWeaknesses：\n\nEven though I am knowledgeable about works related to implicit representation learning, I have difficulty understanding the reasons why the framework proposed in the paper works outperforms existing neural SDF methods. No convincing explanation is given in the paper for this proposed framework to achieve such a large effect of enhancement. (1) In the first stage, every f epochs, this paper splits data X into two subsets with disjoint categories, and then train both data with self-supervised loss and supervised loss respectively. According to my understanding, training the network with ground-truth signed distance values supervision through the supervised loss will give more accurate shape priors. I do not understand the role played by the self-supervised loss here. Even though the paper gives a vague explanation: “episodic training on non-overlapping categories forces the model to develop generalized representations as it cannot overfit to the data.” If the self-supervised loss simply prevents overfitting to the data, there are many common training strategies in the field of machine learning that can prevent overfitting. A more convincing proof of principle for the self-supervised loss is needed here.\n\n(2) I am puzzled by the results of Table 1, whether such a large improvement can be achieved using only unlabeled point cloud data, and what is the reason for the improvement? How is the prediction of /phi(x) guaranteed to be correct if it does not depend on the labeled point cloud. The loss function of Eq. 7 can be equally reduced if it is predicted /phi(x) to all positive or negative signs in Eq. 8. Both SAL and NeuralPull give proofs that they can predict the correct sign, and this paper is unconvincing in this part. I don't foresee any potential negative societal impacts." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 7, 6, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 5 ]

[ "-V0XxKzGkJ8", "S1DsTBBFHv6", "CjJAsWuYtvw", "fKVq1-YA9Z1", "yrZE10XmleEt", "pMw2lbuyEb_", "RMOPfLSKojI6", "kbpn40SChz82", "S1DsTBBFHv6", "NEQ8I_5NU-4", "GC8PjZrarz6", "LBD4iquI7Ir", "DzreTeINLPh", "nips_2022_QK38rpF8RWL", "nips_2022_QK38rpF8RWL", "nips_2022_QK38rpF8RWL", "nips_2022_QK38rpF8RWL", "nips_2022_QK38rpF8RWL" ]

[ "KMhi_C6AxtA", "8Ddh0yuNPjS", "ZNOOVzo99Gc", "IxKkCLm77rF", "vwuZdGYVPiz", "U7PIre2Bww2", "XNVwKYdAiM", "Kp0oifL-DIW", "mLoJGE0-4mY", "ESSOJNSMvR", "cg4Lv7tHP1A", "RIv0Mjxajvf" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We sincerely appreciate your response. We will incorporate your feedback and discuss the relationship with Liang et al. in the final version of the paper. Thank you for your questions and suggestions again!", " Thank you for the explanations.", " Dear reviewers,\n\nWe appreciate your invaluable feedback and constructive suggestions. We are wondering whether our response addressed your concerns. If you have any additional comments, please let us know. We would be happy to address them.", " Thank you for your reviewing efforts and constructive comments. We address the concerns point by point.\n\n> *Comment 1: Comparison with previous works on multiple purchases*\n\nThanks for indicating these papers and we will discuss them thoroughly in the final version of our paper.\n\nThe mentioned papers [1, 2] both considered the multiple purchases setting based on MNL. As a result, **they did not take the effect of ranking into consideration**. Specifically, they characterized the probability of purchasing a set of products according to products' and customers' features only. However, in this work, we consider the setting where customers view the product list sequentially. This is a realistic setting since customers can not obtain the full product list on both websites and smartphones and they always view the products from the top to the bottom of the list. Many works are also based on this setting [3, 4]. As a result, the way to rank products has great effects on the purchasing behaviors of customers, making our work differ fundamentally from theirs.\n\n\n> *Comment 2: Comparison with previous works on the online setting*\n\n- **Compared with other UCB-like online algorithms (e.g., [3, 4])**, the main differences lie in the extra parameter $s\\_t$ (to characterize the distribution of the purchase budget) we introduce in the customer choice model and hence the algorithms and techniques on the regret analysis.\n - Firstly, our online algorithms are all based on the optimal ranking policy if the customers' characteristics are known (demonstrated in Section 4). As a result, the optimal ranking policy has fundamental differences from previous works [3, 4, 5] due to the newly introduced parameter $s\\_t$.\n - Secondly, all UCB-like algorithms share a similar protocol (i.e., optimism in the face of uncertainty principle) while the main differences lie in how to estimate the parameters (i.e., the customer's characteristics in our setting) and how to choose the optimal policy in the uncertainty set of the parameters. To be specific, firstly, we estimate the parameters based on Lemma 5.1 and provide the uncertainty set of the parameters in Propositions 5.2 and 5.4. Secondly, the optimal ranking policy in the uncertainty set is chosen based on Propositions B.1 and B.2 in the appendix of our paper. These two steps become more difficult since we introduce the extra parameter $s\\_t$. By contrast, existing works do not take the purchase budget into account and can not be adopted directly.\n- **There are also other online algorithms based on Thompson sampling (e.g., [6, 7])**. Both types of algorithms (including algorithms based on UCB or Thompson sampling) can effectively balance the trade-off between exploration and exploitation in online settings. While we study a novel online setting, no existing online algorithms could be adopted here directly. As a result, we focus on UCB-like algorithms in this paper and leave the extension to Thompson sampling algorithms as future work.\n- **Compared with other works on multiple purchases (e.g., [1, 2])**, their algorithms can not be adopted directly here. Firstly, their customer choice models do not take the effect of ranking into consideration, which makes the optimal ranking policy fundamentally different. Secondly, these works focused on designing proper offline algorithms and did not consider the online settings.\n\n[1] Tulabandhula et al. \"Multi-purchase behavior: Modeling and optimization.\" arXiv preprint. 2020.\n\n[2] Zhang et al. \"Assortment Optimization Under Multiple-Discrete Customer Choices.\" Available at SSRN. 2021.\n\n[3] Cao et al. \"Dynamic learning of sequential choice bandit problem under marketing fatigue.\" AAAI. 2019.\n\n[4] Chen et al. \"Revenue maximization and learning in products ranking.\" EC. 2021.\n\n[5] Liang et al. \"Sequential dynamic event recommendation in event-based social networks: An upper confidence bound approach.\" Information Sciences. 2021.\n\n[6] Wang et al. \"Thompson sampling for combinatorial semi-bandits.\" ICML. 2018.\n\n[7] Ferreira et al. \"Online network revenue management using thompson sampling.\" Operations research. 2018.", " Thank you for your reviewing efforts and constructive comments. We address the concerns point by point.\n\n> *Comment 1: The paper identifies some limitations of the previous literature and considers a setting that is an “intersection” of several previous setups, which makes their setting more general or realistic compared to each of the previous papers. Yet, for the conceptual contribution, this is an incremental work based on several previous papers.*\n\nAs mentioned in Line 23-30, most related works in the context of ranking products consider the single purchase setting. Several other works consider the multiple purchases setting while their targets are not revenue maximization [1, 2] or they assume that customers always continue viewing the product list after purchasing any product [3]. By contrast, we consider the purchase budget and generalize the existing customer choice models to a more realistic setting, which is novel.\n\n> *Comment 2: The baselines are some previous methods that are designed under different assumptions.*\n\n- Firstly, because we consider a novel setting and no existing works could fit perfectly here, we choose the closest works [3, 4] as baselines to demonstrate the effectiveness of our algorithms.\n- Secondly, our setting is more realistic and general and their works [3, 4] consider the special cases of our setting. We implement their methods based on their assumptions to ensure the solidness of their results so that the comparison between our method and theirs is reliable and rational.\n\n> *Comment 3: Could you briefly explain the technical challenges and contributions compared to Liang et al. (2021)?*\n\nThe main differences between our work and Liang et al. [3] lie in the problem setting (especially the customer choice model) and hence the algorithms and techniques to achieve the regret analysis.\n\n- **The differences in settings** have the following two aspects.\n 1. The most fundamental difference between our setting and theirs is **the purchase budget that constrains the total number of purchases of each customer**. As demonstrated in Line 28-30, [3] assumed that customers always continue viewing the product list after purchasing any product, which is not practical in real scenarios. By contrast, the purchase budget proposed in our paper leads to a different and more practical customer choice model. In addition, our model introduces an extra parameter (i.e., the parameter $s\\_t$ that characterizes the distribution of the purchase budget), which makes our problem more challenging.\n 2. [3] assumed the online retailer will stop recommending products with a certain probability $1 - w\\_t$ to avoid the cost brought by marketing fatigue (i.e., overexposure to unwanted marketing messages [4]). As a result, the parameter $w\\_t$ is a part of the ranking policy instead of customers' characteristics and should be optimized to achieve maximal revenue. In our paper, we focus on the multiple purchases with budgets setting and leave the extension to the case with the marketing fatigue as future work.\n- **The differences in techniques** have the following two aspects.\n 1. For the optimal ranking policy given customers’ characteristics, our optimal ranking policy is based on both the newly introduced parameter $s\\_t$ and other customers' characteristics (i.e., the attention span and the purchase probabilities) as shown in Theorem 4.1. By contrast, they did not take the purchase budget into account so their optimal policy should be based on other customers' characteristics only, which differs from the result in Theorem 4.1 of our paper.\n 2. For the online parts, all UCB-like algorithms share a similar protocol (i.e., optimism in the face of uncertainty principle) while the main differences lie in how to estimate the parameters (i.e., the customer's characteristics in our setting) and how to choose the optimal policy in the uncertainty set of the parameters. Specifically, we first estimate the parameters (including $s\\_t$) based on Lemma 5.1 and provide the uncertainty set of the parameters in Propositions 5.2 and 5.4. Then the optimal ranking policy in the uncertainty set is chosen based on Propositions B.1 and B.2 in the appendix of our paper. By contrast, the parameter $w\\_t$ introduced in [3] is a part of the ranking policy instead of customers' characteristics and need not be estimated from historical data. As a result, our online algorithms are more challenging due to the existence of the extra parameter $s\\_t$ in the customer choice model.\n\n[1] Cao et al. \"Fatigue-aware bandits for dependent click models.\" AAAI. 2020.\n\n[2] Ferreira et al. \"Learning to rank an assortment of products.\" Management Science. 2022.\n\n[3] Liang et al. \"Sequential dynamic event recommendation in event-based social networks: An upper confidence bound approach.\" Information Sciences. 2021.\n\n[4] Cao et al. \"Dynamic learning of sequential choice bandit problem under marketing fatigue.\" AAAI. 2019.", " Thank you for your reviewing efforts and constructive comments. We address the concerns point by point.\n\n> *Comment 1: The major comment is on the time complexity of the algorithms in practice. Please add a discussion on how Algorithms 1 and 2 can put into practice with similar time complexity and appropriate parallelization for each t.*\n\nWe discuss the time complexity of the algorithms as follows.\n\n- For Algorithm 1 in the non-contextual setting, the statistics in Line 6 of Algorithm 1 can be updated at $O(N)$ time complexity. Combining the $O(N \\log N)$ complexity to calculate the optimal ranking policy according to Theorem 4.1, the overall time complexity for each $t$ is $O(N \\log N)$. As a result, the algorithm in this setting does not need parallelization.\n- For Algorithm 2 in the contextual setting, the major overhead is on the calculation of the matrix inversion in Lines 5 and 9 of Algorithm 2. The corresponding time complexity is $O(m\\_x^6 + m\\_y^2)$ where $m\\_x$ is the dimension of customers' features and $m\\_y$ is the dimension of the joint feature of customers and products. As a result, the overall time complexity for each $t$ is $O(N \\log N + m\\_x^6 + m\\_y^2)$. However, the inverse of matrices can be calculated effectively under parallelization [1]. As a result, the actual time complexity can be much smaller.\n\n> *Comment 2: the minor typos.*\n\nThanks for indicating these mistakes, and we will correct them in the final version of the paper.\n\n[1] Quintana et al. \"A note on parallel matrix inversion.\" SIAM Journal on Scientific Computing. 2001.", " Thank you for your reviewing efforts and constructive comments. We address the concerns point by point. \n\n> *Comment 1: According to the purchase probability specified in Eq. (1), the purchase probabilities towards different products are independent of each other. How do you verify this assumption? Please also discuss the corresponding applications.*\n\n- The assumption in Equation (1) is that **the conditional purchase probabilities are independent of each other**. That means if a customer $t$ views the product $k$, the purchase probability $\\lambda\\_{t,k}$ is independent of other products and the position of the product in the ranking list. **This assumption is common and standard in related literature [1-6].** On the one hand, several customer choice models are characterized based on this assumption, including the cascading model [1] and the click chain model [2]. On the other hand, various works have been proposed based on these choice models, as well as the underlying independent assumption, to maximize the revenue [3, 4] or the number of clicks [5, 6].\n- We highlight that **the actual purchase probability of the product $k$ in the ranking list depends both on other products and the position of the product $k$**. Because of the existence of the attention span and purchase budget, the probability that a customer views the product $k$ tends to decrease when the product appears later in the ranking list. In addition, if the products appeared before the product $k$ have high (low) purchase probabilities, it will be easier (harder) for the customer to meet the purchase budget and stop viewing, making the product $k$ less (more) likely to be viewed. As a result, the purchase probability of the product $k$ will be affected.\n- **The assumption in Equation (1) can be satisfied in real-world scenarios**. For example, in online retailer platforms or web click scenarios, as long as the customer views a product/web, the purchase/click probability only depends on his or her own interest in the product/web, making the conditional purchase/click probability independent of other variables. These scenarios are well studied in related literature (e.g., [1,3]).\n\n> *Comment 2: Could you emphasize the major technical contribution of the online algorithm? For example, how does the analysis differ from the existing work? Which part of the single purchase problem cannot be used in this problem?*\n\nGenerally speaking, we consider the more realistic setting (i.e., the multiple purchases with budgets setting) and introduce an extra parameter $s\\_t$ to characterize the distribution of the purchase budget in the customer choice model, which makes the algorithms more challenging. Details are provided as follows.\n\n- Firstly, our online algorithms are all based on the optimal ranking policy if the customers' characteristics are known (demonstrated in Section 4). **Because of the extra parameter $s\\_t$, the optimal ranking policy has fundamental differences from previous works on single purchase settings [3, 4]**.\n- Secondly, all UCB-like algorithms share a similar protocol (i.e., optimism in the face of uncertainty principle) while the main differences lie in how to estimate the parameters (i.e., the customer's characteristics in our setting) and how to choose the optimal policy in the uncertainty set of the parameters. To be specific, firstly, we estimate the parameters based on Lemma 5.1 and provide the uncertainty set of the parameters in Propositions 5.2 and 5.4. Secondly, the optimal ranking policy in the uncertainty set is chosen based on Propositions B.1 and B.2 in the appendix of our paper. **These two steps are more challenging compared with previous methods due to the extra parameter $s\\_t$**. By contrast, existing works on single purchase settings can not be adopted directly here.\n\n[1] Craswell et al. \"An experimental comparison of click position-bias models.\" WSDM. 2008.\n\n[2] Guo et al. \"Click chain model in web search.\" WWW. 2009.\n\n[3] Chen et al. \"Revenue maximization and learning in products ranking.\" EC. 2021.\n\n[4] Cao et al. \"Dynamic learning of sequential choice bandit problem under marketing fatigue.\" AAAI. 2019.\n\n[5] Kveton et al. \"Cascading bandits: Learning to rank in the cascade model.\" ICML. 2015.\n\n[6] Katariya et al. \"DCM bandits: Learning to rank with multiple clicks.\" ICML. 2016.", " > *Comment 3: It is assumed that $V\\_t$ follows the geometric distribution with parameter $1-q\\_t$ and $B\\_t$ follows the geometric distribution with parameter $1-s_t$. Each item costs one unit of budget. I think Theorem 4.1 heavily relies on this assumption. Can the result be generalized to other distributions?*\n\n- Theorem 4.1 is practical because the assumptions are mild and they can cover common realistic scenarios.\n - Firstly, **the assumption that the attention span obeys the geometric distribution is common in related literature**. The cascading models [1] are all based on the assumption that each item in a list is less likely to be viewed by the user with an exponential decay [2], making the attention span obey the geometric distribution. While cascading models are widely adopted (e.g., [6, 7]) to characterize customers' behaviors, it is rational and general to assume the attention span obeys the geometric distribution.\n - Secondly, **the numbers of purchases/clicks are fitted well with the geometric distribution in reality**. [3] showed that the data obtained from Overture during 2003 (including data from Yahoo!, MSN, and AltaVista) are fitted well ($R^2=0.997$) by an exponential decay model (equivalently a geometric distribution). As a result, it is rational and general to assume the purchase budget follows the geometric distribution.\n- We further discuss the possible relaxations on the assumptions as follows.\n - **Relaxing the unit cost assumption**. Suppose that each product has a $e_n$ cost and the customer will stop viewing if the total cost exceeds the purchase budget. By assuming the geometric distribution conditions, following similar proof techniques, the optimal ranking policy in Theorem 4.1 becomes\n $$\n \\frac{\\lambda\\_{\\sigma\\_i^\\*}r\\_{\\sigma\\_i^\\*}}{1 - q + q\\left(1-s^{e\\_{\\sigma\\_i^\\*}}\\right)\\lambda\\_{\\sigma\\_i^\\*}} \\ge \\frac{\\lambda\\_{\\sigma\\_{i+1}^\\*}r\\_{\\sigma\\_{i+1}^\\*}}{1 - q + q\\left(1-s^{e\\_{\\sigma\\_{i+1}^\\*}}\\right)\\lambda\\_{\\sigma\\_{i+1}^\\*}}.\n $$\n - **Relaxing the geometric assumption**. The problem becomes NP-hard under this circumstance because [4] studied the reduced version of the problem (customers purchase at most one product and the distribution of attention span can be other distributions.), which is NP-hard. However, proper approximation algorithms may exist (e.g., the algorithms in [4]) and we leave them as future work.\n\n> *Comment 4: In Section 5, two Theorems specify the regret upper bounds for both non-contextual and contextual problems. Could you also prove that they are both tight?*\n\n**The regret bounds match the best-achievable rate in the literature** as we demonstrated in the corresponding remarks of the theorems. In particular, we study a general case of the previous work [7] and achieve regret bounds with the same rate, indicating the tightness and reliability of our result. In detail, the most important parameters include the number of products $N$ and the number of customers $T$. We highlight the main points as follows.\n\n- For the non-contextual setting, firstly, the regret grows at $\\tilde{O}(\\sqrt{T})$, which is a standard result in online learning algorithms [5]. Secondly, the regret bound is linearly related to $N$, which is the same with the results in cascade bandit models [6] and revenue management literature [4, 7]. As a result, the overall regret bound is $\\tilde{O}(N\\sqrt{T})$, which matches the regret bound of the reduced setting considered in [7].\n- For the contextual setting, firstly, the regret grows at $\\tilde{O}(\\sqrt{T})$, a standard result in online learning algorithms [5]. Secondly, the regret depends on $\\tilde{O}(N)$. This shares the same result with [4], which considered similar linear assumptions on the customers' characteristics.\n\n[1] Craswell et al. \"An experimental comparison of click position-bias models.\" WSDM. 2008.\n\n[2] Breese et al. \"Empirical analysis of predictive algorithms for collaborative filtering.\" UAI. 1998.\n\n[3] Feng et al. \"Implementing sponsored search in web search engines: Computational evaluation of alternative mechanisms.\" INFORMS Journal on Computing. 2007.\n\n[4] Chen et al. \"Revenue maximization and learning in products ranking.\" EC. 2021.\n\n[5] Slivkins, Aleksandrs. \"Introduction to multi-armed bandits.\" Foundations and Trends in Machine Learning. 2019.\n\n[6] Zong et al. \"Cascading bandits for large-scale recommendation problems.\" UAI. 2016.\n\n[7] Cao et al. \"Dynamic learning of sequential choice bandit problem under marketing fatigue.\" AAAI. 2019.", " This paper studies a multi-product purchase problem. Authors design an optimal ranking policy when the online retailer can precisely model customers’ behaviors. Most of the existing work assume that each customer purchases at most one product and stops browsing immediately. This paper proposes a more realistic setting that customers view the product list sequentially and purchase a product when its utility exceeds a certain threshold with a certain purchase budget. In both non-contextual and contextual settings, they provide UCB-like algorithms and theoretically prove that the algorithms achieve \\tilde{O}(\\sqrt{T}) regrets in both settings. Strengths: \nThis paper considers a more practical setting where a single customer can make multiple purchases with certain purchase budget and attention span.\nTheorem 4.1 provides a nice structure of the optimal ranking policy.\nThe study of this ranking problem is comprehensive. It studies both the non-contextual and contextual version.\nThe paper is nicely written.\n\nWeaknesses:\n\nAlthough the paper considers a more practical problem, it still has some limitations: the paper assumes that V_t follows the geometric distribution with parameter 1-q_t and B_t follows the geometric distribution with parameter 1-s_t. Each item costs one unit of budget.\n\n 1.\tAccording to the purchase probability specified in Eq. (1), the purchase probabilities towards different products are independent of each other. How do you verify this assumption? Please also discuss the corresponding applications.\n\n2.\tCould you emphasize the major technical contribution of the online algorithm? For example, how does the analysis differ from the existing work? Which part of the single purchase problem cannot be used in this problem? If it can be emphasized before the main results, it will help to improve the paper.\n\n3.\tIt is assumed that $V_t$ follows the geometric distribution with parameter 1-q_t and B_t follows the geometric distribution with parameter 1-s_t. I think Theorem 4.1 heavily relies on this assumption. Can the result be generalized to other distributions?\n\n4.\tIn Section 5, two Theorems specify the regret upper bounds for both non-contextual and contextual problems. Could you also prove that they are both tight?\n The attention span and the purchase budget are both limited to the geometric distribution. It would improve the paper if they can be generalized to other distributions.", " The authors study the problem of product ranking based on a more realistic situation where customers can have multiple purchases and continues viewing products even after buying a product, both being subject to an overall attention span and overall budget. They characterize the optimal ranking policy and design UCB-like algorithms with a provable \\tildeO(\\sqrt{T}) regret based on both contextual and non-contextual situations. They also show extensive experiments to prove their efficacy on the simulated and real-world datasets.\n The paper is very well written (though with minor typos (see below)) and is quite easy to follow. The related work section throws good light into the existing literature on which this work is based. The thorough theoretical section is impressive and the results look good. \n\nThe major comment is on the time complexity of the algorithms in practice. Section 4 shows the time complexity as O(N Log N). Please add a discussion on how Algorithms 1 and 2 can put into practice with similar time complexity and appropriate parallelization for each t. \n\nMinor typos:\n1. Line 53, 314: rankling -> ranking\n2. Line 210: management\n See above. NA", " The paper studies the problem of product ranking in the following setting (1) customers may purchase more than one product, and (2) customers quit after viewing/purchasing a certain number of products. They first characterize the optimal ranking policy when the customer parameters are known. The paper then investigates the case when customer parameters are unknown. Two UCB-like algorithms with O(\\sqrt{T}) regrets are proposed, one for the non-contextual setting (i.e., all customers share the same parameters), and the other for the contextual setting (i.e., customers have personalized parameters). Finally, the effectiveness of the algorithms is tested by simulations. \n Strength:\nThe paper identifies some limitations of the previous literature and considers a setting that is an “intersection” of several previous setups (mainly Liang et al. (2021), Chen et al. (2021), and Cao and Sun (2019)), which makes their setting more general or realistic compared to each of the previous papers. The paper is complete in the sense that it investigates all the scenarios that have been previously considered (known parameter/non-contextual online setting/contextual online setting) and provides both theoretical analysis and experimental results. I did not check the whole proof, but the theoretical results seem solid and it seems non-trivial to derive the results in this new setting.\n\nWeakness:\nFor the conceptual contribution, this is an incremental work based on several previous papers. The main concepts and ideas have appeared in previous literature. For the experimental result in the main text, the baselines are some previous methods that are designed under different assumptions. I am not sure how meaningful it is to compare these methods when the synthetic customer data are generated according to a new model. \n\nDisclaimer:\nMy evaluation of the theoretical contribution may not be accurate because I was not able to access the full pdf of Liang et al. (2021), which seems to contain quite similar results according to the outline. 1. Could you briefly explain the technical challenges and contributions compared to Liang et al. (2021)? Yes.", " The paper develops vanilla and contextual bandit approaches to maximize revenue given an unknown parametric customer that purchases multiple products.\n One of the major issues with this paper is the extremely light and poor comparison with prior work that diminishes the key contributions. Firstly, multiple purchases have already been modeled in the OR literature that are similar to the MNL (e.g., see \"Multi-Purchase Behavior: Modeling and Optimization\" by Tulabandhula et al, \"Assortment Optimization Under Multiple-Discrete Customer Choices\" by Zhang et al, etc). Of course, some of these works focus on the revenue maximization problem in the offline setting. Given this context, the multiple purchase contribution looks like yet another model among this growing collection.\n\nFor the online setting, in the non-contextual case,there have been many works that follow the same template (define how the user parametrically interacts with a sequence of lists) such as \"Thompson sampling for combinatorial semi-bandits\" by Wang et al. and \"Dynamic learning of sequential choice bandit problem under marketing fatigue\" by Cao et al. Especially the latter work shows almost the same model (sans the budget constraint and multi purchase) with near identical results (characterization of the optimal solution in the offline known behavior case) and deriving regret bounds (albeit sparingly for the contextual case in this particular prior work). Given that this type of proof strategy is well known at this point, it is important to highlight what makes the construction of the algorithm and its analysis difficult. \n\nThese two issues make one believe that the contributions are incremental and the authors should make an effort to highlight differences. See above. Yes." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 6, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 3, 4 ]

[ "8Ddh0yuNPjS", "vwuZdGYVPiz", "nips_2022_wxWTyJtiJZ", "RIv0Mjxajvf", "cg4Lv7tHP1A", "ESSOJNSMvR", "mLoJGE0-4mY", "mLoJGE0-4mY", "nips_2022_wxWTyJtiJZ", "nips_2022_wxWTyJtiJZ", "nips_2022_wxWTyJtiJZ", "nips_2022_wxWTyJtiJZ" ]

[ "G6xJ2DOQ9rC", "Q2qcbRjYATG", "8lThaZGio7yq", "gS6Dbflv5L1", "zDEuVbqM3ct6", "_e6ZNtmnw6t", "vLB3JKPdY9V", "Pnoq1lHGuRa", "6PL5Vr0O2jV", "_AND-rsgIXY", "dmh00jZ2h44", "2CMsU7lGiE", "Tn-xc9G_gf", "mieK-h3iejF", "QqDPLcGSztY", "7I_uvQGeKJu" ]

[ "author", "official_reviewer", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear reviewers, \nAs the author-reviewer discussion period is about to end, we would like to know if you have any additional concerns or questions in light of our responses? If so, we will be happy to address them.", " The reviewer made a valid point in this statement \"Conversely, if the actor's policy is already aligned with the observer's policy, the minimum set of transforms is the Identity transform, and as such doesn't provide any explanation for the agent's behavior.\", but this seems to be the topic for another paper. The point of this paper is to provide explanations when the policy is not coherent with observer's expectations. I am not entirely sure if we should expect the authors to address this point in this paper.\n\nRe: the suboptimal policy. I think that there is nothing incorrect with this method with respect to the suboptimal policies. If the policy is suboptimal, the methods proposed in this paper will thus explain why the policy was suboptimal. This is perhaps another use case for this method, and I would see it a strength of the paper. Don't you think so?", " - Per the reviewer's suggestion, additional clarifications were added to the paper regarding the reliance on meaningful transforms to produce meaningful explanations (85-86 in the recently uploaded version). That being said, the authors wish to highlight the rich and ever-evolving literature on transforms and abstractions that can be used within the framework we offer (e.g. Abel et a. ICML 2018)\n\n- A group of meaningful transforms may yield meaningless explanations - which is why we suggest to bound the search and explore explanations of increasing size. \n\n- Scale was achieved using our suggested extensions to BFS and our suggested heuristics. This compromised completeness, but substantially improved performance (see Figure 4).", " Thank you for addressing the questions. While I am satisfied with most of them, I still have some further questions pertaining to major issues raised in my earlier comments:\n\nRegarding the anticipation gap: In a nutshell, I am still not convinced with the idea of having a set of (minimum) transforms to align a learned policy (here actor's) with a general anticipated policy through the setup highlighted in the paper. While the intuition sounds superficially correct, there is no way to determine if a minimum set of transforms can actually provide the correct explanation for the agent's behavior. From an optimization perspective, if the actor's policy is trapped in a local optimum, introducing/removing something in/from the state-space (like an object that provides a sub-reward) could lead to drastic changes and align it with the observer's policy. However, that tweak (or transform) may not necessarily be a reasonable (or perhaps even a correct) explanation for the initial actor's policy. Conversely, if the actor's policy is already aligned with the observer's policy, the minimum set of transforms is the Identity transform, and as such doesn't provide any explanation for the agent's behavior. ", " I thank the authors for their responses. \n\nQ1 and Q3: With regards to the point about the quality of transforms and explanations, I think this point should be mentioned upfront, and not later in the paper. I think it a major limitation of the paper. Having said that, it facilitates your novel approach. So it may be justified as long as it is declared upfront, while clearly stating the scope of the problem you are dealing with.\nOn a related note, even if a set of intuitively meaningful transforms were selected, would it be possible to end up with less meaningful/meaningless explanations? For example, I imagine it might be possible to end up with a sequence of individually meaningful transforms, which correspond to a not-so-meaningful explanation.\n\nQ2: Regarding minimal length explanations: Thanks for clarifying this point, I may have missed it in the submitted version. Now it makes more sense to me. \n\nMinor comment 4: The nature of environments (long term reasoning + delayed rewards) chosen is fine. The reason I raised the issue of small environments was to clarify whether the authors have been able to scale these approaches. For instance, I imagine the space of possible transforms may become impractically large when dealing with large state/state-action spaces.", " You wrote expert reviews and you asked excellent questions. The authors tried to answer your questions. The reviewers' discussions with the authors will end in a few days. If you'd have further questions to the authors, it would be good to do that asap. This message is written by another reviewer. I am sorry for chasing up, but it would be a shame if this paper was rejected without a thoughtful consideration.", " Thank you for addressing reviewers' comments and questions. I don't have any further questions to you at this stage.", " We thank the reviewer for highlighting elements of the paper that merit further clarification. Questions raised by the reviewer are addressed below.\n\n- Proposed Framework: In our experiments, we used 5 parameterized transforms. The all-outcome deterministation is only highlighted in Appendix 4 as the leading approach. The run-time computations (including those in section 4) include all 5 transforms. Indeed, as stated by the reviewer, and is now emphasized, not all transforms are applicable in all domains. Nevertheless, we show how action effects can be learned in settings in which they are not given as input.\n \n- Comparisons with prior work: In Sreedhanan et al, the only transform that is used is the one that identifies missing preconditions (e.g., the missing fuel constraint in our example). Since such transforms are included in our evaluation, there is a comparison between the approaches in deterministic domains that are included in the paper. We highlight this important point in the current version (lines 125-128).\n\n- Q1 anticipation gap: Our framework can support gaps in both directions. We thank the reviewer for highlighting that this important point is not sufficiently clarified, and is now highlighted in the current version (lines 53-56, 177-180, 226-227) \n\n- Q2 The intention of the statement in lines 106-108 is to highlight that the observer can use off-the-shelf transforms among the rich variety suggested in the literature. This is not to say that the explainer need not use domain knowledge to distinguish between applicable and non-applicable transforms. We have clarified this in the current version (e.g., 275-277) \n\n- Q3 According to the definition by Li, Walsh and Littman, the mapping functions can modify multiple variables. However, to maintain value in terms of explainability, it may be better to modify each variable separately, which is the approach we highlight and use in the paper. \n\n- Q4 Line 327-8: We are assuming the reviewer is referring to our heuristic estimation of grouping transforms to examine their effect. Since this is a heuristic approach, we compromise optimality but improve performance. This is shown in Figure 4 and explained in lines 378-386 , but is now further clarified in the text (line 325).\n\n- Q5 Search resources: the search is capped at a fixed and pre-chosen depth.\n \n- Per the reviewers advise, extending our framework to continuous domains is now mentioned as an interesting avenue for future research. \n\n- All additional comments will be addressed in the final version.", " \nWe thank the reviewer for the supportive feedback and helpful comments which will be used to improve the paper’s clarity. Specifically, according to the reviewer's very helpful advice we will add to the final version a more in-depth account and examples of the produced explanations per domain. In addition we will highlight that the approach presented for learning action preconditions is heuristic and does not offer theoretical guarantees. Counterexamples include settings with latent variables, compound (multi-variable) preconditions etc. This will be clarified in the final version of the appendix. \n", " We thank the reviewer for the helpful comments that will help clarify the main ideas of the paper. \n\n- Q1 and Q3: As we mention in the paper (and now emphasize in lines 274-7) the quality of the transform will dictate the quality of the produced explanations and our ability to find relevant ones. This means that it is up to the user to choose meaningful transforms. To demonstrate, if the method is given the option to select the trivial transform that would 'force' the agent to behave according to the anticipated policy (by removing all other actions from the set of applicable actions in that state), this will yield a policy that \"satisfies\" the anticipated policy but is meaningless for explainability. That being said, the RL and automated planning literature is rich with transforms that accept as input an MDP and can be used 'off-the-shelf' to produce meaningful explanations.\n\n- Q2: We agree with the reviewer w.r.t. the suggested distance measure, and note that this is the measure we describe in the paper and use in our experiments : i.e., we consider the length of the sequence and select explanations of minimal length. We also note that we define a general distance metric for exactly the reasons mentioned by the reviewer, allowing the user to define the distance measure that is most relevant to the setting at hand. \n\n\n- We chose a symbolic state-space search (A*) because the state space is implicitly given by the set of applicable transforms and a deterministic transition function for which the outcome is known and therefore does not need to be learned. Extending our approach to settings in which these assumptions don't hold, requireling an RL algorithm for the search, is an interesting avenue for future work. \n\n- The domains we chose include long-term reasoning and delayed rewards and were therefore challenging for the standard RL we chose for experimentation. \n\n- The only instances we consider in our evaluations are settings in which there is a difference between the anticipated and actual policy. Therefore examining the satisfaction ratio in the original environment is always 0, making it useless to consider the satisfaction ratio relative to the original environment. We will clarify this point. \n", " We thank the reviewer for the insightful and knowledgeable comments that we used to improve clarity of the paper.\n \n- As mentioned by the reviewer, the key idea of our approach is the ability to support a variety of transforms, including those that simplify *and* those that render a more complex problem (e.g. by adding constraints). We thank the reviewer for pointing out that this important point isn't sufficiently clear, and it is now highlighted in the modified version (lines 53-56, 177-180, 226-227) \n\n- Our approach does not guarantee the behavior of the actor is explainable. As we mention in the paper (and now highlight) the quality of the explanations highly depends on the set of transforms that is provided as input. \n\n- We believe our method is useful for various real world problems. While many approaches aim at making sense of the underlying DRL network, we suggest an automated way to produce potential explanations without relying on an understanding of the internal structure and implementation. In fact, the idea for this work came from discussions we had with practitioners and AI researchers that highlighted the need for such a framework. \n\n- As we state in footnote 2, we do not need an observer. The observer's role is merely to highlight the need for explainability \n\n- The statement \"Clearly, for any two policies there exist state and action mappings that can be applied to cause any policy to satisfy another policy\" in lines 274-5 is aimed to emphasize the importance of providing meaningful transforms as input. The trivial transform would be one that forces the agent to behave according to the anticipated policy by removing all other actions from the set of applicable actions in that state (e.g. by disallowing moving right from the initial state in our example). This will yield a policy that \"satisfies\" the anticipated policy but does not contribute to explainability. \n\n- As we mention on page and highlight in the current version, our approach has two key limitations: 1. explanations are only as good as the transforms that are provided as input. 2. we do not directly deal with the translation of the produced explanations to natural language and assume instead that this is something that is straightforward to accomplish.\n", " We thank all reviewers for their helpful feedback on the paper. All comments were used to improve clarity of the paper.\nWe uploaded a revision of the paper that includes the clarifications requested by the reviewers and which are individually addressed below. \n\n", " This paper presents a new framework and algorithm for explainable RL. Given some limited domain information and observed behavior by an actor, the authors propose to search through a space of possible model transformations in order to find a model and associated policy that matches the observed behavior. The transformations then represent some aspect of deviation, and serve as a partial explanation for observed behavior. The transforms are derived from RL literature on state-space aggregation; the search algorithm involves chaining them together. Each node in the search tree must be evaluated by computing a full policy for the transformed model, which can be computationally expensive, and which the authors discuss. The paper has one set of experimental results illustrating an implementation of the ideas. Strengths:\n\n+ The framework is novel\n+ This is a reasonable problem to be working on\n+ The ideas are straightforward, and the paper is clearly written\n+ The experiment seems clear and helpful\n\nWeaknesses:\n\n- While I generally liked this paper, I consistently found myself wanting more. The paper is very \"chatty\" and does not do a good job of balancing exposition of the ideas (which are straightforward) with some sense of application or empirical evaluation (which is very, very thin).\n\n- I ultimately felt the problem (explainable RL) is important, but that the proposed framework should have been more general. I mean this in two specific ways:\n\n1) A more general characterization of the idea could be \"search for a model and corresponding optimal policy that matches observed behavior\". This subtly includes a host of ideas that involve /complexifying/ policies, instead of just /simplifying/ them. For example, you discuss how removing a constraint from a symbolic planning problem might suggest that the agent was unaware of the constraint, but the opposite is also true - you could /add/ constraints to the problem, to similarly better match behavior, that would suggest the agent is laboring under constraints that it doesn't need to. People do this all the time!\n\n2) I am generally dissatisfied by the approach because I feel that it can only explain the /difference/ between the baseline policy and the transformed policies. Suppose, for example, that the optimal set of transforms is the null set -- in other words, the agent is behaving as expected. This does NOT imply to me that the agent's behavior is explainable! In other words, this framework does not contribute any explainability of the base policy. In my mind, this also motivates the more general approach of searching for matching models. \n\n- The framework seems a bit limited to what feels like counterfactual reasoning \n\n- The computational cost is real. As the space of transforms grows, the importance of searching that space effectively becomes increasingly important. You discuss how important a distance metric is, but it's unclear to me how often such a thing exists or is practical to compute. I like the idea of somehow transferring partial solutions or bootstrapping solvers, but these seem to dance around the issue. Ultimately, I'm lead to wonder: will this method ever be useful for real problems?\n\n- The experiments in the paper are underhwhelming. While the single provided experiment is clear and helpful, I feel like a much stronger empirical evaluation is necessary. I would recommend trimming the writing to make room for experiments.\n \n- Why do we need an observer? Why not eliminate that idea and simply state that there is an anticipated policy?\n\n- The claim on lines 274-275 isn't obviously true to me. Can you please explain this further? (I think I understand why you might think it's \"clear\", and I think you might be wrong, so it would be helpful to have it fleshed out) I think the authors could have done a better job of explaining the limitations of their method (although I don't think they tried to hide anything).", " The paper proposes the use of MDP transforms for autonomously producing explanations. The work also introduces and formally defines the RLPE problem and empirically demonstrates the performance of their proposed approach in single and multiagent environments. The article is clear and fairly well written, and the proposed approach seems novel and original. I believe the paper tries to tackle a very relevant and important problem. My main concerns with the work (as listed later) are related to the validity of the assumptions made with respect to the quality of explanations produced by the proposed approach. \n Major comments:\n\n1. The key idea is that an observer has an anticipated policy in mind which is assumed to arise from partial knowledge of the MDP. The explanation then corresponds to an MDP transformation/sequence of MDP transformations whose solution closely matches (satisfies) the anticipated policy. Although this approach might be reasonable in some cases, it is possible that the transformation sequence found to satisfy the anticipated policy may not actually constitute a good explanation. Since there may be multiple transformation sequences whose solution would satisfy the anticipated policy, only some of these may correspond to a meaningful explanation. \n\n2. Regarding the distance metric criterion used: - if the anticipated policy was indeed derived from a transformed MDP whose distance to the original MDP is large, then choosing a transformation sequence with a low distance measure may not be ideal (because the anticipated policy actually corresponds to a transformed MDP with a large distance to the original). It would help to include some lines discussing what motivates the inclusion of the distance metric. Wouldn’t it be better to instead consider for example the length of the transformation sequence and select ones with lower sequence lengths (as smaller lengths might mean simpler explanations)\n\n3. How does one choose a suitable set of transformation functions? This is probably a critical choice because a poor set of transformations may still be able to match the anticipated policy, but may not lead to meaningful explanations.\n\nMinor comments:\n\n1. The figure captions need to be more detailed. Eg: It is not clear what the yellow rectangle/purple ‘x’ in fig 1 mean.\n2. The phrasing of lines 164-165 is confusing\n3. In lines 351-355, I am curious as to why A* was used – was it because it assumes the existence of some heuristic signal which might simulate an observer’s assumptions? Why not use say standard Q learning for example?\n4. It would be good to see results in more complex/high dimensional environments. The chosen environments all seem relatively simple.\n5. The results only report the satisfaction ratio with the transformed MDPs. Reporting the satisfaction ratios on the original environments might better indicate how much the transformation sequence improves the satisfaction ratio relative to the original environment. N/A", " This paper studies explanations of RL policies. The idea is quite slick. An agent executes a policy learned using RL. An observer has some expectations with respect to the behaviour of the agent (e.g. it may expect certain actions to be taken in certain states). The goal of explanations is to explain to the observer why the agent's policy does not match observer's expectations. This may explain to the observer that their expectations are incorrect since they are not compatible with the MDP. The expected behaviour may simply be unfeasible given the MDP, and the goal is to find those infeasible situations and offer them as explanations to the observer. The problem is well formulated, and the results on 12 domains show that the new method is feasible, and it can be implemented even in tasks that don't have a PDDL representation. The paper is very clear and writing if of high quality. The authors took care to introduce all the necessary concepts, and the key terms have accurate formal definitions (e.g., definition 7 is excellent).\n\nThe main idea is innovative, and it appears original. The relevant literature is presented, and discussed in a way that allows the reader to see where this paper sits in the related work.\n\nExample 1 is very good, and it (along with the paragraph in lines 82-94) clarifies the goals. \n\nThe fact that the method is domain independent is a strength.\n\nThe fact that both an intuitive explanation and formal definitions are provided is a plus.\n\nSection 5 is very competent. The authors explain the challenges and propose a feasible solution.\n\nOne weakness is that it would be good to see what the explanations were found on the 12 domains that were evaluated. The results are excellent, but it would be useful if the appendix, for example, showed a few examples of observer's expectations, and how they were addressed by the algorithm. I can imagine that the method works, but a few examples, perhaps one example per domain, would be very useful.\n\nLines 18-24 in the appendix explain how to deal with non-symbolic domains? Will the derivative vector always work? I am asking because perhaps there is a counterexample that could be mentioned or a theorem that could be cited that shows that there is no counterexample.\n\nThis is a strong piece of research and I don't have other questions. The paper is well written, and it was a pleasure to read it. There is no negative societal impact in this work.", " This work proposes an explainable Reinforcement Learning framework, which seeks to explain the discrepancies between the learned \"actor\" policy and an anticipated \"observer\" policy of a partially informed observer. This is done automatically by (an \"explainer\") searching \n over an available set of (state and action) transforms and selecting (a composition) of transforms that tweak elements in the state of the policy (producing counterfactual states), such that the (re-learned) policy in the transformed MDP aligns with the expected policy. Since the authors work on a symbolic (relational) environments, the transforms can given an indication of the key elements that had previously been overlooked by the partially informed observer (which also explains the agent's behavior, hence explainable RL). The authors do an excellent job in formalizing the definitions and explaining the intuitions. Several heuristics are proposed to perform quicker searches over the set of transforms to reach perfect alignment while making minimal changes to the states/actions. The proposed framework is shown to be applicable to a variety of domains including that of single and multi-agent RL environments, and in stochastic settings. Strengths:\n1. This work raises valid questions on explainability in (Deep) RL, which is of great significance, given the black-box nature of the policies and their usage especially in safety critical domains like autonomous driving and treatment recommendation.\n2. The authors have done an excellent job in writing the paper. I thoroughly enjoyed going through the content. The explanations and intuitions are very clear.\n3. The proposed framework seems to be novel and is also generally applicable (agnostic of the RL framework). Empirical evaluations are performed on both single-agent and multi-agent environments with added stochasticity.\n4. The authors have submitted code for reproducibility (although I did not run the code).\n\nWeaknesses:\n1. Results: It is rather unfortunate that the authors chose to devote just half a page to the Results sections (with just one figure) and pushed the rest of the (significant and interesting) results to the appendix. The authors have devoted a lot of space to explain things that might not be required. For instance, Figure 2 is unnecessary and can be substituted with results from the Appendix. Also I would prefer detailed explanations like those in Appendix 4 in the main paper.\n2. Proposed Framework: Although the authors state that they use a RL-setting where the transition function is unknown, some action transforms that they propose work on precondition or postcondition (action effect) relaxation which is readily available in planning domains but NOT in RL domains and must be learned by the policy. Moreover, the experiments only demonstrate explainability on a limited set of transforms like all-outcome determinization (see Appendix 4) and ignore the rest.\n3. Comparisons with prior work: The authors state in lines 126-130 that the work by Sreedharan et. al., 2020 is similar to theirs in deterministic environments. However, there are not comparisons presented for the deterministic experiments. I wonder why.\n4. The first and the second contribution seem to go hand-in-hand: To use model transforms in the explainable RL setup, one needs to define it formally. \n5. Details from the experimental section (like comparisons with previous work, model details, algorithm details) are either vaguely mentioned or are pushed to the Appendix: See Questions 3,4,5\n\nOverall, the paper would benefit a lot from a rewrite, especially the Experiments and the Results sections. 1. lines 82:94 - In both examples, the reason behind the anticipation gap is due to the crucial information missing in the the observer's anticipated policy. How about the other way round: the actor's policy overlooking some crucial information. In other words, is the actor's policy always optimal? If not, the authors should clarify this just to avoid confusion.\n\n2. line 106-108: I am not fully convinced with this statement. Anticipated behavior needs some domain knowledge, no matter how general it is. Moreover, I believe that the more general an anticipated behavior is, the more number of transforms would be required to align both the policies (hence, more retraining in the transformed environments), which in some complex environments might be infeasible. \n\n3. line 185: Do these mapping functions modify multiple random variables X_i of the state or just one?\n\n4. Line 327-328: I failed to understand how the authors can tell this without training the policy in the transformed environment?\n\n5. Is exhaustive search used for all methods: Base, pre-train, pre-cluster? Or do you prune the transforms after a certain distance is reached?\n\nMinor Comments: \n1. To my understanding, there can be different definitions of explainability: for instance, an observer might not have any anticipations, however he/she might be interested in understanding \"how\" (or even \"why\") [1] a particular decision was arrived at. In this work, the authors focus on setups where an observer already has some expected behavior in mind. It would be good if the authors contrast this definition with those of others, or explicitly state that this is just one form of explainability they are dealing with. \n\n2. lines 252-254: Might be good to mention this upfront to avoid confusion. As a reader, I would definitely be in suspense otherwise.\n\n3. Scatter plots: The points should be made bigger and more distinct. Also please make the captions more detailed (like define what X-axis and Y-axis units are). As a reader, it is inconvenient to search for such details in the text.\n\n4. Line 374: We also measured the length of the explanation (i.e. the number of atomic ... ): I couldn't find this result in the main paper. It possible I may have missed it.\n\nline 61: \"is comprised of\" -> comprises\nline 147-148: \"where the set of states\" -> where each state\nline 198: s \\in \\phi_{-1}(\\bar{s})\nline 237: \"as comprised of\" -> as composed of\n\n[1] Neural Logic Reinforcement Learning, Zhengyao Jiang, Shan Luo Proceedings of the 36th International Conference on Machine The authors do propose some limitations and future work to extend their framework in the Conclusion Section. However, to my understanding, there is a key limitation that may have been overlooked: The authors consider a Relational (symbolic) domain, hence a discretized state with limited values. In continuous domains, with the introduction of feature extraction networks, the number of elements in a state (random variables) and its corresponding values would increase, thus increasing the set of transforms required to align the two policies. Will this render the search for transforms infeasible? I understand that this might not be withing the scope of this work (since it is in the preliminary stages), however it might be good to just comment on this for future developments in this direction." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 4, 8, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 4, 5, 4 ]

[ "_e6ZNtmnw6t", "gS6Dbflv5L1", "zDEuVbqM3ct6", "Pnoq1lHGuRa", "_AND-rsgIXY", "2CMsU7lGiE", "6PL5Vr0O2jV", "7I_uvQGeKJu", "QqDPLcGSztY", "mieK-h3iejF", "Tn-xc9G_gf", "nips_2022_32Ryt4pAHeD", "nips_2022_32Ryt4pAHeD", "nips_2022_32Ryt4pAHeD", "nips_2022_32Ryt4pAHeD", "nips_2022_32Ryt4pAHeD" ]

[ "vbUueMh0Ls", "a5v5NABH_xu", "-g1SVc-gZ0A", "sS1f2l02Af2", "6ELRvhhRSyJ3", "mvgmYkVP7p5", "6CQuvsYM5Zu", "qgFh9_8g7q", "kCUXVDmIC-M", "mJXpXEXAqCp", "SGdwMUrtKu", "v-iE6rhvS-v", "_lJ6QFQ-x0J", "mnfNif6bRBL", "u8F0fL41qvF" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I have read over the author rebuttal and the paper changes. These adequately address my main concerns, and so I am happy to raise my score accordingly.\n\nI believe clarity could still be improved, but the issue is not so severe that it should block possible publication. ", " The authors have addressed many of my concerns, including adding more visual evaluations. I am increasing review score to 5.", " I think the author has solved all my doubts, and I think this paper deserves to be accepted by Nips, I am willing to accept this paper strongly.", " Dear Reviewer TtwX:\n\nThanks again for all of your constructive comments and suggestions, which have helped us improve the quality and clarity of this paper!\n\nWe sincerely hope that our added experiments and analyses could address your concerns.\n\nSince the deadline for discussion is approaching, please feel free to let us know if there are any additional clarifications or experiments that we can offer, as we would love to convince you of the merits of our work. We appreciate your suggestions.\n\nBest wishes,\n\nAuthors", " The solution presented leverages text embedding technology which is known to encode human biases. The authors had not fully acknowledged the risks of propagating those risks and negatively impacting historically marginalized groups. This risk was highlighted by 2 technical reviewers.\n\nHowever, another issue not raised by the technical reviewers is that there was no attempt to adversarially test and evaluate the bias propagation properties of the solution. The issues in this space are very well known and acknowledging them is not enough. It should be regular practice and mandatory to actually test and evaluate (there are a plethora of test sets and benchmarks that can be applied) solutions such as these for bias harms against historically marginalized groups and reporting them via something akin to a model card [Model Cards for Model Reporting, Mitchell M, et al 2019). Authors acknowledged that they did not properly document the social impact implications of the bias propagation risk inherent in the text embedding component of the solution and updated the conclusion text of the paper accordingly.\n\nThe issue of not evaluating FFCLIP to measure its propensity to propagate harmful biases cannot be addressed without performing the necessary evaluation work. The issue of not evaluating FFCLIP to measure its propensity to propagate harmful biases cannot be addressed in the existing paper. \nIt would require additional testing which would require substantial lead time and effort. A new version of the paper that included the test methods and results would be needed to address the issue.", " Thank you for your appreciation. I hope our work can help people better understand the semantic space of text and the latent space of GAN. Exploring the relationship between the two spaces can better promote the development of cross-modal generation.", " I appreciate that the authors took the time to carry out the analysis I suggested. As I already indicated in my initial review, I still believe this is a very strong paper with many valuable contributions and insights.", " We sincerely appreciate all reviewers' efforts in reviewing our paper and giving insightful comments and valuable suggestions. We are glad to find that the reviewers generally acknowledge the following novelty and contributions of our work.\n\n- Semantic Alignment: In contrast to the empirical text-visual semantic alignment, our semantic alignment module builds the relationship between text embedding in CLIP space and latent code in the latent space of StyleGAN, so that we can align the text space and latent space adaptively. This automatic alignment helps us to train one model to tackle different text prompts [TtwX, rJnY, 7Kr6]. \n- Experiments: We evaluate our method in multiple datasets, including human portrait, car, and church images. The qualitative and quantitative analysis validated the effectiveness of our method [rJnY, 7Kr6].\n\nAs suggested by the reviewers, we have included the following contents in our revised manuscript to improve our paper. Our modification on the paper has been marked in blue. We summarize the major revision as follows. Our detailed responses can be found in the following response sections to the reviewers.\n\n- More comparison results: We add more visual comparison results between FFCLIP and existing methods. Meanwhile, we add a new human subjective evaluation covering more text prompts to show the effectiveness of our method.[TtwX]\n- Discussions on related works: We add the analysis of the difference between StyleCLIP, HairCLIP, TediGAN, and our method carefully. Meanwhile, we make the discussion for the diffusion model. [TtwX,rJnY]\n- Unseen texts: To show the robustness of FFCLIP, we add visual results for the unseen texts. [7Kr6]\n- Claim support: We adjusted our paper's structure, making the content better understood. [7Kr6]", " ***1. Related works.***\n\nThanks for pointing this out. We have cited the mentioned two papers as related works. For the comparison to FEAT [15], we did not find available implementation. We will definitely compare FFCLIP to FEAT [15] when their implementation is accessible. On the other hand, we note that FEAT introduces an attention mask to edit the region of interests and follows the mapper of StyleCLIP. So FEAT still needs to train one model for one text prompt.\n\n\n\n***2. Clarity.***\n\nWe apologize for the confusion brought by our presentation. We have made significant changes in our abstract and introduction to present our observations and motivations, which give a clear picture of our objectives and intuitions. Meanwhile, we have thoroughly proofread our manuscript and fixed other unclear presentations and grammatical errors. Our modifications are marked in blue.\n\n\n\n***3. Claim support.***\n\nWe thank for your guidance on our paper organization, which makes our core text more supportive for our claims. We have revised accordingly and summarized our revision in the following:\n\n- In Sec. 4.2, we have shown the interpolation analysis in Ln 224-229 and Fig. 5. More results are provided in Fig. 14 and Fig. 15. To further support our latent mapping, we show our results produced by unseen text inputs in Fig. 19 and Fig. 20 in the appendix due to page limit. The results on unseen text inputs support our claim that our latent mapping is effective to align text embedding and latent visual space.\n\n- We have moved the ablation studies on semantic alignment module and number of semantic modulation block to the main text in Sec. 4.4. Moreover, we have tried training the original latent mapper from StyleCLIP by using multiple text prompts. We set k=0 in our experiment to present that we use the original latent mapper (see Ln. 270-273). The results are shown in Fig. 7 where the manipulated results do not faithfully present the semantic guidance from text prompts. The numerical analysis results are shown in Table. 2.\n\n\n\n\n***4. Inaccurate claims.***\n\n- We agree that our illustration that inversion on W+ space benefits editing is not correct. We have replaced this claim by saying `W+ is more effective for identity preserving when we manipulate the image.`\n\n- We agree that StyleCLIP is a one for one scheme for their latent mapper approach while global directions do not suffer from this limit. We have added the illustration in Ln. 35-37 that the global direction method does not employ one for one training while its parameter adjustment and editing direction are manually predefined. \n\n\n\n***5. Unseen texts.***\n\nOur FFCLIP is able to generalize to unseen text when the text prompts describe similar image attributes that have been utilized during training. If we use `blond hair` during training, we are able to produce manipulation results with `red hair` as input text prompt as shown in Fig. 20. On the other hand, we are able to produce results with `blond hair and red beard` as shown in Fig. 20. However, if FFCLIP is not trained on any hair-related prompts, it cannot change the hair color. More visual results with unseen text prompts are shown in Fig. 19 and Fig. 20 where FFCLIP is capable of generalizing if test text prompts and training text prompts describe similar image attributes (e.g., `blond hair` for training and `ginger hair` for test, `happy` for training and `rage` for test).\n\n\n\n***6. StyleCLIP fails on hair color changes.***\n\nWe follow the official setting of StyleCLIP and use the fine parts of latent code to train the mapper. We find that the StyleCLIP performs inferior under `Red hair`, while performing fine for other hair colors. As shown in Figure 25, we compare with StyleCLIP under `white hair` and `blond hair`. FFCLIP performs better than StyleCLIP in preserving unchanged facial attributes (e.g., for `white hair` on the first row, the facial skin color is changed in StyleCLIP. In the second row, the human mouth is closed in StyleCLIP. In the last row, the shape of eyeglass is changed in StyleCLIP). In contrast, our FFCLIP maintains such attributes while only changing the hair color. Also, under the `blond hair`, StyleCLIP produces hair color that resembles yellow rather than blond.\n\n\n\n***7. Limitation discussions.***\n\nWe thank you for the kind suggestions. Our FFCLIP generalizes when the training and test text prompts share similar image attribute descriptions. For different encoders, we have tried our model, which is learned with an e4e encoder to edit latent codes from High-fidelity [43] and Restyle [5] encoders, respectively, as shown in Fig. 21. Our FFCLIP performs well by using different inversion encoders. These results demonstrate that our FFCLIP can be potentially applied to different encoders.\n\n\n***8. Social impact***\n\nWe thank you for pointing out the minority representation concern and have added this aspect in Ln. 287-288.", " ***1. Discussions for StyleCLIP, HairCLIP, and TediGAN.***\n\n- The discussion between FFCLIP and StyleCLIP/HairCLIP has been presented in the first section of our response to `reviewer TtwX`. We suggest `rJnY` to check this section for reference. \n\n- In TediGAN, it makes the text feature close to the latent code and uses the style-mixing operation in StyleGAN to manipulate the image content. The style-mixing operation empirically replaces the specific layer in the latent code with text attribute embeddings. As these embeddings are not aligned well in the visual latent space, TediGAN is not effective to produce semantic abstraction results (e.g., see `Taylor Swift` of TediGAN in Fig. 4). \n\n- Moreover, TediGAN only manipulates the human portrait. This is because the empirical mapping between specific text attribute embeddings and specific layers in latent code is hard to reproduce in other datasets. The corresponding discussions have been added in Section A.5.\n\n\n***2. Discussions with diffusion models.***\n\nDiffusion models have shown great potential in multimodal generation [29][30]. And the most relevant work to our FFCLIP is DiffusionCLIP [21]. DiffusionCLIP fine-tunes the reverse path with the CLIP loss and produces the noises to hijack the sampling process. In contrast to GAN, diffusion models have no semantic latent space (e.g., $W$, $W+$, or $S$ spaces), so it is not straightforward to generate the interpolation results. Meanwhile, the sampling process is time-consuming. Overall, diffusion models are a research direction, and we will take more investigations into them in the future.\n", " \n***1. FFCLIP is similar to CLIP-based image modification systems.***\n\nWhile we agree that both CLIP-based methods (i.e., StyleCLIP and HairCLIP) and our FFCLIP aim to solve the same task (i.e., text-driven image manipulation), we would like to show that the techniques between these methods are very different, which indicates the superiority of our FFCLIP.\n\nStyleCLIP performs an empirical mapping between each text prompt embedding and visual latent space of StyleGAN, so each StyleCLIP model is specifically trained to tackle one text prompt. As a result, the images produced in StyleCLIP based on different text prompt inputs are from different models. In contrast, our FFCLIP establishes an automatic latent mapping (i.e., semantic alignment module) which enables the latent code modulation in visual latent space based on different text prompts. Thus, the results of our FFCLIP are from one single model for each type of image. The HairCLIP also performs an empirical mapping and only focuses on human hair regions, which is limited compared to our FFCLIP which generalizes well in multiple datasets, including human portraits, churches, and cars.\n\nWe have emphasized these differences in Ln. 31-37, Section A.5, and Fig. 18 in the revised manuscript where existing CLIP-based systems are limited to establishing an automatic latent mapping between text embedding space and visual latent space. This limitation is addressed in our FFLIP model, tackling different text prompts for image manipulation.\n\n\n \n***2. Visual difference between StyleCLIP and FFCLIP.***\n\nThe accurate latent mapping of FFCLIP produces visual results highly related to text prompts while the empirical mapping of StyleCLIP does not. As shown in Fig. 4, given the `bald` input, the hair is completely removed in FFCLIP while it still exists in StyleCLIP. Given the `Red hair` input, the color of the hair in FFCLIP is obviously red while it is not the case for StyleCLIP. More visual comparisons in Section A.8 show that FFCLIP produces images more related to the text prompt descriptions than StyleCLIP (e.g., given the `aged 10` as input, the result of FFCLIP is more like a child than that of StyleCLIP in Fig. 23).\n\n\n\n***3. Six image modifications***\n\nAs mentioned in Ln. 231-236, it is hardly to evaluate the performance of image manipulation with a straight quantitative measurement. We choose these six manipulation semantics in Table 1, since the text-relevance of these results can be measured by the classification model as mentioned in [36]. Meanwhile, we have provided thorough human subjective evaluations covering results produced based on four new text prompts('Blue eyes', 'Disgust', 'Dreadlocks hairstyle' and 'Jewfro hairstyle') in Table 4. \n\nAdditionally, we have added more visual comparisons to HairCLIP in Fig. 16 and Fig. 17, as well as visual comparisons to StyleCLIP in Fig. 23, Fig. 24 and Fig. 25. These comparisons indicate FFCLIP is more effective to manipulate images given a wide range of text prompts.\n\n\n\n***4. Writing***\n\nWe apologize for the confusion brought by our presentation. We have thoroughly proofread our manuscript and fixed the unclear presentations and grammatical errors. Our modifications are marked in blue.\n\n\n***5. Significance***\n\nAs illustrated above, our automatic latent mapping between text prompt embedding and visual latent subspace empowers FFCLIP to tackle different text prompts while producing more semantically related results. Both visual and numerical comparisons shown above have indicated the effectiveness of FFCLIP.\n\n\n\n***6. Model size of CLIP***\n\nIn FFCLIP, we follow StyleCLIP to use the ViT-B/32 model to extract text prompt embeddings. We also try to use a larger model (ViT-L/14) and show the results in Fig. 22, which achieves similar performance. We attribute this to the reason that using a base model is sufficient to capture the text representations while using a model does not bring further advantages.\n\n\n\n***7. Humanlike biases of CLIP.***\n\nWe thank for this insightful suggestion and have added this analysis during in limitation discussion in Ln 285-288. As we use the text encoder from CLIP, the humanlike bias may appear in our visual results since our latent mapping connects text embeddings to visual latent space.", " Image manipulation as a task has very foreseeable misuses in enabling fraud, surreptitious behavior, and other similar things. Moreover, the approach seems to be sometimes changing the ethnicity of the person in the input image, e.g. in Figure 1, Stephen Curry's ethnicity seems to have changed in the beard blond mohawk and aged 10 outputs. These sorts of effects are usually biased against minority groups. Remember the hoopla about the depixelator: https://www.businessinsider.com/depixelator-turned-obama-white-illustrates-racial-bias-in-ai-2020-6\n\n As one of the technical reviewers points out, there is essentially nil discussion of potential ethical issues. The application area, although also applied to cars, buildings, etc., is primarily focused on face images and will be difficult to think about if divorced from that application. The authors should most certainly, in detail, expound upon the ethical concerns in the document, but that is only a first step. Stronger guardrails should be considered, including bias mitigation as well as greater transparent documentation (cf. AI factsheets, datasheets, etc.). ", " This paper proposes a new architecture for using CLIP to modify images in coordination with StyleGAN. The system is known as FF-CLIP (Freeform CLIP) and incorporates semantic alignment and injection blocks to identify a semantic subspace in the GAN embedding space. Cross-attention is employed to achieve semantic alignment, while an injection technique previously used in HairCLIP is employed to inject the text embedding semantics into GAN space. The authors provide visual examples of image transformations and provide quantitative evaluations by human subjects indicating that humans prefer FF-CLIP modified images. Originality\nStrengths: The authors choose a relatively novel area of inquiry, that of providing text based guidance to a synthetic image generator, in this case a GAN. This is an area of much innovation at the moment.\nWeaknesses: This seems very similar to other recent CLIP-based image modification systems, especially StyleCLIP. While the authors report outperformance of StyleCLIP in terms of human evaluation, it is difficult for this reader to tell that much of a difference between the StyleCLIP generated images and the FF-CLIP generated images based on the examples provided. The semantic injection technique has itself been used previously in HairCLIP.\n\nQuality\nStrengths: It is an interesting paper and to my knowledge the alignment/injection architecture is novel and might be useful.\nWeaknesses: Evaluations are not robust enough to be convincing to this reader: the authors evaluate only six image modifications based on human preferences. It’s hard to know whether the results are significantly better than those achieved by, e.g., StyleCLIP when the evaluation is narrow.\n\nClarity\nStrengths: Good visualizations, and the math is presented in a straightforward and comprehensible manner.\nWeaknesses: The writing can be hard to follow, with grammatical issues throughout. \n\nSignificance\nStrengths: Synthetic image generation is gaining ground rapidly and this system may help to advance the state of the art.\nWeaknesses: The proposed system mainly consists of components previously used in very similar systems such as StyleCLIP and HairCLIP. If the evaluation of the system were more robust, this might not be an issue, but it is also hard to gauge how much of an advance this model is. Does model size of the CLIP used make any difference? The larger CLIPs do much better on evaluations like ImageNet, so maybe there would be some benefit to using them here? CLIP is known to encode humanlike biases (see Wolfe et al. 2022, ACM FAccT; Birhane et al. 2021, arXiv). It would be good to mention these in a limitations section. How might they affect the system being developed?", " In this paper, an image manipulation method FFCLIP is proposed to edit image semantics based on the text prompt guidance. Following the StyleGAN latent space W for image generation, the alignment between semantics in the latent space W and text encoder is crucial for text-driven image editing. A semantic modulation method is developed to align the visual representations and text semantic embeddings via linear transformation where the parameters are computed based on cross attention computations. This effective alignment improves the previous empirical alignment design so that text prompts with different semantics can be taken for image editing via one model, while the empirical alignment confines each text prompt corresponds to one model. Experiments show that for each dataset (portraits, cars, or churches images), using one model is able to free-formly edit images based on different text prompts. The supplementary videos have also shown the effectiveness. + The alignment is effective to automatically correspond text prompt embeddings to StyleGAN latent Space. This enables different semantical embeddings to be reflected in the visual image representations for manipulations. \n+ The semantic modulation first aligns text-image semantics via semantic alignment and then injects text prompts semantic. This design is reasonable to modify StyleGAN latent space since this space is not disentangled completely at present. Without latent space disentanglement, using the alignment via cross attention computation matches the text-image semantics. \n+ Experiments on three benchmark datasets show that under each dataset, using one model is able to edit image semantics free-form based on different text prompts with single or multiple semantics. The visual results are impressive on both paper and the supplementary video. The numerical results also show the effectiveness of FFCLIP.\n\n- The existing methods TediGAN, StyleCLIP, HairCLIP also edit images based on the text information. A more in-depth analysis shall be taken to enhance the proposed contributions. For instance, TediGAN seems to tackle image editing with different text attributes. StyleCLIP uses one model for a specific text-image editing. HairCLIP focus on hair and can handle different text semantics. These would strengthen why the proposed FFCLIP makes senses and contribute to the cross-modal image manipulation area.\n- A discussion with diffusion models would be helpful to emphasize the importance of editing StyleGAN latent space to benefit future research.\n See weakness. A clear discussion upon previous text-driven methods and more recent diffusion models would strengthen the proposed method. As illustrated in Ln 271, the disentanglement of styleGAN latent space is an open problem. The negative society impact is for face malicious, which can be mitigated via deepfake detection methods.", " The paper proposes an attention-based mechanism for improving CLIP- based StyleGAN editing models. \n\nSpecifically, the paper takes the ‘latent mapper’ approach, where a neural network is trained to predict a latent-code change that would modify specific image attributes described through text. It argues that existing methods are trained to tackle specific texts, and therefore do not need to be aligned with CLIP’s space, limiting their ability to tackle novel texts.\n\nThe authors propose to better align the spaces through an attention mechanism, where the CLIP-text embedding is used to predict both layer and channel importance for latent code changes. This approach allows the authors to train their mapper on a larger collection of texts, creating better alignment between the CLIP and StyleGAN spaces, and enabling more disentangled modifications, with some generalization to unseen texts (e.g. combinations of texts seen during training). Strengths:\n1) The paper introduces a conceptually simple yet well motivated approach for identifying the StyleGAN layers and channels most relevant to the change of specific attributes described through text – specifically, attention. \n2) While there are prior works which deal with attention mechanisms in the context of StyleGAN inversion and editing [1, 2], they are, so far as I am aware, unpublished. However, I would urge the authors to cite these as related work (and consider comparisons to [2], which tackles the same task).\n3) The results are generally of superior quality when compared to existing approaches. In particular, they are more disentangled, and allow for more complex manipulations than the baselines.\n\nWeaknesses:\n\n1) Clarity: The paper itself is very difficult to follow. I had a very hard time understanding the abstract and the introduction, and had to delve into the method and the experiments themselves to get any idea of what the authors are trying to do. The paper is not so complex that this should be required. I urge the authors to, at the very least, run their paper through Grammarly or similar tools.\n\n2) Justification or experimental verification of claims: The core paper contains many claims which are unsubstantiated. In many cases, the supplementary **does** contain experiments which, at least in part, provide backings for these claims. However, they are never referenced from the core text, and if I did not read the appendix I would not be aware of them. These should absolutely be included in the main paper. A few examples:\n\n * The authors claim time and again that their model aligns the CLIP and StyleGAN spaces. The only experiment which possibly hints at this is the interpolation experiment in the appendix. Other than that, it appears that all experiments use the same, or compositions of the texts used during training. \n\n * It is unclear from the paper itself whether the benefit of their approach is a result of the attention mechanism (i.e. improved latent mapper architecture), or the fact that they train for multiple prompts. There is one experiment in the appendix that gives this some backing (Figure 7, the w/o S&T experiment). However, it would also be interesting to see that the original latent mapper can’t be trained conditionally on multiple prompts.\n\n\n3) Some (minor) wrong claims:\n * In the paragraph of L107, the authors suggest that inversion is done into W+ because it is better for editing. This is not the case. Inversion is done into W+ because it allows for better identity preservation. W+ inversions typically behave worse under editing than their W counterparts. See for example e4e [3].\n * The authors claim that StyleCLIP needs to train a different model for each textual prompt. This is only true for their latent mapper approach, but is not actually specified anywhere in the current submission. The ‘Global Directions’ method, for example, does not suffer from this limit. Actually, I would clarify early in the paper that this method specifically aims to improve on the latent mapper approach of StyleCLIP (this also ties to clarity above).\n\n[1] Transforming the Latent Space of StyleGAN for Real Face Editing, Li et al, 2021\n\n[2] FEAT: Face Editing with Attention, Hou et al, 2022\n\n[3] Designing an Encoder for StyleGAN Image Manipulation, Tov et al, SIGGRAPH 2021\n 1) How well does the model generalize to unseen texts? Can a model not trained on hair-related prompts be used to change hair color? What if the only hair-related prompt was ‘blond hair’, would it still work to create red hair? What if the texts contained only ‘blond hair’ but also ‘red beard’, would compositionality in this manner work? If the model truly aligned the CLIP and StyleGAN spaces, one would expect this to be possible.\n\n2) I’m a bit surprised that StyleCLIP fails so badly on hair color changes. Their official models have a purple hair mapper which works fine, and I just tried the global directions in their notebook and was able to generate ginger hair. Is there any chance that you trained their mapper with the fine-layers disabled? \n The limitations and social impact section of the paper is extremely bare-bones, consisting of 2.5 lines. \n\nA few likely limitations might be things discussed in my questions above: How well does the model generalize beyond the training text? \nAnother limitation might be the fact that you train specifically on e4e codes. What if better encoders come along and now, I want to use those? Can you generalize to latent codes derived through optimization? Using another encoder? \n\nOn the matter of social impact, this type of model can lead to harm in more than just the ability to create fake imagery. It can also propagate biases or have negative effects on minority representations. For example, in your Fig 6, the top-right individual’s skin color changes drastically after editing. It is fine that your model has these shortcomings, but the purpose of the limitations / impact paragraph is to be upfront about them.\n" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 8, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 5 ]

[ "kCUXVDmIC-M", "SGdwMUrtKu", "mvgmYkVP7p5", "_lJ6QFQ-x0J", "nips_2022_kb33f8J83c", "6CQuvsYM5Zu", "mJXpXEXAqCp", "nips_2022_kb33f8J83c", "u8F0fL41qvF", "mnfNif6bRBL", "_lJ6QFQ-x0J", "nips_2022_kb33f8J83c", "nips_2022_kb33f8J83c", "nips_2022_kb33f8J83c", "nips_2022_kb33f8J83c" ]

[ "8D6r8rE8fds", "tM3w2MMIA-v", "ILvAMp-05j", "ga2Il6963qG", "VlxYxuTw9e", "nhmDJPyvy6S", "RaHZt0fJwxF", "xYCAg_QDrO" ]

[ "author", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I am glad to help with the questions in my paper.\nAnd I am very grateful for the time you and other reviewers spent reading my work.", " Thanks for the meaningful response. And after reading my colleague's comments, I decided to maintain my scores.", " We would like to thank the reviewers for their input and appreciate their comments.\n\nThe approximate Hessian proposed by (Kim et al., 2020) is very similar to the quadratic gradient but different in some ways: (a) they only used the diagonal elements of the fixed Hessian to build the approximate Hessian, together with a regularization term. They have to decide the parameter in this term. The quadratic gradient takes advantage of all the elements of the fixed Hessian. (b) (Kim et al., 2020) probably cannot be applied to numerical optimization. The underlying theory of quadratic gradient has been proved to meet the converge condition of the fixed Hessian method, so it might be probably used for general optimization problems (future work needs to be done to justify this claim). \n\nAlgorithm 1 is the pseudo-code to implement the enhanced NAG method in the clear. The algorithm in the clear is really the same as the one on ciphertexts, from the logistic perspective. Moreover, the baseline work presented a detailed description of the algorithm incorporating operations on ciphertexts. We have no new contributions to the ciphertext packing and the ciphertext-computation process, so our first mission is to clearly represent the algorithm logistic behind the enhanced NAG. \n\n\nWe implement our privacy-preserving logistic regression training based on the open source code of the baseline method. Our learning-rate setting $\\alpha_{t+1} = (1 + \\sqrt{1 + 4\\alpha_t^2})/2 $ is based on the line 128 in their source code at: https://github.com/kimandrik/IDASH2017/blob/master/IDASH2017/src/TestGD.cpp \n (the first author changed the link from https://github.com/kimandrik/HEML to https://github.com/kimandrik/IDASH2017). \nThe NAG method has many variants and the one that the baseline method used doesn't need to tune the learning rate very much. Although the authors claimed in their paper that they chose a learning rate $\\alpha_t = 10/(t + 1)$, we found no such setting in their open source code.\n\n\nWe don't know the reason why the enhanced Adagrad method had a different result in the iDash dataset. Our guess is that the enhanced Adagrad method might not perform well at the first several iterations because it has no enough prior knowledge to get a good learning-rate setting (the raw Adagrad has a less serious problem with this) but catches up with the raw Adagrad after it has enough quadratic gradients to obtain its learning rate. It might be probably the case that the raw Adagrad performs very well in the iDash dataset and when the enhanced Adagrad method finally catches up, there is no much room for both methods to improve in their performance.\nWe should not have included the enhanced Adagrad method, which is not related very much to the topic of this paper and whose performance we don't fully understand. Maybe we should leave it to future work.\n\nFor a fair comparison, we adopt the same parameters of the HE setting as the baseline work. The security parameter $\\lambda$ is determined by the parameters $\\log N$ and $\\log Q$ according to the security estimator of (Albreht et al. 2015). (Kim et al. 2018) derived a lower-bound on the ring dimension as $N \\ge \\frac{\\lambda + 110}{7.2} \\cdot \\log Q$ to get $\\lambda$-bit security level. Since HEAAN uses the complex number to facilitate the FFT computation, it needs another $N$ slots to store the complex conjugates. The formula is actually $N \\ge 2 \\cdot \\frac{\\lambda + 110}{7.2} \\cdot \\log Q$ for HEAAN.\nThe results with $\\lambda = 128 $ can be obtained if we set $\\log N = 17$ and $\\log Q = 1200$.\n\n\nIn table 2, that the auc score of Ours on nhanes3 is too low is probably because the nhanes3 is a too large dataset and only 3 iterations is not enough to achieve a decent auc score. We doubted it was a typo before and therefore implemented the bootstrapping in our code to perform more iterations, just to see the further outcomes. After many experiments, the results show that enough iterations enable the enhanced method to have a comparable auc score compared to the baseline method. Here is one running result: https://anonymous.4open.science/r/IDASH2017-245B/IDASH2017/Debug/No.vCPU2_RAM16GB_Datasetnhanes3_kdeg5_fold5_numIter17_nohup.out\n So we don't think it is a typo. \n\n\n\n(Albreht et al. 2015) M. R. Albrecht, R. Player, and S. Scott. On the concrete hardness of learning with errors. Journal of Mathematical Cryptology, 9(3):169{203, 2015 \n\n(Kim et al. 2018) Kim, M., Song, Y., Wang, S., Xia, Y., and Jiang, X. (2018b). Secure logistic regression based\n262 on homomorphic encryption: Design and evaluation. JMIR medical informatics, 6(2):e19.", " We would like to thank the reviewers for their input and appreciate their comments.\n\nOur method and the baseline method have very similar computation processes and our method adopts the ciphertext packing technique proposed by the baseline work. Therefore, the two works have very similar consumption of memory in the HE domain. \n\nFor some large-scale datasets such as the MNIST dataset, the calculation of $\\tilde B$ indeed needs to walk through the whole dataset. However, in these cases, we usually adopt the mini-batch version of the NAG method rather than the full batch version and partition the large-scale dataset into multiple same-size batches. The mini-batch version of the enhanced NAG method would be an open future work.\n\nWe don't know the reason why the convergence speed of Enhanced Adagrad is worse than the raw Adagrad. Our guess is that the enhanced Adagrad method might not perform well at the first several iterations because it has no enough prior knowledge to get a good learning-rate setting (the raw Adagrad has a less serious problem with this) but catches up with the raw Adagrad after it has enough quadratic gradients to obtain a better learning rate. It might be probably the case that the raw Adagrad performs very well in the iDash dataset and when the enhanced Adagrad method finally catches up, there is no much room for both methods to improve in their performance.\n\n\nThe SFH method, as an extension of the fixed Hessian method, has one main drawback that it cannot be used on some datasets like the MNIST datasets, in which case the simplified fixed Hessian is singular (The fixed Hessian method also has this weakness). This is one reason that the SFH method, as well as the fixed Hessian method, might not be applied to more general NNs. Another important reason is that it might be difficult or even impossible to find a \"fixed\" good lower bound of the Hessian matrix for the SFH method. On the other hand, the quadratic gradient can be constructed from the Hessian matrix directly, which doesn't rely on finding a fixed replaced matrix, and can be invertible in any case. This suggests that quadratic gradient might be able to be applied to more general NNs training like CNN, LSTM or Transformer. ", " We would like to thank the reviewers for their input and appreciate their comments.\n\n\nThe motivation why we proposed such a gradient variant is that quadratic gradient might unite the first-order gradient (descent) method and the second-order Newton's method, probably substituting and superseding the line-search method used in Newton's method. We think that the two enhanced methods might be super-quadratic algorithms (we might be wrong but we believe so) although we cannot prove it now. \nWe proposed the quadratic gradient with the hope of constructing something that possesses both the merits of the gradient descent method and Newton's method. We think that quadratic gradient can enhance Newton's method and fill the gap between the gradient methods and Newton's method.\n\n\nWe did try to make some comparisons with the work [1]. However, [1] used the mini-batch version of NAG while we adopt the full batch version of NAG. Therefore, It might be difficult to design experiments to fairly compare the two different types of NAG methods. We would like to leave the mini-batch version of the enhanced NAG method to future work, in which we of course would like to take [1] as the baseline work. Python experiments have already shown that the enhanced NAG outperforms the original NAG even in the mini-batch version. Our work and our baseline work are both based on a single model, whereas [2] is not. Therefore, it may be inappropriate to compare our work with [2].\n\n\nIt is true that the enhanced method in the iDash dataset of figure 1 is not robust and may be worse than the baseline method. we don't know the reason. Our guess is that the enhanced Adagrad method might not perform well at the first several iterations because it has no enough prior knowledge to get a good learning-rate setting (the raw Adagrad has a less serious problem with this) but catches up with the raw Adagrad after it has enough quadratic gradients to obtain a better learning rate. It might be probably the case that the raw Adagrad performs very well in the iDash dataset and when the enhanced Adagrad method finally catches up, there is no much room for both methods to improve in their performance.\n\n\nThe enhanced NAG method has worse accuracy on the Edinburgh dataset probably because it can only be performed for 3 iterations while the baseline method was performed for 7 iterations. ", " This paper studied the problem of privacy-preserving logistic training on encrypted data. The quadratic gradient is proposed to implement logistic regression training in the homomorphic encryption domain. The proposed method can be seen as an extension of the simplified fixed Hessian and an enhancement of the Adaptive Gradient Algorithm (Adagrad). The implemented homomorphic logistic regression training obtains a comparable result by only 3 iterations. Strengths: \n\nThis paper studies an important problem. Privacy-preserving logistic regression training is one popular method to protect the training data privacy, especially when logistic regression is ubiquitous in the real world.\nThe paper provides extensive experimental details and implemented codes that are helpful for reproducibility. \n\nWeakness:\n\nThe writing is not clear to distinguish between the proposed methods and previous methods. Most of section 3 are previous works, instead of proposed methods. For example, section 3.1 about the Simplified Fixed Hessian method is actually from previous works. It is better to write it in a background section. Section 3.2 seems to be the proposed method. Thus, it should be highlighted and clarified using diagrams, and clear descriptions. More importantly, it is not clear to know the motivation why the authors propose a quadratic gradient. What are the observations and insights that we have to using quadratic gradient? \n\nTypos: for example: lines 183-184. Ower-->owner\n\nMore comparisons are needed. Although the authors mentioned [1], it is required to have a result comparison with [1] since the techniques are applicable to logistic regression training. It is also better to compare with [2]. \n\nThe results are not robust or generalized. For example, the enhanced method in the iDash dataset of figure 1 is not robust and may be worse than the baseline method. It would be better to explain more about the reason. Otherwise, it may show that the proposed method is not generalized to other datasets. Also, in table 2, the proposed method has worse accuracy than the baseline method on the Edinburgh dataset. \n\n[1] Han, K., Hong, S., Cheon, J., & Park, D. (2019). Logistic regression on homomorphic encrypted data at scale. In Proceedings of the AAAI conference on artificial intelligence (pp. 9466–9471).\n\n[2] Bergamaschi, F., Halevi, S., Halevi, T., & Hunt, H. (2019). Homomorphic training of 30,000 logistic regression models. In International Conference on Applied Cryptography and Network Security (pp. 592–611).\n\n - -", " This paper presents a faster gradient variant to implement logistic regression training in a homomorphic encryption domain. The results show the new optimization method could speed up the convergence of training on small datasets. Strength:\n1. This paper is well-written and clearly organized, including sufficient theoretic analysis of the proposed Simplified Fixed Hessian method. I like such a solid line of work.\n2. The targeted topic – privacy-preserving domain of logistic regression is very promising and deserves insightful hard work to resolve the application of homomorphic encryption.\n3. The results of convergence speed are clear and convincing.\n\nWeakness:\n1. The experiments are somewhat not enough, considering the lack of experimental support for the claim in line 44 “without compromising much on computation and storage.” It will be better if a detailed comparison of computation and storage is presented.\n2. The algorithm may lack of generalization to some large-scale datasets, considering the calculation of $\\bar{\\math{B}}$ needs to walk through the whole dataset, which is quite resource-hungry\n3. Lack of further analysis of the results of the experiment, such as in Figure 1(a), why the convergence speed of Enhanced Adagrad is worse than the raw Adagrad.\n 1. In Figure 1(a), why the convergence speed of Enhanced Adagrad is worse than the raw Adagrad?\n2. I am curious about the consumption of memory in the HE domain, it will be better if the authors include a comparison between the proposed method and the baseline method.\n3. I like the idea of the second-order optimization and wonder whether the SFH method could be applied to more general NNs like CNN, LSTM or Transformer?\n Yes, the authors have included the limitations in line 119, which includes (a) the numerical condition of the SFH method and (b) the singular problem for some high-dimensional sparse matrix datasets.", " This study suggests an enhanced gradient method on logistic regression with homomorphic encryption (HE)\nThe contents of the paper generally follows (Kim et al., 2018), so for who read the paper the contents are familiar.\nThe others modified existing algorithm by replacing learning rate with quadratic gradient, which is a variant of simplified fixed Hessian.\nExperimental results show that the proposed method converges better than existing method in (Kim et al., 2018). Strengths\n- In table 2, It is empirically shown that the proposed method can achieve similar accuracy compared to (Kim et al., 2018) with much less computation time. (the ratio of the computation time is bigger than 7/3 for most datasets, which seems because bigger $logq=60$ was used for the proposed method)\n- By transferring the role of computing $\\tilde{B}$ to the data owner, the proposed method does not require more multiplicative depth compared to (Kim et al., 2018).\n- The paper seems clear and easy to follow.\n\nWeaknesses\n- The novelty seems rather shallow; (Kim et al., 2020) has already proposed an approximate Hessian which is very similar to quadratic gradient method. The authors should check the paper.\n- Algorithm 1 seems rather meaningless. The algorithm should incorporate operations on ciphertexts, which deal with ciphertext packing.\n\n(Kim et al., 2020) Kim, M., Lee, J., Ohno-Machado, L., & Jiang, X. (2019). Secure and differentially private logistic regression for horizontally distributed data. IEEE Transactions on Information Forensics and Security, 15, 695-710. 1. Parameter setting is an important issue when using HE, because parameter search is extremely unfriendly with HE. In algorithm 1, the authors set $\\alpha_{t+1}=(1+\\sqrt{1+4\\alpha_{t}^2})/2$, which is different to the setting in (Kim et al., 2018), which is $\\alpha_t=10/(t+1)$. Can the parameter choice be justified?\n\n2. In the experiments, iDash dataset showed different results than other datasets. Can it be explained?\n\n3. Can the results with $\\lambda=128$ be given?\n\n4. In table 2, the auc score of Ours on nhanes3 is too low. Is it a typo? The authors have not address the limitations of their work. Because the study is about privacy-preserving logistic regression, it seems to have a positive societal impact.\n\nAs mentioned above, the biggest limitation of their work is that there is no significant improvement compared to the existing methods." ]

[ -1, -1, -1, -1, -1, 4, 5, 3 ]

[ -1, -1, -1, -1, -1, 3, 4, 5 ]

[ "tM3w2MMIA-v", "ga2Il6963qG", "xYCAg_QDrO", "RaHZt0fJwxF", "nhmDJPyvy6S", "nips_2022_6tRhLrki6b8", "nips_2022_6tRhLrki6b8", "nips_2022_6tRhLrki6b8" ]

[ "WEbZTNlkNkK", "hVn3xoeeAhV", "5yp6nkGP0l", "JWrqHrAPWC9", "kjfx6mn0QHy", "FNxnYXkdU6q", "5cyuhiz-vb0", "A7tXgkTIXdv", "NquNO11iH4_", "FTzsTun_sD", "QKOdb7Yh-hH", "RcIV1Gt4jSV" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I would like to thank the authors for addressing my concerns, and I raised my rating based on the responses.", " Thanks for addressing my concerns!\n\nI want to clarify that for the last point:\n> We appreciate the reviewer's suggestion regarding a more thorough comparison with [Sedghi et al., 2019] in the intractable scenarios, which we will add in the next revision.\n\nI'm suggesting doing more comparison with [Sedghi et al., 2019] when it is tractable, not the other way around.\n\nOtherwise, thanks for the response!", " Thank you for addressing my concerns!", " We thank reviewer Cy9m for the feedback and comments.\nIn addition to answers below, we invite the reviewer to check out the top-level post.\n\n> The originality of the proposed framework lacks significance, since using tensor decomposition to decompose a CONV layer into sequential smaller ones is not novel.\n\nDecomposing a kernel tensor of a convolutional layer is indeed not a novel part of our work. Our main contribution is that we find a decomposition that allows us to control singular values of the decomposed layer efficiently, and we rigorously prove the validity of our method. We provide the reasoning about significance of downstream tasks leading to the need of singular values control emphasized in the top level post.\n\n\n> The related work contains too many topics.\n> I suggest making Section 2 more concise and the research gap more obvious.\n\nWe thank the reviewer for these suggestions. We will be sure to improve the related work section in accordance with your suggestions.\n\n\n> This work does not give a clear strategy to find the proper TT ranks, which is of great significance for TT decomposition.\nalso\n> About the choice of TT ranks. How to choose proper ranks is a vital research topic for tensor decomposition, but it is not discussed in this article. I wonder how the ranks are determined in this paper. The selection is based on experimental results? If yes, there should be an ablation study about it.\n\nThank you for pointing out this issue. The ranks were chosen as the maximum number of channels divided by a small constant c (such as 2-4) for each layer to control the performance by a single hyperparameter c for simplicity. Such rank policy assumes decomposing only the largest layers, and keeps the smallest layers intact. We will adjust text to make these details clear and add the ablation study w.r.t. the rank values as you suggest.\n\n\n> The experiments are insufficient and lack discussion and ablation study.\n> I think experiments on two models using CIFAR-10 are not enough. I think the results will be more convincing if more models (e.g., ResNet-18/50) and larger dataset (at least CIFAR-100) are considered.\n> The results are listed in the Table without further discussion\n\nWe provide justification of the design choices and selection of evaluation protocols in the top-level post. We, however, agree that the paper will benefit from more experiments with resnet-type architectures and plan to add experiments on CIFAR-100 dataset as you suggest. Moreover, we already plan to add more discussion and ablation study as we pointed out to other reviewers.\n\n\n In our work we focused on the study of network architectures with large convolutional layers.\n\n\n> About the novelty. Including TT, Tucker-2, CP, and Tensor Ring (TR) are also decomposition methods widely utilized to compress the CONV layers. I wonder why TT is employed in this work but not other decomposition methods?\n\nThis is a great question, which we touch on in LL. 183-184 and also plan to elaborate in detail in the revised version. The short answer is that not all tensor decompositions of kernel tensors admit efficient computation of singular values. In our setting, TT serves well for this purpose, but CP and TR decompositions are incompatible by design for controlling singular values.\n\n\n> I think the first column in the right part of Table 1 should be “ACC.” instead of “AC.”? The definition of COMP. is also missing, it is not clear how to calculate it and the meaning of the number.\n\nThank you also for pointing out issues with \"ACC\" and \"COMP\". The latter denotes the compression ratio in terms of parameters count (line 265).\n\n\n> line 288 – 321. I think it is better to move this part to the appendix and use the space to add more experiments, discussion of the results, ablation study of rank, etc.\n> Sections 5.1 & 5.2 are too short\n\nThank you for this and other suggestions regarding clarity and readability. We will make sure to update Section 5.", " We thank reviewer 9EwE for the feedback and comments.\nIn addition to answers below, we invite the reviewer to check out the top-level post.\n\n> Theoretical claims could be better explained/justified. It's not obvious upon reading this how all the theoretical contributions are related to the work. Theorem 1 and lemma 1 are related to TT framework, and theorem 2 is about explicit singular value formula for strided convolution. To help clear some ambiguity, it might be helpful to put the lemma in appendix and expand up the technical details of theorem 1 and the importance of it for the framework. Then explain how all the theoretical contributions fit into algorithm (1).\n\nIndeed, Theorem 1 and Lemma 1 are related to the TT framework. In particular, Theorem 1 suggests that one can apply a method of choice to a smaller kernel K2 instead of K. Theorem 2 is focused on the generalization of exact computation of all singular values [Sedghi et al., 2019] to the case of strided convolutions, which often appear in practice. Since computation of all singular values is both time and memory consuming, our approach is particularly useful in this scenario. Anyway, we thank the reviewer for the suggestion regarding the readability. We will fix it in the next revision of the paper.\n\n\n> I believe the paper would benefit from additional experiment, similar to the one in Figure (1), which would include speed up versus some performance metrics (accuracy, ECE). This would be very useful from a practitioner's standpoint\n\nThank you for this suggestion. We found that the choice of the rank r in terms of the number of channels m yields the best results when r = m/c, where c = 2-4 (as in Figure 1). However, we agree that the dependence of the performance on the rank could be very useful for a reader and plan to add the plot to supplementary materials. \n\n\n> Could you please provide some context w/ respect to Figure 1? Such as if you have speed up of x amount, could that lead to requiring less memory in GPU compute? For example, say a researcher only has access to 8 GB GPU could they compress the network by a certain factor to fit onto their GPU.\n\nIndeed, using our framework leads to less memory for small ranks. In particular, the gain is quadratic with respect to the ratio m/r, where m is the number of channels and r is the TT-rank. Say, if m/r=3, then our approach requires 9 times less memory. This is important for networks with large number of input/output channels. For example, if m = 4096 and n = 16 (spatial dimension), then storing n x n x m x m padded kernel tensor requires ~34GB, while our method would only require ~4GB. In the next revision, we will add a figure similar to Figure 1, but with memory requirements.\n\n> Strided convolutions are a large part of Generative networks in GANs, do you think your work could be built upon to study mode collapse in GAN's based on the singular value composition? As well, did you consider study these types of models in your paper?\n\nWe believe so. We actually plan to address this matter in our future work. Similar attempts have been done, e.g., in [Liu et al., 2019], but using heuristics for computing singular values.", " We thank reviewer eWcT for the feedback and comments.\nIn addition to answers below, we invite the reviewer to check out the top-level post.\n\n> title of the work is not well aligned with the actual content.\n\nThank you for pointing out this concern. We agree that the title could be improved. Tentatively, \"Towards practical control of singular values of convolutional layers\" would reflect the merits of the proposed framework better. In case of positive decision, we will work with ACs to change the title.\n\n\n> the experiment section seems a little bit weak to only compare with SOC only (Table 1) and the vanilla setting (Table 2). The effect of the proposed approaches can be better demonstrated If more experiments can be added.\n\nIn our experiments, we considered 3 principled approaches: exact computation of all singular values, direct parametrization of all singular values (SOC) and constraining the largest singular value (e.g., computing it with power iterations and subsequent division of the tensor). To the best of our knowledge, we investigated state-of-the-art methods in all categories. In case the reviewer can suggest a reference that we could use in our study, we would be happy to consider it in the next revision.\n\n\n> As an additional question, I'm wondering why the constraint discussed in Section 4.2 does not include a term to deal with K2 and why is the constraint useful without controlling K2.\n\nThe central matrix, K2, is controlled by clipping, iterative method, or SOC, while the frame matrices K1 and K3 are orthogonalized approximately with the help of auxiliary loss. According to Theorem 1, if K1 and K3 are orthogonal, the singular values of the entire convolution will match the singular values of the convolution defined by K2, which are controlled efficiently by the method of choice.\n\n\n> Lastly, I would suggest expanding the clipping part discussed in Section 5.2 to a more comprehensive comparison between the proposed method and [1] (perhaps adding some comparisons when [1] is tractable in order to show both the efficiency and accuracy of the proposed method).\n\nWe appreciate the reviewer's suggestion regarding a more thorough comparison with [Sedghi et al., 2019] in the intractable scenarios, which we will add in the next revision.", " We thank reviewer EXfn for the feedback and comments. \nIn addition to answers below, we invite the reviewer to check out the top-level post.\n\n> The assumptions of the lemma and theorems are not specified clearly. Do they apply to all kinds of convolutional layers?\n> Does it mean the stride equals the kernel size? Many convolutional layers may not satisfy such a requirement.\n\n\nThank you for the comment, we will be sure to edit the paper and write it more explicitly.\nTheorem 1 is rather general. The key assumption is the orthogonality of K1 and K3. As for the map given by K2, we only assume its linearity, which covers different convolution types.\nIn Theorem 2, we follow [Sedghi et al., 2019] and assume that the convolution is periodic. As opposed to that paper, our generalization is applicable for strided convolutions (s>1). The only assumption we impose on s is that the image size n is divisible by s (or n = 0 (mod s)), which is natural for strided periodic convolutions.\n\n\n> The experiments of computational complexity are too limited. A detailed comparison (in terms of, for example, running time) between the proposed method and prior methods should be added.\n\n\nWe consider 3 types of methods: using clipping [Sedghi et al., 2019], several iterations of power method [Gouk et al., 2020] and the exact parametrization [Singla and Feizi, 2021b]. Time performance for the first two methods are presented in Figure 1 and Table 2. \nTo reinforce empirical study, we will add a figure similar to Figure 1 for the SOC method and present run time ablation of several new architectures. For example, our preliminary results show that clipping singular values of all layers of resnet-50 is almost 5 times slower than doing so using our framework with the rank value 256.\n\n\n> The correctness of the singular values (SVs) using the proposed method should be validated empirically.\n\n\nAs correctly pointed out by the reviewer, the result from [Sedghi et al., 2019] works only for stride equal to 1. To validate correctness of our approach, we performed the following sanity check: we generated random orthogonal matrices K1, K3 and random K2, assembled a single core K from them and then constructed the full matrix of the linear map for small enough number of channel and image size to fit into computer memory. Then we computed singular values of this matrix by calling np.linalg.svd and compared it with the results obtained through our equations. All the experiments showed that they are equal up to machine epsilon. We thank the reviewer for pointing out the paper [Liang et al, 2021].", " We thank the reviewers for their time, valuable comments and constructive criticism. Quoting the reviews: the work is on \"important problems to the ML/AI community\" (Reviewer 9EwE), the presentation is \"clear\" (Reviewer eWcT), the experiments part demonstrates \"the benefits of applying the proposed method\" (Reviewer eWcT) and the \"significance of proposed framework\" (Reviewer 9EwE). \"The lemma and theorems are clearly stated, and the proofs are detailed\" (Reviewer Cy9m).\n\nBefore giving detailed answers to the questions raised by the reviewers in the comment section, we briefly reiterate the main idea of our paper and highlight the motivation behind our numerical experiments.\n\nOur main contribution is a framework for convolutional layer representation that allows us to reduce complexity of controlling its singular values with a method of choice (such as exact computation using FFTs [Sedghi et al., 2019], direct parametrization [Singla and Feizi, 2021b], etc.). The importance of efficiently controlling singular values stems from the practical needs typically solved through such control: the demand for certifiable robustness of deep models, stability of training, to name a few. The methods for singular values control mentioned above exhibit poor scaling with the growth of the number of convolutional layer channels. Our framework permits exploiting any of these methods in their most favorable performance regime. In our experiments, we apply our framework with these methods and demonstrate that different architectures (WideResNet, LipConvNet) benefit from using our approach. \n\nEach method employed within our proposed framework carries over the evaluation conventions used by the authors. That is, finding the definitive set of networks, datasets, and metrics, to unify the findings, is a hard problem in its own right. On top of that, our approach to controlling singular can be used with a variety of policies (such as truncation, division, etc.). We attempted to demonstrate the most important selection of the axes of study, however, it is only natural that some important experiments were omitted. Nevertheless, we agree with comments of the reviewers that the paper would benefit from some more experiments, which we do plan to add in the revised version and which we discuss in the comment section. ", " The authors of this paper offer a method to compute the singular values (SVs) of convolutional layers efficiently. They propose a method to decompose the matrix $\\mathcal{K}$ representing a convolutional layer to smaller matrices $\\mathcal{K}^{(1)} \\mathcal{K}^{(2)} \\mathcal{K}^{(3)}$ and show that the SVs of $\\mathcal{K}$ can be expressed by the union of the SVs of some smaller matrices related to $ \\mathcal{K}^{(2)}$. ## Strengths\n- The decomposition of the matrix for convolutional layers is neat.\n- The experimental results on clean and robust accuracy are improved with the proposed method.\n\n## Weaknesses\n- The assumptions of the lemma and theorems are not specified clearly. Do they apply to all kinds of convolutional layers?\n- It seems that Theorem 2 requires $n \\equiv 0\\ (\\text{mod}\\ s)$, which means the spatial size $n$ has to be divisible by the stride $s$. Does it mean the stride equals the kernel size (i.e., $s = k$)? Many convolutional layers may not satisfy such a requirement.\n- The experiments of computational complexity are too limited. A detailed comparison (in terms of, for example, running time) between the proposed method and prior methods should be added.\n- The correctness of the singular values (SVs) using the proposed method should be validated empirically. For example, the SVs computed by the proposed method can be compared to those from [1]. Note that the method from [1] may only apply to convolutional layers with a stride equaling 1. For other strides, an alternative comparison is [2] by using the inequalities of matrix norms: $r\\|A\\|_\\alpha\\leq\\|A\\|_\\beta\\leq s\\|A\\|_\\alpha$, i.e., by empirically showing that the largest singular value from the proposed method can be bounded by the $\\ell_1$ norm or $\\ell_\\infty$ norm from [2].\n\n[1] Sedghi H, Gupta V, Long PM. The singular values of convolutional layers. arXiv preprint arXiv:1805.10408. 2018 May 26.\n\n[2] Liang Y, Huang D. Large norms of CNN layers do not hurt adversarial robustness. InProceedings of the AAAI Conference on Artificial Intelligence 2021 May 18 (Vol. 35, No. 10, pp. 8565-8573). Please see the Weaknesses above for the questions. The limitations are not sufficiently discussed. For example, the assumptions of the lemma and theorems are not specified clearly.", " The work proposed a less expansive approach to calculating the singular values of convolutional layers. The proposed approach builds on the assumption that modern neural networks are highly overparametrized in such a way that a sparser surrogate network could achieve similar performance and the method of Tensor-Train (TT) decomposition. The work further empirically shows that a network's robustness could be improved by adding additional orthogonality constraint terms derived from the proposed approach and clipping calculated singular values. Strengths:\nThe overall presentation of the work is clear. The relationships with prior arts are carefully discussed. And the experimental part clearly demonstrates the benefits of applying the proposed method and also discusses many technical details.\n\nWeaknesses:\nThe reviewer found that the title of the work is not well aligned with the actual content. The title indicates that a more efficient approach for calculating singular values of convolutional layers will be proposed, one would expect to directly use the proposed method to calculate singular values of some given network (like the algorithm proposed in [1]). However, the calculation described in this work heavily relies on the decomposition (K = K1 ∘  K2 ∘  K3) and it is not clear to the reviewer how to decompose a given convolutional kernel to such form (please correct me if I'm wrong). Rather, the reviewer believes that the major accomplishment of the work lies in designing networks/constraints to improve the robustness of networks.\nBesides, the experiment section seems a little bit weak to only compare with SOC only (Table 1) and the vanilla setting (Table 2). The effect of the proposed approaches can be better demonstrated If more experiments can be added. \n\n[1] Hanie Sedghi, Vineet Gupta, and Philip M. Long. The singular values of convolutional layers, 2019\n My major concerns are discussed in the Weaknesses section. \n\nAs an additional question, I'm wondering why the constraint discussed in Section 4.2 does not include a term to deal with K2 and why is the constraint useful without controlling K2.\n\nLastly, I would suggest expanding the clipping part discussed in Section 5.2 to a more comprehensive comparison between the proposed method and [1] (perhaps adding some comparisons when [1] is tractable in order to show both the efficiency and accuracy of the proposed method). N/A", " This paper proposes an efficient method to compute eigenvalues of convolutional layers based on a sparsity-driven approach. The proposed work achieves by proposing a novel framework that compresses the layer representation (section 3.2) based on a tensor decomposition. The authors provide theoretical justification in Lemma 1 and Theorem 1 of their proposed framework. In addition, empirical evidence is provided to demonstrate how effective their tensor decomposition across a wide range of architecture and metrics. \n\nThe contributions are listed as the following:\n1). Proposes a novel framework Tensor-Train (TT) decomposition to compute singular values that reduce computational complexity.\n2). Extend previous work on the exact computation of singular values to strided convolutions\n3). Demonstrated significance of proposed framework with varying control over the singular values on a few CNN architectures by comparing their method to the baseline across some important metrics (accuracry, generalization error, and adversarial robustness). Strengths-\n1). Works on important problems to the ML/AI community.\n2). Approves upon previous work by reducing the computation complexity and extending work to strided convolution. \n3). Convincing empirical evidence that this framework is effective.\n\nWeakness-\n1). Theoretical claims could be better explained/justified. It's not obvious upon reading this how all the theoretical contributions are related to the work. Theorem 1 and lemma 1 are related to TT framework, and theorem 2 is about explicit singular value formula for strided convolution. To help clear some ambiguity, it might be helpful to put the lemma in appendix and expand up the technical details of theorem 1 and the importance of it for the framework. Then explain how all the theoretical contributions fit into algorithm (1).\n\n2). I believe the paper would benefit from additional experiment, similar to the one in Figure (1), which would include speed up versus some performance metrics (accuracy, ECE). This would be very useful from a practitioner's standpoint\n 1). Could you please provide some context w/ respect to Figure 1? Such as if you have speed up of x amount, could that lead to requiring less memory in GPU compute? For example, say a researcher only has access to 8 GB GPU could they compress the network by a certain factor to fit onto their GPU. \n\n2). Strided convolutions are a large part of Generative networks in GANs, do you think your work could be built upon to study mode collapse in GAN's based on the singular value composition? As well, did you consider study these types of models in your paper? \n Limitations are in section 6, assumptions are reasonable. ", " This article proposed a framework based on the Tensor Train (TT) decomposition to decrease the complexity of computing a given convolutional layer's singular values (SVs). The key idea is to decompose the original convolution layers into low-rank factors and calculate the SVs of the factors with smaller sizes instead of the original kernel tensor. The main paper and supplementary materials give detailed proofs of the lemma and theorems. The framework is evaluated on accuracy, robustness, and calibration. The experiments are conducted on LipConv and WideResNet-28-10, using CIFAR-10 as the dataset. Strength\n1. The lemma and theorems are clearly stated, and the proofs are detailed.\n\nWeakness\n1. The originality of the proposed framework lacks significance, since using tensor decomposition to decompose a CONV layer into sequential smaller ones is not novel.\n2. The related work contains too many topics, which instead blurs the key point of this article. It makes the research gap and the motivation of the proposed framework unclear.\n3. This work does not give a clear strategy to find the proper TT ranks, which is of great significance for TT decomposition.\n4. The experiments are not comprehensive and lack discussion and ablation study.\n 1. Section 2. As mentioned in the weakness part, too many topics are mentioned in this section. Though the scope of topics mentioned in this section is enormous, each of them only has short content, which makes the critical point unclear. Especially for the last two (viz. Robustness and Calibration), I think they are metrics to evaluate the framework in the experiments, thus it is not necessary to mention them in the related work section. I suggest making Section 2 more concise and the research gap more obvious.\n2. About the novelty. Including TT, Tucker-2, CP, and Tensor Ring (TR) are also decomposition methods widely utilized to compress the CONV layers. I wonder why TT is employed in this work but not other decomposition methods? \n3. About the choice of TT ranks. How to choose proper ranks is a vital research topic for tensor decomposition, but it is not discussed in this article. I wonder how the ranks are determined in this paper. The selection is based on experimental results? If yes, there should be an ablation study about it. \n4. The experiments are insufficient. I think experiments on two models using CIFAR-10 are not enough. I think the results will be more convincing if more models (e.g., ResNet-18/50) and larger dataset (at least CIFAR-100) are considered.\n5. The results lack analysis. Sections 5.1 & 5.2 are too short, and the results are listed in the Table without further discussion. It will be better if more analysis is provided. Besides, I think the first column in the right part of Table 1 should be “ACC.” instead of “AC.”? The definition of COMP. is also missing, it is not clear how to calculate it and the meaning of the number.\n6. line 288 – 321. I think it is better to move this part to the appendix and use the space to add more experiments, discussion of the results, ablation study of rank, etc.\n None" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 7, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 3, 4 ]

[ "5cyuhiz-vb0", "FNxnYXkdU6q", "kjfx6mn0QHy", "RcIV1Gt4jSV", "QKOdb7Yh-hH", "FTzsTun_sD", "NquNO11iH4_", "nips_2022_T5TtjbhlAZH", "nips_2022_T5TtjbhlAZH", "nips_2022_T5TtjbhlAZH", "nips_2022_T5TtjbhlAZH", "nips_2022_T5TtjbhlAZH" ]

[ "wRVABRkCO_s", "D8R2jAik_Ri", "wNwd4nTgUJ8", "xbUU9aItzB", "Dl-fesxKio_", "dYh_t4AhUb", "9mcS3Cajvzd", "e_lsy98jWb", "oNEd7qLAp1g", "2dJRI1nNtSh", "bPluvFd_feQ", "Xv5xBVStvD", "TfOaOCTVgWM", "SwXPFbHFFd" ]

[ "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " The author provides additional experimental results, showing the scalability of HCL on existing object-level learning methods (ORL), which supports their claims and address my main concerns. So, I increase my score.\n\nI would recommend the authors add these results to the main text to support the effectiveness of HCL.", " In the additional experiments, the authors show that their proposed method is quite general and can be combined with many existing methods such as MoCo, ORL, and Dense-CL. The performance can be consistently improved by 1~3%.\n\nThese results strengthen the paper, and have addressed my main concerns. The intuition provided by the authors also makes sense.\n\nWhile the performance improvement seems small, given the novelty and generality of the proposed method, I'd like to recommend accept.", " Dear Reviewer 78go,\n\nThank you for your time and efforts in reviewing our paper!\n\nWe kindly remind that the discussion period will end in a few days, and thus we just wonder whether we could have the last chance to address your further concerns or questions (if you have any). We are sincerely glad to improve our paper under your suggestions!\n\nThank you very much!\n\nAuthors", " Dear Reviewer SzXC,\n\nThank you for your time and efforts in reviewing our paper!\n\nWe sincerely hope our response successfully addresses your concerns and answers your questions.\n\nWe just wonder if we could have the last chance to address your further concerns or questions, and we are glad to improve our paper under your further suggestions (if you have any).\n\nThank you very much!\n\nAuthors", " Thank you for your clarifications and additional experiments. \n\nThe authors added an additional comparison with DenseCL where they showed their method to improve COCO results, too, which strengthens the paper. Thus, I increase my rating.\n\n\nMy main concern remains that more recent SSL methods achieve much better classification accuracy on ImageNet and improvements of the hyperbolic loss compared to a MoCo+bbox baseline are small. The main increase in performance does seem to come from using object regions as the baseline using them increases significantly over MoCo compared to adding the additional loss. But I tend to agree that ImageNet, as an object-centric datataset, is not an ideal benchmark. \n\nIf the main goal of the paper is to improve out-of-context detections, and quantifying label uncertainty, then the paper would benefit from a more detailed quantitative evaluation of them. For the claimed key features of their method, only limited quantitative evaluation is conducted (e.g. only comparison to MoCo). \n\n", " Thank you for your detailed feedback. To mitigate the raised concerns, we either conduct the requested experiments or explain the reasons why the suggested experiment may not be a fair comparison below.\n\n**\"Performance gains of using hyperbolic loss might be due to using additional information, i.e. detections\"**\n\nWe agree that comparing with the original MoCo-v2 is not enough to demonstrate the effectiveness of using hyperbolic loss, therefore, in our experiments (e.g. Table 1), we also have another baseline HCL/$\\mathcal{L}\\_{\\text{hyp}}$ that takes the object regions as the input while not using hyperbolic loss (Line 205-206). (We notice that the name of this variant HCL/$\\mathcal{L}\\_{\\text{hyp}}$ does not explicitly reflect the fact that it uses bounding boxes and could have caused confusion. We will use a more accurate name like MoCo+bbox in our next version.) As shown in Tables 1 and 2, this baseline outperforms MoCo on the downstream tasks by learning cleaner object representations. However, without any objective imposed on the scene images, the performance is still inferior to the proposed HCL. \nWe also report another ablation in Table 4 where we replace the hyperbolic distance in the loss function with a Euclidean distance, which leads to not just ineffective but detrimental results. We believe that these results together demonstrate that the improvements are indeed because of our novel objective rather than the detections.\n\n**\"Dense-CL achieves similar performance without relying on detection labels for pre-training but is missing.\"**\n\nWe train Dense-CL with and without our hyperbolic objective on the COCO dataset by following settings in the Dense-CL paper and evaluate the pretrained model on object detection and instance segmentation. To confirm that the improvements are due to the hyperbolic loss, we also report the results of Dense-CL with ground truth object proposals. The results are shown in the table below. We can see that using hyperbolic loss consistently improves the performance of Dense-CL.\n\n| COCO detection | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ | COCO segmentation | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ |\n|----------------------------|------|------|------|----------------------------|------|------|------|\n| Dense-CL | 39.6 | 59.3 | 43.3 | Dense-CL | 35.7 | 56.5 | 38.4 |\n| Dense-CL+GT-Bbox | 41.3 | 61.5 | 44.7 | Dense-CL+GT-Bbox | 37.5 | 59.5 | 40.4 |\n| Hyperbolic Dense-CL | 42.5 | 62.5 | 45.8 | Hyperbolic Dense-CL | 38.5 | 60.6 | 41.4 |\n\n**\"I'd like to see some scores on a dataset of similar size to ImageNet.\"**\n\nWe train Dense-CL on the full OpenImage dataset for 75 epochs and the results are shown in the table below. The trend stays the same.\n\n| COCO detection | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ | COCO segmentation | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ |\n|----------------------------|------|------|------|----------------------------|------|------|------|\n| Dense-CL | 38.2 | 58.9 | 41.6 | Dense-CL | 34.8 | 55.3 | 37.8 |\n| Dense-CL+GT-Bbox | 41.1 | 61.5 | 44.4 | Dense-CL+GT-Bbox | 37.2 | 58.3 | 39.7 |\n| Hyperbolic Dense-CL | 42.1 | 62.6 | 45.5 | Hyperbolic Dense-CL | 38.3 | 59.4 | 40.6 |\n\n**\"HCL requires supervision. Selective search avoids annotations but it decreases performance.\"**\n\nWe agree. However, unsupervised object discovery and detection is an active research area and has gained decent progress, e.g. [1]. We believe that using the proposals generated by these methods could further diminish the gap, which we leave as future work\n\n**\"MoCo-V2 [1] achieves an accuracy of 67.5% for 200 epochs, 71.1% after 800 epochs, DINO [2] even 75.3%. HCL achieves only an accuracy of 58.5% despite using the additional information.\"**\n\nAs also mentioned by the reviewer, these numbers are not directly comparable since these models have different focuses from us and are trained on the ImageNet-1K dataset which is object-centric. \n\nWe have shown that the proposed HCL is generic and able to combine with any existing methods, including MoCo, ORL and Dense-CL as requested by reviewers. We also admit that our proposed idea has its limitations. For instance, we find that the learned representations do not improve on the fine-grained class classification as shown in Appendix B.2. However, we want to kindly note that as we state in the paper, our goal is ***not*** to develop another state-of-the-art self-supervised learning method but a step towards learning representations for images depicting not just objects. As we show in the paper, such representations allow us to achieve results that were not approachable before, such as using image-object similarity to detect out-of-context objects, and using representation norms to quantify label uncertainty. \n\n[1] Vo, Van Huy, et al. \"Large-scale unsupervised object discovery.\" NeurIPS 2021.", " 1 - 3: thanks for suggesting, we will clarify and add the corresponding details in our next version.\n\n4: the general hyperparameters such as learning rates are tuned using MoCo-v2 instead of HCL. We did use a cosine learning rate scheduler during the pretraining phase.", " We would like to thank the reviewer for the positive comments and rating!\n1. To address the major concern, we conduct an experiment using ORL. We train ORL with and without our hyperbolic objective on the COCO dataset following the settings in the paper (800 epochs) and evaluate it on object detection and instance segmentation. The results in the table below show that using our hyperbolic objective improves the performance. Similar to MoCo, methods like ORL only focus on learning object representations while paying insufficient attention to scene images. We show that it is beneficial to handle the representations for scene images additionally. We hope our work could make a step towards learning representations for all images beyond objects.\n| COCO detection | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ | COCO segmentation | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ |\n|-----------------|------|------|------|-----------------|------|------|------|\n| ORL \t| 40.3 | 60.2 | 44.4 | ORL \t| 36.3 | 57.3 | 38.9 |\n| Hyperbolic ORL | 41.4 | 61.4 | 45.5 | Hyperbolic ORL | 37.3 | 58.5 | 40.0 |\n\n2. Please find our HCL/$\\mathcal{L}_{\\text{hyp}}$ with SS bbox on OpenImage below to support the claim. \n| | VOC | IN-100 | INPMix | IN-1k |\n|--------------------------------|-------|--------|--------|-------|\n| HCL/$\\mathcal{L}_{\\text{hyp}}$ | 71.82 | 75.33 | 52.02 | 56.58 |\n| HCL | 74.31 | 78.14 | 53.21 | 58.12 |\n\n3. Calculating hyperbolic loss itself takes nearly the same time as a normal contrastive loss. The only overhead in training is one additional forward pass to get scene representations. We further measure the time per iterations during training: MoCo takes 0.616 sec/iter while HCL takes 0.757 sec/iter under 4 P6000 GPUs.\n", " **\"why the objects are the root nodes\"**\n\nTo be accurate, when we mention objects we consider classes of objects, since in object-focused representation learning, different objects of the same class are often clustered together. In general, there are more scenes than classes of objects. A scene image can contain multiple kinds of objects and hence the number of scene images can be combinatorially many. A real example of this is the COCO dataset, which has over 300K images but only less than 200 classes of objects. Last, objects are more general and ambiguous when shown alone in the image world. As more contexts are given, they become more specific. Each class of object can occur in different contexts and thus form a hierarchy starting from it. Therefore we pick the objects as the root.\n \n**\"why the norm of representation will be large when there are multiple objects\"**\n\nThis is an expected result from our hyperbolic objective. Consider an example that learns representations of 3 regions $r_1$ (contain obj1, obj2, and obj3), $r_2$ (contain obj2, and obj3), and $r_3$ (contain obj2, obj3, and obj4): to minimize the hyperbolic distance $d(r_1, r_2) + d(r_2, r_3)$, it gives us the smaller distance when putting $r_2$ at the origin and $r_1$ & $r_3$ at the boundary compared with putting $r_1$ or $r_3$ at the origin. This is because of equation (3), which tells us that the distance between two boundary points is twice the distance between one to the origin. Therefore, the hyperbolic loss places regions with more objects closer to the periphery, with larger norms.\n\nWe also experimented with the *scene*-centric hierarchy as shown in Table 4. Qualitatively, we saw that the model overfits to make the norms of some scene regions to be smaller but they are not consistent across images and do not generalize to unseen images. Quantitatively, it yields worse performance. We appreciate that the reviewer asks these questions on the intuition and will make our best effort to improve on this in future versions.\n", " **\"Empirical evaluation seems insufficient...\"**\n\nAlthough we build our method mainly on MoCo, the idea of hyperbolic objective can easily slot into other contrastive learning frameworks. For instance, as suggested by the reviewer, ORL [1] learns *object representations* from scene images and shows better downstream performance than MoCo when pretrained on COCO. We conduct experiments using ORL with and without our hyperbolic objective on the COCO dataset following the settings in [1], and evaluate the pretrained model on object detection and instance segmentation. We report the results in the table below. It shows that our proposed hyperbolic objective further improves ORL and supports our claim that learning representations for scene images in hyperbolic space is beneficial to downstream performance.\n\n| COCO detection | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ | COCO segmentation | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ |\n|---------|------|------|------|-----------------|------|------|------|\n| ORL \t| 40.3 | 60.2 | 44.4 | ORL \t| 36.3 | 57.3 | 38.9 |\n| Hyperbolic ORL | 41.4 | 61.4 | 45.5 | Hyperbolic ORL | 37.3 | 58.5 | 40.0 |\n\nApart from ORL, as suggested by Reviewer-L2gv, we also add an experiment with Dense-CL [2]. Dense-CL is a contrastive learning framework that is not specifically designed for scene images but generally achieves better object detection results than MoCo. As shown in the table below, we observe improved performance when training Dense-CL with our hyperbolic objective. Together with the experiment on ORL, we believe that these results demonstrate that our proposed hyperbolic loss is generic enough to boost any existing contrastive learning methods.\n\n| COCO detection | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ | COCO segmentation | $\\text{AP}$ | $\\text{AP}_{50}$ | $\\text{AP}_{75}$ |\n|----------------------------|------|------|------|----------------------------|------|------|------|\n| Dense-CL | 39.6 | 59.3 | 43.3 | Dense-CL | 35.7 | 56.5 | 38.4 |\n| Hyperbolic Dense-CL | 42.5 | 62.5 | 45.8 | Hyperbolic Dense-CL | 38.5 | 60.6 | 41.4 |\n \n**\"Comparison to MoCo-v2 seems unfair...\"**\n\nWe agree that comparing with the original MoCo-v2 is unfair as it takes the full image as the input. We were aware of that, therefore, in our experiments (e.g. HCL/$\\mathcal{L}\\_\\text{hyp}$ in Table 1), we gave MoCo advantages by using the object regions as the input (Line 205-206). We notice that the name of this variant HCL/$\\mathcal{L}\\_{\\text{hyp}}$ does not reflect this explicitly and could have caused confusion. A more proper name should be MoCo+bbox. We will address this in our next version.\nThis variant improves the downstream performance by learning cleaner object representations. However, without any objective on the scene images, the performance is still inferior to the proposed HCL. The other supporting evidence is in Table 4. When we replace the hyperbolic distance in the loss function with a Euclidean distance, we observe worse performance than MoCo. Therefore, the improvement is from leveraging the hyperbolic objective rather than having cropping.\n\n**\"The definitions in L105-111 do not seem to form a tree.\"**\n\nThanks for pointing this out! We agree that in this example it is not a tree so the reference to a forest is not accurate. We tried to refer to it as a hierarchy and will be more careful with this in our future version!\n\n[1] Xie, Jiahao, et al. \"Unsupervised object-level representation learning from scene images.\" NeurIPS 2021.\n\n[2] Wang, Xinlong, et al. \"Dense contrastive learning for self-supervised visual pre-training.\" CVPR. 2021.", " We thank the reviewers for their thoughtful feedback. It is encouraging that the reviewers found learning representations for scene images to be important and relevant to the community (R-SzXC), our idea of using hyperbolic space to be novel (R-SzXC), interesting and promising (R-L2gv), and well-motivated (R-78go, R-SzXC), which is corroborated by our improved downstream performance (R-78go, R-L2gv) and the application of the useful property of representation norms to several problems, and our writing to be clear and easy to follow (R-SzXC).", " The paper aims to improve contrastive learning for multi-object scenes. In addition to making single-object representations close when objects are similar, the paper seeks to encourage multi-object scenes that share similar objects to also be close in the representation space. However, a given number of objects can be composed into exponentially many possible scenes, making it challenging to learn scene representations in the Euclidean space. Therefore, the proposed method maps the scene representations to a hyperbolic space, which is better at handling combinatorial explosion, and proposes a hyperbolic loss. Experiments show that the hyperbolic loss leads to 1~2% improvement in downstream classification, detection, and segmentation tasks. It is also shown that the learned scene representation can be used to quantify label uncertainty and detect out-of-context objects without further training. - Strengths\n - SSL works well on images containing one dominant object, but has limitations on multi-object images. The paper tackles this limitation and is relevant to the community.\n - The proposed hyperbolic loss is quite novel and well motivated. It also leads to an interesting property of the representation that a larger norm indicates more object types in the image.\n - The paper is well written. It is easy for me to understand the high-level idea behind using the hyperbolic space although I am unfamiliar with the exact mathematical definitions.\n- Weaknesses\n - Empirical evaluation seems insufficient. As mentioned in the Related Work section, quite a few models have been proposed to improve SSL on multi-object datasets, but none of them are included as a baseline. As an example, ORL[1] achieves 59% top-1 accuracy on ImageNet-1k when pretrained on COCO, while the proposed method only achieves ~55%.\n - Comparison to MoCo-v2 seems unfair, because MoCo-v2 only receives the full image as input while the proposed method takes object regions.\n - The definitions in L105-111 do not seem to form a tree. Consider an image $s$ with three objects $a$, $b$, and $c$, and a region $r$ covering objects $a$ and $b$. Then $a$, $r$, and $s$ form a cycle, so it is not a tree.\n\n[1] Unsupervised Object-Level Representation Learning from Scene Images. (https://arxiv.org/pdf/2106.11952.pdf) Please see my main concerns listed in Weaknesses. Additionally, I have the following two minor questions:\n- I did not understand why the objects are the root nodes (rather than the scenes).\n- Is there an intuitive explanation why the norm of representation will be large when there are multiple objects? Limitations and potential negative societal impact have been addressed.", " This paper proposed a hyperbolic contrastive objective function (HCL) to formulate the object-centric scene hierarchy for self-supervised learning on scene images. The main motivation of the paper is that the hyperbolic space is more suitable to embed the hierarchical structure than\n Euclidean space. Using the ground truth or Selective search to obtain objects, this paper extends another branch on MoCo to constrain the similarity of scene crops and object crops in the hyperbolic space. The paper shows superior performance on downstream visual tasks when compared with its baseline method. HCL also shows interesting properties on label uncertainty quantification and out-of-context object detection. Strengths:\n1. The paper utilizes the hyperbolic space to formulate the scene-object relationship, which builds up another way to represent scene images (small norms represent objects and large norms represent scenes).\n2. The paper achieves better downstream tasks than its baseline.\n\nWeakness:\n1. The experimental results only contain the comparison with baseline. Several relevant papers [1,2], which focus on the problem of self-supervised learning on scene images and also use Selective Search to acquire objects, are not mentioned in the experimental section. \n2. The paper only trained HCL for 200 epochs, it is not clear whether the performance gain can be maintained when training for more epochs (800ep). \n\n\n[1] Xie, Jiahao, et al. \"Unsupervised object-level representation learning from scene images.\" Advances in Neural Information Processing Systems 34 (2021): 28864-28876.\n[2] Li, Zhaowen, et al. \"UniVIP: A Unified Framework for Self-Supervised Visual Pre-training.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022. 1. Train HCL for 800 epochs and compare HCL with ORL and other Selective Search-based methods. This result will be more important to support the claim of hyperbolic loss.\n2. The paper claims in Line 213 that \"HCL would improve more on the dataset with more objects per image\", which is not sound enough. On OpenImages, the paper only compares HCL w/ and w/o hyperbolic loss when using the ground truth bounding boxes (which can not be acquired during self-supervised learning). The authors should provide the performance of HCL/${L_{hyp}}$ with SS to support the claim.\n3. Is the additional hyperbolic loss time-consuming? Yes.", " The authors address the problem of contrastive representation learning of objects and scenes simultaneously. To this end, they employ the Poincaré embedding to model a hierarchy from simple (single object) towards more complex (multi object, scenes) images.\nIn the experiment it is shown that HCL improves over MoCo-V2 [1]. The method is trained on COCO (118,000 images) or OpenImages (212,000 images) for 200 epochs. Strengths:\n- The idea of using hyperbolic geometry in conjunction with contrastive learning is interesting and promising.\n- Results indicate the proposed method works: Quantitative improvements as well as representation norms correlating with number of labels.\n\nWeaknesses:\n- Performance gains of using hyperbolic loss are small and improvements might be due to using additional information, i.e. detections, instead of only the images.\n- Relevant baselines are missing from Table 1. For detection for example [3, 4] achieve similar performance without relying on detection labels for pre-training.\n- The claimed performance improvement is only shown over a weak baseline (MoCo-V2 on a small dataset). Performance in general does not seem competitive with current SSL models. For example, MoCo-V2 [1] achieves an accuracy of 67.5% when trained on ImageNet-1K for 200 epochs (71.1% after 800 epochs), the more recent DINO [2] even 75.3%. HCL achieves only an accuracy of 58.5% despite using the additional information of where objects are in an image. (This is of course difficult to compare due to using a different pre-training dataset, but a proper comparison to other SSL models would be needed here).\n- The used datasets are small for SSL. To show that this method is useful in practice, I'd like to see some scores on a more competitive benchmarks. E.g. by using a dataset of similar size to ImageNet.\n- Compared to other contrastive methods, HCL requires supervision. While selective search is proposed as a way to avoid reliance on ground truth, it decreases performance. \n\nMinor remarks:\n- \"...treated using the same lens\": This contradicts the claims of the next sentences\n- Fig. 4 should indicate standard deviations.\n- The precise task on the VOC dataset is unclear since there are multiple. I assume multi-label classification on Pascal VOC 2011 is meant but this should be explicitly stated.\n- L189: MoCO-V2 should be trained using the hyperparameters from [1] and not the ones that work best for HCL (i.e. learning rate etc). MoCo-V2 is trained using a cosine scheduler which was apparently not being used here.\n\n\nThe paper presents an interesting idea of applying contrastive learning on multi-image scenes using poincare embeddings and promising first results. However, the experiments fail to convince me. \nThere is a large gap between this method's and state-of-the-art performance in self-supervised representation learning, which raises concerns regarding the utility of the method.\n\n[1] Chen et al. Improved Baselines with Momentum Contrastive Learning\n[2] Caron et. al. Emerging Properties in Self-Supervised Vision Transformers\n[3] Wang et al. Dense Contrastive Learning for Self-Supervised Visual Pre-Training \n[4] Xiao et al. Region Similarity Representation Learning A more extensive comparison to other SSL methods would be necessary, especially to other methods that focus on object-level contrastive learning and/or that use object detection as additional information such as HCL. Limitations are briefly addressed. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 4, 4 ]

[ "e_lsy98jWb", "2dJRI1nNtSh", "TfOaOCTVgWM", "Xv5xBVStvD", "dYh_t4AhUb", "SwXPFbHFFd", "SwXPFbHFFd", "TfOaOCTVgWM", "Xv5xBVStvD", "Xv5xBVStvD", "nips_2022_QUyasQGv1Nl", "nips_2022_QUyasQGv1Nl", "nips_2022_QUyasQGv1Nl", "nips_2022_QUyasQGv1Nl" ]

[ "Iqv7b_vbV0s", "17WxtGrX02f", "lR-dLdnjlQx", "T9jEMgCUaPj", "hoYPOajmWoB", "T_7lFQLVOsn", "r9jEOhjCEe0", "-t4_W1NiIl9", "y__7ENcrDyX", "OjCy0h5dYLA", "ccs5Eihfwyj", "IvAE_8aqd3X" ]

[ "official_reviewer", "author", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for the revisions. I will increase the score.\n\n", " Thanks for your feedback. The range of training noise is: *vision-language nav.* ($0.19$ SPL), *image-goal nav.* ($0.50$ SPL), *audio-goal nav.* ($0.22$ SPL), *object-goal nav.* ($0.42$ SPL). Most of the numbers in Table 3 are beyond the range of noise. \n\nIn addition, to better address your concern and avoid misleading, we rephrased our statements related to the experimental results:\n\n- L17-19: We empirically demonstrate that, compared with learning each visual navigation task individually, our multitask agent achieves comparable or even better performance with reduced complexity.\n\n- L336-337: Compared with other task-specific competitors [2, 5, 6, 25], VIENNA achieves comparable results on *audio-goal nav.* and *object-goal nav.*, and performs better \non *image-goal nav.* and *vision-language nav.* tasks.\n\n- L347: This indicates that investigating inter-task relatedness may help to strengthen the generalizability of navigation agents.\n\n- L366-367: We compare this design against two variants in Table 4b, and find such a strategy is conducive to the performance.\n\n- L374-375: Several variants of multitask planner $f_{MTP}$ (*cf.* Eq. 9) are compared in Table 4d. The two-layer shared trunk design is adopted, due to its relatively better performance.\n\nThe main paper is updated, and the revised parts are highlighted in red.", " While the paper proposes a good benchmark, the experiment section includes various inaccurate or wrong claims that certainly need to be revised. I raised concerns about improvements being in the range of training noise. The rebuttal provided the standard deviation, but it turned out that the standard deviation was for one of the tasks (the VLN task) which was not mentioned in my initial review. \n\nI am going to lower the rating since the inaccurate statements in the experiments section need to be revised. I will be fine with acceptance if the revision is done.\n\n ", " Thank you authors for taking the time to provide further analysis and clarifications. The response has solved all my concerns. I agree with the authors that the proposed multimodal multitask embodied navigation is a promising direction. A multi-modal navigation agent deserves much more attention.", " Thanks for your feedback. The variance mentioned in our rebuttal is for the VLN task. \nThere are a number of factors that can influence the performance variance, such as task setting, \nnetwork architecture, learning algorithm, training iteration, batch size, success criterion, \nand so on. For instance, [1] focuses on point navigation, which is even not among our four navigation tasks. \nThe success threshold in point navigation is 0.2 m, and in our setting is 1.0 m. Thus our SPL is more tolerant of training variance. \nMoreover, our batch size is much larger than [1, 2]; our batch size is $4\\times32=128$ (see Table I of our supplementary document) \nwhile that of [1] is $6$. Note that large batch size will make training more stable. In addition, [1, 2] only trained for around 75M frames \nand [2] plots the variance at the same iterations of different training runs. However, we train our agents for around 180M frames, and \nreport the number of the best checkpoints from different training runs. After reaching convergence with enough training frames, the variance \nbetween the best checkpoints from different runs is small. Overall, directly comparing training statistics of different methods with different \ntask settings and hyperparameters, seems less informative. ", " Thanks for the response. My comments about the improvement being in the range of training noise are neither subjective nor unfair. They are actually objective and backed up by previous works. The range of training noise for these types of methods is quite large. Please refer to Table 1 in [1] and Figure 3 in [2] as examples. The variance reported in the rebuttal is surprisingly low compared to previous work (roughly an order of magnitude difference). I would like to ask the authors to explain how they managed to reduce training noise this much. \n\n[1] Wijmans et al., How to Train PointGoal Navigation Agents on a (Sample and Compute) Budget, 2020.\n\n[2] Weihs et al., AllenAct: A Framework for Embodied AI Research, 2020.\n", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n\n#### **Q1. Training noise (including \"The difference ... is within the range of training noise ($8.3$ vs $8.8$ for object goal nav. or $10.6$ vs $11.3$ for audio goal nav.).\", \"Statements such as L345\", \"Numbers in Tables 4b and 4d ...\").**\n\n**A1:** We had run the same experiments five times, under the same hyper-parameter setting (but used different random seeds that initiate the network parameters and dataset shuffling). We found the range of training noise is typically less than 0.2 SPL.\n\nThe SPL improvements ($8.3$ vs $8.8$, $0.5\\uparrow$, $10.6$ vs $11.3$, $0.7\\uparrow$) in ablation experiments are significant and constant. Prior works [7, 45, 46, 49, 91] report improvement within a similar range ($0.1\\sim0.7\\uparrow$) in the ablation studies. Moreover, for all the baselines involved in our experiment, we have tried our best to get the highest score and our method is not extensively tuned. The judgment of \"...are within the range of noise\" is subjective and unfair. \n\nFor statements such as L345: \"$\\text{VIENNA}_\\text{ST}$ suffers from relatively large performance drop\", here we report $14.4$ SR drop ($33.0$->$18.6$), while the SR drop for $\\text{VIENNA}_\\text{MT}$ is only $12.5$ ($35.0$->$22.5$). We believe such gap ($14.4$ -> $12.5$ SR) is clearly beyond the range of noise. \n\n---\n\n#### **Q2. Model selection.**\n\n**A2:** Thanks for your careful review. We train all models for around 180M frames. Similar to [25], we select the checkpoint for evaluation with the best SR on val_unseen. We will add the details in the final version.\n\n---\n\n#### **Q3. L226: what is \"epoch embedding\" ?**\n\n**A3:** Sorry for this confusion. $\\mu_{1:t}$ are temporal position encoding. As the Transformer is used to capture long-term dependencies over the historical observations (at different navigation epochs (decision steps) $t$) in the current navigation episode, temporal position encoding, as a standard module of Transformer, is needed here. Related statements will be improved. \n\n---\n\n#### **Q4. How is MDPPO different from DDPPO?**\n\n**A4:** The main differences are two-fold:\n1. MDPPO balances the training samples from different tasks.\n2. MDPPO first averages the gradients of task-specific heads in the corresponding task process group, and then broadcasts the gradients to other task process groups. While DDPPO always averages the gradients of all parameters across all processes.\n\n---\n\n#### **Q5. What are Navigation Error (NE) and Oracle success Rate (OR) ?**\n\n**A5:** These metrics are widely used in the field of navigation (please see [8, 25]). Navigation Error (NE) is the geodesic distance between the position where the agent stops and the target position. Oracle success Rate (OR) is the rate that the closest position to the target position along the navigation trajectory is inside the range of success. \n\n---\n\n#### **Q6. The sequence length for the Transformer is 100.** \n\n**A6:** Thanks for the careful review. To save the GPU memory, we preprocess all visual observations through the visual/depth encoder described in L305-307. We also cache the $e_{1:t-1}, e_{1:t-1}$, and $Q_{1:t-1}$ tokens. It makes the network only need the current observation rather than the whole observation sequence to infer the next action. In the training phase, we split up a batch to multiple GPUs and accumulate the gradients to update the parameters. We will add the details in the supplementary material.\n\n", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n\n#### **Q1. Dataset samples.**\n\n**A1:** Sorry for this confusion. In the supplementary, we have already provided some audio rendering samples (please see `audio_rendering.mp4`) and navigation results in some sample environments (please see `dataset_examples.mp4`) of our dataset. Moreover, our dataset is built upon Matterport3D environments, which are widely used in our field. To better address your concern, we update our supplementary material with a new demo video, `more_dataset_examples.mp4`. This new demo video shows two sample groundtruth navigation epochs for each navigation task. Our dataset shall be released.\n\n---\n\n#### **Q2. Just a new task including the input types from the four tasks.**\n\n**A2:** Here the key is that we introduce a multitask navigation setting, where the agent is taught to master four different navigation tasks. As we clarified in L27-31, the prior works concentrate on designing a specific method for a certain navigation task, which is contrary to natural thinking that the agent should be smart enough to execute different tasks involving varying modalities with different optimal policies. We only address the novelty of such a multitask setting. Mentioning our dataset contains four navigation tasks is just to clarify our task setting. Moreover, our VXN is not just created by including the input types from the four tasks. We standardized the settings of the four tasks and developed a real-time continuous biannual acoustic simulator to support audiovisual-rich environment rendering (L156-177).\n\n---\n\n#### **Q3. Sometimes utilizing more modality leads to a poor performance for some model.**\n\n**A3:** Based on our method, we have already provided some experiments regarding the impact of multimodal sensory. For example, in Table. 4(a), we have shown that RGB and Depth information are relatively less informative in *audio-goal nav.*, but they are crucial for *vision-language nav.*. And the integration of different modalities leads to relatively better performance (L360-363). We agree that \"Sometimes utilizing ... for **some model**\". However, conducting a large-scale study on different navigation models to investigate the influence of different modalities seems beyond the scope of this work. As a very early attempt toward multi-task navigation, our work comes with many open questions, including how to make better use of multimodal sensory information. It is impossible to solve all of them in a pioneering work. \n\n---\n\n#### **Q4. The proposed model with more inputs should at least outperform these models with less input information.**\n\n**A4:** Current SOTAs for different navigation tasks involve a lot of task-specific designs, such as map building, large-scale vision-language pre-training, global + local policy, neural graph planner, and different training strategies. The view of the input information is the only factor for the performance is too narrow. Requiring our model to beat all current task-specific SOTAs seems unfair. Moreover, in Table 3 (a-d), we have already provided extensive comparisons between multi-task methods and single-task methods, based on the same architectures (*i.e.*, Seq2Seq and our VIENNA), as well as other navigation agents [5, 6, 2, 25]. \n\n---\n\n#### **Q5. Suggested citations.**\n\n**A5:** Thanks for your suggestion. We are happy to cite these papers in our final version. \n", " We thank you for your time and valuable comments. Below we answer the main concerns raised in the review and would be happy to provide further clarification if suitable.\n\n#### **Q1. What kinds of knowledge can be reused and how to reuse this knowledge?** \n\n**A1:** Thanks for your careful review. Yes, in *image-goal nav.*, $\\tau_{A}$ does not contain any information about what kind of images should be found. However, as $\\tau_{A}$ is trained during *audio-goal nav.*, it embeds certain knowledge that is specific for *audio-goal nav.*, *e.g.*, $\\tau_{A}$ could respond to certain audio signals that are crucial for navigation. Therefore, during *image-goal nav.*, $\\tau_{A}$ can help the agent to notice and better utilize those informative audio signals. In the supplementary, Fig. II and Fig. III provide some visualization results, where the attention maps over the visual/audio observation queried by different task embeddings are given. As seen in Fig. II, the task embeddings $\\tau_{I,T,L}$ indeed attend to some crucial visual landmarks (L84-88), which are essential for the success of navigation. $\\tau_{A}$ tends to respond to acoustic pressure changes which typically happen at the connection areas between rooms. Thus audio signals attended by $\\tau_{A}$ can reveal the room layout, and hence helps the agent to better understand the surrounding environment. In summary, the task embeddings $\\tau_{I,T,L,A}$ encode task-specific knowledge which can make the agent aware of different navigation-related information from RGBD and audio perception. \n\n---\n\n#### **Q2. Explain the meaning and benefits of the vectors $\\mu_{1:t}$ in section 4.1.**\n\n**A2:** Sorry for this confusion. $\\mu_{1:t}$ are temporal position encoding. As the Transformer is used to capture long-term dependencies over the historical observations (at different navigation epochs (decision steps) $t$) in the current navigation episode, temporal position encoding, as a standard module of Transformer, is needed here. Related statements will be improved. \n\n---\n\n#### **Q3. It would be an interesting future research direction for considering different kinds of rewards for different tasks.**\n\n**A3:** We totally agree. Currently, for the sake of simplicity, we directly adopt the same reward function for the four navigation tasks. But it is indeed interesting and necessary to investigate more task-specific reward designs and some other training objectives which are aware of the multitask and multimodal nature of VXN. We will discuss this point in the final version. Overall, we feel the proposed multimodal multitask embodied navigation is a promising direction, which also comes with many intriguing questions. \n", " This paper proposes VXN, a large-scale 3D indoor dataset for multimodal, multitask navigation in continuous and audiovisual complex environments. It can conduct four embodied navigation tasks, including image-goal navigation, audio-goal navigation, object-goal navigation, and vision-language navigation. Moreover, the authors devise a framework named VIENNA to simultaneously learn four navigation tasks within a single unified parsing-and-query scheme. Experiments show that the VIENNA outperforms the baselines among four navigation tasks. # Strengths\n1. The authors are the first to innovatively combine four navigation tasks and propose a dataset that can simultaneously adopt them.\n2. The authors propose an agent that can solve the four navigation tasks using one single model without switching among different models and the model size is considerable.\n3. The proposed VIENNA agent leverages multisensory input for navigation. Input in different modalities provides supplementary information. This setting is more practical in the real world, where robots use multi-modal information for finishing their tasks.\n4. The proposed methods outperform the existing SOTA in every single task by leveraging multisensory input and multi-task learning. Also, the authors have conducted a thoughtful ablation study to evaluate the effectiveness of each component and claim.\n\n# Weaknesses\n1. My main concerns are what kinds of knowledge can be reused and how to reuse this knowledge? In Section 4.3, the authors claim that the knowledge re-usage is conducted by \\tau. However, in image-goal navigation, \\tau_A does not contain any information about what kind of images should be found. So how can \\tau_A help to retrieve target image-related audio for navigation? More explanations are needed.\n2. Some details are missing. Please explain the meaning and benefits of the vectors \\mu_{1:t} in section 4.1. \n3. VIENNA adopts the same reward function for the four navigation tasks. However, the reward function design will be different for different navigation tasks. For example, in object-goal navigation, a positive reward should be given when an object with goal-related semantics is found. It would be an interesting future research direction for considering different kinds of rewards for different tasks.\n My main concerns are what kinds of knowledge can be reused and how to reuse this knowledge? Please explain more about this question. Yes, the authors adequately addressed the limitations and potential negative social impact of their work.", " This paper proposed a new visual navigation benchmark that combines containing information from different modalities. Then the authors propose a modular model for the proposed benchmark including Episodic Encoder to encode the history, Target Parser to interpret the target, and a planner to predict the navigation action. Strengths:\n\n1. The proposed task itself is a timely movement in navigation area. With the advancement in individual navigation task, it is natural to consider tasks with input of more modalities. \n\n2. Considering the complexity of the task, the proposed modular model is a great baseline. The modular structure is designed via analyzing the task component. The architecture itself also shows some intuition on the problem. For example, the author shows a good demo about how to handle input from different modalities.\n\n3. Both the paper and the appendix are detailed and well-written.\n\nWeakness: \n\n1. The main contribution is a proposed dataset, but it does not provide the full dataset or a sample in the supplemental material.\n\n2. The authors claim the task includes four navigation tasks. Actually, it is just a new task including the input types from the four tasks.\n\n3. One serious issue in navigation task is that sometimes utilizing more modality leads to a poor performance for some model. Therefore I think it is necessary to ablate different modality input and test the performance. For example, check the paper mentioned in Section 4.1.2 of [1]. There are limited ablation study in section 5.2. \n\n4. The paper should include more SOTA models on the four navigation tasks as baselines. The proposed model with more inputs should at least outperform these models with less input information. \n\n\nSuggested citation:\n[1] A survey on visual navigation for artificial agents with deep reinforcement learning\n[2] Vision-and-Language Navigation: A Survey of Tasks, Methods, and Future Directions\n[3] Core Challenges of Social Robot Navigation: A Survey\n See Weakness\n\n Yes, they discussed that in the appendix.", " The paper proposes a unified model for 4 popular navigation tasks (image-goal navigation, object-goal navigation, audio-goal navigation, vision-language navigation). A Transformer based architecture is utilized to combine these 4 tasks. The target signal (image, audio, etc.) is basically used as the query. The paper also proposes a dataset that supports all 4 tasks. The experiment section provides results for single-task and multi-task settings and provides comparisons with task-specific baselines. **Strengths:**\n- The paper takes a step towards unified models for Embodied AI. This is an important direction since agents should be able to perform various tasks simultaneously.\n\n- The proposed dataset, which supports multiple types of navigation, will be useful for the community.\n\n**Weaknesses:**\n- The weakest part of the paper is its experiment section. The conclusion that are drawn from the experiments are not accurate.\n\n&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; (1) The difference between most of the single-task and multi-task results is within the range of training noise (8.3 vs 8.8 for object goal navigation or 10.6 vs 11.3 for audio goal navigation). The results of these types of training algorithms vary greatly depending on the initialization, sampling and various other factors. It is great that the multi-task model works as well as the single-task models. However, claims such as \"VIENNA also beats other task-specific competitors\" are not correct. \n\n&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; (2) Statements such as L345: \"VIENNA_ST suffers from relatively large performance\" are not accurate. If the training noise is considered the drop is the same for single-task and multi-task settings. \n\n&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; (3) Numbers in Tables 4b and 4d are within the range of noise. No conclusion can be drawn from these tables. Statements such as \"such strategy greatly boosts the performance\" are not accurate. \n\n&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; I will consider raising the score if these statements are corrected in the revision.\n\n- It is not clear how models are chosen for evaluation. Is it the model that achieves the best performance on the validation set, trained for a specific number of epoch, or other criteria? \n\n\n - L226: what is \"epoch embedding\" ?\n\n\n- How is MDPPO different from DDPPO? Does it just balance the task samples? \n\n\n- What are Navigation Error (NE) and Oracle success Rate (OR) ?\n\n\n- The sequence length for the Transformer is 100. That means there is a huge memory consumption, and the sequence might not fit into a GPU. Is there any specific trick used ? Yes, the limitations are discussed adequately. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 4, 5 ]

[ "17WxtGrX02f", "lR-dLdnjlQx", "hoYPOajmWoB", "y__7ENcrDyX", "T_7lFQLVOsn", "r9jEOhjCEe0", "IvAE_8aqd3X", "ccs5Eihfwyj", "OjCy0h5dYLA", "nips_2022_ZMrZ5SC2G3_", "nips_2022_ZMrZ5SC2G3_", "nips_2022_ZMrZ5SC2G3_" ]

[ "zL7DDChiGN", "pFxb30vbaDO", "8BpEvd9mV3G", "TM61FMGNgP", "JGmNNuwTwZ7", "7n_HnkA1apf", "h7bzZFIW7V9", "rCysc4n2BnK", "XD09fisWSOf", "9LLTASey98" ]

[ "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you again for your valuable comments. As the discussion period is closing soon, could you please take a look at our response and reevaluate the submission? Please let us know if there is any further question about the submission. We look forward to hearing from you.", " Given the upcoming OpenReview deadline, we were kindly wondering whether our response and new experiments have addressed your concerns, and we would greatly appreciate a reply.", " We thank the reviewer for their constructive feedback and insightful ideas for further improvement. We hope that our response will address your concerns.\n\n\n**wrt suggested baselines.** We would like to kindly disagree with the statements provided by the reviewer. The listed references are for very different settings. Our goal is to tackle federated training for participants with heterogeneous capacity and produce generic global inference models, a very practical scenario described in HeteroFL and FjORD. In this setting, the capacity of each device is collectively constrained by **memory**, **computation budget** and **communication overhead**, which accords with real-world practice, e.g., deployment over multi-generation devices. We model system heterogeneity through rescaling network width by $p$, which directly reduces the communication and computational overhead by $p^2$ and memory consumption by $p$.\n\n**LotteryFL** and **FedMask** focus on a very different problem setting: **1.** as discussed in Sec. 1 of both papers, they aim to learn **personalized** models, a fundamentally different task not aiming for producing global models. **2.** They cannot tackle system heterogeneity. As described in Sec 3.1 in LotteryFL and Sec 3.4 in FedMask, they require all clients to **run the full model** as the initial training stage, indicating a uniform device capacity is required. Hence, their performance is incomparable with us. We have added these papers to the related work.\n\n**FedHM** cannot handle the described heterogeneity setting either, as it lacks the ability to scale memory consumption. As described in Sec 2.1 & 2.2 of FedHM, it factorizes a kernel of shape $m\\times n$ (where $m$ and $n$ are input and output channels respectively) into two tensors of shape $m\\times r$ and $r\\times n$. As such, the network still has the same width $n$ after factorization, indicating it is not able to vary the peak memory consumption (the large intermediate feature maps and their associated gradient computation are the bottlenecks). This makes direct comparison unfair due to unaligned device capacity requirements. In addition, FedHM is a pre-print work without code publicly available to reproduce its results. \n\n**wrt novelty and advantages over previous low-rank methods.** Unlike previous methods, our approach **never performs explicit low-rank factorization** but instead only uses this notion **conceptually**. Our method significantly differs from previous works in terms of **formulation**, **training strategy** and **problem scope**. In our case, the low-rank nature of deep models serves only as a theoretical foundation for using a unified neural basis to express knowledge and compose heterogeneous models. As described in Sec. 2.2 & 2.4, FLANC directly learns the basis and coefficients from scratch rather than factorizes them from existing kernels. \n\nThe proposed neural composition has several advantages compared to previous methods performing real low-rank decomposition: 1. it avoids approximation errors of factorization, which will harm the performance. Meanwhile, it can be applied to every layer for better complexity scaling. As discussed in Sec. 2.2 of FedHM, factorization inevitably introduces **an approximation error** that will be accumulated and propagated to subsequent layers. This makes their approach only applicable to the last several layers and much less practical for real-world deployment, as early layers can also become computational and memory bottlenecks, for example, when dealing with large images. 2. our method can handle system heterogeneity by constructing client models with different widths, whereas factorization methods cannot achieve the same. As discussed, factorization requires the resulting tensors to have aligned input and output dimensions (e.g., $m\\times r$ and $r\\times n$) with the original kernel (e.g., $m \\times n$), which cannot change run-time width to adjust memory consumption. FedDLR and FedPara further assume a uniform processing capacity over devices. These make previous approaches infeasible for dealing with system heterogeneity. We have included this discussion in the supplementary file.", " **wrt complexity analysis.** Computation complexity is discussed in detail and compared in Sec. 2 (Sec. 3 for the updated version) and Table 2 of the supplementary material. For communication complexity, our method expresses a kernel of shape $k^{2} \\times Sp \\times Tp$ (with rescale ratio $p$) as a neural basis $V_{\\text{share}}$ of shape ${k^{2} \\times R_{1} \\times R_{2}}$ and coefficients $U_{p}$ of shape ${R_{2} \\times Sp/R_{1} \\times Tp}$. Thus, the total parameters required by our approach is ${k^{2}R_{1}R_{2}+(R_{2}/R_{1})STp^{2}}$. By properly setting the values of $R_{1}$ and $R_{2}$, we can achieve an on-par or better efficiency compared to existing solutions. We have added further detailed analysis in the supplementary file. An empirical comparison is provided in the last two columns of Table 1 in the original manuscript. We changed the column name to \"communication cost\" to make it more clear.\n\nFor the convergence analysis, we have included an empirical study in Figure 1 of the supplementary file. One can see that our approach has a faster/on-par convergence speed and achieve better accuracy compared to previous solutions. We agree that theoretical analysis will be definitely helpful. However, we would like to mention that the theoretical convergence analysis is rather onerous in our setting because our method involves optimizing heterogeneous architectures (width), while most previous FL algorithms and theorems only consider shape-aligned models. For the same reason, HeteroFL [16] and FjORD [17] are also not able to conduct such analysis. \n\n**wrt more evidence on knowledge sharing.** As we compose individual weight fragments as linear combinations of the neural basis, it indeed has a similar effect as pruning if all values in the corresponding coefficients (a column of $U_{p}$) are close to zero. To show that our method enables better knowledge sharing, we report the statistics of the mean absolute value for each column in the coefficient matrix. As illustrated in Figure 2 of the supplementary file, values are not small and zero-centered, indicating knowledge stored in the basis is well-shared across models.\n\n**wrt unique complexity levels.** To answer this question, we consider a simulated experiment on CIFAR10 where (1). we double the number of complexity levels (i.e. $p\\in \\\\{ 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1 \\\\}$), and (2). each participant in a communication round has a unique complexity level. We report the results in Figure 3 of the supplement file. One can see that our approach can still stably outperforms existing solutions. While it is difficult to conduct an experiment considering a large scale of devices with distinct complexity levels (because, for most ratio $p$, rescale model width will not result in integer channel numbers), we speculate it would be challenging since the capacity-specific coefficient (only shared among one device) will be biased towards its own data. To this end, the introduced pre-clustering strategy, which quantizes complexity levels, is important to stabilize the training. \n\n", " **wrt suggestions on limitations.** Thanks for your helpful suggestions! We discuss the limitations on the mentioned aspects below and have added them to the manuscript accordingly. \n\n- In our experiments, we demonstrated that our approach can enable federated training over at least eight capacity groups, which covers a wide range of devices in practice (from 1.5\\% to 100\\% in terms of computational and communication overheads and 12.5\\% to 100\\% in terms of memory). However, we acknowledge that it will be challenging to handle many capacity groups at very fine-grained levels, especially when the group size is further limited. In this case, the learned coefficients will be potentially biased towards the corresponding particular group of devices. The provided pre-clustering strategy is required for quantizing complexity levels. \n\n- Without defense techniques, privacy leakage is known to be a common challenge for almost all FL methods. Different from existing algorithms which will disclose global statistics over the entire user group, our method will reveal statistics with respect to the specific capacity groups. However, we do believe our approach offers better privacy protection by design, as information leakage cannot happen without the simultaneous leakage of both neural basis and coefficients. Advanced techniques are also required to combine and decode the information. Further combining our approach with advanced privacy-preserving techniques, such as differential privacy and homomorphic encryption, will be an interesting direction for future exploration.\n\n- When the resource constraint changes within a single communication round, the device may not necessarily be able to support the current model and the server has to either exclude or drop those \"stragglers\" in case of timeout. One intuitive way to tackle this situation is to simply send all coefficients to the clients and let the clients switch to a suitable model upon its resource allocation, but meanwhile, this induces higher communication costs. It might be also interesting to improve the straggler-resilience of our approach. We leave this extension for future work.", " Thanks very much for your valuable comments. We are glad that you recognize the significance of the topic, broad applicability and promising results of the method, and good writing of this paper. We address the concerns in the following text and have changed the manuscript accordingly.\n\n**wrt communication overhead.** The communication overhead is reported as \"model size'' in the last two columns of Table 1. We have changed the column name to \"communication cost'' to avoid confusion. One can see that our approach can achieve better overall efficiency compared to previous solutions. We also add a detailed complexity analysis in the supplementary file. \n\n**wrt training rounds.** We included a discussion on training rounds in the supplementary material. As shown in Figure 1, our approach has a faster/comparable convergence speed and achieves better accuracy compared to previous solutions.\n\n**wrt experimental results with error bar.** As explained in Checklist 3(c), it is computationally expensive to report error bars for all experiments given a limited time frame because our evaluations involve training 192 individual models. We do try to minimize random effects by fixing all seeds and using [PyTorch deterministic algorithms](https://pytorch.org/docs/stable/generated/torch.use_deterministic_algorithms.html#torch.use_deterministic_algorithms) for a fair comparison. However, we agree that the multi-run experiment will make our results more convincing. Therefore, we conduct 5 times of experiments with different random seeds on CIFAR10 and measure the variance. The corresponding results are reported in Figure 4 of the supplementary file, which shows our method can consistently outperform existing solutions.\n\n", " We thank the reviewer for their helpful comments and valuable time spent reviewing our manuscript. We are glad that the reviewer acknowledges the contribution, effectiveness and extensive experiments of this paper. We address the concerns below and have also updated our manuscript accordingly.\n\n**wrt error bars.** We agree that adding error bars will indeed make our quantitative evaluations more convincing. To this end, we conduct five experiments with different random seeds on CIFAR10 and report the results in Figure 4 of the supplementary file. These results show our method can stably outperform existing solutions, and the performance improvement is beyond the error range.\n\n**wrt real devices.** As discussed in the supplementary file (original version, lines 76-81), due to the lack of mature software support, we did not benchmark the performance on real devices. We instead abstract the resource constraints as model width for simplicity and demonstration purposes. Constructing an accurate mapping from hardware specifications to the ratio $p$ requires solving engineering challenges and we leave it for future work. However, it is possible to roughly map real devices to complexity level $p$ based on the GPU memory capacity. We include some examples of popular GPU/device types in the following:\n|Device type | Memory (G) | ratio $p$ | \n|---|---|---|\n| RTX 3090 | 24 | 1.0 |\n| Nvidia V100 | 16 | 1.0 |\n|RTX 3080 | 10 | 1.0 | \n|Radeon RX 580, RTX 3070Ti, RTX 3060Ti, RTX 2070 |8 | 0.75 | \n|Arc A380, RTX 2060 | 6| 0.5|\n|GTX 1060 |6|0.5|\n|GTX 970, IPhone 13 | 4| 0.25|\n|Quadro K4000, IPhone 8 Plus |3|0.25|\nby supposing running a full model with 10GB memory requirement. We have included this discussion in the supplementary file. We would also like to mention some public benchmarking results (e.g. https://ai-benchmark.com/ranking_deeplearning_detailed.html) for real deployment.", " Practical federated learning (FL) needs to handle heterogenous resource constraints among participants. Existing solutions mostly rely on pruning a global model in each client, which would cause uneven contributions to the global model weights among different clients. The paper proposes a mechanism that factorizes the global model weights into two low-rank tensors, where one of the tensors is unified across all the clients (called neural basis) and the other tensor varies according to clients’ resource. The paper also proposes a regularization term to encourage the basis vectors to be orthogonal with unit term. The evaluation shows the proposed mechanism outperforms two existing solutions, HeteroFL and FjORD. Strengths\n-------------\n1. The paper proposes a reasonable solution to an important problem in FL.\n2. The paper proposes a mechanism that generalizes pruning-based solutions to this problem.\n3. The proposed regularization term is interesting.\n\nWeaknesses\n----------------\n1. The paper misses important baselines in this area. Specifically, the paper should also compare its solution against LotteryFL (Li et al., 2020), FedHM (Yao et al., 2021), and FedMask (Li et al., 2021). These three solutions aim to address the same problem, and they report better accuracy than the paper. \n2. The novelty is incremental. The idea of using low-rank factorization to address system heterogeneity has been proposed by FedHM (Yao et al., 2021). The general idea of using low-rank factorization for FL was proposed by FedDLR (Qiao et al., 2021) and FedPara [47]. While the detail of factorization might be different, it is unclear if the proposed factorization technique is better than other existing ones.\n3. There is no analysis on computation and communication complexity. Similarly, there is no convergence analysis. The paper should provide an analysis of the proposed mechanism, and it would be much better to do the same against related solutions in this space.\n 1. Can you provide more evidence to support the claim that the shared neural basis enables more knowledge sharing than pruning among clients? If the values in the coefficient matrix are small, isn’t it effectively similar to pruning?\n2. How will the proposed method work if each device has a unique complexity level? Will the training still converge?\n The paper does not provide meaningful discussions on its limitations, and it would be good to see the discussion on the following aspects:\n1. How will the proposed mechanism work with fine-grained complexity levels?\n2. What are the privacy implications of sharing the coefficient matrices?\n3. What if the resource constraint changes within a communication round (e.g., other applications running)?\n", " This paper presents the design of All-In-One Neural Composition, which can formulate networks at different complexities with one unified neural basis that's shared among clients. FL systems have suffered from the problem of system heterogeneity where the service providers would either sacrifice model capacity or data accessibility. This paper provides the FLANC framework that provides systematic support to train complexity adjustable neural networks and evaluated on a wide range of statistical data heterogeneity and system heterogeneity. Strength: \n1. Proposed a runtime method to construct the compressed model instead of applying after the training process compared to other low-rank techniques.\n2. Conducted extensive experiments to show the effectiveness of the proposed method. \n\nWeakness:\n1. Didn't include error bars in the evaluation results. The results reported may not be statistically confident without any error bars. The authors could add randomness experiments on some small scale experiments. 1. In the evaluation section, the authors varied the $p$ to simulate heterogeneous systems. It's good to also include some real cases including the exact CPU/GPU that might result in the different $p$ (i.e. the limitations of computation power on each device to result in the limitation on model size). Yes", " This paper presents FLANC, a model decomposition method for the heterogeneous devices in Federated Learning (FL). The basic idea is to change the model size/complexity by varying the ratio of channels. Strengths\n1.Better supporting of heterogeneous devices (e.g., IoT and mobiles) is an important research topic in FL.\n2.FLANC is generally applicable to other models and datasets. \n3.FLANC shows promising results compared to HeteroFL and FjORD.\n4.This paper is well-written and easy to follow. \n\nWeaknesses\n1.Only the metric of accuracy is evaluated. It is better to consider other important aspects of FL, e.g., communication overheads. \n2.Evaluation results are from one-run experiment only, which is less convincing. How does FLANC perform with regards to other FL aspects such as training rounds and communication overheads? None" ]

[ -1, -1, -1, -1, -1, -1, -1, 5, 6, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, 4, 2, 2 ]

[ "rCysc4n2BnK", "rCysc4n2BnK", "rCysc4n2BnK", "rCysc4n2BnK", "rCysc4n2BnK", "9LLTASey98", "XD09fisWSOf", "nips_2022_wfel7CjOYk", "nips_2022_wfel7CjOYk", "nips_2022_wfel7CjOYk" ]

[ "p6enO84TBFX", "0lAQd8EJE1T", "fgznnBgP7cX", "yaByflM5XZB", "BwPgyctBuXE", "MbelBBlkyt4", "w5bHfYptqB", "SJjCG9ZvYwq", "vyQLyeX7ITA" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks again for your time and your constructive criticism!", " Thank you for your responses, especially the clarification regarding pruning algorithms. I appreciate the addition of post-pruning results in the final version, as well as the EC2 results added in the supplement. Given that my main concern was these comparisons, I have increased my score to 7.", " **TO ALL REFEREES**\n\nWe updated in OpenReview the file corresponding to the full paper (body+ supplementary material). The 13 first pages correspond to the body of our submission. The only difference between this new file and the previous one (original submission) is\nthe addition of section E.7 (pages 41-43). \n\nThis section reports a comparison between our method and EC2, a method to optimize the average depth from [*Near-optimal bayesian active learning with noisy observations*, Golovin et al, NIPS 2010]; this comparison was suggested by the third referee (code Bn48) \n", " Thank you for your comments. We are happy that you found our novel interpretability metric interesting and useful. We also thank you for the list of pointers to additional literature that we will definitely take into consideration when preparing the final version. \nBelow, we address the issues raised in your review.\n\n**QUESTIONS:**\n\n**Why is there no comparison between the proposed algorithm and algorithms from the literature that optimize depth? Given the demonstrated compatibility of small depth and small explanation size, this seems like a relevant baseline.**\n\nReply: We assume that you refer to the algorithms proposed in the papers cited in (Lines 96-106). We note that most of these papers do not present experiments, they are essentially purely theoretical.\n\nThe main reason why we did not make this comparison is that we did not believe that a raw implementation of the algorithms in these papers would lead to competitive results with CART (or another standard algorithm) in terms of accuracy. One reason for our belief is that although our algorithm, without the use of the FactorExpl (setting it to 0), has an optimal approximation guarantee (assuming P != NP) with respect to the minimization of the depth, its accuracy in this case (FactorExpl=0) is low. Indeed, as shown in the leftmost graph of Figure 2 its accuracy is about 8 points on average lower than the average accuracy achieved when FactorExpl is close to 1. We believe that the same poor accuracy would be seen with the raw implementation of the algorithms proposed in the literature. \n\nSo in order to have fairer comparisons, in the theoretical part, we are comparing our algorithm with the algorithms that minimize the depth in terms of theoretical bounds, and on the practical side, we compare our algorithm with CART, a standard algorithm for building decision trees with good accuracy.\n\nThat said, following your suggestion, we have implemented one of the methods that optimize the average depth, the EC2 algorithm from [*Near-optimal bayesian active learning with noisy observations*, Golovin et al., NIPS 2010]. When tested on the same datasets we used for our experimental analysis, it achieved average accuracy equal to 76.6% while CART and SER-DT (our algorithm) achieved more than 82%, as shown in the last line of Table 1. Moreover, in terms of average explanation size EC2 achieves 3.68 while SER-DT achieves 2.93 and CART 3.97. Finally, in terms of average depth EC2 achieves 4.62 while SER-DT achieves 4.31 and CART 4.70. \nIn summary, SER-DT performs much better than EC2 on all metrics. \n\nWe updated the supplementary material (Section E.7, pages 41-43) to include Tables 9 and 10 covering this experiment. \n\n**What is the significance of the example weights in the problem definition? Most commonly, we consider unweighted prediction problems, which are equivalent to using constant weights. The theorem as given allows us to choose these constant weights arbitrarily small, in effect letting the log n term vanish. This seems counterintuitive.**\n\nReply: The inclusion of weights is very common in the literature about building optimal decision trees which is referred to in Lines 96-106. In terms of interpretability, this flexibility may be interesting since it allows to prioritize the explanation of some classes by assigning large weight to the examples in the chosen classes.\n\nRegarding the theoretical results, more precisely Theorem 1, notice that the weights are only taken into account for the average depth/explanation size, in which case the additive log term in our result is multiplied by the sum of the weights. So this makes both bounds in Theorem 1 actually invariant to rescaling the weights (and the same is true for the multiplicative guarantee of Observation 1). \n\n**OTHER ISSUES**\n\n**The presented algorithm is simple yet shown theoretically and practically to achieve its goal. It would be useful though to discuss why the proposed splitting criterion based on reducing the number of discrepancy pairs leads to this result, as this as well as the other steps of the algorithm do not seem to directly relate to explanation size.**\n\nReply: We will add this discussion to the final version. \n\n**However, there are some missing implicit definitions and assumptions. Most importantly, the underlying problem definition seems to assume that the resulting trees have to perfectly classify the given training data**.\n\nReply. Indeed, on lines 125 and 126 (in the section describing the theoretical model) we explicitly say that we consider the exact classification model, namely the case where the decision tree must correctly classify all the objects in the instance, i.e. each object is required to reach some \nleaf associated to its correct class. We will nonetheless emphasize better this choice of the model in the final version of the paper. \n\n", " Thank you for your comments. We are happy that you appreciated the topic, the novel metric, and the theoretical results. \nBelow, we address the issues raised in your review.\n\n**QUESTIONS**\n\n**Why is there such high variance in accuracy results (Table 1) between SER-DT and CART? Why is the reported accuracy is higher for SER-DT than CART for a number of datasets (e.g. dry bean, eeg eye estate)? This seems to imply that regularizing for explanation length actually increases performance.**\n\nReply: We believe that this variance (including better results for some datasets) is an intrinsic characteristic of decision trees induction rather than a weakness of our method/experiments. In fact, it is well documented in the literature that decision trees may be very sensitive to (small) perturbations in the training set and we understand that they are also (considerably) sensitive to the choice of the splitting criterion. For instance, by replacing the Gini criterion with the Entropy criterion in CART, as we did in Table 8 (p. 34 of suppl. Material), we observe the same behavior that you mentioned in terms of variance: for 7 out of 20 datasets there is a non-negligible variance (absolute difference larger than 1%) between CART with Gini (Table 8) and CART with Entropy (Table 1). \n\nOur gains in accuracy in some datasets are indeed interesting as you pointed out and might show some gain due to the regularization effect. However, the main conclusion that we draw from our experiments is that SER-DT is much better in terms of explainability (measured by explanation size and avg depth) and competitive in terms of accuracy.\n\n**How was FactorExpl=0.97 chosen for the experiments? Are there any guidelines for selecting this parameter in practice?**\n\nReply: The parameter FactorExpl can be used to trade off accuracy and explainability: a larger value for FactorExpl makes the algorithm favor more accurate predictions while reducing FactorExpl leads to trees that are easier to interpret (smaller explanation size). In general, the best choice depends on the user's goal and application. A user might also create a utility function that trades-off accuracy and interpretability and apply a grid search on a validation set to find a value for FactorExpl that optimizes such function.\n\nThat said, our approach was to use the corpus of 20 datasets to estimate a possible default value for FactorExpl when employing our method. Based on Figure 2, and the experiments reported in Section E.2 (Suppl. Material, p. 31), where several values of FactorExpl are tested, we conclude that values in the range [0.95,0.99] provide significative gains in terms of interpretability while incurring small or no loss in terms of average accuracy. Thus, we recommend using 0.97 as a default value.\n\n**OTHER ISSUES**\n\n**Comparisons with Pruning algorithms. While the experiments include comparisons with CART, the paper could be improved by including comparisons with methods that reduce tree complexity, such as pruning.**\n\nReply: Thanks for raising this issue, which also allows us to elaborate some more on our empirical study.\nPlease, note that our experiments already include a pre-pruning strategy, consisting in limiting the depth of the tree (which we bound to 6)\n\nIn terms of post-pruning strategies, we understand that a standard one consists of allowing trees of unlimited depth/size and then keep removing leaves according to some criterion that takes into account the model complexity and mainly the expected gain in accuracy (e.g. Reduced Error Pruning). The critical point is how to control the maximum depth, which is a key parameter in view of interpretability. In fact, from our experiments in the appendix (Table 6 and 7, pp. 32 and 33) one sees that without the bound on the height, the resulting trees have a maximum depth above 20 and an average depth above 10. Since these trees have, in general, higher accuracy ( explainability has its price) with respect to the ones obtained upper bounding the maximum depth (Table 1, section 6) it appears unlikely that pos-pruning will significantly reduce the depth.\n\nAnother possibility is to limit the depth of the tree, as we did in Table 1 of Section 6, and then apply post-pruning to the resulting trees. We are planning to add this experiment to the final version. That said, based on our experiments with unlimited depth, we are not very optimistic that this strategy will significantly improve the explainability for both CART and SER-DT, while maintaining and/or improving the accuracy. Moreover, the post-pruning makes the method a bit more complex (eg. the necessity of a validation set and/or more hyperparameters). In any effect, post-pruning is a good attempt and it is worth trying! \n\n**Error bars and/or significance testing in Table 1 would be helpful**\n\nReply: On page 35 of suppl. material, we present boxplots for the experiments in Table 1. \nWe will emphasize it in the body of the paper.\n", " Thank you for your comments. We are happy that you appreciated the topic and the novel metric that we introduced. \nBelow, we address the issues raised in your review.\n\n**ISSUES**,\n\n**The numerical results in Section 6 are not very convincing in the performance comparison**\n\nReply: We do not see why the numerical results are not convincing. In Table 1, for 12 out of the 20 datasets, SER-DT is at least as good as CART in terms of testing accuracy while CART is at least as good as ours in 11 datasets. Moreover, the average accuracy of our method is actually slightly larger than that of CART and the largest difference in accuracy is in our favor (87.4% for our algorithm vs 80.1% for CART on the Sensorless dataset).\nHowever, In terms of explanation size our algorithm gives a very significant (around 25%) average reduction compared to CART.\n\nWhen FactorExpl is set to 0.99 (see Table 5 of suppl. material, page 32) the accuracy of our algorithm matches or outperforms that of CART (results on Table 1) in 15 out of the 20 datasets; in the 5 datasets where CART wins, its advantage is at most 0.3% on 4 datasets (so negligible), and 2% on only 1 dataset. Even with this stricter setting of parameter, the explanation size of our algorithm is better or equal to that of CART in all but one dataset, and again provide significant improvement (e.g. avg explanation size 1.94 vs 4.29f or Default, and 1,89 vs 4,30 for Poker). \n\nWe believe that we provide strong evidence that our method is competitive in terms of accuracy while yielding a significant advantage in terms of explainability.\n\n**This paper presents some theoretical bounds in relating explanation size to tree depth in average and worst cases. But it is not clear how tight these bounds are. (They seem to be rather loose bounds).**\n\nReply: As explained below, replying to one of your questions, our worst-case bound of Theorem 1 is tight. Moreover, both bounds in Observation 1 and in Theorem 3 are also tight assuming P ≠ NP (see discussion in lines 249-252).\n\n**QUESTIONS**\n\n**For the example in Section 6, FactorExpl is set to be 0.97. In general, how this hyperparameter should be tuned?**\n\nReply: The parameter FactorExpl can be used to trade-off accuracy and explainability: a larger value for FactorExpl makes the algorithm favor more accurate predictions while reducing FactorExpl leads to trees that are easier to interpret (smaller explanation size). In general, the best choice depends on the user's goal and application. A user might also create a utility function that trades-off accuracy and interpretability and apply a grid search on a validation set to find a value for FactorExpl that optimizes such function.\n\nThat said, our approach was to use the corpus of 20 datasets to estimate a possible default value for FactorExpl when employing our method. Based on Figure 2, and the experiments reported in Section E.2 (Suppl, Material, page 31), where several values of FactorExpl are tested, we conclude that values in the range [0.95,0.99] provide significative gains in terms of interpretability while incurring small or no loss in terms of average accuracy. Thus, we recommend using 0.97 as a default value.\n\n**For the above hyperparameter, is there significant room to have better choices so that the explanation size drops more, while the performance may stay competitive or even better in generalization?**\n\nReply: Yes! As an example, for Anuran dataset, if we use FactorExpl=0.9, rather than FactorExpl=0.97, the explanation size drops from 4.78 to 3.85 (a reduction of almost 20%) while the accuracy varies just a little, dropping from 94.8% to 94.6%. For this dataset CART achieves 94.7% of accuracy and an average explanation size equal to 5.24. These numbers were extracted from Table 1 and Table 5 (suppl. material, p. 32)\n\nMore generally, Table 5 shows that setting FactorExpl=0.95 gives 32% average reduction in explanation size compared to CART with loss of only 0.35% in average accuracy. Furthermore, by setting FactorExpl=0.9 we obtain an even bigger 38% average reduction in explanation size compared to CART with a loss of 1.1% in average accuracy\n\n**How tight are the theoretical bounds in Section 4?**\n\nReply: We would like to point out that the worst-case bound in Section 4, as given in Theorem 1, is indeed tight. This is made precise by the lower bound in Theorem 2, which shows the necessary trade-off one has between optimizing explanation size and depth, i.e. improving upon the bound on the depth we achieve in Theorem 1 can only be attained at the cost of a logarithmic factor loss in the explanation \nsize. \n\nMoreover, our guarantee results are also tight with respect to what is possible with polynomial time algorithms. As noted in Observation 2, Theorem 1 also implies that O(log n)-approximation simultaneously with respect to both depth and explanation size is achievable in polynomial time (which is in fact the best possible approximation under the assumption P ≠ NP).\n", " This paper studies the interpretable decision tree by a metric called \"explanation size\", then presents some theoretical results about this size in relating to the tree depth in the average and worst cases. The paper proposes a practical algorithm using adjusted Gini-index for tree splitting, based on a hyperparameter that differentiates whether using the existing split variable or using a new variable. Numerical experiments are conducted for multiple datasets. 1. Interpretable decision tree has been an interesting topic, which is usually measured by the tree depth or the number of terminal nodes. Explanation size is a new interesting metric in measuring the splitting rule complexity. \n\n2. This paper presents some theoretical bounds in relating explanation size to tree depth in average and worst cases. But it is not clear how tight these bounds are. (They seem to be rather loose bounds).\n\n3. The authors propose a practical algorithm based on an adjusted Gini-index, which also sounds reasonable. It is desirable to see how effective such algorithm may construct the interpretable decision trees that are smaller explanation size while maintain competitive prediction performance. The numerical results on Section 6 are not very convincing in the performance comparison. 1. For the example in Section 6, FactorExpl is set to be 0.97. In general, how this hyperparameter should be tuned? \n\n2. For the above hyperparameter, is there significant room to have better choices so that the explanation size drops more, while the performance may stay competitive or even better in generalization? \n\n3. How tight are the theoretical bounds in Section 4?\n The algorithm based on adjusted Gini-index seems to be a plausible approach, but the results as illustrated in Section 6 do not show significant lifting power. In Figure 2, when FactorExpl = 0.97, explanation size drops a bit dramatic, but performance also drops in a non-negligible way. It is desirable to see more convincing results with competitive performance. ", " The paper introduces a metric for evaluating decision trees based on explanation size. Using this metric, The authors establish theoretical bounds on identifying trees with both optimal depth and explanation size, and develop an algorithm, SER-DT, for regularizing decision trees based on explanation size. The proposed algorithm shows improvement in reducing explanation while maintaining similar performance when compared to a competing method.\n \n**Strengths:**\n* The proposed definition of explanation size is natural and intuitive. Decision trees are used in a number of applications for their interpretable properties; the proposed method improves on this interpretability and therefore could be of high interest to the community.\n* The paper has a good theoretical exploration of the tradeoff between tree depth and explanation size.\n\n**Weaknesses:**\n* Comparisons with Pruning algorithms. While the experiments include comparisons with CART, the paper could be improved by including comparisons with methods that reduce tree complexity, such as pruning.\n* High variance of results in Table 1 for test accuracy (see questions below). It would be beneficial if the authors could clarify these points. Error bars and/or significance testing in Table 1 would be helpful.\n\n**Miscellaneous Minor Issues / Suggestions:**\n* In table 1, it would be helpful to define what the bolded results indicate in the table caption.\n* Typo in Line 85: \"interpretabilty\"\n* Typo in Line 212: \"Explanaible\"\n* Typo in Line 302: \"intrepretability\"\n* Grammar in Line 303: \"upper and lower bound\"\n\n**Summary:**\nThe paper introduces a novel approach to improving decision tree interpretability. While the paper has room for improvement regarding experimental results and comparisons with pruning methods, the strong theoretical analysis makes me lean towards acceptance.\n * Why is there such high variance in accuracy results (Table 1) between SER-DT and CART? Why is the reported accuracy is higher for SER-DT than CART for a number of datasets (e.g. dry bean, eeg eye estate)? This seems to imply that regularizing for explanation length actually increases performance.\n* How was FactorExpl=0.97 chosen for the experiments? Are there any guidelines for selecting this parameter in practice? Limitations have been adequately discussed in the paper.", " The paper proposes explanation size as a novel measure to capture the interpretability of a decision tree. The explanation size of a leaf is defined as the number of distinct attributes occurring in nodes from the root to the leaf. This is an intuitively sensible notion, as it captures the size of the decision rule corresponding to the leaf. The metric is then lifted to whole trees by either considering the average or worst-case explanation size among all leafs.\n\nAs the first major contribution, the authors give a tight characterization of best possible guarantees achievable by a decision tree on the trade-off of simultaneously optimizing explanation size and the traditional criterion of tree depth. In particular, a theorem is given that states that for all datasets there are trees which have optimal explanation size and a depth within a factor of 2 of the optimal depth plus a logarithmic term in the sample size. This is complemented by a lower bound that shows that there are problem inputs for which depth and explanation size are different for all binary trees by a logarithmic factor in sample size. While not mentioned explicitly, these results seem to refer to trees that achieve zero classification error.\n\nMoreover, the authors present a greedy top-down tree induction algorithm called Short Explainable Rules (SER-DT) that aims to find minimum explanation size trees by using a novel splitting criterion called weighted pairwise misclassification. This algorithm guarantees an O(ln n) approximation for binary decision trees of approximately optimal average / worst-case explanation size and depth, and the experiments over 20 datasets indicate that the new algorithm is competitive with the commonly used CART algorithm. The introduced explanation size is a simple, apparently useful, yet, to my knowledge, novel metric to measure the interpretability of decision trees. However, note that this notion is closely related to rule sizes (as in number of queries in a rule), which is considered in the rule learning literature, e.g.,\n* Ignatiev, Alexey, Filipe Pereira, Nina Narodytska, and Joao Marques-Silva. “A SAT-Based Approach to Learn Explainable Decision Sets.” In International Joint Conference on Automated Reasoning, 627–45. Springer, 2018.\n* Proença, Hugo M., and Matthijs van Leeuwen. “Interpretable Multiclass Classification by MDL-Based Rule Lists.” Information Sciences 512 (February 2020): 1372–93.\n* Probably has been considered in early rule learning work as well; I recommend checking the survey “Seperate-and-conquer Rule Learning” by Furnkranz for an overview of work from the 1990s.\n \nThe presented algorithm is simple yet shown theoretically and practically to achieve its goal. It would be useful though to discuss why the proposed splitting criterion based on reducing the number of discrepancy pairs leads to this result, as this as well as the other steps of the algorithm do not seem to directly relate to explanation size. In this context it would also be useful to discuss the relation to tree optimization that minimizes the total size of the tree (number of nodes), e.g.,\n\n* Bessiere, Christian, Emmanuel Hebrard, and Barry O’Sullivan. “Minimising Decision Tree Size as Combinatorial Optimisation.” In International Conference on Principles and Practice of Constraint Programming, 173–87. Springer, 2009.\n \nRelated to that, the empirical study, while overall showing good accuracy/explanation size trade-offs relative to CAR, does not contain a comparison with a method that directly optimizes depth, which seems relevant given the theoretical results of the paper, and the cited empirical work that assesses that depth is indicative of interpretability. A further caveat is that theoretical and empirical results might relate to different variants of the algorithm: the parameter FactrorExpl seems to not play a role in the theoretical analysis. However, it is tuned for the experiments.\n \nThis relates to the clarity of the presentation, which is overall good. However, there are some missing implicit definitions and assumptions. Most importantly, the underlying problem definition seems to assume that the resulting trees have to perfectly classify the given training data. This is a reasonable definition. However, it is different from the usual ML problem, in which either tree pruning or other forms of regularization are applied, allowing the returned tree to have non-zero classification error. See for example:\n\n* Hu, Xiyang, Cynthia Rudin, and Margo Seltzer. “Optimal Sparse Decision Trees.” In 33rd Conference on Neural Information Processing Systems, 9, 2019.\n \nWith this definition, it is also implicitly assumed that the there are perfectly classifying trees, which is not necessarily guaranteed in the usual statistical settings.\n \nOther minor issues the term “n” is used without definition (e.g., Theorem 1), and, as mentioned, the hyper-parameter “FactorExpl”, which seems to be introduced as an afterthought in the empirical section.\n Why is there no comparison between the proposed algorithm and algorithms from the literature that optimize depth? Given the demonstrated compatibility of small depth and small explanation size, this seems like a relevant baseline.\n \nWhat is the significance of the example weights in the problem definition? Most commonly, we consider unweighted prediction problems, which are equivalent to using constant weights. The theorem as given allows us to choose these constant weights arbitrarily small, in effect letting the log n term vanish. This seems counterintuitive.\n Besides the above mentioned limitations in terms of comparison to other tree optimisation paradigms, there is also a lack of guarantees / discussion for the tradeoff between explanation size and accuracy – once such a tradeoff is allowed by considering, as usual, no perfect classification.\n" ]

[ -1, -1, -1, -1, -1, -1, 5, 7, 6 ]

[ -1, -1, -1, -1, -1, -1, 4, 3, 3 ]

[ "0lAQd8EJE1T", "BwPgyctBuXE", "nips_2022_Lp-QFq2QRXA", "vyQLyeX7ITA", "SJjCG9ZvYwq", "w5bHfYptqB", "nips_2022_Lp-QFq2QRXA", "nips_2022_Lp-QFq2QRXA", "nips_2022_Lp-QFq2QRXA" ]

[ "OASJ0s3lzcm", "mfHcjVRflKg", "xAlrZyaT58N", "AvplZjYa8rs", "MAgWr0LFMdR", "NV5bg0taw05", "tqQFp_MLiU", "0rvtF-iYsbv", "Ro09zGEyvHw", "NzTfeGbhSkd", "Paa1Sju5CNJ" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear reviewer, we have answered your questions in the author response and also uploaded a revised manuscript by following your suggestions for paper writing. We hope that we have addressed all your concerns. Do you have any further assessment (or concerns) of our work? Thanks for your kind consideration.", " I thank the authors for the detailed reply. I will keep my original rating. ", " We sincerely thank the reviewer for providing the thoughtful review. Below are our responses. \n\n**R1-Q1: The overall process and idea are exactly the same as PointPillar.** \n**R1-A1:** In outdoor 3D detection, Pointpillar [16] and SECOND [45] represent two mainstream paradigms, and almost all the well-known methods adopted these two basic paradigms and improved some modules in these two frameworks, such as CenterPoint [51] (detection head), SST [7] (3D backbone), VoTR [22] (3D backbone) and PillarNet [31] (2D encoder). Pointpillar directly converts the point cloud into 2D pillars and only utilizes 2D CNNs to build the network, which is more efficient but yields unsatisfied performance since all the operations are performed in 2D and the 3D structure information can not be well extracted. SECOND rasterizes the points into 3D voxels and extracts features through a 3D convolution backbone, which maintains the 3D structure and thus achieves better performance. \n\nHowever, the 3D CNNs in backbone can not provide sufficient receptive field, which is crucial for large-scene 3D detection. Moreover, the shared weight attribute of CNN makes it unable to model the local regions adaptively, while the sparse and irregular points change violently in different areas and need to be considered dynamically. Currently, the window-based transformer, which has revolutionized 2D image processing, shows a powerful ability to capture long-range information and is adaptive to the input, providing a potential solution for the above problems. \n\nIn our work, we make great efforts to design a novel 3D transformer backbone suitable for point cloud 3D detection while leveraging the incredible power of window-based transformers. To make a fair comparison, we adopt the SECOND paradigm and replace its pivotal 3D CNN backbone with our Mixed-scale Sparse Voxel Transformer (MsSVT), which achieves significant improvements, **+6.22, +15.02, +16.62** for the vehicle, pedestrian, and cyclist respectively on the challenging Waymo Open Dataset. Moreover, we overcome many difficulties when introducing window-based transformers into 3D voxels through our novel architecture design and technical contribution.\n\n1) **We conquer the ununiform sampling bias problem through mixed-scale window design and balanced multi-window sampling strategy.** Current window-based transformers achieve great success by applying an attention mechanism in a single-scale large window. However, the memory occupation cubically grows when migrating to 3D voxel space. Thus we have to sample a certain number of voxels in the window to reduce computation costs. Unfortunately, this simple sampling strategy will miss significant nearby voxels. It tends to sample more distant voxels when the object has few voxels (e.g., far-away objects only contain 1-5 voxels more likely to be irreversibly dropped). Meanwhile, it cannot collect enough distant voxels from enlarging the receptive field when it comes to dense areas and will bias these dense voxels (e.g., dense background area). To solve this problem, we divide the local region into mixed-scale windows and adopt balanced multi-window sampling strategy: collecting all the voxels in the small window to avoid loss of fine-grained information while using FPS to obtain a uniformly sampled distant voxel set in the large window, as shown in Figure 1(c).\n\n2) **We leverage the scale-aware head attention to achieve effective mixed-scale information aggregation.** It is not trivial to simultaneously capture the fine-grained details and long-range contextual information through the transformer. In our early exploration, putting all the nearby and distant voxels together and making the network learn to attend them alone do not bring improvements because of the diverse distribution of voxels from mixed-scale windows. In our work, we present the Scale-aware Head Attention to explicitly make different attention heads in charge of attending to information within a particular range (window). In this way, we solve the problem of ununiform distribution and significantly boost the performance. In addition, we also design a new Scale-aware Relative Position Encoding to enhance position information in different attention heads.\n\n3) **We significantly reduce the memory and computation cost by chessboard sampling and sparse implementation.** In general, the unacceptable memory and computation cost caused by the cubically growing queries and keys when applying attention in 3D voxels significantly limit the development of the 3D transformer backbone. In our work, we present the balanced multi-window sampling strategy, which can reduce the number of keys. Besides, we also present a novel chessboard sampling to reduce the number of queries without loss of information, which significantly reduces the memory and improves the speed, as shown in Table 5. In addition, we implement all the operations in MsSVT sparsely and accelerate them in parallel on GPU.", " We sincerely thank the reviewer for providing thoughtful review and positive feedback. Below are our responses to the questions and suggestions raised by the reviewer.\n\n**R2-Q1: The motivation is a little inaccurate.** \n**R2-A1:** Thank you for your insightful comments. Your opinion on the multi-scale is very professional. In 3D detection, a large receptive field is essential to accurately regress various objects and recognize far-away sparse objects leveraging long-range contextual information. Meanwhile, fine-grained geometric details are crucial to improving objects' localization accuracy and distinguishing foreground objects from great false positives. \n\nHowever, we found that directly applying the attention mechanism in a large window will blur out the fine-grained details, while restricting attention range in a small window leads to an insufficient receptive field. Inspired by this phenomenon, we propose the mixed-scale window design, which can keep finer granularity by applying self-attention in densely sampled nearby voxels within small windows and simultaneously expand the receptive field by attending to roughly collected distant voxels. This way, the problem of the sparsity and irregularity of LiDAR points distribution and the scale variance of different instances can be alleviated. \n\n1) As for the challenge of the ununiform distribution of point clouds, MsSVT can gather long-range contextual information to accurately detect the far-away objects in the absence of fine-grained information (e.g., for the vehicle only contain 1-5 points, we can recognize it and correctly infer the box from its surroundings such as other vehicles and the road), as shown in appendix (E). Meanwhile, our single-stage detector outperforms the SOTA two-stage detectors PV-RCNN++[34] without refining one-stage boxes by complicated RoI module as in the latter, demonstrating our strong ability to utilize fine-grained details to improve the localization accuracy. \n\n2) Though not as apparent as in the 2D images, the absolute scale variance also challenges 3D detection (e.g., the large vehicle can be 15m-30m long while pedestrian only ranges from 0.5m-1m in the Waymo Open Dataset). Previous work such as SST[7] achieves impressive results on small objects by avoiding down-sampling to maintain fine-grained features. In contrast, our method achieves strong results on small and large objects. Notably, we achieve remarkable improvements by **+4.73, +1.34** for vehicle and pedestrian in terms of LEVEL2 mAP compared with SST[7], which uses single scale window, demonstrating the significant superiority of the mixed-scale window design. \nIn addition, we have revised the sentence in the abstract to avoid misunderstanding.\n\n**R2-Q2: Additional results on KITTI test set.** \n**R2-A2:** Due to limited space, we do not report the results of the KITTI test set in the main paper. We submit our results to KITTI's official test server and provide the results below. Our method beats the superior PV-RCNN++ by $0.6$ mAP. The results on KITTI demonstrate that our MsSVT has excellent generalizability to adapt to different datasets. We will add the results in the final version.\n\n| Method\\\\mAP@Car | Easy | Mod | Hard |\n|-----------------|:-----:|:-----:|:-----:|\n| SECOND | 84.65 | 75.96 | 68.71 |\n| PV-RCNN | **90.25** | 81.43 | 76.82 |\n| PV-RCNN++ | 90.14 | 81.88 | 77.15 |\n| MsSVT-SS (ours) | 90.04 | **82.10** | **78.25** |\n\n**R2-Q3: Better to put two sections about sampling together, the paper needs polishing and fixing some minor typos.** \n**R2-A3:** Thank you for your suggestion. We agree that putting sections of Balanced Multi-window Sampling and Chessboard sampling together can make it more transparent and easy to understand. We have updated the methodology, carefully polished our writing, and fixed the typos in the attached revision.", " **R1-Q2: The multi-scale idea is the same as Voxel-FPN, but the processing backbone is replaced by a transformer.** \n**R1-A2:** Thanks. **Voxel-FPN** [15] is a valuable work in 3D detection and has been involved in the attached revision. Voxel-FPN adopts a multi-scale voxelization strategy to rasterize the input point clouds into voxels with different voxel sizes and utilizes an FPN network to aggregate the multi-resolution feature maps. **Pillar-in-Pillar** [40] further solves the misalignment problem in multi-scale voxelization by leveraging a center-aligned voxelization strategy with overlapped sub-voxel partition. \nOur **MsSVT** is very different from these multi-scale voxelization methods.\n\n1) **We gather mixed-scale information from different windows rather than apply multiple voxelizations.** First of all, our mixed-scale windows are different from the multi-resolution voxels in two aspects: i) The basic unit of our windows is still a high-resolution voxel, while Voxel-FPN pools all the information in a significant voxel, in which case the local structure will be blurred irreversibly. For example, the low-resolution voxelization will convert an object into a solid cube, while our large window roughly collects high-resolution voxels on its surface and thus can still retain the local structure thanks to the well-designed sampling strategy. ii) Our windows are much larger than the multi-resolution voxels (e.g., we have two window sizes (1.2m, 2.8m) while Voxel-FPN adopts three voxel sizes (0.16m, 0.32m, 0.64m)). This way, our MsSVT can obtain sufficient receptive benefit from the large window more directly and efficiently. \n\n2) **MsSVT can capture mixed-scale information in a single layer while Voxel-FPN relies on a complicated architecture.** Previous multi-scale voxelization methods must first adopt multiple voxelizations, then stack 3D CNNs for different resolutions to extract multi-scale feature maps, and finally utilize the FPN network to fuse the pyramid feature maps and obtain the multi-scale features. Technically, the multiple voxelizations will bring disastrous computational costs to the sparse voxel operation. While our **MsSVT** only voxelizes the point clouds at once at the beginning, then maintains the resolution without down-sampling as SST [7]. We can capture multi-scale information in a single layer by making voxels learn to attend to each other in mixed-scale windows, which has two advantages: i) our mixed-scale windows are naturally overlapped with each other so that we do not have the misalignment problem as discussed in **Pillar-in-Pillar** and can further save the additional shift window operation which is commonly required by window-based transformers. ii) Without the need for multiple voxelizations, our model is more flexible and efficient and can be plugged into any single resolution layer to obtain multi-scale features.\n\n**R1-Q3: This article is poorly written and needs careful polishing, such as line 5, line 32.** \n**R1-A3:** Thanks. We have carefully polished our writing and fixed the grammatical errors in the attached revision. ", " **R2-Q4: More experiments of mixed-window.** \n**R2-A4:** As shown below, we conduct a series of ablative experiments by increasing or decreasing the number of key windows and attention head groups allocated to each window. All models are trained for 12 epochs on 20\\% Waymo data. We measure the latency on Tesla-V100 GPU and Unbuntu-16.04, Python 3.7, Cuda-10.2, and Pytorch-1.8. Compared with two windows (M1), more windows (M2, M3, M4) do not improve performance but increase the runtime latency. In our Scale-aware Head Attention, we distribute all feature channels and attention heads among the key windows to make different head groups in charge of a particular scale. Thus too scattered key windows will lead to fewer channels for each head group, which can weaken the representation ability of the single-scale features. Meanwhile, a single window (M5, M6) lacks multi-scale information and leads to low accuracy. Moreover, (M2, M3, and M4) also demonstrate that allocating more heads to the oversized windows significantly affects the accuracy of small objects. These experiments prove that our current combination (M1) can bring superiority of the mixed-scale window into full play and make a trade-off between speed and accuracy.\n\n| Strategy | Comb | Num Heads | Veh / Ped / Cyc | Lat (ms) |\n|----------|-----------|-----------|:-------------------:|:--------:|\n| M1* | (3,7) | (4,4) | $72.37/75.99/67.90$ | 121 |\n| M2 | (3,5,7) | (2,3,3) | $71.94/75.76/67.07$ | 137 |\n| M3 | (3,5,7) | (2,2,4) | $72.17/75.45/67.01$ | 139 |\n| M4 | (3,5,7,9) | (2,2,2,2) | $72.04/75.38/66.53$ | 157 |\n| M5 | (3) | (8) | $71.46/74.39/65.55$ | 98 |\n| M6 | (7) | (8) | $72.06/75.20/66.33$ | 112 |\n\n**R2-Q5: More experiments of sampling strategy.** \n**R2-A5:** We conduct more experiments by adopting different sampling strategies for queries and keys. All models are trained for 12 epochs on 20\\% Waymo data. As shown below, compared with CBS(query)+FPS(key), full adoption of FPS brings high latency and incurs a slight performance penalty on vehicles and pedestrians. Full adoption of CBS leads to faster speed and lower accuracy. In contrast, the CBS(query)+FPS(key) combination finds a sweet spot between latency and accuracy, where CBS significantly reduces the computation cost for query sampling and avoids the information loss caused by uncertain voxel updating. At the same time, FPS has a more vital ability to retain geometric structure.\n\n| Strategy | Veh / Ped / Cyc | Lat (ms) |\n|----------|:-------------------:|:--------:|\n| CBS+FPS* | $72.37/75.99/67.90$ | 121 |\n| FPS+FPS | $72.02/75.57/67.91$ | 143 |\n| CBS+CBS | $71.83/75.28/67.25$ | 107 |\n| FPS+CBS | $71.88/75.04/67.33$ | 118 |", " **R2-Q6: Difference with the mentioned methods.** \n**R2-A6:** We are very different from the mentioned methods. We will first briefly revisit them and then elaborate on our differences. In addition, all the mentioned works have been involved in the attached revision.\n\n1) **Every View Counts** replaces the commonly used cuboid-shaped voxel representation with Hybrid-Cylindrical-Spherical (HCS) Voxels by changing $R=\\sqrt{x^2 + y^2 + z^2}$ in the Spherical coordinates system into $r=\\sqrt{x^2 + y^2}$ which is adopted in Cylindrical coordinate system, then performs detection on both Bird Eye View (BEV) and Range View (RV) in the unified voxel representation. In comparison, **MsSVT** uses the cuboid-shaped voxel and performs detection on BEV. We focus on how to gather voxels and apply an efficient attention mechanism in multiple windows rather than on designing the voxel representation.\n\n2) **Reconfigurable Voxels** changes the local neighbor searching of each voxel from finding its nearest four neighbors into a random walk scheme, which gets four gathered voxel sets connected to the center voxel as the neighbors through a complex pre-defined rule without learning parameters. In comparison, **MsSVT** explicitly divides the local neighbors into large and small regions by a more efficient and straightforward distance partition. Then the voxels learn to attend to their neighbors with more flexibility, thus leading to more powerful feature extraction. In addition, **MsSVT** models the relationship in local voxel sets where all the voxels in the window, even not connected, can be attended to rather than reconfiguring the neighbors for a single voxel where only connected voxels are considered.\n\n3) **It's All Around You** introduces the Cylindrical Coordinates to 3D detection to leverage the natural scanning pattern from LiDAR sensors and propose a range-guided convolution to address the problem that similar objects appear across different bins depending on the range when adopting Cylindrical Coordinates. While **MsSVT** follows the traditional Cartesian Coordinates and divides the scene into normal cells, we conquer the sparsity and irregularity of voxels by mixed-scale window transformers. The motivation and solution are very different.\n\n4) **Voxel-FPN** adopts a multi-scale voxelization strategy to rasterize the input point clouds into voxels with different voxel sizes and utilizes an FPN network to aggregate the multi-resolution feature maps. **Pillar-in-Pillar** further solves the misalignment problem in multi-scale voxelization by leveraging a center-aligned voxelization strategy with overlapped sub-voxel partition. \nOur **MsSVT** is very different from these multi-scale voxelization methods.\n * **We gather mixed-scale information from different windows rather than apply multiple voxelizations.** First of all, our mixed-scale windows are different from the multi-resolution voxels in two aspects: i) The basic unit of our windows are still high-resolution voxels, while Voxel-FPN pools all the information in a significant voxel, in which case the local structure will be blurred irreversibly. For example, the low-resolution voxelization will convert an object into a solid cube, while our large window roughly collects high-resolution voxels on its surface and thus can still retain the local structure thanks to the well-designed sampling strategy. ii) Our windows are much larger than the multi-resolution voxels (e.g., we have two window sizes (1.2m, 2.8m) while Voxel-FPN adopts three voxel sizes (0.16m, 0.32m, 0.64m)). This way, our MsSVT can obtain sufficient receptive benefit from the large window more directly and efficiently. \n * **MsSVT can capture mixed-scale information in a single layer while Voxel-FPN relies on a complicated architecture.** Previous multi-scale voxelization methods need first to adopt multiple voxelizations, then stack 3D CNNs for different resolutions to extract multi-scale feature maps, and finally utilize the FPN network to fuse the pyramid feature maps and obtain the multi-scale feature map. Technically, the multiple voxelizations will bring disastrous computational costs to the sparse voxel operation. While our **MsSVT** only voxelizes the point clouds at once at the beginning, then maintains the resolution without down-sampling as SST[7]. We can capture multi-scale information in a single layer by making voxels learn to attend to each other in mixed-scale windows, which has two advantages: i) our mixed-scale windows are naturally overlapped with each other so that we do not have the misalignment problem as discussed in **Pillar-in-Pillar** and can further save the additional shift window operation which is commonly required by window-based transformers. ii) Without the need for multiple voxelizations, our model is more flexible and efficient and can be plugged into any single resolution layer to obtain multi-scale features.", " We sincerely thank the reviewer for providing thoughtful review and positive feedback. Below are our responses to the questions and suggestions raised by the reviewer.\n\n**R3-Q1: More experiments of the number of groups for multi-scale attention.** \n**R3-A1:** As shown below, we conduct a series of ablative experiments by increasing or decreasing the number of key windows and attention head groups allocated to each window. All models are trained for 12 epochs on 20\\% Waymo data. Compared with two windows (M1), more windows (M2, M3, M4) do not improve performance but increase the runtime latency. In our Scale-aware Head Attention, we distribute all feature channels and attention heads among the key windows to make different head groups in charge of a particular scale. Thus too scattered key windows will lead to fewer channels for each head group, which can weaken the representation ability of the single-scale features. Meanwhile, a single window (M5, M6) lacks multi-scale information and leads to low accuracy. Moreover, (M2, M3, and M4) also demonstrate that allocating more heads to the oversized windows significantly affects the accuracy of small objects. These experiments prove that our current combination (M1) can bring superiority of the mixed-scale window into full play and make a trade-off between speed and accuracy.\n\n| Strategy | Comb | Num Heads | Veh / Ped / Cyc | Lat (ms) |\n|----------|-----------|-----------|:-------------------:|:--------:|\n| M1* | (3,7) | (4,4) | $72.37/75.99/67.90$ | 121 |\n| M2 | (3,5,7) | (2,3,3) | $71.94/75.76/67.07$ | 137 |\n| M3 | (3,5,7) | (2,2,4) | $72.17/75.45/67.01$ | 139 |\n| M4 | (3,5,7,9) | (2,2,2,2) | $72.04/75.38/66.53$ | 157 |\n| M5 | (3) | (8) | $71.46/74.39/65.55$ | 98 |\n| M6 | (7) | (8) | $72.06/75.20/66.33$ | 112 |\n\n**R3-Q2: Could the model scale to multi-frame?** \n**R3-A2:** Yes, our model can easily scale to multi-frame. We scale the model to multiple frames following SST. Due to limited time, we trained 12 epochs on 20\\% Waymo. As shown below, the performance of our multi-frame model is much better than that of the single frame, which shows the great potential of our method. In fact, MsSVT is compatible with multi-frame and other tricks since the input and output of our 3D backbone network are normal voxels.\n\n| Frame | Veh / Ped / Cyc |\n|:-----:|:-------------------:|\n| 1f | $72.37/75.99/67.90$ |\n| 3f | $75.78/79.96/72.44$ |\n\n**R3-Q3: Experiments with more two-stage architectures will be interesting.** \n**R3-A3:** Thank you for your advice. We add the result of LidarRCNN as shown below. Furthermore, we will test more two-stage methods in the future. The performance of MsSVT is much better than the LidarRCNN baseline (about 5-7 mAP) and is comparable to MsSVT-CT3D. It proves that our method can be widely applicable to different architectures.\n\n|Method\\\\mAP | Vel\\_L1| Vel\\_L2|Ped\\_L1 |Ped\\_L2 |Cyc\\_L1 | Cyc\\_L2|\n|:------:|:------:|:------:|:------:|:------:|:------:|:------:|\n|MsSVT-SS| 77.18 | 68.75 | 80.25 | 72.88 | 73.75 | 70.96 |\n| CT3D | 76.30 | 69.04 | -- | -- | -- | -- |\n| MsSVT-CT3D | 78.41 | 69.74 | **82.34** | **74.71** | **75.74** | **73.72** |\n| LidarRCNN(2x) | 73.5 | 64.7 | 71.2 | 63.1 | 68.6 | 66.1 |\n| MsSVT-LidarRCNN | **78.62** | **69.87** | 82.26 | 74.68 | 75.58 | 73.57 |\n\n\n**R3-Q4: More details of chessboard sampling.** \n**R3-A4:** Chessboard sampling is essentially an equal interval sampling strategy. First, we divide the entire voxel mesh space into four characters alternately without considering sparsity. Fig.3 is an example of division on a 2D plane. The \"cross\" character represents the position where the X coordinate is odd, and the Y coordinate is odd (odd-odd), and \"circle\", \"triangle\", and \"square\" represent even-even, odd-even, and even-odd, respectively. The similar combinations of odd and even can also be extended to three dimensions to get a sampling rate of power-of-2 (we apply it on two dimensions like Fig.3 and do not sample on the Z-axis). After that, we select the \"cross\" voxels in the first attention layer, which means all the non-empty voxels in the \"cross\" position will be fetched and fed to the attention layer to serve as queries. In the second attention layer, we choose \"circle\". In the third, we choose \"triangle\". And so on. Chessboard sampling has high efficiency and can significantly reduce memory. Moreover, all non-empty positions can be preserved completely after multiple stacked layers, reducing the uncertainty of updating query voxels.\n\n**R3-Q5: More discussion of the potential negative societal impact will be useful.** \n**R3-A5:** Thanks. The misleading 3D detection will result in disastrous consequences such as car crashes. We should continue improving the reliability and robustness of 3D detection.", " This paper presents a novel Mixed-scale Sparse Voxel Transformer to capture both types of information simultaneously by the divide-and-conquer philosophy. Experiments on waymo show promising results. 1. The general idea of this article is to extract features through multi-scale transformers in point cloud voxels, and then perform regression through 2D CNN. First of all, the overall process and idea are exactly the same as PointPillar. Second, this multi-scale idea is the same as Voxel-FPN[2], but the processing backbone is replaced by a transformer. So from this point of view, the author needs to think carefully about the novelty of this article.\n\n[1] Lang A H , Vora S , Caesar H , et al. PointPillars: Fast Encoders for Object Detection From Point Clouds[C]// 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2019.\n\n[2] Wang B , An J , Cao J . Voxel-FPN: multi-scale voxel feature aggregation in 3D object detection from point clouds[J]. 2019.\n\n2. This article is poorly written and needs careful polishing, such as line 5, line 32. Refer to part Strengths And Weaknesses. Refer to part Strengths And Weaknesses.", " This paper proposes a backbone, dubbed MsSVT, for exploiting mixed-scale sparse voxel transformer for LiDAR-based 3D detection. It devises chessboard sampling and balanced multi-window sampling strategies to obtain queries and a set of keys from different scales and then uses multiple attention heads for different scale-aware groups. The mixed-scale features are aggregated for multi-scale scene understanding. Experiments demonstrate the efficacy of the proposed method and the qualitative analysis with expected attention weights shows the role of the mixed-scale design. Strengths:\n- The motivation for designing mixed-scale voxel feature extraction is reasonable.\n- The proposed method not only shows impressive performance compared to other methods but also turns out to be efficient with the customized sampling designs. It is important for the practical use of LiDAR-based 3D detectors.\n- The illustration, such as Fig. 2 and 5, clearly show the design methods and the functionality of mixed-scale voxelization feature extraction.\n- It shows great potential for improving the detection performance of small objects, such as pedestrians and cyclists, in the Waymo experiments.\n\nWeaknesses:\n- The motivation for the necessity of mixed-scale voxelization is a little inaccurate.\n\nLarge-scale outdoor scenes do not feature significant variance in instance scales, from my perspective, at least compared to 2D object detection in images. A more reasonable explanation should be related to the ununiform distribution of LiDAR point clouds? Due to the sparsity and irregularity of LiDAR points distribution, a voxel-based 3D detector needs customized designs for voxelization to tackle the difficulty of detecting small objects and far-away objects. Of course, I think the scale variance of different instances is also a problem in 3D although it is just one reason for the necessity of mixed-scale voxelization.\n\nHere also needs a literature review for different voxelization methods in previous works, for example:\n\nEvery View Counts: Cross-View Consistency in 3D Object Detection with Hybrid-Cylindrical-Spherical Voxelization, NeurIPS 2020\n\nReconfigurable Voxels: A New Representation for LiDAR-Based Point Clouds, CoRL 2020\n\nIt's All Around You: Range-Guided Cylindrical Network for 3D Object Detection\n\nContext-Aware Dynamic Feature Extraction for 3D Object Detection in Point Clouds (Pillar-in-Pillar)\n\nVoxel-FPN: Multi-Scale Voxel Feature Aggregation for 3D Object Detection from LIDAR Point Clouds, Sensors 2020\n\n- Technical contribution: This paper contributes more engineering techniques, including mixed-scale voxelization, multi-scale heads, and efficient sampling implementation. From the perspective of novel technical contributions and new insights to the community, the contribution is just above the borderline.\n\n- Experiments: There are only results on the validation set both on Waymo and KITTI. Although the results on the validation set of Waymo are commonly used for comparison, the validation results on the KITTI are usually not convincing enough. Additional results on the test set would strengthen the experiment part.\n\n- Minor typos: The paper needs polishing and fixing some minor typos, such as line 123 prsent -> present, line 125 regrard -> regard, line 197 wrt -> w.r.t or with respect to. The methodology part can be also improved. For example, the two sections about sampling are not put together, which makes the reader confused about their relationship and the main philosophy of different sampling methods for queries and keys (It is clarified until the beginning of Sec. 3.2). - Does the implementation only try the mentioned two-scale case? How about the results for other alternative designs? For example, using the same sampling strategy for both queries and keys, and using more scales for mixing?\n The author analyzes the limitations and societal impacts adequately.", " This paper proposes a new transformer architecture for Lidar-based 3D object detection. Previous windows-based transformers utilize large windows to capture the long-range context information but ignore the negative effect of blurring fine-grained details. This is especially true for 3D point cloud cases where the point downsampling is performed and sparse and distant points are selected (further blurring fine-grained details). To alleviate this, the authors propose to design a multi-scale transformer architecture and set up key windows of different scales in which different windows contain the same amount of downsampled points. Scale-aware head attention is also proposed to divide the attention head into multiple groups and aggregate after inner group computation with the query. Additionally, the authors further propose a chessboard sampling strategy to iteratively sample different query voxels in order to reduce the computational cost while maintaining similar accuracy performance. In the end, the final models are evaluated on the KITTI and Waymo datasets and achieve SOTA results. S1: The overall design is sound and relatively novel. This work nicely extends the Single-Stride Transformer [1] to work with voxel data. Concretely, SST only works with pillar (a long elongated voxel) representation to maintain efficiency. Extending windows-based transformers to the voxel representations come with an efficiency challenge due to the larger amount of voxels inside a key window. The authors nicely address this by proposing multi-scale window attention and chessboard query sampling strategy. The overall approach significantly improves the SST baseline and sheds light on efficient transformer design with 3D point cloud data. \n\nS2: The approach is well ablated on two popular datasets and achieves SOTA results compared to published methods. \n\nS3: The paper is generally well written and easy to follow. \n\nW1: There is no ablation on the number of groups for multi-scale attention (currently set to two). To further verify the motivation, the authors need to investigate the accuracy/speed tradeoff with a larger number of groups.\n\nW2: Current model only works with single-frame data. Could it scale to multi-frame? \n\nW3: Experiments with more two-stage architecture will be interesting (minor, this could be done later). Q1: On line 180, the authors mentioned that the model selected one of the four characters as the sampling location. How are these chessboards generated? Is it purely random? The authors need to provide more details. \n\nQ2: Please address the weakness I listed above. Partially. More discussion of the potential negative societal impact like the earlier adoption of not-yet validated autonomous vehicles (or misleading 3D detection performance) will be useful. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 5, 4, 5 ]

[ "MAgWr0LFMdR", "0rvtF-iYsbv", "Ro09zGEyvHw", "NzTfeGbhSkd", "Ro09zGEyvHw", "NzTfeGbhSkd", "NzTfeGbhSkd", "Paa1Sju5CNJ", "nips_2022_hOVEBHpHrMu", "nips_2022_hOVEBHpHrMu", "nips_2022_hOVEBHpHrMu" ]

[ "B2etkGOKyTa", "ktP5WeL2qCd", "kWWMAVNq1Sl", "fy7PTl-Rdh4", "CKgqkYSply5", "-7RD21LPnsC", "IYM5kYYqLl7", "5HOS7HEzO3B", "ylXW3eGgez_", "I3GqaYfjSr_" ]

[ "official_reviewer", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for the clarification.\n\nI have raised the score to 7.", " We use $p()$ to denote the ground-truth probability distribution,\nand $q()$ to denote the corresponding estimated probability distribution.\nHere, $q(a|y)$ is an estimation of $p(a|y, x)$.\nSorry for the confusion.\n\nIt's hard to tell whether using $q(a|y, x)$ will be better.\nSince the data with specific $x$ and $y$ will be much fewer, \nwhich may lead to overfitting and larger approximation error.\n\nBoth $q(a|y)$ and $q(a|y, x)$ formulation fit within our framework, \nand the choice depends on the specific problem.\nExperimentally, we found that using $q(a|y)$ is simpler and performs well in our case.", " Hi, I checked this paper \"Heterogeneous Collaborative Filtering without Negative Sampling for Recommendation. AAAI 20.\"\nI don't think Heterogeneous feedback and the delayed feedback (this submission) are the same problem.\nCould you provide more thoughts?", " About Q6, q(a|y)? or p(a|y)?\n\nOK, practically you approximate p(a|y, x) with a p(a|y), how much information will be lost in such approximation may I ask?", " Thanks for your kind and patient review of our paper.\nWe try our best to answer each question in detail within the character limit.\n\n### Q1: How many actions do you consider in your experiments?\n\nIn the Criteo dataset, we consider one type of user action, i.e., conversion,\nwith 7 different revealing times as described in the supplementary material,\nso there are 1*7=7 actions (we count different revealing times as different actions to simplify discussion).\n\nIn the Taobao dataset, we consider 3 types of actions, i.e., conversion, cart, and favorite,\nwith 5 different revealing times, so there are 3*5=15 actions.\n\n### Q2: How will you deal with a large number of different actions?\n\nThe computational complexity increase is mainly caused by the number of different revealing times,\nas analyzed in the response to Reviewer fM2F Q3.\n\nThe reason is that practically we can utilize all the available action information at\nthe same revealing time, which only needs forward and backward propagation once.\nAnd the computational increase caused by the number of outputs (actions) is\ntypically negligible compared with the feature network.\n\n### Q3: How do you deal with discrete input values (y)?\n\nWe have added a new Figure 1 to depict the calculating procedure visually.\n\nThe procedure for calculating equation (4) is:\n\n1. The CVR probability $q_{\\theta}(y|x)$ is calculated normally with one forward pass of network $q_{\\theta}$,\n which produces the estimation of $p(y=0|x)$ and $p(y=1|x)$.\n\n2. $q_{\\phi}(a_j|x, y, \\delta_j)$ takes $x$, $\\delta_j$ and $y$ as inputs.\n Specifically, we first encode $x$ with an encoding network $Encode(x)=e_x$,\n where $e_x$ denotes an embedding of $x$. \n Then, we concatenate $e_x$ with one-hot representations of $y$ ([1, 0] and [0, 1] for CVR),\n respectively, e.g., $e_x | [1, 0]$ and $e_x | [0, 1]$ (since we need to take sum over different $y$).\n We take $e_x | [0, 1]$ (corresponds to $y=1$) as an example, \n this vector is then fed into a MLP with $m$ output heads that corresponding to probabilities of $m$ actions.\n\n3. The predicted probabilities are used to calculate the GDFM loss $\\mathcal{L}_{\\delta_j}$.\n\n### Q4: Why do you use a large batch size?\n\nWe tune the batch size on the vanilla method and keep it fixed when we compare other methods.\nOur practice suggests that a very small batch size will lead to severe overfitting to very recent data\nand will slow down training speed significantly.\n\n### Q5: Elaborate on the limitations and potential solutions.\n\nAs stated in the paper,\nthe main limitation of our approach is the increase of data samples,\nas analyzed in the response to Reviewer fM2F Q3.\nSince the main problem is the lack of conversion labels,\nsuch an increase in computational complexity is acceptable.\nBesides, our current implementation utilizes data parallel training,\nwhich will not be significantly slower as long as the computational resource is sufficient.\n\nWe can also subsample the data stream randomly to reduce computational burden if necessary,\nwhich is a common practice in recommendation systems.\n\n### Q6: Consideration of the implementation complexity of the method.\n\nThe training procedure of GDFM can be implemented efficiently with\nvectorized computation as in our code.\nThere may be some engineering problems related to constructing the required data stream.\nSpecifically, our approach needs to duplicate a click sample at each revealing time\nand get corresponding action labels,\nwhich is technically tractable but not quite compatible with some existing offline training frameworks.\n\n### Q7: The experimental improvements are relatively small.\n\nThe absolute improvements of GDFM compared with the best baselines\nare about 0.1% AUC, 0.17% PR-AUC on the Criteo dataset,\nand 0.35% AUC, 0.2% PR-AUC on the Taobao dataset,\nwhich is generally considered significant in recommender systems.\nAnd the improvements are statistically significant with $p \\ll 0.01$.\n\nWith the development of machine learning based recommender systems in recent years,\nthe potential room for improvement restricted within the static dataset is significantly reduced,\nwhich is the main force driving the emergence of research considering delayed feedback.\nIn learning with delayed feedback, the room for improvement lies between the static model and the\nOracle model (streaming training without delayed feedback),\nwhich is about 2% AUC in our cases.\nThe absolute improvement of GDFM will improve as this delayed feedback gap enlarges.\nFor example, we observe that the delayed feedback problem is\nmore severe on the items with a high price,\nwhich requires more time to decide to pay;\nthe average feedback delay will also increase if we use larger $\\delta_y$.", " Thanks for your kind and patient review of our paper.\nWe try our best to answer each question in detail within the character limit.\n\n### Q1: Are there any online experiments?\n\nWe have conducted offline experiments on private datasets from our cooperative partner,\nand the results are promising to prompt us to an online deployment.\nHowever, the development is not yet complete, and we are still working on it.\n\n### Q2: What is the architecture used in the experiments?\n\nWe use hashed user ID and item ID to train embeddings end-to-end,\nthen the embeddings are concatenated to form the input of a MLP,\nthe outputs of this MLP serve as embeddings of $x$.\nWe have included a new figure of the overall framework in the revision of our paper,\nand the feature encoder network is depicted in the supplementary material.\n\n### Q3: Time complexity analysis?\n\nAlgorithm 2 is to calculate the joint distribution $p(a, y)$,\nwhich can be achieved by an $O(N)$ ($N$ is the number of samples) counting over the dataset.\nSince we assume the distribution $p(a, y)$ is relatively stable,\nwe only need to run the algorithm once on an offline dataset.\nThus, the computational complexity of Algorithm 2 is\nnegligible and will not affect the streaming training stage.\n\nThe main increase in computational complexity is\ncaused by Algorithm 1: Introducing multiple revealing times requires to\ninsert multiple duplicated samples into the data stream.\nThis leads to an O(number of different revealing times) increase\nof training data.\n\nThus, the overall computational burden is O(number of revealing times)\nof duplicated data.\nSince the primary problem is the lack of timely labels,\nand the increase of data can be greatly alleviated\nby data parallel, the overall cost is affordable.\n\n### Q4: Are there any related work considered ideas similar to the paper?\n\n* Using entropy between user action and conversion label to measure the\n information carried by the action.\n\nTo the best of our knowledge, we are the first to use entropy\nto measure the information carried by the actions.\n\n* Considering the time gap and sample complexity into designing the weight for the action.\n\nSuch a problem only matters in online learning with delayed feedback,\nand existing literature does not consider the distribution drift along with time.\nSome related work also involves losses corresponding to different actions,\nbut they use equal weights[2] or treat the weights as independent hyper-parameters[1].\n\n[1] Chen, et al. Efficient Heterogeneous Collaborative Filtering without Negative Sampling for Recommendation. AAAI'20.\n\n[2] Ma, et al. \"Entire space multi-task model: An effective approach for estimating post-click conversion rate.\" SIGIR'18.\n\n### Q5: Why does the assumption \"$rank(M) = n$\" holds for real-world problems?\n\nConsidering conversion $y$ and cart action $a$.\nUsing the fact that $p(a=0|y)+p(a=1|y)=1$,\nwe can solve that $p(a=0|y=0)=p(a=0|y=1)$ and $p(a=1|y=0)=p(a=1|y=1)$ must hold **exactly** if $rank(M) < n$,\nwhich is nearly impossible naturally.\n\n$rank(M)=n$ is a necessary but not a sufficient condition to make $p(y|x)$ recoverable (with low error),\nand it does not imply a strong relationship.\nThe reason is that the estimation of $p(a|x)$ is not perfect,\nand the error will be amplified by $M$.\nSo we further propose to use conditional entropy as a measure of relationship strength.\n\n### Q6: The relationship between $p(y|x)$, $p(a|y)$, and $p(a|x)$.\n\nBy definition, for a fixed $\\delta$ (omitted in the following equations),\nwe have\n$$\np(a|x) = \\sum_y p(a|y, x) p(y|x)\n$$\nand practically we approximate $p(a|y, x)$ with a $q(a|y)$ which\ndoes not depend on $x$. We will further clarify this point in the paper.\nHere, we are maximizing the likelihood of $p(a|x)$ to\nlearn $p(y|x)$ *using $q(a|y)$ as a bridge*,\nso $q(a|y)$ works like a proxy between $p(a|x)$ and $p(y|x)$.\n\n### Q7: The significance of the delayed feedback problem in real-world recommender systems.\n\nExtremely long delay (several months) does exist in real-world recommender systems (but rare).\nPractically, delay from hours to 1 week occupies a considerable portion,\nand we provide some statistics from our partner and some previous literature here:\n\n1. E-commerce (our partner): With $\\delta_y=14$ days,\n 28% of the conversions happen after 1 hour, and 15% of conversions happen after 1 day.\n Our preliminary online experiments indicate that simply dropping the conversions with > 1-hour delay\n leads to significant performance improvement,\n which is indeed a degenerated case of GDFM with only one revealing time.\n\n2. Display advertisement (Criteo[1]): With $\\delta_y=30$ days, 70% of conversions happen after 1 hour,\n 50% of conversions happen after 1 day, and 13% of conversions happen after 14 days.\n [1] provides more detailed information.\n\n[1] Chapelle, et al. Modeling Delayed Feedback in Display Advertising. KDD'14.\n\nThe Reviewer fuKP also agrees that \"This is a very important problem.\"", " Thanks for your detailed review and suggestions on improving the paper.\nWe try our best to answer each question in detail within the character limit.\n\n### Q1: What are the differences between the delayed feedback problem and the heterogeneous feedback problem?\n\n1. **The training schema is different**.\n Streaming training with feedback delay already differs \n from static training without considering heterogeneous labels.\n For example, in offline training, the missing labels will not be revealed during training,\n and we do not need to consider conflict labels (e.g., negative label changes to positive label).\n\n2. **Some distinct problems arise from feedback delay**.\n Tackling new labels is not as straightforward as it seems to be at the first glance.\n 1. Suppose a sample has been already used as a negative sample, and it converts later,\n *how* to deal with this sample?\n If we simply ignore it, then we have used the wrong label;\n if we insert a duplicate with a positive label, then the data distribution $p(x)$\n changes (negative samples appear once, but positive samples may appear twice),\n and the label conflict still exists, how to repair it?\n 2. Another problem is *when* to use a sample.\n Since we are not working with a static dataset passively,\n we can choose the revealing time freely,\n and this requires us to define a schedule explicitly for revealing the labels.\n\n3. **User actions play an intrinsically different role in learning with delayed feedback**:\n In the setting of learning with heterogeneous feedback,\n as we discussed in response to Reviewer fM2F Q4, user actions work more like\n *complementary information to the conversion labels*.\n In the setting of learning with delayed feedback,\n we need to *rely on user actions to extract information related to conversions*\n when ground-truth conversion labels have not been revealed yet.\n\nThese distinct differences lead to different motivations and methodologies of\ndelayed feedback methods compared with heterogeneous feedback methods.\n\n### Q2: What are the differences between GDFM and EHCF?\n\n1. EHCF does not consider specific problems in learning with delayed feedback as\n discussed in the previous question.\n\n2. As pointed out by Reviewer fM2F and fuKP, our main contribution is providing a\n novel probabilistic perspective to analyze the delayed feedback problem,\n and come up with a practical method to measure the information carried by\n user actions. These are novel points rooted in the delayed feedback problem and\n are not considered by EHCF.\n\n3. We agree that in our current implementation of GDFM,\n $p(a|x)$ also relates with $p(y|x)$ linearly.\n However, this formulation comes from our probabilistic model naturally\n with clear interpretability and establishes the base of the following analysis.\n The linear mapping introduced by EHCF lacks such probabilistic insight.\n\n4. The training methods are different, which leads to different results:\n GDFM learns $p(a|y)$ explicitly,\n whereas the meaning of linear transformation learned by EHCF\n is unclear.\n\n### Q3: Experimental comparison between GDFM and heterogeneous feedback methods such as EHCF.\n\nAs analyzed in the previous questions,\nwe can not compare GDFM with EHCF directly since EHCF does not support duplicated samples and\nchanging labels in the delayed feedback setting.\n\nWe agree that using trainable linear layers to capture relationships between user actions\nis an applicable idea in the delayed feedback setting with user actions.\nSo we implemented an architecture equipped with the Transfer-based Multi-Behavior Prediction layer\nas proposed in the EHCF paper\nand used the same duplicating and revealing strategy as in GDFM to conduct a reasonable comparison.\nWe denote this as the \"Linear relation\" method.\nWe evaluate the performance on the Taobao dataset.\n\nThe performance of the Linear relation method is:\n\nAUC: 63.4±0.9%, PR-AUC: 50.1±1.5%, NLL: -470±4.6%\n\nand GDFM is:\n\nAUC: 79.4±0.5%, PR-AUC: 80.7±0.9%, NLL: 49.6±3.1%\n\nThe results support that utilizing the relationship between user actions and conversions with a proper sampling strategy\nwill improve performance on AUC and PR-AUC.\nHowever, since the Linear relation method does not consider label changing,\nthe NLL is significantly worse. And the AUC and PR-AUC metrics of GDFM are also better than EHCF based method.\n\nThe experimental results and discussion about some related heterogeneous feedback methods [1, 2, 3]\nare added to the paper. \n\n[1] Chen, et al. Efficient Heterogeneous Collaborative Filtering without Negative Sampling for Recommendation. AAAI'20. \n\n[2] Chen, et al. Graph Heterogeneous Multi-Relational Recommendation. AAAI'21.\n\n[3] Jin, et al. Multi-behavior Recommendation with Graph Convolutional Networks. SIGIR'20.\n\nWe have added a new figure depicting our approach's overall design and procedure in\nrevision of our paper according to your suggestion.", " The authors introduce a generalized feedback model in order to use delayed labels. This is very relevant in e-commerce platforms where a specific action we care about (for example buying a product) can happen after some time from the first interactions with the platform. Generally this is an important problem in e-commerce platforms. Is related basically, to attribution mechanism which is very important when one considers to build a training dataset from click-stream data. The authors compare their approach with other similar approaches on to two datasets. The authors observe improvements using their approach. This is very important problem. The way is tackled by the authors is interesting and they try to clarify all the points of their approach. By adding and modeling the intermediate actions they can capture and propagate the delayed feedback.\n\nThere is novelty in the approach as it considers temporal distributions and is the main one.\n\nI have some doubts of whether such an approach can be easily implemented in a real use case. No such on-line experiments are described in the paper and essentially the paper builds on such a use-case. By also checking the exact results in the supplemental material improvements there is some relatively small improvements.\n - I am not sure I got on how many actions you consider in your experiments. In on-line platforms we can have quite large number of different actions. How you deal with this?\n- Did not get in the architecture when you say that you concatenate one-hot encoded y. For y \\in {0, 1} what exactly you concatenate? Could you clarify?\n- I see in the experiments you use a quite large batch size. How you came up with this value? Yes the authors discuss briefly limitations and giving some idea of overcoming it, but they do not really elaborate on the type of the solution.", " In this paper, based on the assumption that post-click user behaviors are informative to conversion rate prediction and can be used to improve timeliness, the authors propose a generalized delayed feedback model (GDFM) that unifies both post-click behaviors and early conversions as stochastic post-click information. Based on GDFM, they further establish a novel perspective that the performance gap introduced by delayed feedback can be attributed to temporal and sampling gaps. They measure the quality of post-click information with a combination of temporal distance and sample complexity. The training objective is re-weighted accordingly to highlight informative and timely signals. The experimental performance results show their model’s effectiveness. *Positive points*\n1. Recommendation is one of the most important applications of machine learning.\n2. The proposed method achieves good performance. \n3. The method is proposed based on a thorough analysis.\n\n*Negative points*\n1. The proposed method is not novel enough. The authors assert that previous literature concentrates on utilizing early conversions to mitigate delayed feedback problem and propose a generalized delayed feedback model (GDFM) that unifies both post-click behaviors and early conversions as stochastic post-click information. Indeed, what they tend to address can be defined as heterogeneous feedback problem and there are some relationships between different feedback types. Besides, there have already been some works such as EHCF that addressed this problem via multi-task learning and linear transformation, whose solution is very similar to this work.\n\n[1] Chen et al. Efficient Heterogeneous Collaborative Filtering without Negative Sampling for Recommendation. AAAI 20.\n\n2. The baselines are not enough. It is necessary to compare with some important and highly related heterogeneous collaborative filtering recommendation models such as EHCF.\n\n3. The presentation should also be improved. For example, there is not model framework in their methodology part as their proposed method is with multi-target. I strongly suggest a figure that can illustrate their overall design. \n Please answer my questions corresponding to the negative points: (1) Model novelty; (2) Missing baselines.\nSee the detailed comments above. Some limitations are mentioned and I think such this algorithm-driven paper for improving user experience in recommendation system does not have negative societal impact.", " This paper aims to alleviate the delayed feedback problem in conversion rate prediction (CVR) via proposing a new method: generalized delayed feedback model (GDFM). After clicking the item url, it might take months for a user to really purchase the item. Hence, the positive sample might be treated as negative sample in the training and this problem could bias the model.\n\nInstead of only relying on observed labels, their key idea is to introduce other user behaviors or actions like put the item into shopping cart as an auxiliary information or proxy to better predict the conversion.\n\nAccording to entropy between the conversion label and an action, they design a weight to reflect how informative the action is. Besides, they also consider the time gap and sample complexity into designing the weight for the action.\n\nThey conduct experiments over two public datasets and propose detailed evaluations. Strengths:\n\n(1) Since years ago, papers of recommender systems have become some sort of LEGO game -- like how to put a CNN over a DNN etc., Unlike those papers, this one really analyze the impact of user actions and clearly present the generation process in a probability graph way, which looks reasonable to me. I really enjoy this kind of papers.\n\n(2) Using entropy between user action and conversion label to measure the information carried by the action seems reasonable. In addition, they also consider time gap and sample complexity into designing the weight for the action, which shows the comprehensiveness of their thinking. My question (also presented in the next section) is that are these factors firstly considered by this paper?\n\nWeakness:\n\n(1) The experiments could be further enhanced:\n\n(a) Is there any online experiments?\n\n(b) What is the architecture used in the experiments? there are no clues in the paper.\n\n(2) Will algorithm 2 significantly slower the training? Where is the time complexity analysis? \n\n (1) Using entropy between user action and conversion label to measure the information carried by the action seems reasonable. In addition, they also consider time gap and sample complexity into designing the weight for the action, which shows the comprehensiveness of their thinking. My question (also presented in the next section) is that are these factors firstly considered by this paper? did any related work consider these factors?\n\n(2) In 167: \"Since rank(M) < n requires that some rows of M are linear combination of the others, which rarely happens in real-world problems\". So you are saying rank(M) = n holds for most of real-world problems, may I ask why? \n\nIn this specific situation, what is the physical meaning of rank(M) = n? does that mean user action and conversion has a very strong relationship? like a user must purchase the item in the shopping cart?\n\nin 160, \"We can recover p(y|x) from p(a|x) if and only if rank(Mx) = n.\" My opinion is that rank(Mx) = n is a very strong condition and also we don't need to 100% recover p(y|x) from p(a|x), does I understand right? \n\n(3) In section 3.2.2, I understand that how much information an action carry about the conversion can be measured by the entropy between them and I see H (y|a) in Equation (5). However, in 195: \"Since we are estimating p(y|x) through a proxy distribution p(a|y)\". May I ask where does p(a|y) come from? could you show the relation of p(y|x), p(a|y) and p(a|x) in some sort of equations, I am a bit confusing here.\n\n In Section 2, they said: \"However, the ground-truth conversion labels are available only after a long delay: A user may purchase several months later after a click event x.\"\n\nWell, several months? that is a bit against my life experience. \n\nDoes this delay of several months a common situation?\n\nI guess it would be better to show the delay distribution from a real-world CVR system so that we know how serious this delay problem can be and how important this paper's contribution can be.\n\nBut I understand that it may not be appropriate to show that due to company's policy.\n\nExpected to see that though!" ]

[ -1, -1, -1, -1, -1, -1, -1, 6, 3, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, 3, 5, 4 ]

[ "ktP5WeL2qCd", "fy7PTl-Rdh4", "ylXW3eGgez_", "-7RD21LPnsC", "5HOS7HEzO3B", "I3GqaYfjSr_", "ylXW3eGgez_", "nips_2022_IvJj3CvjqHC", "nips_2022_IvJj3CvjqHC", "nips_2022_IvJj3CvjqHC" ]

[ "0VJcsckZsN", "-Xhq1d_xWzz", "sAilVEEfL3", "L0oRfmtBOID", "dvgo5Kd5Me", "_5hNC_wA9i", "jc2SdJPknx", "Lcc4HmGfKC2", "iz6ZyEtRnk", "nHR4QH99Ce", "aaNE8zrDq2e", "SmOcQwgUvZ-", "_liLFMmB_w6", "yywQQNI6Oy6", "DcNV_wqAHjN", "_nkmP0-G_H_", "KEbbpws-wpg", "9HJF5hNHbl1G", "jFzCCEmU5l", "vQK7RJ1VyZd", "FDx9AT1Nc1Y", "jiLHLzzqtjQ", "SEcVhXRsehm", "IerZYHjNIUi", "7t3AKpquFKw", "vEn7sc5sa6m", "1USh4cjTLPp", "Qgz9CE4k0QrZ", "5sg1IBU24pn", "2SyiNX-aV5u", "gduagZVCegM", "6-F1huulKSq" ]

[ "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear Reviewer 6Fb8,\n\nThanks for discussing with us and agreeing that our response addresses some of your concerns. Thank you for approving the $\\textbf{contribution}$ of our proposed Transformer and $\\textbf{practical significance}$ of our work. We will kindly cite and introduce U-Transformer in the revision.\n\nBest regards,\n\nAuthors", " Dear Reviewer nC4p,\n\nThanks for discussing with us and agreeing that our response well addresses your concerns. Thank you for approving the $\\textbf{motivation}$, $\\textbf{novelty}$ and $\\textbf{significant contribution}$ of our work for spectral compressive imaging. We will kindly cite and introduce 3DT-Net in the revision. \n\nBest regards,\n\nAuthors", " Dear Reviewer BuNS,\n\nThanks for discussing with us and agreeing that our response well addresses your concerns. Thank you for highly praising the $\\textbf{novelty}$, $\\textbf{motivation}$, $\\textbf{contribution}$, and $\\textbf{reproducibility}$ of our work. We will release all the codes and pre-trained models to the public for further research.\n\nBest regards,\n\nAuthors", " We thank all reviewers and area chairs for their time and valuable comments. All source code and pre-trained models will be made publicly available for further research. After discussing with reviewers and providing more clarifications/results/analyses, we would like to give a brief response.\n\n(a) Reviewer BuNS, nC4p, and 6Fb8 all hold a $\\textbf{positive}$ side for our work. \n\nReviewer BuNS as an expert in the field of snapshot compressive imaging highly praises the motivation, novelty, improvements, and reproducibility of our work. Reviewer nC4p has no doubt that our work has novelty and significant contribution for spectral compressive imaging. Reviewer 6Fb8 agrees with the contribution of our proposed Transformer and the practical significance of our work. Yet, reviewer 6Fb8 still has concerns about our unfolding framework. Thus, we provide further clarifications and experimental results to address the concerns of reviewer 6Fb8. \n\n(b) Reviewer Jov1 states that our DAUHST is not better than USRNet in terms of Params and FLOPS, and our method is a combination of existing works. $\\textbf{However, all these concerns have been covered in our rebuttal.}$\n\nFirstly, in the experiments of our response, DAUHST significantly outperforms USRNet by $\\textbf{2.08 dB}$ while costing $\\textbf{0.24 M Params and 12.22 G FLOPS less}$ than USRNet. Secondly, we provide detailed comparisons between our DAUHST and the three works as reviewer Jov1 mentions (USRNet, CAT, and MST) in our response. They are fundamentally different in $\\textbf{motivation}$, $\\textbf{contribution}$, $\\textbf{technique}$, etc. We also conduct comprehensive experiments to show the significant advantages of our method. Thus, we highly recommend reviewer Jov1 to read our corresponding responses carefully.\n\nBest regards,\n\nAuthors", " Thanks for your reply. As you mention that “guiding the unfolding\nwith the ill-posedness of the measurement operator is not significant.” We would like to explain the contribution of our unfolding framework DAUF to you. \n\nAs we analyze in `A-1` (a) of ` Response to Reviewer 6Fb8 - Part 1`, Our DAUF is fundamentally different from existing deep unfolding frameworks. Previous unfolding methods do not estimate the degradation patterns and ill-posedness degree from the highly related CASSI system to guide the iterative learning. In contrast, we formulate a principled degradation-aware unfolding framework (DAUF) to address this issue. our DAUF estimates parameters from the compressed measurement and physical mask in the CASSI system. Then the parameters, which capture critical cues of CASSI degradation patterns and ill-posedness degree, are fed into each iteration to contextually scale the linear projection and provide noise level information for the denoising network.\n\n$\\textbf{Our degradation guiding scheme does significantly improve the performance.}$ In Table 2(c) of our main paper, we conduct ablation study to compare our DAUF with different unfolding frameworks. We also list the results here in the following table. As can be seen that our DAUF dramatically surpasses previous deep unfolding frameworks DNU, ADMM, and GAP by 2.59, 1.69, and 1.63 dB. This evidence demonstrates the impressive effectiveness and contribution of our DAUF for deep unfolding framework.\n\n| Framework | DNU | ADMM | GAP | DAUF |\n| - | - | - | - | - |\n| PSNR | 34.62 | 35.52 | 35.58 | 37.21 |\n| SSIM | 0.930 | 0.942 | 0.943 | 0.959 |\n\nWe hope to further discuss with you whether your concerns have been addressed or not. If you still have any unclear parts of our work, please let us know. Thanks.\n\nBest regards,\n\nAuthors", " Thanks for your response. Now we answer your questions.\n\n\n$\\textbf{Firstly}$, we have provided the quantitative comparisons between USRNet and DAUHST in `A-1` (d) of `Response to Reviewer Jov1 - Part 1` . We also list the results here in the following table. DAUHST-share means using weights sharing operation like USRNet. It can be observed that our DAUHST significantly outperforms USRNet by $\\textbf{2.08 dB}$ while only requiring $\\textbf{89.7}$% (2.08 / 2.32) Params and $\\textbf{69.0}$% (27.17 / 39.39) FLOPS. Our DAUHST-share significantly surpasses USRNet by $\\textbf{1.60 dB}$ while only costing $\\textbf{31.5}$% Params and $\\textbf{69.0}$% FLOPS. All these results demonstrate the effectiveness superiority and efficiency advantage of our DAUHST over USRNet.\n\n| Method | PSNR | SSIM | Params (M) | FLOPS (G) |\n| - | - | - | - | - |\n| USRNet | 35.13 | 0.942 | 2.32 | 39.39 |\n| DAUHST-share | 36.73 | 0.955 | 0.73 | 27.17 |\n| DAUHST | 37.21 | 0.959 | 2.08 | 27.17 |\n\n$\\textbf{Secondly}$, we do not understand the logical causal relationship between our statement that “USRNet is based on CNN, showing limitations in capturing long-range dependencies. DAUHST based on Transformer addresses this issue. Our HS-MSA jointly develops two branches” and your conclusion that our method is a combination of existing work. In fact, we have already stressed the differences between our DAUHST and the three works you mentioned (i.e., USRNet, CAT, and MST.) in ` Response to Reviewer Jov1 - Part 1` and ` Response to Reviewer Jov1 - Part 2`. They are fundamentally different in $\\textbf{motivation}$, $\\textbf{contribution}$, $\\textbf{technique}$, etc. We also conduct comprehensive experiments to show the significant advantages of our method. \n\nWe highlight our technical novelty and contributions in two parts, $\\textbf{deep unfolding framework}$ and $\\textbf{Transformer}$. Please refer to `A-1` of ` Response to Reviewer 6Fb8 - Part 1` for details. Besides, the other reviewers’ concerns about our $\\textbf{motivation}$ and $\\textbf{contribution}$ have been addressed. \n\nWe hope to further discuss with you whether your concerns have been addressed or not. If you still have any unclear parts of our work, please let us know. Thanks.\n\nBest regards,\n\nAuthors", " Thank you so much for the response.\n\nAlthough I've read the feedback from the authors, my main concern remains that the proposed method's novelty and gain are limited. For instance, both parameters and FLOPs are not better than USR. \n\nMoreover, the authors mention in the response that \"USRNet is based on CNN, showing limitations in capturing long-range dependencies. DAUHST based on Transformer addresses this issue. Our HS-MSA jointly develops two branches\", which also demonstrates the proposed method as a combination of existing work. Therefore, the novelty raised by the authors is overclaimed. ", " I would like to thank the authors for addressing my comments. I don't have any concerns about the motivation of this paper now. I also have no doubt that this work has its novelty and significant contribution from the spectral compressive imaging point of view, as demonstrated by the authors' explanation and excellent experimental results. However, when the scope of consideration is enlarged to the hyperspectral image reconstruction level, the general idea of the transformer as the prior plus unfolding technique has been proposed. Although the exact task or some detailed consideration of unfolding framework and denoiser prior network is different between this paper and the prior work, the essential conceptual difference from the neural information processing point of view is not significant. Therefore, I still consider this paper as a borderline paper for NeurIPS but lean toward weak acceptance.", " Dear Reviewer Jov1,\n\nWe thank you for your previous review time and valuable comments. Until now, the other three Reviewers have replied to us that their concerns including the $\\textbf{motivation}$, $\\textbf{contribution}$, and limitation of our work are mostly addressed. We also believe our response to you has covered your concerns. We hope to further discuss with you whether your concerns have been addressed or not. If you still have any unclear parts of our work, please let us know. Thanks.\n\nThe author-reviewer discussion period will end on August 9. We are still waiting for your reply. \n\nBest regards,\n\nAuthors", " I would like to thank the authors for their effort to provide an extensive response in explaining the technical novelties and providing new experiments. It is clarified now that the proposed U-shaped architecture is superior to alternative U-shaped transformers and ViT for denoising and the design choices are important based on the provided ablation. Thus, I raise my score by one. \n\nAlthough this work has practical significance, I still believe that this work has limited technical novelty. This work relies on deep unfolding/unrolled networks for inverse imaging, and guiding the unfolding with the ill-posedness of the measurement operator is not significant. \n", " I would like to thank the authors for addressing my comments. I don't have any concerns about the motivation of this paper now. I also have no doubt that this work has its novelty and significant contribution from the spectral compressive imaging point of view, as demonstrated by the authors' explanation and excellent experimental results. However, when the scope of consideration is enlarged to the hyperspectral image reconstruction level, the general idea of the transformer as the prior plus unfolding technique has been proposed. Although the exact task or some detailed consideration of unfolding framework and denoiser prior network is different between this paper and the prior work, the essential conceptual difference from the neural information processing point of view is not significant. Therefore, I still consider this paper as a borderline paper for NeurIPS but lean toward weak acceptance.", " I have read the author's feedback. My confusion regarding some details and the concerns raised by other reviewers are well-addressed. The author's responses are well organized and experimentally supported, which is convincing. Thanks for their effort. Here is my response to the author’s rebuttal.\n\n(i) The motivations and novelties are excellent.\n\nI have investigated snapshot compressive imaging for decades. To the best of my knowledge, this is the first Transformer-based deep unfolding method in snapshot compressive imaging. This work contributes a novel deep unfolding framework and an interesting Transformer for snapshot compressive imaging. The proposed DAUF can perceive CASSI degradation to adjust the iterative learning. The proposed HS-MSA computes spatial self-attention through shuffle operation, capturing long-range dependencies while costing cheaper.\n\n(ii) The improvements over state-of-the-art methods are very significant. \n\nAs reported in Table 1, the proposed DAUHST dramatically outperforms previous deep unfolding methods by over 4 dB and state-of-the-art method by 0.78 dB.\n\n(iii) The reproducibility can be ensured. \n\nI have checked the submitted code and models. The reported results can be exactly reproduced. I believe the subsequent open-source works will significantly benefit the community and further research of snapshot compressive imaging.\n\nBearing the above considerations in mind, I highly recommend this paper to be accepted.", " Dear Reviewer 6Fb8,\n\nWe thank you for your previous review time and valuable comments. We have provided corresponding responses and results, which we believe have covered your concerns about the technical novelty, comparisons with U-Transformer, ablation for the choice of U-shaped architecture, limitation, and ablation of robustness evaluation.\n\nWe hope to further discuss with you whether your concerns have been addressed or not. If you still have any unclear parts of our work, please let us know. Thanks.\n\nBest regards,\n\nAuthors", " Dear Reviewer BuNS,\n\nWe thank you for your previous review time and valuable comments. We have provided corresponding responses and results, which we believe have covered your concerns about the placement of visual results, reshape operation of $\\mathbf{R}$, the vectorized and shifted operations, generality of DAUF, and FLOPS of BIRNAT.\n\nWe hope to further discuss with you whether your concerns have been addressed or not. If you still have any unclear parts of our work, please let us know. Thanks.\n\nBest regards,\n\nAuthors", " Dear Reviewer Jov1,\n\nWe thank you for your previous review time and valuable comments. We have provided corresponding responses and results, which we believe have covered your concerns about the novelty, motivation, ablation of $\\alpha$ and $\\beta$, removing HS-MSA, ablation of self-attention with three-stage architecture, position of the auxiliary variable, comparison of complexity for attention alternatives, weight sharing operation, difference between training and testing, limitation, and receptive fields of non-local branch.\n\nWe hope to further discuss with you whether your concerns have been addressed or not. If you still have any unclear parts of our work, please let us know. Thanks.\n\nBest regards,\n\nAuthors", " Dear Reviewer nC4p,\n\nWe thank you for your previous review time and valuable comments. We have provided corresponding responses and results, which we believe have covered your concerns about the novelty, motivation, comparisons with 3DT-Net and MST, method description, ablation of stage number, spectral ranges, and more experiments with more infrared spectrum.\n\nWe hope to further discuss with you whether your concerns have been addressed or not. If you still have any unclear parts of our work, please let us know. Thanks.\n\nBest regards,\n\nAuthors", " Dear Reviewer,\n\nYou concerns about the novelty and motivations are critical and can convince me to reject the paper. Please read the author's rebuttal to see if your concerns have been addressed properly.\n\nAC", " Thanks for your valuable comments\n\nCode and models will be made public\n\nWe argue that our DAUHST is fundamentally different from USRNet [1], CAT [2], and MST [3]\n\n`Q-1:` Comparison with USRNet\n\n`A-1:` Firstly, using MAP theory to build energy function and HQS algorithm to obtain an unfolding inference are two common strategies in deep unfolding methods [4,5,6]. These methods all generate $x_k$ , $z_k$ in an iterative manner. These are not the contributions of us or USRNet. Our DAUHST and USRNet are different in \n\n(a) Research topic, degradation pattern, and motivation\n\nUSRNet is designed for super-resolution (SR). The degradation in low-resolution image is caused by a blur kernel, downsampling, and an additive noise. In contrast, our DAUHST is designed for snapshot compressive imaging (SCI) reconstruction. The degradation of SCI is mainly caused by mask-modulation, dispersion, and integration-compression. The degradation patterns and mathematical models of SR and SCI are different. Since using MAP theory for deep unfolding methods requires task-specific mathematical degradation models, the established energy function and subsequent formulation of USRNet and DAUHST, especially the closed-form solutions are fundamentally different. Please compare Eq. (1) - (7) in [1] and Eq. (1) - (10) in our paper. USRNet adopts a very sophisticated SR-specific closed-form solution in Eq. (7) of [1] to update $z_k$ . In contrast, we formulate a computationally efficient SCI-specific closed-form formulation based on the characteristic of sensing matrix in Eq. (10) of our paper, which can update $x_k$ in one shot. All these lead to the large variance in the iterative learning, including the formulation, input, and output of each iteration\n\n(b) The estimation method, implication, and function of the estimated parameters\n\nSee the third subpart of Sec. 3.3 in [1], the hyperparameter module of USRNet directly adopts the noise level $\\mathbf{σ}$ and scale factor $\\mathbf{s}$ as inputs. Plus, the blur kernel $\\mathbf{k}$ is directly applied in the subsequent iterative learning. In real practice, these degradation parameters are usually not given in advance and thus need manual tweaking. As a result, USRNet suffers from poor generality. In application, usually only the degraded image is given. Yet, the hyperparameter module does not take the low-resolution image as input. Thus, the estimated parameters do not capture the feature and degradation pattern from the low-resolution image but only represent the manually tweaked parameter $\\mathbf{σ}$ and $\\mathbf{s}$ to function as a ‘slide bar’ to control the input and output of each iteration. In contrast, our estimator directly operates and extracts information from the compressed measurement and physical mask. Hence, the estimated parameters can capture the feature and CASSI degradation pattern from the degraded image. Besides, the mask is usually given in advance. Thus, DAUHST does not need manual tweaking and enjoys better generalization ability\n\n(c) Technique\n\nUSRNet is based on CNN, showing limitations in capturing long-range dependencies. DAUHST based on Transformer addresses this issue. Our HS-MSA jointly develops two branches. The local branch extracts local contents and the non-local branch models long-range interactions through shuffle operation. Besides, all the networks in each iteration of USRNet share the same weights. This forces a single model to fit different image processing functions of different iterations. Yet, the representing ability of a single model is limited. Thus, this weights-sharing operation limits the progressive image restoration performance, especially in SCI reconstruction that deals with sophisticated and severely ill-posed CASSI degradation. In contrast, DAUHST does not share weights of networks. Thus, DAUHST enjoys powerful representing ability to simulate the progressive SCI reconstruction across stages\n\n(d) Experiment \n\nWe perform ablations to compare with USRNet in the following table. USRHST indicates replacing U-Net in USRNet with our HST. DAUHST-share means sharing weights across stages like USRNet. Three-stage architecture is adopted. DAUHST-share outperforms USRHST by 1.06 dB, showing our DAUF is more suitable for SCI. USRHST surpasses USRNet by a large margin with less Params and FLOPS, which stems from the capacity of HST to model long-range dependencies. DAUHST outperforms DAUHST-share by 0.48 dB, showing that weights sharing operation sacrifices the representation ability\n\n| Method| PSNR | SSIM | Params (M) | FLOPS (G) |\n| - | - | - | - | - |\n| USRNet | 35.13 | 0.942 | 2.32 | 39.39 | \n| USRHST | 35.67 | 0.947 | 0.69 | 26.30 |\n| DAUHST-share | 36.73 | 0.955 | 0.73 | 27.17 |\n| DAUHST | 37.21 | 0.959 | 2.08 | 27.17 |\n\n`Reference`\n\n[4] Nonlinear image recovery with half quadratic regularization. In TIP 1995\n\n[5] Fast Image Deconvolution using Hyper-Laplacian Priors. In NeurIPS 2009\n\n[6] Multi-Scale Patch-Based Image Restoration. In TIP 2015", " `Q-2:` Comparison with CAT\n\n`A-2:` Our DAUHST is different from CAT in\n\n(a) Non-local self-attention mechanism\n\n$\\textbf{CAT does not use shuffle operations to capture long-range dependencies.}$ In Sec. 3.1.2 of CAT [2], the cross-patch self-attention (CPSA) partitions each single-channel feature map into patches. Then CPSA treats each patch $\\in \\mathbb{R}^{N\\times N}$ as a token to compute self-attention. CPSA is the same as the global multi-head self-attention (MSA) in ViT except that CPSA computes self-attention in a single channel at a time while global MSA calculates self-attention with all channels. In other words, CPSA is a depth-wise separable global MSA. Yet, this scheme limits the representing capacity and easily causes inaccurate matching because the representations and interactions of other channels are neglected when computing self-attention in a specific channel. In contrast, our HS-MSA exchanges the spatial positions of pixel vectors in different patches through shuffle operations. Then HS-MSA treats each pixel vector $\\in \\mathbb{R}^{C}$ as a token to calculate self-attention within each patch, see Fig. 3(d). Subsequently, an unshuffle operation is exploited to restore the original positions of tokens. By this means, HS-MSA establishes long-range dependencies\n\n(b) Network depth, memory and computational costs\n\nThe global and local self-attention of CAT are cascaded in a successive manner. There are three self-attention units in a basic block, see Fig. 2 (b) in [2]. This leads to two issues. Firstly, the local contents and global interactions are not simultaneously captured. Secondly, the depth of CAT is deepened, introducing difficulties into the training process, increasing the memory and computational costs, and lowering down the model inference speed. In contrast, HS-MSA simultaneously develops two parallel branches to extract local contents and non-local interactions, without increasing the depth and costs. Thus, HST is more cost-effective, efficient, and easier to train\n\n(c) Motivation and technique\n\nCAT is proposed as a backbone for high-level vision tasks. In contrast, HST is designed as a U-shaped structure to be plugged into unfolding framework for SCI reconstruction. Besides, CAT adopts absolute position embedding and patch embedding layer while HST applies learnable position embedding\n\n(d) Experiment\n\nWe adopt the two self-attention proposed by CAT, i.e., Inner-Patch Self-Attention (IPSA) and CPSA to replace HS-MSA in HST to conduct ablations in the following table. Our HS-MSA costs less Params, FLOPS, and training time but enjoys higher performance and faster inference speed, showing the advantages of HST\n\n| Method | PSNR | SSIM | Params (M) | FLOPS (G) | Train Time (h) | Test Time (ms) |\n| - | - | - | - | - | - | - |\n| IPSA + CPSA | 33.14 | 0.917 | 0.49 | 10.37 | 32 | 42 |\n| HS-MSA | 34.05 | 0.930 | 0.48 | 9.72 | 24 | 29 |\n\nWe will follow your advice to cite USRNet [1] and CAT [2], and add these results in the revision\n\n`Q-3:` Comparison between HST and MST\n\n`A-3:` In fact, the FFN and FPN-style connection of HST and MST both follow previous works, such as Swin Transformer, U-former, PVT, etc. However, we do not claim this part as our contributions. We state that HS-MSA is our contribution. So we keep the same flow as MST [1] for fair comparison of self-attention mechanism to show the advantages of HST. HST is different from MST in\n\n(a) Motivation\n\nMST is motivated by the fact that HSI representations are spatially sparse while spectrally self-similar. Thus, MST captures the inter-dependencies in spectral dimension while circumventing the HSI spatial sparsity nature. Our HST is proposed to jointly model local and non-local interactions with a low computational cost in spatial dimension, which alleviates the limitations and combines the advantages of local and global MSA. Hence, our HST fits the HSI spatial sparsity nature better\n\n(b) Technique\n\nMST treats each single-channel feature map $\\in \\mathbb{R}^{H\\times W}$ as a token and computes self-attention in channel wise. HST treats each pixel vector $\\in \\mathbb{R}^{C}$ as a token and calculates self-attention in spatial wise. Thus, HST can capture more fine-grained pixel-level HSI self-similarity. The position embedding of MST is produced by CNN while that of HST is additive learnable parameters\n\n(c) Performance\n\nIn Tab. 2(b), HS-MSA yields 0.23 dB improvements over S-MSA. Yet, this margin is just for one stage and without position embedding. In the following table, we plug MST and HST into DAUF and increase the number of stages. PSRN / SSIM are reported. The improvements of HST over MST enlarges as the number of stages increases. In particular, DAUHST-9stg outperforms DAUMST-9stg by 1.35 dB\n\n| Stage | 1 | 3 | 5 | 7 | 9 |\n| - | - | - | - | - | - |\n| DAUMST | 34.01 / 0.927 | 36.47 / 0.954 | 36.89 / 0.958 | 36.95 / 0.959 | 37.01 / 0.959 |\n| DAUHST | 34.36 / 0.932 | 37.21 / 0.959 | 37.75 / 0.962 | 38.20 / 0.968 | 38.36 / 0.967 |", " `Q-4:` Ablation study of setting both $\\alpha$ and $\\beta$ as learnable parameters\n\n`A-4:` We conduct the ablation as you recommend in the following table. We adopt DAUHST-3stg as Baseline-3 but $\\alpha$ is set as learnable parameters and $\\beta$ is not used. If $\\alpha$ and $\\beta$ are both learnable parameters, the improvements are marginal, i.e., 0.02 dB when $\\beta_k$ adds with $x_k$ and 0.13 dB when $\\beta_k$ concatenates with $x_k$ . However, our DAUF gains by 0.72 dB, which surpasses the degradation-unaware schemes by over 0.59 dB. This evidence suggests that capturing CASSI degradation patterns and ill-posedness degree is informative for the iterative learning. Thanks for your advice, we will add this ablation in the revision\n\n| Method | $\\beta_k$ with $x_k$ | PSNR | SSIM | Params (M) | FLOPS (G) |\n| - | - | - | - | - | - |\n| Baseline-3 | None | 36.49 | 0.952 | 2.03 | 26.23 |\n| Both Learnable | add | 36.51 | 0.952 | 2.03 | 26.23 |\n| Both Learnable | concate | 36.62 | 0.953 | 2.03 | 26.29 |\n| DAUF | concate | 37.21 | 0.959 | 2.08 | 27.17 |\n\n`Q-5:` Question about removing HS-MSA\n\n`A-5:` In Fig.3 (b), removing HS-MSA indicates that the first layer normalization, HS-MSA, and the first skip connection are all removed and replaced by an identity operation. Sorry for confusing, we clarify this point in the revision\n\n`Q-6:` Why does Tab. 2(b) adopts a one-stage architecture?\n\n`A-6:` The memory bottleneck of global self-attention is one of the reasons. In this ablation study, we focus on comparing different self-attention mechanisms. Thus, we reduce the effect of multi-stage iterative learning by adopting a single-stage structure. By the way, we are glad to share the ablation study on three-stage architecture in the following table. Baseline-4 indicates removing HS-MSA from DAUHST-3stg. Different position embedding schemes are removed for stronger comparison. Our HS-MSA outperforms G-MSA, S-MSA, and SW-MSA by 0.95, 0.78, and 0.66 dB.\n\n| Method | Baseline-4 | G-MSA | SW-MSA | S-MSA | HS-MSA |\n| - | - | - | - | - | - |\n| PSNR | 35.37 | 35.84 | 36.13 | 36.01 | 36.79 |\n| SSIM | 0.938 | 0.948 | 0.952 | 0.950 | 0.956 |\n| Params (M) | 1.11 | 1.35 | 1.35 | 1.35 | 1.35 |\n| FLOPS (G) | 18.55 | 28.91 | 26.24 | 24.68 | 27.17 |\n\n`Q-7:` Question about the auxiliary variable\n\n`A-7:` The different positions of the auxiliary variable lead to different unfolding inferences and subsequent iterative learning. We introduce $z$ into the image prior term. In the iteration, the solution $x$ is firstly handled while the auxiliary variable $z$ is subsequently solved. USRNet introduces the auxiliary variable into the data term. Then in the iteration, the auxiliary variable $z$ is firstly solved while the solution $x$ is secondly handled. Please refer to `A-1` of `Response to Reviewer Jov1 - Part 1` for more comparisons between DAUHST and USRNet.\n\n`Q-8:` Question about the comparison of complexity for attention alternatives\n\n`A-8:` In fact, we have compared the memory and computational complexity of using different self-attention mechanisms in Tab. 2(b) and the second subpart of Sec. 3.4. In Tab. 2(b), Params indicates the memory complexity while FLOPS indicates computational complexity. Besides, we also provide theoretical analysis of computational complexity in Sec. 2 of the supplementary. We are glad to list the theoretical computational complexity in the following table. Suppose the input size as $H \\times W \\times C$. In implementation, $H = W = 256$, $M = 8$, $C = 28$. Our HS-MSA only requires 0.89% computational costs of G-MSA but also captures global spatial interactions, showing its efficiency advantage.\n\n| Self-Attention | Computational Complexity |\n| - | - |\n| G-MSA | $4H\\hat W C^2+2(H\\hat W)^2C$ |\n| SW-MSA | $4H\\hat W C^2+2M^2H\\hat WC$ |\n| S-MSA | $4H\\hat W C^2+2H\\hat WC^2/N$ |\n| HS-MSA | $4H\\hat W C^2+M^2H\\hat WC+H^2\\hat W^2C/M^2$ |\n\n`Q-9:` Questions about weights sharing, training and testing phases\n\n`A-9:` Different stages do not share parameters or weights although they use the same HST architecture because weight-sharing operation limits the representing capacity of the whole network. Note that DAUHST outperforms SOTA methods with less Params even without weight-sharing operation, see Tab. 1 of the paper. There is no difference between training and testing phases. The test input should go through all stages.\n\n`Q-10:` Comparison of training and inference time\n\n`A-10:` We admit that the performance improvement of our method comes with increasing training and testing time. However, we compare DAUHST with SOTA methods on the same GPU in the following table. The training and testing time of DAUHST is moderate while the improvement of DAUHST is significant.\n\n| Method | DNU | TSA-Net | GAP-Net | MST-L | DAUHST-3stg |\n| - | - | - | - | - | - |\n| PSNR | 30.74 | 31.46 | 33.26 | 35.18 | 37.21 |\n| SSIM | 0.863 | 0.894 | 0.917 | 0.948 | 0.959 |\n| Train (h) | 253 | 69 | 61 | 100 | 70 |\n| Ineference (ms) | 558 | 68 | 60 | 90 | 76 |", " `Q-11:` Does the non-local branch capture relatively long-range or global dependencies?\n\n`A-11:` We claim that the non-local branch captures global dependencies. See Fig. 3 (d). For each patch, after the shuffle operation, all patches in the global area are extracted a token to this patch for calculating self-attention. In other words, the non-local branch calculates self-attention inside each patch with tokens that come from all patches in the whole image. Besides, the local branch computes self-attention with all tokens inside a patch. Thus, the interactions between any two tokens in the whole image can be established and the global dependencies can be captured.", " Thanks for your valuable comments, now we answer your questions one by one.\n\nAll source code and pre-trained models will be made publicly available for further research.\n\n`Q-1:` Explanation of our technical novelty and contributions\n\n`A-1:` We highlight our technical novelty and contributions in two parts, deep unfolding framework and Transformer.\n\n(a) Deep unfolding framework\n\nOur DAUF is fundamentally different from existing deep unfolding frameworks. As analyzed in Line 5-6 and 105-106, previous unfolding methods do not estimate the degradation patterns and ill-posedness degree from the highly related CASSI system to guide the iterative learning. In contrast, we formulate a principled degradation-aware unfolding framework (DAUF) to address this issue. As mentioned in Line 74-78 and 139-142, our DAUF estimates parameters from the compressed measurement and physical mask in the CASSI system. Then the parameters, which capture critical cues of CASSI degradation patterns and ill-posedness degree, are fed into each iteration to contextually scale the linear projection and provide noise level information for the denoising network. The ablation study in the third subpart of Sec. 3.4 and Tab. 2(c) shows that our DAUF significantly outperforms previous unfolding frameworks, i.e., DNU, GAP, and ADMM by 2.59, 1.69, and 1.63 dB. This evidence demonstrates the impressive effectiveness and contribution of our DAUF. Besides, As shown in Fig.1 and Tab.1, our DAUHST outperforms previous deep unfolding methods by over 4 dB.\n\n(b) Transformer\n\nOur HST is fundamentally different from previous Transformers including those that have been used in other low-level vision tasks. As analyzed in Line 68 - 71, the computational complexity of Global Transformer is quadratic to the spatial size of the input map. This burden is non-trivial and sometimes unaffordable. The receptive fields of local Transformer are limited within position-specific windows. To tackle these problems, we propose HS-MSA that simultaneously develops two branches, i.e., a local branch capturing local content inside patches and a non-local branch modeling long-range dependencies through shuffle operation. Our HS-MSA can enjoy larger receptive fields and relatively cheaper computational costs. In Tab. 2(b) and the second subpart of Sec. 3.4, our HS-MSA outperforms G-MSA and SW-MSA by 0.42 and 0.30 dB. The improvements of our HS-MSA will enlarge when the number of stages increases. \n\nIn addition, our HS-MSA is different from S-MSA of MST in\n\n(i) Motivation. S-MSA is motivated by the fact that HSI representations are spatially sparse while spectrally self-similar. Thus, MST captures the inter-dependencies in spectral dimension while circumventing the HSI spatial sparsity nature. Our HS-MSA is proposed to simultaneously model local and non-local interactions in spatial dimension, which alleviates the limitations and combines the advantages of local and global MSA. Hence, our HS-MSA fits the HSI spatial sparsity nature better than S-MSA. \n\n(ii) Technique. S-MSA treats each single-channel feature map $\\in \\mathbb{R}^{H\\times W}$ as a token and computes self-attention in channel wise. Our HS-MSA treats each pixel vector $\\in \\mathbb{R}^{C}$ as a token and calculates self-attention in spatial wise. Therefore, our HS-MSA can capture more fine-grained pixel-level HSI self-similarity. Besides, the position embedding of S-MSA is generated by CNN while our position embedding is set as learnable parameters.\n\n(iii) Performance. In Tab. 2(b), our HS-MSA achieves 0.23 dB improvement over MST. Nonetheless, this margin is just for one stage and without position embedding. As shown in the following table, we conduct an ablation study by plugging MST and HST into our DAUF and increase the number of stages. PSNR / SSIM are reported. As can be seen that the improvement of HST over MST enlarges as the number of stages increases. In particular, our DAUHST-9stg significantly outperforms DAUMST-9stg by 1.35 dB, suggesting the advantage and effectiveness of our HST.\n\n| Stage | 1 | 3 | 5 | 7 | 9 |\n| - | - | - | - | - | - |\n| DAUMST | 34.01 / 0.927 | 36.47 / 0.954 | 36.89 / 0.958 | 36.95 / 0.959 | 37.01 / 0.959 |\n| DAUHST | 34.36 / 0.932 | 37.21 / 0.959 | 37.75 / 0.962 | 38.20 / 0.968 | 38.36 / 0.967 |", " `Q-2:` Comparison with U-Transformer [1]\n\n`A-2:` We argue that our DAUHST is completely different from U-Transformer. In fact, the only thing they have in common is that they both adopt U-shaped structure. Yet, the U-shaped structure is proposed by U-Net [2] and has been widely applied. We do not claim this as our contribution. Our DAUHST and U-Transformer are different in\n\n(a) Motivation and research topic\n\nU-Transformer aims to address the conceptual limitations and model spatial relationships between anatomical structures. Our DAUHST is proposed to perceive CASSI degradation patterns to adjust the iterative learning, and jointly capture local and non-local dependencies of spatially sparse HSI representations. U-Transformer is designed for medical image segmentation while DAUHST is customized for SCI reconstruction\n\n(b) Technique\n\n(i) We firstly focus on comparing the self-attention mechanism. U-Transformer mainly proposes two attentions, multi-head self-attention (MHSA) and multi-head cross-attention (MHCA). MHCA is applied to the skip connection between encoder and decoder to filter out non-semantic features and allow a fine spatial recovery. It is not self-attention. The MHSA is a vanilla global multi-head self-attention. Its computational costs are quadratic to the spatial dimension of the input map. This is a huge burden and sometimes unaffordable. Thus, only a single MHSA is applied at the lowest resolution of the encoder in U-Transformer. In contrast, as analyzed in Sec. 2.3, our HS-MSA jointly develops two branches. The local branch captures local contents by computing self-attention within local patches. The non-local branch models long-range dependencies by globally shuffling tokens and then calculating self-attention between tokens from different patches. Thus, the computational complexity of our HS-MSA is much lower than MHSA. Besides, U-Transformer only employs a single MHSA layer. In contrast, DAUHST plugs HS-MSA into the basic block as a key component to build up the whole network. So the long-range dependencies can be repeatedly captured and enhanced by DAUHST. Hence, our DAUHST can model more robust and stronger non-local interactions than U-Transformer\n\n(ii) All details of DAUHST and U-Transformer are completely different. For instance, the components of downsampling and upsampling. U-Transformer has four levels while DAUHST has three. DAUHST is unfolded from the MAP energy function based on SCI degradation model in Eq. (1) and (2) of the paper. While U-Transformer learns an end-to-end implicit mapping of segmentation. Thus, DAUHST is more intuitively interpretable by explicitly characterizing the image priors and the CASSI system imaging model. DAUHST uses layer normalization while U-Transformer uses batch normalization. And so on. In a nutshell, DAUHST and U-Transformer are two completely different things\n\n(c) Experiment\n\nWe conduct experiments to compare DAUHST and U-Transformer in the following table. Our DAUHST-3stg dramatically surpasses U-Transformer by 6.14 dB while only costing 21% FLOPS, suggesting the significant superiority of DAUHST over U-Transformer.\n\n| Method| PSNR | SSIM | Params (M) | FLOPS (G) |\n| - | - | - | - | - |\n| U-Transformer | 31.07 | 0.861 | 6.79 | 129.21 | \n| DAUHST-3stg | 37.21 | 0.959 | 2.08 | 27.17 |\n\nWe will cite [1] and add these results in the revision\n\n`Q-3:` Ablations of the design choices for the U-shaped structure\n\n`A-3:` Thanks for your advice, we conduct the ablation as you recommend. Specifically, we simply apply a multi-head vision Transformer, i.e., ViT [3]. Besides, we also change the overall architecture to a single-scale structure without downsampling and upsampling. Three-stage structure is adopted. The results are listed in the following table, where $\\dagger$ denotes using single-scale architecture, OOM indicates out of memory issue raised by GPU, and ViT* denotes downsampling the input images to $\\frac{1}{4}$ size due to the memory limitation. As can be seen that the computational cost of directly applying ViT is unaffordable for our GPU. DAUHST$^\\dagger$ yields 1.44 dB improvement than ViT*$^\\dagger$ while costing less FLOPS, suggesting the effectiveness of HS-MSA. DAUHST surpasses DAUHST$^\\dagger$ by 0.92 dB. This evidence shows that U-shape is a better choice of architecture for SCI reconstruction\n\n| Method| PSNR | SSIM | Params (M) | FLOPS (G) |\n| - | - | - | - | - |\n| ViT$^\\dagger$ | OOM | OOM | OOM | OOM | \n| ViT*$^\\dagger$ | 34.85 | 0.933 | 0.35 | 36.12 | \n| DAUHST$^\\dagger$ | 36.29 | 0.951 | 0.35 | 27.30 | \n| DAUHST | 37.21 | 0.959 | 2.08 | 27.17 |\n\nWe will add this ablation in the revision\n\n`Reference`\n\n[1] U-net transformer: Self and cross attention for medical image segmentation. In International Workshop on Machine Learning in Medical Imaging 2021.\n\n[2] U-net: Convolutional networks for biomedical image segmentation. In MICCAI 2015.\n\n[3] An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale. In ICLR 2021.", " `Q-4:` Question about discussing the limitations of this work\n\n`A-4:` In fact, we have discussed the limitations of our work in Sec. 5 of the supplementary. The main limitation of our work is that the performance improvement of our method comes with lowering down the inference speed and increasing the model complexity. Specifically, the Params, FLOPS, and depth of network increase with the stage number of DAUHST. For instance, compared with DAUHST-1stg, DAUHST-9stg achieves 4.00 dB improvement but requires 8.18$\\times$ FLOPS, 8.42$\\times$ Params, and 4.04$\\times$ inference time. To tackle this limitation, we will study how to improve the restoration performance without increasing the model complexity and sacrificing the inference speed. However, as shown in Tab. 1 and Sec. 3.2 of the main paper, our DAUHST significantly outperforms other state-of-the-art methods while using cheaper computational and memory costs.\n\n`Q-5:` Question about evaluating the robustness of the model\n\n`A-5:` In fact, we have done ablation to evaluate the robustness of our method in Sec. 4.2 and Tab. 1(b) of the supplementary. After training the network, we fix its parameters. In the testing phase, we change the mask by randomly cropping it with size 256×256 from the real mask of size 660×660 to evaluate the robustness of DAUHST for different signal modulations. We directly copy the results in Tab. 1(b) of the supplementary to the following table, where Mask-0 indicates the original mask used in the training phase. Compared with the two SOTA methods TSA-Net that degrades by 7.51% on average and DGSMP that degrades by 13.91% on average, our DAUHST-3stg declines by much smaller margins, i.e., only 2.03% on average. These results suggest that DAUHST does not need to be re-trained from scratch when the measurement model changes because DAUHST only sacrifices marginal performance that can be ignored. In other words, our DAUHST is more robust and flexible for large-scale SCI reconstruction.\n\n| Method| TSA-Net| DGSMP | DAUHST-3stg |\n| - | - | - | - |\n| Mask-0 | 31.46 $\\downarrow$ `0.00%` | 32.63 $\\downarrow$ `0.00%` | 37.21 $\\downarrow$ `0.00%` |\n| Mask-1 | 29.18 $\\downarrow$ `7.24%` | 28.50 $\\downarrow$ `12.66%` | 36.43 $\\downarrow$ `2.10%`|\n| Mask-2 | 29.10 $\\downarrow$ `7.50%` | 27.87 $\\downarrow$ `14.59%` | 36.55 $\\downarrow$ `1.77%`|\n| Mask-3 | 29.01 $\\downarrow$ `7.79%` | 27.91 $\\downarrow$ `14.47%` | 36.38 $\\downarrow$ `2.23%`|", " Thanks for your comments. \n\nCode and models will be released to the public.\n\n`Q-1:` Explanation of our motivation and contribution\n\n`A-1:` We highlight our novelty and technical contributions in two parts, deep unfolding framework and Transformer\n\n(a) Deep unfolding framework\n\nOur DAUF is different from previous unfolding methods in Snapshot Compressive Imaging (SCI), e.g., GAP, DNU, and ADMM. Previous methods do not estimate CASSI degradation pattern and ill-posedness degree (defined in `A-4` of `Response to Reviewer nC4p - Part 2`)\n to guide the iterative learning. To address this issue, we formulate DAUF to estimate parameters from the compressed image and physical mask, and then use these parameters to adjust each iteration. In Tab. 2(c), DAUF outperforms DNU, ADMM, and GAP by 2.59, 1.69, and 1.63 dB. In Fig.1, DAUHST outperforms other unfolding methods by over 4 dB\n\n(b) Transformer\n\nOur HST is different from previous Transformers. In Line 68 - 71, the computational complexity of Global Transformer is enormous. The receptive fields of local Transformer are limited within position-specific windows. To tackle these issues, we propose HS-MSA to jointly develop two branches. The local branch captures local content inside patches and the non-local branch models long-range dependencies through shuffle operation. Thus, HS-MSA can enjoy larger receptive fields and relatively cheaper computational costs. In Tab. 2(b), HS-MSA outperforms G-MSA and SW-MSA by 0.42 and 0.30 dB. We provide comparisons between HS-MSA with S-MSA in `A-3` of `Response to Reviewer nC4p - Part 2`\n\n`Q-2:` Comparison with 3DT-Net [1]\n\n`A-2:` DAUHST is different from 3DT-Net in\n\n(a) Research topic\n\n3DT-Net is proposed for Hyperspectral Image Super-Resolution (HSISR). It aims to capture a low-resolution HSI and a high-resolution multispectral image, e.g., RGB image, and fuse them into a resultant image with high spatial and spectral resolution simultaneously. This task is more like image fusion or synthesis than restoration. The main degradation of HSISR is low resolution in spatial and spectral dimensions. In contrast, DAUHST is proposed for Snapshot Compressive Imaging Reconstruction (SCIR). It aims to restore the latent 3D HSI cube from the compressed 2D measurement, see Line 34 - 38. The degradation of SCIR is modulation and compression caused by CASSI system. To the best of our knowledge, DAUHST is the first Transformer-based unfolding method for SCIR\n\n(b) Motivation and technique\n\n(i) Unfolding Framework. The unfolding framework of 3DT-Net is based on proximal gradient algorithm and observation models of LR-HSIs and HR-MSIs. 3DT-Net does not estimate degradation pattern and ill-posedness degree from input LR-HSIs and HR-MSIs to direct the iterative learning. In contrast, our unfolding framework starts from half-quadratic splitting algorithm and CASSI mathematical model, which makes the subsequent formula derivation completely different from that of [1]. Please compare Eq. (1) - (9) in [1] and Eq. (1) - (10) in our paper. In Line 74 - 78, DAUF implicitly estimates informative parameters from the compressed measurement and physical mask. Then DAUF feeds the parameters, which capture key cues of CASSI degradation patterns and ill-posedness degree, into each iteration to adaptively scale the linear projection and provide noise level information for the denoising prior network. Besides, 3DT-Net employs some CNNs to solve the data term, e.g., the four channel or spatial operators in Eq. (6) - (9) of [1]. In contrast, we formulate a computationally efficient mathematical closed-form solution to handle data term in Eq. (10)\n\n(ii) Denoiser Prior Network. 3DT-Net adopts the Swin-Transformer layer and 3D convolution as the two key components of its prior network to exploit the spatial-spectral correlations. The adopted window-based multi-head self-attention (W-MSA) only calculates the self-attention within position-specific windows, showing limitations in capturing long-range dependencies. Besides, the prior network of 3DT-Net adopts a single-scale architecture without downsampling and upsampling the spatial resolution, which shows limitations in extracting multi-scale contextual information. In contrast, we customize a novel HS-MSA to alleviate the limitation of W-MSA. HS-MSA develops a non-local branch to model long-range dependencies through shuffle operations. In addition, HST adopts a three-level structure to capture multi-scale contextual information that is critical for HSI reconstruction. Plus, 3DT-Net shares weights across stages, limiting the representation capacity. DAUHST employs different parameters in different iterations to better fit the sophisticated SCI reconstruction\n\nWe will cite and introduce 3DT-Net in revision. We are glad to conduct experiment to compare with 3DT-Net but we have not found any codes of 3DT-Net on github\n\n`Reference`\n\n[1] Learning A 3D-CNN and Transformer Prior for Hyperspectral Image Super-Resolution. Arxiv", " `Q-3:` Comparison between HS-MSA and S-MSA\n\n`A-3:` HS-MSA is fundamentally different from S-MSA in\n\n(a) Motivation\n\nS-MSA is motivated by the fact that HSI representations are spatially sparse while spectrally self-similar. Thus, MST captures the inter-dependencies in spectral dimension while circumventing the HSI spatial sparsity nature. HS-MSA is proposed to jointly model local and non-local interactions with a low computational cost in spatial dimension, which alleviates the limitations and combines the advantages of local and global MSA. Hence, our HS-MSA fits the HSI spatial sparsity nature better\n\n(b) Technique\n\nS-MSA treats each single-channel feature map $\\in \\mathbb{R}^{H\\times W}$ as a token and computes self-attention in channel wise. HS-MSA treats each pixel vector $\\in \\mathbb{R}^{C}$ as a token and calculates self-attention in spatial wise. Thus, HS-MSA can capture more fine-grained pixel-level HSI self-similarity\n\n(c) Experiment\n\nIn Tab. 2(b), HS-MSA is 0.23 dB higher than S-MSA. Yet, this margin is just for one stage and without position embedding. In the following table, we plug MST and HST into DAUF and increase the number of stages. PSRN / SSIM are reported. The improvements of HS-MSA over S-MSA enlarge as the number of stages increases. In particular, DAUHST-9stg outperforms DAUMST-9stg by 1.35 dB\n\n| Stage | 1 | 3 | 5 | 7 | 9 |\n| - | - | - | - | - | - |\n| DAUMST | 34.01 / 0.927 | 36.47 / 0.954 | 36.89 / 0.958 | 36.95 / 0.959 | 37.01 / 0.959 |\n| DAUHST | 34.36 / 0.932 | 37.21 / 0.959 | 37.75 / 0.962 | 38.20 / 0.968 | 38.36 / 0.967 |\n\n`Q-4:` What are CASSI degradation patterns and ill-posedness degree? Why are they important?\n\n`A-4:` (a) See the measurement and GT HSIs in Fig. 4 of the paper. The CASSI degradation patterns and ill-posedness degree are that the original HSIs are compressed from a 3D cube to a single 2D image, the scene is severely distorted and blurred, and many artifacts are introduced into the measurement. In Line 34 -38, this degradation stems from the CASSI process that uses a coded aperture and a disperser to modulate the spectral signals at different wavelengths, and then mixes all modulated signal to generate a 2D compressed measurement\n\n(b) The subsequent iterative learning is based on MAP theory that is highly related to the CASSI degradation model, see Eq. (2) of the paper. Thus, the two main phases unfolded from the MAP-based energy function Eq. (2) in each iteration, i.e., linear projection that requires scale factor in Eq. (10) and denoiser prior that requires noise level information in Eq. (11), are also closely correlated to the CASSI degradation pattern and ill-posedness degree. Yet, previous unfolding methods naively set these two parameters as constants or learnable parameters, which neglects the connection between CASSI system and the iterative learning. To tackle this issue, DAUF estimates the two parameters from the physical mask and compressed measurement. Then the parameters capturing key cues of CASSI degradation patterns and ill-posedness degree are exploited to adaptively scale the linear projection and provide noise level information for the denoiser prior. As shown in Tab. 2(c), our DAUF outperforms DNU, ADMM, and GAP by 2.59, 1.69, and 1.63 dB. As shown in Fig.1, DAUHST significantly outperforms previous deep unfolding methods by over 4 dB\n\n`Q-5:` Details about the parameter estimation\n\n`A-5:` Instead of using hand-crafted formulation or image prior that needs manual tweaking and suffers from poor generality, we adopt a learnable estimator to implicitly and automatically estimate the informative parameters from the measurement and sensing mask. The details of the estimator is described in Line 138 -142. The shifted measurement concatenated with the sensing matrix undergoes a conv1x1, a strided conv3x3, a global average pooling, and three fully connected layers to obtain the parameters. In other words, $\\alpha$ and $\\beta$ are estimated end-to-end by passing the measurement and sensing matrix through the estimator. You can also refer to Line 338 - 346 of code `DAUHST.py` in the supplementary for implementation\n\n`Q-6:` What determines $\\mu$ and $\\tau$?\n\n`A-6:` In Line 109 - 110, $\\tau$ is a hyperparameter balancing the importance between data term and prior term. In Line 113, $\\mu$ is a penalty parameter that forces x and z to approach the same fixed point. $\\mu$ and $\\tau$ are both hyperparameters that need to be set. Some previous unfolding frameworks such as GAP and ADMM set them as constants (=1). Some (e.g., DNU) set them as learnable parameters. In contrast, our DAUF set them as informative parameters that are estimated from the CASSI system. In Line 132 - 133, we set $\\alpha_k = \\mu_k$ and $\\beta_k = \\mu_k / \\tau_k$ . $\\alpha_k$ and $\\beta_k$ are estimated from the physical mask and compressed measurement. Then $\\mu_k$ and $\\tau_k$ are determined by $\\alpha_k$ and $\\beta_k$ , i.e., $\\mu_k = \\alpha_k$ and $\\tau_k = \\alpha_k / \\beta_k$", " `Q-7:` The influence of the number of stages\n\n`A-7:` In fact, we have conducted this ablation in Sec. 4.1 and Tab. 1(a) of the supplementary. We also list the results here in the following table. The performance improves when we gradually increase the stage number. We notice that a 3-stage DAUHST can achieve a very impressive PSNR result of 37.21 dB.\n\n| Stage | 1 | 3 | 5 | 7 | 9 |\n| - | - | - | - | - | - |\n| PSNR | 34.36 | 37.21 | 37.75 | 38.20 | 38.36 |\n| SSIM| 0.932 | 0.959 | 0.962 | 0.968 | 0.967 |\n| Params (M) | 0.73 | 2.08 | 3.44 | 4.79 | 6.15 |\n| FLOPS (G) | 9.72 | 27.17 | 44.61 | 62.05 | 79.50 |\n\n`Q-8:` The spectral ranges covered by the images in the synthetic datasets are narrow. Experiments with more infrared spectrum.\n\n`A-8:` (a) We use the same datasets to evaluate the SCI reconstruction performance as previous snapshot compressive imaging reconstruction methods such as GAP-Net, DGSMP, TSA-Net, and PnP-DIP-SCI for fair comparison.\n\n(b) We are glad to conduct the experiment as you recommend. We adopt the Botswana dataset (https://www.ehu.eus/ccwintco/index.php/Hyperspectral_Remote_Sensing_Scenes) that contains more infrared spectra as you suggest. The spectral wavelength range of the Botswana dataset is 400 nm - 2500 nm. We uniformly select 28 out of 145 spectra and randomly crop patches with a spatial size of 256×256 from the Botswana dataset as training samples. The results are listed in the following table. Our DAUHST still outperforms other SOTA methods while requiring the least computational cost. These results demonstrate the cost-effective advantage and generalization ability of our DAUHST.\n\n| Method| GAP-Net | TSA-Net | MST-L | DAUHST-3stg |\n| - | - | - | - | - |\n| PSNR | 29.36 | 31.52 | 31.78 | 32.45 | \n| SSIM| 0.705 | 0.735 | 0.737 | 0.751 |\n| Params (M) | 4.27 | 44.25 | 2.03 | 2.08 |\n| FLOPS (G) | 78.58 | 110.06 | 28.15 | 27.17 |", " Thanks for your valuable comments, now we answer your questions one by one.\n\nAll source code and pre-trained models will be made publicly available for further research.\n\n`Q-1:` Move the visual results of DAUHST, HDNet, and BIRNAT from the supplementary to the main paper.\n\n`A-1:` Due to space limitation, we present these comparisons in the supplementary. Thanks for your advice, we will add these results to the main paper in the revision.\n\n\n`Q-2:` Explanation of the reshape operation of $\\mathbf{R}$ in Line 156 of the main paper.\n\n`A-2:` $\\mathbf{R}$ is reshaped from $\\mathbb{R}^{H \\times (W+d(N_\\lambda - 1)) \\times N_\\lambda}$ to $\\mathbb{R}^{H (W+d(N_\\lambda - 1)) N_\\lambda}$\n\n\n`Q-3:` Explanation of the vectorized and shifted operations in Line 98 of the main paper.\n\n`A-3:` Please refer to Sec.1 of the supplementary for the mathematical model of CASSI. \n\n(a) Vectorized operation\n\nThe vectorized operation is detailed in Line 28 - 33 of the supplementary. It concatenates all the columns of a matrix as one single vector. Specifically, define $\\tilde{\\mathbf{X}} \\in \\mathbb{R}^{H\\times (W+d(N_\\lambda - 1))\\times N_\\lambda}$ as the shifted version of the original HSI signal $\\mathbf{X} \\in \\mathbb{R}^{H\\times W \\times N_\\lambda}$ . Denote the vectorized operation as $\\text{vec( )}$. Then $\\mathbf{x}$ in Line 98 can be formulated as \n\n$\\mathbf{x} = \\text{vec}([\\tilde{\\mathbf{x}}^{(1)}, ..., \\tilde{\\mathbf{x}}^{(N_\\lambda )}])$,\n\nwhere $\\tilde{\\mathbf{x}}^{(n_{\\lambda} )} = \\text{vec}(\\tilde{\\mathbf{X}}(:, :, n_\\lambda ))$ and $[..., ...]$ indicates the concatenating operation\n\n(b) Shifting operation\n\nThe shifting is caused by the disperser in CASSI. The shifted operation is detailed in Line 13 - 21, and Eq (2) of the supplementary. After passing through a disperser, the 3D HSI cube $\\mathbf{X}' \\in \\mathbb{R}^{H\\times W \\times N_\\lambda}$ becomes tilted and could be considered as sheared along the $y$-axis. Define $\\mathbf{X}'' \\in \\mathbb{R}^{H\\times (W+d(N_\\lambda - 1))\\times N_\\lambda}$ as the tilted cube, and $\\lambda_c$ as the reference wavelength, i.e., $\\mathbf{X}'[:, :, n_{\\lambda_c} ]$ is not sheared along the $y$-axis. Then the dispersion is formulated as\n\n$\\mathbf{X}''(u, v, n_{\\lambda}) = \\mathbf{X}'(x, y+d(\\lambda_n - \\lambda_c), n_{\\lambda})$ ,\n\nwhere $(u, v)$ indicates the coordinate system on the detector plane, $\\lambda_n$ denotes the wavelength of the $n_{\\lambda}$-th spectral channel, $d$ represents the shifting step, and $d(\\lambda_n - \\lambda_c)$ signifies the spatial shifting for the $n_{\\lambda}$-th channel on $\\mathbf{X}'$ . Thus, the shifted version $\\tilde{\\mathbf{X}}$ of the original HSI cube $\\mathbf{X}$ can be similarly formulated as \n\n$\\tilde{\\mathbf{X}} (u, v, n_{\\lambda}) = \\mathbf{X}(x, y+d(\\lambda_n - \\lambda_c), n_{\\lambda})$ .\n\n`Q-4:` Comparison of DAUF, GAP, and ADMM on CNN-based methods\n\n`A-4:` Thanks for your advice. We conduct the ablation study as you recommend in the following table. Three-stage architecture is adopted. For each stage, the same U-shaped CNN as GAP-Net and ADMM-Net is adopted. It can be observed that our DAUF significantly outperforms GAP and ADMM by 2.75 and 2.32 dB in PSNR, 0.046 and 0.038 in SSIM. These results demonstrate the impressive effectiveness and promising generalization ability of our DAUF. \n\n| Method | GAP | ADMM | DAUF |\n| ---------- | ------ | --------- | -------- |\n| PSNR | 32.06 | 32.49 | 34.81 | \n| SSIM | 0.892 | 0.900 | 0.938 |\n\n`Q-5:` Question about the FLOPS of BIRNAT. \n\n`A-5:` Yes, you are right. BIRNAT suffers from enormous FLOPS because it adopts an RNN architecture that recurrently processes images for many times (28 times for HSIs in the official implementation of BIRNAT). ", " This paper introduces a hyperspectral image reconstruction method based on a deep unfolding method and a Half-shuffle Transformer (HST). The deep unfolding method estimates parameters from the image and uses them to direct the iterative learning. The HST captures both local contents and non-local dependencies with relatively low computation cost. The proposed method was evaluated on both synthetic and real image datasets and demonstrated excellent performance over a few other methods. Ablation studies were also provided to show the contribution of key components in the proposed method. This is a solid paper. Each proposed component in the whole method structure seems to be working, and when putting together, they produce the best hyperspectral image reconstruction performance reported so far. However, I also have several concerns about this paper.\n\nFirst, the proposed DAUHST method has its novelty in combining transformer and deep unfolding for HSI restoration. However, the contribution can only be considered incremental since a similar idea (transformer as prior + unfolding) has been proposed for hyperspectral image super-resolution in November 2021, which is closely related to the reconstruction or restoration task: Learning A 3D-CNN and Transformer Prior for Hyperspectral Image Super-Resolution. Furthermore, both deep unfolding and transformer have been adopted separately for hyperspectral image processing. Take the self-attention HS-MSA module in the proposed Half-Shuffle Transformer (HST) as an example, it can be considered an extension of the S-MSA in MST-L [81]. Table 2 (b) also shows that the performance improvement of HS-MSA over S-MSA is marginal. \n\nSecond, the introduction section hasn't clearly described the motivation of the degradation-aware unfolding framework. It simply says previous methods do not estimate CASSI degradation patterns and ill-posedness degree. Please clearly define what are CASSI degradation patterns and ill-posedness degree and why they are important to the estimation process.\n\nThe method description also needs to be improved as well. In Figure 2, the parameter estimator takes the compressed measurement and the sensing of the CASSI system as inputs and produces \\alpha and \\beta. How is the estimation done? The details are missing. In lines 127-129, \\mu and \\tau are iteration-specific parameters. How their values are determined in each iteration? \n\nTable 1 shows that the 9 stages DAUHST produces the best results. An analysis of the influence of the number of stages on the final performance shall be given. Please address the comments in the Strengths And Weaknesses. The spectral ranges covered by the images in the adopted synthetic datasets are narrow. Please consider experiments with more infrared spectrum. ", " This paper proposes a degradation-aware unfolding framework (DAUF) where the parameters are estimated by the input image and physical mask, which can serve as a guidance for each iteration stage towards the final output. Among each iteration stage, two parts, e.g., a linear projection and denoising network, perform successively based on maximum a posteriori (MAP). Specifically, the denoising network builds on Transformer-type framework replacing the vanilla self-attention mechanism with two branches, local and non-local branch, to extract the local and long-dependency representations. Strengths:\nThe paper is clearly written and the logic flow is easy to follow. The method sufficiently utilizes the potential prior knowledge in the input image and the mask to guide the reconstruction process. For the denoising sublayer, local window based and shuffle based self-attention are leveraged to capture local and long-range dependencies. Overall, the approach achieves over 4 dB higher performance than SOTA deep unfolding based methods, and 0.78 dB than SOTA.\n\nWeaknesses:\nIn my opinion, the authors combine three approaches to establish their method [1,2,3]. To be specific, the authors of [1] also explore a deep unfolding network based on MAP and HQS and then get two parameters, alpha and beta, to generate x_k and z_k iteratively. With respect to the two-branch attention paradigm, the local attention based on windows and long-range attention based on shuffle operation have already put forward in [2] but in successive manner instead of parallel. For the flow of transformer, this paper follows most parts of [3], e.g., FFN part and FPN-style connection. To sum up, I doubt the novelty of the method. If authors are inspired by these papers, it would be better to include them in the reference. If I am wrong, please correct me.\n\n[1] Deep Unfolding Network for Image Super-Resolution, CVPR 2020.\n[2] CAT: Cross Attention in Vision Transformer, arxiv 2021.\n[3] Mask-Guided Spectral-Wise Transformer for Efficient Hyperspectral Image Reconstruction, CVPR 2022.\n 1, For the input of denoising network, beta_k is stretched to concatenate with x_k following the Eq. 12, and in Tab 2(d) the learnable alpha is studied. I wonder if beta and alpha can be both set as learnable parameters and achieve a compatible result, i.e., learnable beta is also stretched as the original method do or just be added into x_k . In that case, the method would not be degradation-aware.\n2, In 3.4, HS-MSA is remove in the first two subparts. Is it substituted by identity operation? DAUHST-3stg is used to perform ablation studies except for self-attention mechanism (DAUHST-1stg). Is it because the memory bottlenecks of global self-attention?\n3, In Eq. 3, auxiliary variable z is introduced to replace x in the image prior term R(*), but this replacement occurs in the data term in Eq4. of [1]. What is the difference?\n4, It would be better to provide the comparison of complexity for attention alternatives.\n5, The DAUF works in an iterative manner. Is the same HST used or not for different stages? Is there any difference between training and test phase? For example, should the test input go though all stages?\n[1] Deep Unfolding Network for Image Super-Resolution, CVPR 2020.\n The method works in an iterative manner where there is a Transformer-type HST in each stage, which may lead to a long training and inference time. In addition, the non-local branch captures relatively long-range dependencies but not globally. ", " This work proposes a novel unfolding Transformer-based algorithm for hyperspectral image reconstruction in CASSI system. There are two key components of the proposed method: \n\n(i) degradation-aware unfolding framework perceiving the CASSI degradation pattern and degree of ill-posedness, and\n\n(ii) half-shuffle Transformer capturing local contents and non-local dependencies jointly. \n\nHalf-shuffle Transformer is plugged into degradation-aware unfolding framework to establish the proposed degradation-aware unfolding half-shuffle Transformer. Strengths:\n\n(i) This work proposes the first Transformer-based unfolding method for HSI reconstruction in snapshot compressive imaging. \n\n(ii) The idea is novel and interesting. The degradation-aware unfolding framework changes the general unfolding paradigm of previous works (e.g., ADMM-Net, GAP-Net) by estimating parameters from CASSI system to adapt the iterative learning. Besides, the elaborately customized half-shuffle Transformer combines the advantages of local and global Transformers while using moderate Params and FLOPS.\n\n(iii) The performance is pretty impressive. DAUHST outperforms SOTA algorithms by large margins while using less Params and FLOPS. In particular, DAUHST achieves over 4dB improvements than previous unfolding methods. \n\n(iv) The experiments are comprehensive and the ablation study is well-designed. The comparisons in Table 1, Figure 4, and Figure 5 including 14 SOTA methods, which is very convincing. The ablation studies in Table 2 sufficiently evaluate the effectiveness of the proposed techniques. The in-depth visual analysis in Figure 6 reveals some important insights of unfolding frameworks for SCI.\n\n(v) The writing is good and easy to follow. Especially in Section 2.1. The mathematical notation and formulation are clear, rigorous, and neatly arranged. In addition, the presentation is well-dressed.\n\n(vi) The reproducibility can be guaranteed. I have check the submitted codes and models, and run the demo. The results in Table 1 of the main paper can be reproduced. The implementation details are described in Section 3.1. Meanwhile, the authors have claimed that they will release the code and models to the public. I believe this work can significantly benefit the community. \n\nWeakness:\n\n(i) The authors provide visual comparisons of DAUHST, HDNet, and BIRNAT in the supplementary but the main paper lacks these important comparisons. Why not move these results to the main paper?\n\n(ii) In Line 156 of the main paper, the mentioned reshape operation of R is unclear and should be explained.\n\n(iii) In Line 98 of the paper, the “vectorized” and “shifted” operations need more explanations.\n\n(iv) It would be better to evaluate the generality and extensibility of DAUF. For instance, replacing the HST by the same CNN of GAP-Net and ADMM-Net. This ablation can show whether the proposed DAUF fits CNN-based denoising networks or not. In Table 1, I am not sure why the FLOPS of BIRNAT is so large? Is it because BIRNAT employs an RNN architecture? The authors have discussed the limitations and social impacts in the supplementary material. \nThis work does not have any foreseeable negative social impacts.", " this submission deals with designing unfolding based architecture for supervised learning of spectral compressive imaging (SCI). Compared with SOTA, it proposes to explicitly integrate the ill-posedness of the acquisition (degradation and mask) into each block (iteration) for data consistency and denoising. The denoising network also uses a U-shape transformer with half-shuffle multihead self-attention to capture both local and non-local contents. The experiments outperform SOTA in terms of both memory, computer, and reconstruction fidelity. Strength\npractical significance: the gains achieved are significant compared with the reported SOTA methods\npractical novelty: this is the first work deploying transformers as the denoiser for SCI.\nclear writing: the paper is well written and the idea is clear\n\nWeakness\nlimited technical novelty: The main novelty of this work is to propose a U-shaped transformer with half–shuffle multi-head self-attention for the denoising network in deep unfolding architectures for SCI. Deep unfolding is well established. Also, there are several works reporting superiority of transformers against CNNs for denoising and low level computer vision tasks, and it is not surprising to observe similar gains for SCI; see e.g., [Peit et al’21].\n\n[Peit et al’21]Petit O, Thome N, Rambour C, Themyr L, Collins T, Soler L. U-net transformer: Self and cross attention for medical image segmentation. InInternational Workshop on Machine Learning in Medical Imaging 2021 Sep 27 (pp. 267-276). Springer, Cham.\n This work can be strengthened with more ablations that explains the design choices for the U-shaped transformer. For example, what if one simply uses a multi-head vision transformer instead of U-shaped architecture?\n \nThe limitations are not included in the submission. The limitations need to be discussed. For example, it seems that the entire network needs to be trained from scratch each time the measurement model changes. The robustness of the model also needs to be discussed in terms of introducing hallucinations. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 4, 8, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 5, 3 ]

[ "IerZYHjNIUi", "Lcc4HmGfKC2", "SmOcQwgUvZ-", "nips_2022_r9b6T088_75", "nHR4QH99Ce", "jc2SdJPknx", "iz6ZyEtRnk", "_nkmP0-G_H_", "2SyiNX-aV5u", "IerZYHjNIUi", "KEbbpws-wpg", "Qgz9CE4k0QrZ", "6-F1huulKSq", "gduagZVCegM", "2SyiNX-aV5u", "5sg1IBU24pn", "5sg1IBU24pn", "2SyiNX-aV5u", "2SyiNX-aV5u", "2SyiNX-aV5u", "2SyiNX-aV5u", "6-F1huulKSq", "6-F1huulKSq", "6-F1huulKSq", "5sg1IBU24pn", "5sg1IBU24pn", "5sg1IBU24pn", "gduagZVCegM", "nips_2022_r9b6T088_75", "nips_2022_r9b6T088_75", "nips_2022_r9b6T088_75", "nips_2022_r9b6T088_75" ]

[ "MScvLL49pSd", "GrpV_qZdL9", "PykriOpU1So", "4RjQVaF2Pk", "HefFB1GX-aen", "nZp-0IKiIX", "ivWHAJjwo1g", "DPt8GD_jrx9", "eOjYt4iVWKG" ]

[ "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear reviewers,\n\nWe first thank you again for your valuable comments and suggestions. In the previous replies, we have tried our best to address your questions point by point and supplemented more experiments.\n\nWe sincerely look forward to your reply to our response. And we are open to any discussion to improve our paper.\n\nBest wishes!\n\nThe authors.\n\n", " Hi dear Reviewer 3trj,\n\nWe have further revised our manuscript following your detailed feedback and uploaded the revised version. Please let us know if you have more questions or discussions for us! Thanks again!\n\nThe authors.", " **Q7: In what domains would you expect the PTIE paradigm to be similarly effective? Any imperfect-information setting? Is cooperation required? Multi-players (beyond 2)?**\n\nA7: We expect the PTIE paradigm is suitable for all imperfect-information games where Actor-Critic algorithms can be applied, and it is not limited to games featured with cooperation or multi-players since the aim is to utilize the global information.\n\n**Q8: You state that games are randomly generated and played twice ... Did you consider playing each game 6 times, once for each possible landlord hand (3) and each algorithm (2)?**\n\nA8: Thanks for the advice! In our submitted version, we mainly follow the setting of DouZero to make a fair comparison. In the revision, we have supplemented the extra experiments following your suggestions and the result is as follows:\n\n| A \\ B | PerfectDou | PerfectDou | DouZero | DouZero |\n|---|---|---|---|---|\n| | WP | ADP | WP | ADP |\n| PerfectDou | - | - | 0.544 | 0.150 |\n| DouZero |0.456 | -0.150 | - | - |\n\n**Q9: Lines 316-327 - What do you mean by frames? Do you mean training iterations? or epochs**\n\nA9: We are sorry for the confusion. The term `frames` mainly follows the common usage in the RL literature (also see in [1,2]). In fact, it simply means game frames, in terms of RL words, also known as observations or interaction steps. Therefore `1e9 and 2.5e9 frames` means we trained the network after obtaining 1e9 and 2.5e9 steps of observations. We have revised it as `steps` in our revision to make it clear.\n\n[1] Mnih V, Kavukcuoglu K, Silver D, et al. Playing atari with deep reinforcement learning[J]. arXiv preprint arXiv:1312.5602, 2013.\n[2] Yarats D, Fergus R, Lazaric A, et al. Mastering visual continuous control: Improved data-augmented reinforcement learning[J]. arXiv preprint arXiv:2107.09645, 2021.\n\n**Q10: What type of machine were the inference times computed on?**\n\nA10: Sorry for missing such information! The inference times were computed on a single core of Intel(R) Xeon(R) Gold 6130 CPU @ 2.10GHz. We have now supplemented it into the main text.\n\n**Q11: The meaning of \"The inference time of each AI could be attributed to its solution and implementation in the playing time\"**\n\nA11: In this sentence, we want to explain the reason why the inference time of each AI varies. As explained in lines 359-374, the result is caused by their different solutions and implementations.\n\n**Q12: What does it mean for a player to be \"leaky and unreasonable\"? / What do you mean by \"more aggressive and less thinking\" exactly? /Similarly for \"guessing and supressing\", \"better at card combination\" and \"more calm\" on the next lines.**\n\nA12: We think the answers can be found in Appendix D.2 and D.3, where we show detailed qualitative comparisons between Douzero and PerfectDou, in-depth statistical analysis and a few detailed playing examples to give more evidence why PerfectDou can beat DouZero. \n\n**Q13: For example, if one DouZero peasant is paired with one PerfectDou peasant against another agent, how well does this work?**\n\nA13: Thanks for your great suggestion! This is a very interesting problem and unfortunately we missed it by simply following the competition setting of DouZero for fair comparisons. Extra experiments have been carried out in the revision (Appendix D.6) and the results of Landlord against Peasants are as following:\n\n| Peasant → | PerfectDou+DouZero | PerfectDou+DouZero | PerfectDou | PerfectDou | DouZero | DouZero |\n|---|---|---|---|---|---|---|\n| **Landlord↓** | WP | ADP | WP | ADP | WP | ADP | WP | ADP |\n| **PerfectDou** | 0.424 | -0.448 | 0.389 | -0.606 | 0.452 | -0.375 |\n| **DouZero** | 0.395 | -0.534 | 0.363 | -0.676 | 0.421 | -0.465 |\n\nIn the experiment, two peasants are played by PerfectDou and DouZero respectively and the landlord is played by PerfectDou or DouZero, using 100,000 randomly generated games and each game is played 6 times as before.\nSome conclusions could be drawn from the table: when playing as the peasant, PerfectDou can better cooperate with its teammate than DouZero. And when playing as the landlord, PerfectDou outperforms DouZero against all types of opponents. \n\n**Q14: Ablation study - If I am understanding correctly, Vanilla PPO doesn't have access to the perfect information features or the node. What is this testing exactly?**\n\nA14: One of the main differences between PerfectDou and DouZero is that DouZero is a value-based method while PerfectDou utilized an actor-critic algorithm - PPO, this experiment aimed to illustrate the improvement of PerfectDou vs DouZero is not arisen from simply replacing the underlying algorithm as PPO, the node reward and the PTIE both play significant roles.", " **Q1: Lines 380- 389 - What is a \"bomb\" in the context of DouDizhu?**\n\nA1: Yeah this is a special term of DouDizhu and we have a brief introduction of 'bomb' in Appendix B.1 Line 577. In short, the bomb is a kind of card's category, such as 3333, 4444 or 5555, this kind of action is special because it suppresses all other kinds of categories (except rocket) and it will double the score. Playing the bomb will bring the privilege by suppressing the opponent's action while it also brings the risk of losing more scores if the player's other cards are not strong. It is necessary for the experienced player to find out the balance.\n\n**Q2: Could you clarify the explanation of the result with high WP and negative ADP again? I didn't follow the explanation on lines 311-315.**\n\nA2: Sorry for the confusion. A potential reason for high WP and negative ADP is that the agent is reckless to play out the bigger cards (like bombs) without considering the left hand. For example, consider the case when **AI1** always chooses to suppress by playing out its bomb and the opponent **AI2** only plays bomb when its left cards are good. In that case, if the left hand cards of **AI1** are similar or better than **AI2**, **AI1** can win most games with small scores. However, in the opposite scenario, where **AI2**'s left cards in hand are better than **AI1**, **AI1** and **AI2** both play out the bombs, making the score be doubled several times and **AI1** would lose plenty of scores. This could be one example of high WP and negative ADP caused by the ai player's wrong strategy. This can be further clarified in the revision.\n\n**Q3: It wasn't clear to me what matters more, winning or advantage points. In a typical single game, is the goal simply to win, or does the reward (like the size of the pot in poker) actually depend on the advantage of the players at the end? Or is it important in a series of games where the scores for the players are added up until someone gets to a certain score total, or something?**\n\nA3: Sorry for your confusion about the rules. As explained in Line 287-289 and Line 579-588, when human players play DouDizhu the Average Difference in Points (ADP) is more important than the winning percentage (WP). The goal of this game is to achieve as many scores as possible. In the real competition of DouDizhu, a series of games are played and the scores of players are added up, after all games end, the player with the highest score wins the game. \n\n**Q4: And this work is just focused on a single game of DouDizhu? It seems like the true primary goal should be winning, and the advantage only measures how close it was. I believe though, it has been observed with other superhuman AIs, like in Go, that they play to win, and often the best chance of winning is accompanied by a very small winning margin in the end.**\n\nA4: The answer to this question actually relates to the scoring rule of the game. In our work, we focused on building an AI which could play real DouDizhu competition with human players, where ADP is much more important, as mentioned above (Q2A2). Normally, the base score of the game is 2 for the landlord and 1 for each peasant, and when the landlord loses the game, it loses 2 scores and vice versa. However, because of the existence of `Bomb`, the score can be doubled. Some strategies like not playing bombs when the ranks of other cards in hand are small can avoid losing large scores.\n\n**Q5: In your case, the RewardlessDou has a better WP against DouZero(~1e10) than PerfectDou. If WP is most important, then the node rewards appear unnecessary.**\n\nA5: As explained above, from the main point of this paper, WP is **less important** than ADP since we want to win higher scores in series of games. Additionally, in our experiments, all AI systems are trained to maximize ADP by taking it as the basic reward (as stated in Line291). \nFurthermore, there is another evidence from Line 314 to 315 in the paper showing the reasonable range of WP value when we only want to maximize ADP, where we analyzed the statistics of online human matches and showed that the WP of the human player is usually kept in a range of 0.52 ∼ 0.55 when the player tries to maximize ADP. \n\n**Q6: Are there principles you used in your feature engineering that would be applicable in other, different domains?**\n\nA6: Thanks for the good question! We believe part of the features in card representation matrix (Figure 2) such as the number of cards in hand can be easily transferred to other games such as Mahjong or Texas Hold'em. For the node representation, we believe most of the features such as current cards in hand, last moves and cards in the opponent's hand are common features in card games and can be applied to other games as well. \n\n", " **Q1: no much difference between PTIE and CTDE.**\n\nA1: Essentially, we think you are right. L38-39 has claimed that the \"Perfect-Training-Imperfect-Execution (PTIE) framework, a variant of the popular Centralized-Training-Decentralized-Execution (CTDE) paradigm\". Although they both utilize global information, technically, the main difference is their form of global information. In detail, most of previous CTDE works focus on allocating the observations and actions across agents; by contrast, PTIE concentrates on the range of the information itself in imperfect-information games, which does not make any requirement on agents' joint observations or actions.\n\nAs stated in Line 532 Appendix A, where we further discussed related works of training with global information, we are the first to formulate the idea for training agents on imperfect-information games, making the idea explicitly useful for more kinds of imperfect-information games.\n\n**Q2: \"I doubt if the PTIE framework plays an important role in this work. I wonder if the Douzero gets better performance if it also combines the feature design and the node reward.\"** \n\nA2: The concern is already addressed in the ablation studies, Table 4. In Line 335-338, we design the battle among **ImperfectDouZero** (DouZero with our proposed imperfect-information features) and **ImperfectDou** (PerfectDou with only imperfect features as inputs for the value function.) and **RewardlessDou** (PerfectDou without node reward) and even **Vanilla PPO** (Naive actor-critic training with imperfect-features only and without additional reward). We try to disentangle all important components in our proposed method to validate the effectiveness of each part.\n\nFor your question, the analysis can be referred to the battles between **ImperfectDouZero v.s. RewardlessDou** and **ImperfectDouZero v.s. Vanilla PPO**. Note that DouZero cannot use the perfect information since it will play in a cheating style if doing so (it is a value-based method thus it only has the value function and no policy function to distill). ImperfectDouZero uses the same imperfect features of PerfectDou, RewardlessDou does not include the node reward and Vanilla PPO does not include the node reward and PTIE. From Table 4, we can conclude that compared with Vanilla PPO, RewardlessDou shows a significant improvement under the help of PTIE when playing against ImperfectDouZero.\n\nThe above analysis will be further revised and supplemented into the final version.\n", " **Q1: This paper only focuses on the card play phase. The strategy in the bidding phase may also follows influence the whole performance of the AI agent.**\n\nA1: Random selection is used in the bidding phase following the setting of DouZero to make a fair comparison. In practice, a bidding network used in the bidding phase is trained to predict the winning probability with the initial hand.\n\n**Q2: Inference time concern.**\n\nA2: The inference time consists of two parts, feature processing procedure and model inference. We test that the network inference time of DouZero is 2.2 ms(pytorch) and the feature extraction time is 0.39 ms while the network inference time of PerfectDou(tensorflow) is 5.0 ms and the feature extraction time is 3.6 ms. As stated in Line 370-371, PerfectDou is a bit slower than DouZero due to the more complex feature processing procedure and model structure, which can be largely optimized into neglectable computation cost from practical implementation, such as changing the source code from Python to C++, which is common for AI deployment. \n\n**Q3: \"Is the perfect-information-imperfect-execution training paradigm a general structure for imperfect information games? In other words, can it be used for solving other imperfect-information games, such as other poker games?\"**\n\nA3: We are sorry for not including such a discussion in the main text, more discussions are given in Appendix F in the revised version, which will be further supplemented into the main text in the future version. In this paper, due to the amount of work, we mainly focus on one of hard poker games, DouDizhu, but we surely believe the technique will boost AI works on other imperfect-information games such as Texas Hold'em or Mahjong due to the success of utilizing global information in many multi-agent challenges.\n\n**Q4: Does it just train one policy network for both peasants and a landlord? Or does it train a policy network for each player?**\n\nA4: This is covered in the paper. As stated in Appendix D.1, Line 611-613, \"During self-play, we find a better practical solution for DouDizhu is to keep three different models for Landlord and two Peasants separately which is only updated by their own data against the latest opponent model.\" The three models mean Landlord, Peasant before Landlord and Peasant after Landlord.\n", " This paper mainly focuses on the DoDizhu Game. It proposes the Perfect-Training-Imperfect-Execution(PTIE) learning framework to train a robust agent called PerfectDou. Specifically, under the actor-critic framework, it uses imperfect information to feed the actor and uses perfect information to feed the critic. Combined with the new representation (Card, Node, and Action) and reward design, it trains the agent which can beat previous AI on DoDizhu and achieve the SOTA performance. In addition, they conduct ablation experiments to verify that the PTIE framework, feature design, and node reward all contribute to the final performance. Originality\nThis work proposes the three main parts: Perfect-Training-Imperfect-Execution (PTIE) learning framework, a new representation on card, node, and action, and a new node reward design. Combining the three parts can train the AI with SOTA performance in DouDizhu game. However, I do not see much difference between the PTIE and the CTDE, and the latter two are more dependent on the human experience. So, I think the originality of this paper is limited.\n\n\nQuality\nFrom an engineering perspective, I think this is a good work.\n\nClarity\nI think this paper is written clearly. \n\nSignificance\nThe AI trained by the method proposed in this work can achieve the SOTA performance in the Doudizhu game. However, this framework may only be applicable to Doudizhu because the feature and reward design play a vital role, but they can only be used in the Doudizhu game. 1. I do not see much difference between the perfect-training-imperfect execution (PTIE) paradigm and the centralized-training-decentralized-execution. Both of them seem to use the global state to train the critic and partial observation to train the actor.\n\n2. I doubt if the PTIE framework plays an important role in this work. I wonder if the Douzero gets better performance if it also combines the feature design and the node reward. I think this work has no potential negative societal impact.", " This paper proposes a SoTA DouDizhu AI system named PerfectDou that dominates the game. They adopt a perfect-training-imperfect-execution framework. It uses the global information to guide the training process. During the actual gameplay, only imperfect information can be used. Furthermore, they also do some feature engineering on card and action representations. When training the AI agent, they adopt PPQ with GAE by self-play in a parallel training system. Finally, extensive experimental results show that PerfectDou can achieve SoTA performance. Strengths: The idea of perfect-information-imperfect-execution paradigm for training imperfect-information games is interesting. It can effectively use the perfect information for training and distill it into policy network, which can only use imperfect information. To further improve the performance of DouDizhu AI agent, they also characterize card and game features to represent the perfect and imperfect information. These may be the main contributions of this paper. The structure of the paper is well, and this paper is easy to follow. This paper indeed provides a novel method for games with competition and collaboration.\n\nWeaknesses: This paper only focuses on the card play phase. The strategy in the bidding phase may also influence the whole performance of the AI agent. Another slight problem is inference time. As the experimental results show, although the inference time of PerfectDou is much fast, the inference time is slower than DouZero.\n 1.\tIs the perfect-information-imperfect-execution training paradigm a general structure for imperfect information games? In other words, can it be used for solving other imperfect-information games, such as other poker games?\n2.\tDoes it just train one policy network for both peasants and a landlord? Or does it train a policy network for each player?\n This paper does not claim the limitations and potential negative societal impact. Maybe the decision in the bidding phase needs to be considered in the future. ", " This paper presents PerfectDou, a novel AI agent for the game of PerfectDou. This agent uses a training paradigm introduced by the authors called Perfect Training Imperfect Execution (PTIE) where in an actor-critic framework the critic has access to the exact state of the game, including all hidden information, while the actor/policy only has access to the imperfect information that players normally have access to. The networks representing the actor/critic are trained using PPO with GAE. The paper details the features used as input to the networks, additional reward information that is included to guide the policy. The PerfectDou agents is then evaluated against other published DouDizhu agents, including the current state-of-the-art, DouZero. These results demonstrate that PerfectDou can beat these previous agents at the game and should now be considered the state of the art agent at the game.\n Strengths - \n- The domain in question, DouDizhu, is an interesting one combining many interesting characteristics: competition, cooperation, and imperfect-information. The success of this agent represents an advancement in these areas and I think this is significant enough to warrant sharing with the broader AI/ML community. \n- To my knowledge, the perfect-training-imperfect-execution (PTIE) paradigm introduced by the authors is novel and the experimental results demonstrate that it contributes to the success of the agent. This paradigm could be useful in other similar imperfect-information settings. \n- The high-level presentation of the methods is generally clear, with a few execeptions noted below. \n- It is clear that the underlying work was carefully and thoroughly done, and is of high quality. \n\nWeaknesses: \n- The paper is singularly focused on the domain of DouDizhu. It remains up to the reader to imagine how any of the insights from this work might translate to other domains and problems. I think that the work would be strengthened if it included some of this discussion in the paper itself. \n- With the exception of PTIE, this largely appears to be an engineering feat specific to DouDizhu, and it is unclear how many contributions are significant elsewhere. All of the algorithms and methods appear to be drawn from previous work, and while there is value in generating this productive combination for this domain, it could be stronger. \n- Ablation study - If I am understanding correctly, Vanilla PPO doesn't have access to the perfect information features or the node reward. What is this testing exactly? \n- The low-level clarity of the writing was poor at times, and there are several sentences (noted below) where I couldn't determine what was being communicated.\n\n\nMinor Feedback: \n- Line 41 - \"when deploy the...\" should be \"when deploying the...\"\n- Line 143-144 - \"In addition, the optimality of RL is .... \" - This sentence doesn't make sense to me.\n- Line 187 - should read \"... the imperfect features are a subset of the perfect features.\"\n- Line 257-258 - you state that CFR is not appropriate for DouDizhu due (in part) to the \"mixed-game property\". There is at least one example that I am aware of where CFR was used for this type of mixed-game setting. In [Mazrooei, Parisa, Christopher Archibald, and Michael Bowling. 2013. “Automating Collusion Detection in Sequential Games”. Proceedings of the AAAI Conference on Artificial Intelligence] CFR was used to train players in 3 player poker, and two of those players were trained to collude/coordinate with each other, sharing their reward. CFR was able to train successful agents in this case. \n- Line 298 - You state that games are randomly generated and played twice, once with each algorithm controlling the landlord, and once controlling the two peasants. I assume that the landlords get the same hand in each case? Did you consider playing each game 6 times, once for each possible landlord hand (3) and each algorithm (2)? It seems this could reduce the variance of the game that you refer to on line 303. \n- Lines 316-327 - What do you mean by frames? Do you mean training iterations? or epochs? \n- Line 357 - What type of machine were the inference times computed on? \n- Lines 357-259 - \"The inference time of each AI could be attributed to its solution and implementation in the playing time.\" I don't understand what this sentence is saying. \n- Line 374 - What does it mean for a player to be \"leaky and unreasonable\"? \n- Lines 380- 389 - What is a \"bomb\" in the context of DouDizhu?\n- Line 381-382 - \"...and tends to control the game even the Peasants play more bombs;\" should this be: \"... and tends to control the game even when the Peasants play more bombs\"?\n- Line 386 - What do you mean by \"more aggressive and less thinking\" exactly? Similarly for \"guessing and supressing\", \"better at card combination\" and \"more calm\" on the next lines.\n - Could you clarify the explanation of the result with high WP and negative ADP again? I didn't follow the explanation on lines 311-315. \n- It wasn't clear to me what matters more, winning or advantage points. In a typical single game, is the goal simply to win, or does the reward (like the size of the pot in poker) actually depend on the advantage of the players at the end? Or is it important in a series of games where the scores for the players are added up until someone gets to a certain score total, or something? And this work is just focused on a single game of DouDizhu? It seems like the true primary goal should be winning, and the advantage only measures how close it was. I believe though, it has been observed with other superhuman AIs, like in Go, that they play to win, and often the best chance of winning is accompanied by a very small winning margin in the end. In your case, the RewardlessDou has a better WP against DouZero(~1e10) than PerfectDou. If WP is most important, than the node rewards appear unnecessary. \n- Are there principles you used in your feature engineering that would be applicable in other, different domains? \n- In what domains would you expect the PTIE paradigm to be similarly effective? Any imperfect-information setting? Is cooperation required? Multi-players (beyond 2)?\n The main limitation that stands out to me is that this work assumes that it is playing with its same agent in the other peasant seat. One of my big questions is how well the agents do in other pairings. For example, if one DouZero peasant is paired with one PerfectDou peasant against another agent, how well does this work? I understand that this is perhaps beyond the scope of this work, but I think that it should be made clear in the paper itself. I don't see any potential negative societal impact that should have been addressed. \n" ]

[ -1, -1, -1, -1, -1, -1, 6, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, 3, 4, 4 ]

[ "nips_2022_Blbzv2ZjT7", "eOjYt4iVWKG", "4RjQVaF2Pk", "eOjYt4iVWKG", "ivWHAJjwo1g", "DPt8GD_jrx9", "nips_2022_Blbzv2ZjT7", "nips_2022_Blbzv2ZjT7", "nips_2022_Blbzv2ZjT7" ]

[ "XCsQOTm7EO", "3y5yTqJvioi", "XaakeppozZ-", "bjd-Q8vXJ_h", "x9coXOnGxD", "d9AnOMFhyVw", "kC0IL_SmOGQ", "-sbat-U9AG", "LVcqdde0NZj", "7QmE59LCp7z", "rYlseSeDM4R", "HA20apUD-XF", "Sl_aXdWGuIL", "roJ5XXilQ3", "n0L6VJYeTZS" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank the reviewer for their response and constructive feedback, as well as for considering our rebuttal and increasing the score for our paper. We will make sure to include the evaluation of smoothness and injectivity, as suggested by the reviewer. We will also make sure to include an analysis of the different initialization schemes of the random network in the final version.", " I thank the authors for the additional clarifications. They were helpful for further understanding.\n\nQ2: I think the additional evaluation of smoothness and injectivity is an important addition. They should be added to the paper. I would be also interested in a comparison between different networks.\n\nQ7: I think we are talking about the same methods. E.g. functional maps require descriptors in order to find the map C in the spectral domain. Initial descriptors are often found using local methods. Then, a global correspondence that aligns local descriptors is found in the spectral domain. But I agree that this distinction is not clear and the border between local and global is not clearly defined, as some descriptors are found using global methods, as it is the case here, depending on the backbone.\n\nQ9 was about the network initialization for the first part of the paper (neural bias for pointwise features). I would imagine that the network initialization scheme has an impact on the result (given that the point embeddings are generated purely based on this random initialization) and still think that an analysis of different schemes would make the paper better.\n\nAll in all, (1) the rebuttal did improve clarity of the work and (2) an important experiment was added that supports the assumptions of Theorem 1. I increased my score to 7 as I think this paper should get accepted.", " **Q6. Our method slightly outperforms the DiffusionNet-based methods**\n\nWe would like, first, to clarify that \"WSupFMNeT + DiffusionNet\" is the\nmethod we used for Stage 1 of our method (see implementation details in\nSection B of the Supp. Materials), and the maps predicted by this method\nare used for Stage 2. We will make this clear in the revision. We use\nthe same method based on unsupervised functional maps in all of our\nexperiments to keep our method simple.\n\nSecond, we believe that a 2cm improvement in error, or about a 25%\nincrease in accuracy, constitutes a significant improvement, especially\nfor such difficult problems. Moreover, our improvement is not restricted\nto a particular benchmark or dataset, but is verified broadly on several\nchallenging datasets and tasks (point cloud matching (KeyPointNet\ndataset), non-rigid non-isometric shape matching (SMAL and SHREC’20\ndatasets), part segmentation (ShapeNet Part dataset) and keypoint\ndetection (KeyPointNet dataset)). Finally, our method is fundamentally\ndifferent from previous approaches and, we believe, constitutes a\nconceptual contribution.\n\n**Q7. Figure 4 shows the results of NeuroMorph**\n\nWe have shown the results of NeuroMorph because, to the best of our\nknowledge, it is the most recent, state-of-the-art method at the time of\nwriting the manuscript. As we clarified in the previous answer,\n\"WSupFMNeT + DiffusionNet\" is the method we used for Stage 1, and its\nresults are shown in Figure 4 under the label \"Stage 1\".\n\nNevertheless, we will be happy to add the results of other methods in\nour error figure.\n\n**Novelty is limited, and slight improvement in performance for the\nexperiment in Table 2**\n\nWe believe that a 25% increase in performance represents a significant\nimprovement. In addition, as we shown throughout the main manuscript and\nthe Supp. Materials, our methods improve upon the state-of-the-art\nmethods on multiple benchmarks, including rigid shape correspondence (up\nto 44% improvement for some classes), shape segmentation transfer (with\nan increase of up to 8% in IOU for some classes), non-rigid shape\nmatching, and keypoint detection.\n\nOn the other hand, we argue that our method is also conceptually novel.\nAs attested by other reviewers, we demonstrate, for the first time, the\nutility of neural prior for shape correspondence, and introduce an\neffect that we call the Neural Correspondence Prior. This effect was not\nobserved in prior literature, and we believe that it can lead to\nfollow-up works, especially since it is substantiated by significant\npractical utility in our experimental results. We note also that the\nreviewer **4Seq** found the method “novel and interesting”, and the\nreviewer **ZBSs** found the idea “novel and well explained”. We will be\nhappy to further clarify our conceptual and practical contribution in\nthe final version.\n\n**Exposition** \n\nWe thank the reviewer for finding our work presenting\n“simple interesting idea” and the paper “well written”.\n\nWe will incorporate *all of the* writing suggestions from the reviewer,\nincluding making more clarifications, and discussing the link between\nour method and the student/teacher paradigm.\n\nAs we have demonstrated throughout the main manuscript, in the\nsupplementary materials, and in our response, our paper observes, for\nthe first time, the NCP effect, and proposes an algorithm to exploit it.\nOur method achieves state-of-the-art results on multiple benchmarks, as\nevidenced by all the other reviewers. We believe that these points\naddress the reviewer’s concern and thus, we kindly ask the reviewer to\nreconsider their rating.", " We thank the reviewer for their detailed and thoughtful comments and suggestions. We invite the reviewer to consider the general feedback that we provided to all reviewers in the \"High Level Summary\" answer. Below are our answers to the reviewers’ questions. Due to the 5000 character limit, and in order to fully address the reviewers’ comments, we have divided our response into two parts.\n\n**Q1. Neural bias with pointwise MLP**\n\n Thank you for the suggestion. Please\nnote that the main goal of Section 3.1 is to highlight our observation\nthat the structure of the network, even when untrained, provides a prior\nfor the produced features. We used DiffusionNet to illustrate this\npoint, following the Deep Image Prior work \\[1\\], which only\ndemonstrated this effect on one, commonly used, state-of-the-art\narchitecture.\n\nAt the same time, we stress that we only used this observation as a\n*motivation* for our main proposal (Section 4), built from the *Neural\nCorrespondence Prior,* described in Section 3.2.\n\nWe have evaluated the Neural Correspondence Prior and our proposed\nalgorithm with five different backbone architectures, including\nDiffusionNet, PointMLP, DGCNN, PointNet++, and ResidualMLP, which is a\npointwise MLP. Please see Table 1 of the Supp. Materials.\n\nWe will be happy to reword and possibly rename Section 3.1, as\nrequested.\n\n\\[1\\] Dmitry Ulyanov, Andrea Vedaldi, and Victor Lempitsky. Deep image\nprior. arXiv:1711.10925, 2017.\n\n**Q2. Link between Neural bias with pointwise MLP** \n\nAs mentioned above, we\nview the neural bias as a general motivation to our approach,\nhighlighting the fact that the structure of neural networks imposes a\nparticular prior on the types of features that they produce. We used the\nneural prior to illustrate this effect as it is especially striking when\nthe networks are untrained. However, we do not use it in our\nexperimental results, which are based on Algorithm 1, described in\nSection 4. We will clarify this in the final version.\n\n**Q3. Terminology of teacher / student networks** \n\nWe avoided this\nterminology, as it is borrowed from the knowledge distillation\ncommunity, where the goal is to transfer the “knowledge” of a bigger\nnetwork (in term of size and parameters) (teacher) to a smaller network\n(student).\n\nThis is not the case for our method, and using such a terminology can\npotentially be misleading, especially to readers from other communities.\nFirst, Stage 1 of our algorithm uses an off-the-shelf unsupervised shape\nmatching method that can be either learning based (such as unsupervised\nGeomFMaps) or even axiomatic (such as Smooth Shells, see Table 2 of the\nSupp. Materials), and no condition on the size or type of a network is\nmade.\n\nSecond, the purpose of the Stage 1 is to produce a set of approximate\nmaps, which are then refined in Stage 2. To the best of our knowledge, while\nin the student/teacher paradigm, the student is trained to learn exactly\nthe same predictions by the teacher network, our method relies on the\nNCP effect, which we demonstrate for the first time for shape matching.\nThus, the goal of Stage 2 is to *improve* or refine the maps computed in\nStage 1, which is fundamentally different from the standard\nteacher/student paradigm, where the goal is to *replicate* the results\nof a larger model by a smaller one.\n\nNevertheless, we agree that a conceptual link does exist and will be\nhappy to cite relevant works, and clearly state the difference of our\nsetting.\n\n**Q4. Expecting the teacher network to be untrained** \n\nAs mentioned in our\nfirst response, the neural bias section (Section 3.1) was just a\nmotivation for our method, which we explained and developed in Section 4\nand Algorithm 1, based on the Neural Correspondence Prior effect that we\ndiscovered and explained in Section 3.2.\n\nWe would like to emphasize that the results in Section 3 are only an\nexploratory study, and that the results in it motivate (as the title of\nthe section suggests) the method that we introduce in Section 4. Such a\nseparation has been noticed and appreciated by other reviewers such as\n**ZBSs**. We will be happy to further clarify the nature of the relation\nand separation between these sections.\n\n**Q5. Performances of the teacher network on point clouds** \n\nThank you for\nthe question. The performance of the method used for Stage 1 in our\nalgorithm (called teacher by the reviewer) is provided in Figure 2 in\nthe Supp. Materials, under the label Ours (Stage 1).\n\n", " **Q6. Is the statement provided by the reviewer correct?** \n\nThe first part of\nthe statement is not correct. First, we do not necessarily need a\nfeature extractor for Stage 1, any off-the-shelf unsupervised shape\nmatching method could work.\n\nPlease see Table 2 in the Supp. Materials where we included a\ndemonstration of this: we used 4 different methods for Stage 1, one of\nwhich is Smooth Shells, which is an axiomatic and not a learning-based\nmethod.\n\nSecond, we do not always rely on the quasi-isometry assumption in Stage\n1, as for example in the Rigid Shapes experiment (Section 5.1.1 of the\nmain manuscript), where the network is trained only with the bijectivity\nloss (see Section B of the Supp. Materials for more details on the\nimplementation), and no near-isometry assumption is made.\n\nFor the second part of the statement, our Stage 2 does indeed solve for\nerrors related to non-isometric matches, as well as other types of\nerrors, introduced by artifacts in Stage 1. Figure 1 in the main\nmanuscript supports this statement, where the network is able to denoise\nmaps that are corrupted by purely random noise, up to 75% (i.e., 75% of\nthe entries of the map are noise).\n\n**Q9. Analysis of different initialization schemes** \n\nWe are not sure to\nfully understand the reviewer’s question. If by initialization schemes\nthe reviewer means the method used in Stage 1 to get the\n\"artifact-laden\" maps, we did such a study in Table 2 of the Supp.\nMaterials, where we tested 4 different initialization methods (Smooth\nShells, Unsup GeomFMaps, Deep Shells, and NeuroMorph), and showed that\nthe method always works, and does not depend on the choice of Stage 1.\n\nIf by random initialization, the reviewer means the different\ninitialization schemes of a neural network (such as normal\ninitialization \\[8\\], Xavier initialization \\[9\\], Kaiming\ninitialization \\[10\\], etc.), we want to emphasize that we used the\ndefault initialization in Pytorch for all our networks (which is a\ncombination of Xavier initialization, and Kaiming initialization).\n\nFurthermore, please note that our Algorithm 1, stated in Section 4.1.\nand used in all of our results, does not use features produced by a\nrandomly initialized network (described in Section 3.1), but rather the\noutput of an unsupervised correspondence method that we refine in our\nStage 2.\n\n\\[8\\] Y. LeCun, L. Bottou, G. B. Orr, and K. R. Muller, Efficient\nbackprop, In G. B. Orr and K. R. Muller, editors, Neural Networks:\nTricks of the Trade, pp. 9-50, Springer, 1998\n\n\\[9\\] Glorot, Xavier, and Yoshua Bengio. \"Understanding the difficulty\nof training deep feedforward neural networks.\" Proceedings of the\nthirteenth international conference on artificial intelligence and\nstatistics. JMLR Workshop and Conference Proceedings, 2010.\n\n\\[10\\] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving\ndeep into rectifiers: Surpassing human-level performance on ImageNet\nclassification. In Proceedings of the IEEE international conference on\ncomputer vision, pages 1026–1034, 2015.\n\n**Limitation and Negative Impact** \n\nWe will be happy to expand upon the\nlimitations section. As mentioned above (in the answer to Q8), our method tends to break when\nthe maps in Stage 1 either have no structure, or when they are\nsymmetrically inverted. Moreover, since our method is general, it might\nnot be the best choice, e.g., for near isometric categories, where,\nspecialized methods could perform better. In contrast, we target\ndifficult non-rigid non-isometric datasets, where existing methods tend\nto fail.\n\nPlease note that we provided a section on societal impact in Section G\nof the Supp. Materials, however, as the reviewer said, we could not see\nany immediate negative impact.\n\n**Exposition** We thank the reviewer for finding our paper “good,\ninteresting and well written”.\n\nWe will be happy to incorporate writing suggestions from the reviewer,\nincluding more clarifications, rearranging the sections, and correcting\nthe spelling mistakes.", " **Q2. About Theorem 1**\n\nWe thank the reviewer for this comment. As mentioned in our response to\n**ZBSs**, our main motivation behind Theorem 1 is to highlight the fact\nthat, given smooth feature embeddings, if we add the injectivity\ncondition, the maps extracted using the nearest neighbors in the feature\nspace tend to be smooth. As smoothness is a generally desirable\nproperty, and the frequency bias shown in prior works, such as \\[1\\]\nsuggests that neural networks are biased towards low frequency (and thus\nsmooth) functions, we provide this result as a partial explanation for\nthe Neural Correspondence Prior, which we have observed, for the first\ntime, in our work.\n\nRegarding injectivity, although we agree with the reviewer that such a\nproperty is not trivial, and might need to be specifically enforced\n(using, for example, invertible networks \\[2\\]). However, we observe\nthat when training a network using contrastive learning, such as NCE\nloss, the latter forces the networks to produce embeddings that are\nunique for each point, in order to minimize the NCE loss, which can be\nconsidered a form of injectivity.\n\nLast but not least, we agree with the reviewer that the conditions of\nthe theorem are not trivial. Furthermore, as mentioned in our response\nto **ZBSs**, we do not consider this theorem as a key contribution of\nour work. We would therefore be happy to paraphrase it as simply a\nhigh-level motivation for our approach, if the reviewers deem\nappropriate.\n\nFinally, we include here the results of the experiments suggested by\n**ZBSs**, and also by the reviewer, which is checking the smoothness and\ninjectivity of a randomly initialized network. For this, we performed\nthe following experiment. We first computed the embeddings produced by a\nrandomly initialized DiffusionNet network for the 20 test shapes in the\nFAUST remeshed dataset.\n\nTo evaluate the smoothness of the embedding, we computed the standard\nDirichlet energy of both the embedding produced by the network and the\noriginal embedding of the shape in $\\mathbb{R}^3$ (the 3D coordinates of\nthe shape’s vertices), using the following formula:\n$$E_{Dirichlet}(G) = \\frac{1}{n} \\sum_{i=1}^n \\frac{G_i^{\\top} W G_i}{G_i^{\\top} A G_i},$$\nwhere $G$ is the embedding in question of dimension $n$, while $W$ and\n$A$ are, respectively, the standard stiffness and mass matrices,\ncomputed using the classical cotangent discretization scheme of the\nLaplace-Beltrami operator \\[3\\]. We computed the Dirichlet energy over\nthe whole test set and found it equal to **47.2** (the average) for\ncoordinate functions (original shape embeddings in $\\mathbb{R}^3$),\nwhile it is equal to **13.1** for embeddings produced by the network.\nThis shows that the latter are smoother than embeddings in the original\nspace.\n\nFor injectivity, we computed for each point of the embedding, the\ndistance to its nearest neighbor, and took *the minimum* across all\npoints of a shape. To make the comparison between the original embedding\nin $\\mathbb{R}^3$ and the embedding produced by the network fair, we\nnormalized both embeddings to the unit sphere. We find that on average,\nthe minimum distance between points in the original 3D space is\n**0.0004**, while for the feature embedding, given by the network it is\nequal to **0.0015**. This shows that the network is injective, and that\ndistances between points are larger than in the original domain.\n\nWe will be happy to incorporate this result in the final version.\n\n\\[1\\] Rahaman, Nasim, et al. \"On the spectral bias of neural networks.\"\nInternational Conference on Machine Learning. PMLR, 2019.\\]\n\n\\[2\\] Behrmann, J., Grathwohl, W., Chen, R. T., Duvenaud, D., and\nJacobsen, J.-H. Invertible residual networks. In International\nConference on Machine Learning, pp. 573–582, 2019.\n\n\\[3\\] Ulrich Pinkall and Konrad Polthier. Computing discrete minimal\nsurfaces and their conjugates. Experimental mathematics, 2(1):15–36,\n1993\n\n**Q8. Where the proposed method breaks?** \n\nWe observed that our method fails\neither when the maps in Stage 1 are total noise and have no structure,\nor when the maps are symmetrically inverted (e.g., mapping left to right\non human or animal shapes), in which case it is difficult to recover a\nground truth map from this initialization, since structurally such maps\nare identical to the ground truth.\n\nRegarding partial shapes, we thank the reviewer for this suggestion, and\nwe think this is an interesting direction for future research. We\nbelieve that our method will still work in this setting, but additional\nattention must be paid to partiality, either by using a partiality\ncriterion such as the one used in our keypoint detection experiment, or\nby using a special network for detecing the overlap region, such as the\none introduced by DPFM \\[7\\].\n\n\\[7\\] Souhaib Attaiki, Gautam Pai, and Maks Ovsjanikov. DPFM: Deep\npartial functional maps. In 2021 International Conference on 3D Vision\n(3DV). IEEE, December 2021.", " We thank the reviewer for their detailed and thoughtful comments and suggestions. We invite the reviewer to consider the general feedback that we provided to all reviewers in the \"High Level Summary\" answer. Below are our answers to the reviewers’ questions. Due to the 5000 character limit, and in order to fully address the reviewers’ comments, we have divided our response into three parts.\n\n\n**Q1. Intuition for Stage 2 in our algorithm** \n\nThank you for your comments\nand suggestions. Our intuition for Stage 2 is threefold.\n\nFirst, and motivated by the results of Section 3.2 (the NCP effect), we\nshowed that neural networks tend to have difficulty overfitting to\ncorrupted artifact-laden inputs (neural networks have high noise\nimpedance), and in the process of over-fitting an approximate map by a\nneural network, the intermediate maps are of **better quality** than the\ninput (L163-166 of the main manuscript), which gives us the idea of\nusing artifact-laden maps as supervision for a network, and capitalizing\non the NCP effect to recover better maps.\n\nSecond, and as we mentioned in Section 4.1, when we have a collection of\napproximate maps, their errors tend to be inconsistent, and training a\nnetwork to adapt to them adds an extra layer of regularization, as the\nnetwork cannot adapt to all inconsistent errors on all pairs at once.\n\nFinally, in our formulation of Stage 2, we learn one feature embedding\nper shape, and compute correspondences via nearest neighbor search\nbetween feature embeddings. This introduces an additional layer of\nregularization, as it makes it difficult for the network to learn a\nfeature embedding, which can adapt to errors in the maps between all the\n*pairs of shapes.*\n\nWe thank the reviewer for this comment and will be happy to clarify this\nintuition in the final revision.\n\n**Q.3 Is the usage of term “noise” appropriate?**\n\nWe thank the reviewer for this question. The use of this term comes from\nour experiment in Section 3.2, where real random noise was used to\ndemonstrate the NCP effect, and we have adopted the same terminology\nthroughout the paper. With respect to the maps produced by Stage 1, we\nagree with the reviewer that they are not pure noise and that they\ncontain some structure. Perhaps a more appropriate term would be\n\"approximate\" or \"artifact-laden\" maps. We will make the necessary\nchanges in the revision to reflect this idea.\n\n**Q4. Are many-to-one mappings theoretically allowed?** \n\nIf the question refers to mappings between shapes, then yes, both in theory and in\npractice many-to-one mappings across shapes are allowed. Note that even\nif the individual feature embeddings are injective, the nearest neighbor\nmapping between them might not be, and the smoothness of the\ncorrespondence is not hindered by this.\n\nOn the other hand, if the question refers to many-to-one feature\nembeddings, then, indeed, as mentioned by the reviewer, we need to\nassume it theoretically, since otherwise the nearest neighbor\ncorrespondence in feature space is not even well-defined. However, in\npractice, our method works directly without requiring or enforcing\ninjectivity of feature embeddings.\n\n\n**Q5. Insights of Section 3 and local operators**\n\nThank you for the comment.\nPlease note that in addition to DiffusionNet and PointMLP, we have\nprovided in Table 1 in the Supp. Materials additional results using\nseveral other backbones: PointNet++, DGCNN and ResidualMLP. The latter\nis a true local backbone, as it applies multiple MLPs to each point\nindividually without pooling (PointNet applies pooling at latter\nstages). As can be seen from this table, *all methods* improve the\nresults of Stage 1, indicating that the NCP property holds very broadly.\nHowever, we have observed that using an advanced network such as\nDiffusionNet (which is global by design) tends to yield the best results\nfor 3D meshes for example.\n\n**Q7. Advantages/downsides for doing local then global matching?** \n\nCan the reviewer provide some examples of such methods? To the best of our\nknowledge, learning-based shape matching methods all start by finding a\nglobal map (either by using functional maps or by considering the\nmatching problem as a dense semantic segmentation problem), and then\nthey try to refine the map locally using techniques such as ZoomOut\n\\[4\\], PMF \\[5\\], ICP \\[6\\], etc.\n\n\\[4\\] Simone Melzi, Jing Ren, Emanuele Rodolà, Abhishek Sharma, Peter\nWonka, and Maks Ovsjanikov. 2019. ZoomOut: spectral upsampling for\nefficient shape correspondence. ACM Transactions on Graphics 38, 6\n(2019), 1–14\n\n\\[5\\] M. Vestner, R. Litman, E. Rodola, A. Bronstein, and D. Cremers.\nProduct manifold filter: Non-rigid shape correspondence via kernel\ndensity estimation in the product space. In Proc. CVPR, pages 6681–6690,\n2017.\n\n\\[6\\] Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher,\nand Leonidas Guibas. Functional Maps: A Flexible Representation of Maps\nBetween Shapes. ACM Transactions on Graphics (TOG)", " **Q2. Utility of Theorem 1**\n\nWe thank the reviewer for this comment. The\nmotivation behind Theorem 1 is to highlight the fact that, given smooth\nfeature embeddings, if we add the injectivity condition, the maps\nextracted using the nearest neighbors in the feature space tend to be\nsmooth. As smoothness is a generally desirable property for maps, and\nthe frequency bias shown in prior works, such as \\[3\\] suggests that\nneural networks are biased towards low frequency (and thus smooth)\nfunctions, we provide this result as a partial explanation for the\nNeural Correspondence Prior, which we have observed, for the first time,\nin our work.\n\nNevertheless, we agree with the reviewer that this theorem is not\nrelated directly to the fact that the mapping is given by a neural\nnetwork. Furthermore, we do not consider this as a key theoretical\ncontribution of our work. We would therefore be happy to paraphrase it\nas simply a high-level motivation for our approach, as suggested by the\nreviewer.\n\nRemark, however, that we believe the result still does hold for d\\<3.\nFor d=1, there are no smooth injective embeddings of 2d manifolds, and\nthus the theorem does not apply (as it requires such an embedding by\nassumption). For 2d, *if* the feature embeddings are smooth and\ninjective, then the nearest neighbor map will generically be smooth up\nto sets of measure zero. We will be happy to provide more details on the\nargument, if necessary.\n\nFurthermore, following the reviewer’s suggestion, we evaluated the\nsmoothness and injectivity of a randomly initialized network.\nSpecifically, we first computed the embeddings produced by a randomly\ninitialized DiffusionNet network for the 20 test shapes in the FAUST\nremeshed dataset.\n\nTo evaluate the smoothness of the embedding, we computed the standard\nDirichlet energy of both the embedding produced by the network and the\noriginal embedding of the shape in $\\mathbb{R}^3$ (the 3D coordinates of\nthe shape’s vertices), using the following formula:\n$$E_{Dirichlet}(G) = \\frac{1}{n} \\sum_{i=1}^n \\frac{G_i^{\\top} W G_i}{G_i^{\\top} A G_i},$$\nwhere $G$ is the embedding in question of dimension $n$, while $W$ and\n$A$ are, respectively, the standard stiffness and mass matrices,\ncomputed using the classical cotangent discretization scheme of the\nLaplace-Beltrami operator \\[4\\]. We computed the Dirichlet energy over\nthe whole test set and found it equal to **47.2** (the average) for\ncoordinate functions (original shape embeddings in $\\mathbb{R}^3$),\nwhile it is equal to **13.1** for embeddings produced by the network.\nThis shows that the latter are smoother than embeddings in the original\nspace.\n\nFor injectivity, we computed for each point of the embedding, the\ndistance to its nearest neighbor, and took *the minimum* across all\npoints of a shape. To make the comparison between the embedding in\n$\\mathbb{R}^3$ and the embedding produced by the network fair, we\nnormalized both embeddings to the unit sphere. We find that on average,\nthe minimum distance between points in the original 3D space is\n**0.0004**, while for the feature embedding, given by the network it is\nequal to **0.0015**. This shows that the network is injective, and that\ndistances between points are larger than in the original domain.\n\nWe will be happy to incorporate this result in the final version.\n\n\\[3\\] Rahaman, Nasim, et al. \"On the spectral bias of neural networks.\"\nInternational Conference on Machine Learning. PMLR, 2019.\\]\n\n\\[4\\] Ulrich Pinkall and Konrad Polthier. Computing discrete minimal\nsurfaces and their conjugates. Experimental mathematics, 2(1):15–36,\n1993\n\n**Exposition** \n\nWe thank the reviewer for finding our paper “simple, well\nexplained and well demonstrated”. We also thank the reviewer for\nacknowledging that our work is the first to demonstrate the utility of\nthe neural prior for shape correspondence.\n\nWe will incorporate *all of the writing suggestions* from the reviewer,\nincluding more clarifications, fixing the font size and removing the\nunnecessary abbreviations.", " We thank the reviewer for their detailed and thoughtful comments and suggestions. We invite the reviewer to consider the general feedback that we provided to all reviewers in the \"High Level Summary\" answer. Below are our answers to the reviewers’ questions. Due to the 5000 character limit, and in order to fully address the reviewers’ comments, we have divided our response into two parts.\n\n\n**Q1. Correspondences evaluated on FAUST** \n\nThank you for the suggestion. In\nour work, we focus on difficult non-rigid non-isometric datasets, where\nexisting methods tend to fail. This is because, on near-isometric\ndatasets such as FAUST or SCAPE, current unsupervised methods can\nexploit the assumption of near-isometry and achieve good results.\n\nNevertheless, as suggested, below we include a comparison of our method\non the FAUST remeshed and SCAPE remeshed datasets, using the same\ntrain/test split used in all previous works. The notation X on Y means\nthe method is trained on X and tested on Y.\n\nAs input for our Stage 2, we use WSupFMNet + DiffusionNet \\[1\\] (first\nline of the table), which is the same method used in the main manuscript\nfor all our experiments. For our method (Stage 2), we use the same\nimplementation as the one used for the SMAL dataset, described in\nSection 5.1.2 of the main manuscript.\n\nAs shown in this table, even on a near-isometric dataset, our Stage 2\nimproves upon the initial maps in all categories, by 18.4% on average.\nNevertheless, we remark that in such settings it is more advantageous to\nuse specialized methods, such as ZoomOut \\[2\\], that directly exploit\nthe near-isometry assumption.\n\nWe will be happy to include this result and discussion in the final\nversion.\n\n| Method | FAUST on FAUST | SCAPE on SCAPE | FAUST on SCAPE | SCAPE on FAUST |\n|:-----------------------------------|:--------------:|:--------------:|:--------------:|:--------------:|\n| WSupFMNet + DiffusionNet | 3.8 | 4.4 | 4.8 | 3.6 |\n| WSupFMNet + DiffusionNet + ZoomOut | 1.9 | 2.6 | 2.7 | 1.9 |\n| NCP (ours) | 3.0 | 3.5 | 4.2 | 2.9 |\n| NCP (ours) + ZoomOut | 1.9 | 2.4 | 2.6 | 1.9 |\n\n---\n\n\\[1\\] Nicholas Sharp, Souhaib Attaiki, Keenan Crane, and Maks\nOvsjanikov. Diffusionnet: Discretization agnostic learning on surfaces.\nACM Trans. Graph., 01(1), 2022.\n\n\\[2\\] Simone Melzi, Jing Ren, Emanuele Rodolà, Abhishek Sharma, Peter\nWonka, and Maks Ovsjanikov. 2019. ZoomOut: spectral upsampling for\nefficient shape correspondence. ACM Transactions on Graphics 38, 6\n(2019), 1–14", " We thank the reviewer for their detailed and thoughtful comments and suggestions. We invite the reviewer to consider the general feedback that we provided to all reviewers in the \"High Level Summary\" answer. Below are our answers to the reviewers’ questions. \n\n\n\n**Q1. Is the loss in line 260 differentiable?** \n\nThank you for your comment. In our implementation, $\\Pi_{MN}$ is a soft matrix computed using Eq. (5) in the Supp. Materials. This makes the whole operation differentiable. We will clarify this in the revision.\n\n**Q2. Is early stopping an important step in 4.2?** \n\nTo clarify, as shown in\nFigure 1 of the main manuscript, when using a single pair of shapes (as\nin Section 4.2), if no early stopping is used, the network will\neventually overfit to the noisy map, making early stopping necessary.\n\nHowever, when using a collection (the setting in Section 4.1), as\nmentioned on L187-190 of the main manuscript, the collection provides an\nadditional layer of regularization, making early stopping unnecessary.\nSince *all* of our results, except those explicitly mentioned in Table\n2, are produced using the approach described in Section 4.1, we do not\nrely on early stopping in practice.\n\nIn Table 2 we presented results with both methods (Ours, which uses the\ncollection) and (Ours, Test-Time Optimization, using the method\ndescribed in Section 4.2, applied on each pair independently). As can be\nseen from this table, the results when using the collection are better.\nFurthermore, this method is also faster since it does not require\ntest-time optimization on each shape individually.\n\nIn summary, early stopping is only required when considering individual\nshape pairs. In our experimental results, we are given access to a\ncollection of training shapes, and thus we use the method in Section\n4.1, which makes early stopping unnecessary. We will be happy to make\nthis more explicit.\n\n**Q3. About the notation of Theorem 1** \n\nWe use $N(M)_x$ to denote the image\nof the mapping $N(M)$ at some point $x$ ($N(M)$ is the image of the\nnetwork $N$ applied to the surface $M$). An alternative, possibly more\nstandard notation, would be to use $N(M)|_x$, i.e., the mapping $N(M)$,\nrestricted to $x$. We will be happy to make this change.\n\n**Q4. Repeating the second stage multiple times, i.e steps 2-5 in the\nalgorithm** \n\nYes, it is possible to repeat Stage 2 several times, and we\nobserved that there is a slight improvement in some cases, but most\noften it stagnates after the first iteration. We experimented with this\nand chose to keep the method simple and use only one iteration (thus,\navoiding an additional tunable hyperparameter). We will be happy to\nprovide illustrations of this phenomenon.\n\n**Q5. The main difference between 4.1 NCP and 4.2 test time denoising**\n\nThe difference between the methods in Section 4.1 and 4.2 lies in the\namount of training data available. The method proposed in Section 4.2 is\nused when we only have a single pair of shapes and an approximate map\nbetween them as input. In this case, we train a network to overfit to\nthis input map and use early stopping to achieve improvement in\naccuracy.\n\nThe method in Section 4.1 is used when we have a collection of shapes at\ntraining time (as is the case in *all of our experiments*, except the\none marked “test-time optimization” in Table 2 of our main manuscript).\nIn this case, in Stage 1, we use an unsupervised method to get an\ninitial set of maps. In Stage 2, we then use these approximate maps as\nsupervisory signal, as described in Algorithm 1. We advocate this method\nin case of collections because 1) it avoids early stopping, 2) it leads\nto more accurate results, and 3) it is faster as no test time\noptimization is necessary, and the network, once trained, can be used\ndirectly to predict high quality maps on unseen shape pairs.\n\n**Exposition** \n\nWe thank the reviewer for the suggestions regarding the\nexposition. We will incorporate *all of the* writing suggestions from\nthe reviewer, including making more clarifications, and enlarging the\nfont size in the figures. We also thank the reviewer for finding our\nwork “novel and interesting”.", " We thank the reviewers for their constructive comments. We find the\nsuggestions to be very helpful for improving the quality of our work,\nmaking it clearer and more convincing.\n\nBefore responding to individual concerns, we stress the following\ncontributions of our work:\n\n**(1)** We show, for the first time, that when trained using\napproximate, artifact-laden maps for supervision, the features learned\nby neural networks lead to correspondences that are more coherent and\nare of higher quality than the input, including on difficult non-rigid\nnon-isometric shape pairs. We call this effect Neural Correspondence\nPrior \\[**4Seq**, **41ct**\\]. As remarked by \\[**ZBSs**\\] our work\ndemonstrates, for the first time, “neural prior for shape\ncorrespondence”.\n\n**(2)** We demonstrate that an untrained recent state-of-the-art neural\nnetwork for 3D shapes can produce pointwise features that are on par\nwith complex axiomatic local descriptors \\[**ZBSs**, **41ct**,\n**2gYm**\\]\n\n**(3)** Based on these insights, we develop a two-stage algorithm for\nunsupervised 3D non-rigid shape matching that achieves SOTA results in a\nbroad range of difficult matching scenarios including non-isometric and\npoint cloud matching, as well as other tasks such as part segmentation\ntransfer and 3D keypoint detection \\[**ZBSs**, **41ct**\\].\n\nWe believe that all of the suggested changes can be easily done within a\nminor revision and we will make sure to address all of the comments and\nconcerns in the final version. We will also release our code and data\nfor full reproducibility of our results and to facilitate future work in\nthis area.", " This paper proposed an unsupervised shape matching method, where the core idea is to first generate noisy maps from existing unsupervised shape matching methods, and refine them by learning pointwise features from the noisy maps, and build a new map by matching those features. The new map is empirically more accurate than the input noisy maps. Experiments are conducted to support the claim.\n The reviewer finds the work novel and interesting. The main concerns are as follows:\n\n1. How is the loss in line 260 differentiable with respect to the network parameters? Since it appears that Pi_MN lies in the set of permutations, which is a discrete set.\n2. In section 3.2 it says early stopping is needed for training the random-initialized network to learn features. However, it appears that early stopping criterion is only proposed in 4.2 but not 4.1. Is it true that 4.2 is not an optional step of denoising, but actually an important step for early stopping?\n\n\nMinor issues on presentation: \n3. The notations of Theorem 1 (lines 201-204) look a bit confusing. Does N(M)_x mean the mapping N restricted on M applied on x \\in M? \nIf so, I wonder if N(M)_x a standard notation, or if N|_M(x) is more standard? Since in the former, N(M) could mean the image of M under N.\nIf not, what does this notation mean? \n4. The fonts in the figures could be improved, in particular, they are way too small compared to the body text, and it seems that there is space.\n 1. Is it possible if one repeats the process of learning features from a map and matching the features to produce a map, i.e., steps 2-5, would one get further improvement? \n2. What is the main difference between 4.1 NCP and 4.2 test time denoising? In 4.2 do you train an extra network beyond that already trained in 4.1 NCP? Is the purpose of 4.2 to propose an early stopping criterion for NCP?\n N/A", " This paper applies the idea of deep prior to predict 3D correspondences. It does so using two ideas, which are demonstrated experimentally in the first part of the paper: first, it shows that randomly intialized diffusionNet features actually provide better results than spectral and SHOT descriptors, and combined with fonctional maps even improve over learned metods; second, it shows that when training a network to predict features to fit noisy correspondences, the quality of correspondences/features obtained at the beginning of training are actually better than the noisy target. This naturally leads to a method to predict correspondences, obtaining features from a randomly initialized network, then training a second one to predict them and stoping early (using a cycle consistency loss to decide when) I liked this paper, the idea is simple, well explained and well demonstrated. To the best of my knowledge using neural prior for shape correspondence is novel, if this is indeed the case I think the paper should clearly be accepted.\n\nAs for weaknesses:\n- Why aren't correspondences evaluated on FAUST? I would really want to see this evaluation, which would also ease comparison with other methods.\n- smaller weaknesses:\n* I liked the separation of section 3 and 4, but then section 4 points several times to section 5 for important details about the method, I think this makes the reading more complicated than needed, please move all details about the method to section 4.\n* I am not a fan of theorem 1. It is actually not related directly to the fact that the mapping are neural nets, it would need a demonstration that this is the general case (i.e. with random weights) for the neural net architecture considered, and both formulation and demonstration in the supmat are very handwavy (for example the theorem is clearly false for d<3, which doesn't appear anywhere). I would thus suggest to completely remove it, or at least not call it a theorem for which I would like a much more rigorous demonstration\n* too many unnecessary abbreviations make the text harder to read (FR, SR, NCP, NCP-UN, UM, RN not counting the ones for previous methods ), I would remove at least 50% of them and be sure to regularly remind the reader of the meaning of the ones kept (none, or maybe only NCP would be great)\n* fig 2 is not readable in the printed version See weaknesses (in particular FAUST evaluation) yes", " The authors analyze the power of random features from 3D encoders and use it to provide methods for point cloud matching, non-isometric shape matching on meshes, part segmentation transfer and keypoint transfer. It is shown that the random features of several architectures provide a strong prior that automatically resolves matching errors in the early iterations of training. Together with a novel stopping criteria, this leads to a method for refining dense correspondences between shapes. Strengths:\n- The paper presents a lot of insight into features extracted from 3D operators. The strength of random features was known before (in CNNs) but this is the first time, it was analyzed for 3D architectures on point clouds/meshes\n- The described neural correspondence prior in combination with the cycle loss as early-stopping criteria is an interesting and strong mechanism\n- There are a lot of state-of-the-art results beaten here (or on par): point cloud matching, shape matching on non-isometric shapes, part segementation transfer, 3D keypoint detection on point clouds\n- The paper is well written\n\nWeaknesses:\n- The paper raises a lot of questions (see below), I am not sure if I fully understood the effect of the second stage of the network. It would be good if the authors made an additional effort describing the main intuitions.\n- Theorem 1 seems to be not that important to me. The crucial parts are the assumption of smooth encoders and injectivity, which are often not given for existing methods (especially local encoders like PointNet). The consequence of smooth encoders and injectivity is pretty straight-forward. It would be more interesting if the authors would additionally show that the used encoders are indeed injective and smooth.\n- It seems to me that the term \"noise\" is used in a hand-wavy fashion in this work. I would appreciate a more clear definition of \"noise\" and comparisons between different types of noise if they are applied artificially. I am not convinced that the output of stage 1 of the approach should be called \"noisy\". The errors seem to be more systematic.\n- This paper seems to be divided into to main messages, (1) the analysis of random features/neural correspondence prior, and (2) Theorem 1 and its application using the respective networks (DiffusionNet and PointMLP + fmaps). This makes the paper hard to follow in some parts.\n\nEven if the weaknesses list is longer, I think this is a good paper. I liked reading it and it gave me several insights and a few ideas, which is a good sign. In order to make it really great I would encourage the authors to work a bit more on the structure, discussions of main implications and several details that need to be answered, see below. - Are many-to-one mappings theoretically allowed / is it just assumed that there is an injective mapping from shape to feature space, as in the requirement of Theorem 1?\n- Related to the last question: DiffusionNet is a method that incorporates global information through the global diffusion mechanism. However, other networks, such as PointNet and variants are inherently local, meaning that many-to-one feature mappings will be much more likely, even for isometric shapes. Does the method require a global backend, such as as DiffusionNet (or seemingly PointMLP, not so sure on this one) to work, do the insights in Section 3 only hold for those backends, and in case of a local operator, would an additional consensus method (like [1]) help?\n- Would the following statement be correct: The first part of the method finds dense correspondences based on a global feature extractor and fmaps and relies on the near-isometry assumption. Refining the random features during test time is able to resolve errors made due to non-isometric correspondences (in this case, \"noise\" would not be a reasonable description of such errors). Is this due to the local nature of the random features? \n- Many correspondence methods first do local feature matching and then resolve mistakes by introducing global information in a second stage. Here, it seems to be the other way around. Could the authors discuss the implications of this and which advantages/downsides this variant has?\n- I would like to know where the proposed method breaks - how mismatching do the shapes have to be? Since the method seem to rely on a global feature extractor backend, how well does it work on partial meshes? Could a similar technique as in the keypoint extractor be applied?\n- I think the paper would benefit from an analysis of different initialization schemes, when using random features. In the end, this seems to be the main part of the paper.\n\n[1] Fey et al.: Deep Graph Matching Consensus, ICLR 2020\n\nMinor:\n- l. 61: Correspondnece\n- l 281: does not relies\n- l 285: \"point cloud dataset that provide\"\n- Figure 2 labels are way too small\n- Content of the supplementary materials should be explicitly referenced in the main paper (most important: keypoint application). The authors shortly mention some limitations of the method, as it depends on the results of the applied step 1. Discussion of limitations could be improved.\nPotential negative societal impact is not discussed but I also see no immediate reason to do so. ", " An unsupervised shape correspondence method is proposed :\n\n1. Inputs : training set of shapes (without ground truth)\n2. Train an off-the-shelf unsupervised matching \"teacher\" network on the training set\n3. Train a \"student\" network from scratch on the training set in a supervised manner using the \"teacher\" predictions as ground truth\n4. Use the \"student\" network to establish correspondences between unseen shape pairs\n\nThis method is motived by two empirical observations :\n\n1. \"Neural bias\" : It experimentally shows that features extracted with a randomly initialized DiffusionNet produce good matching performances on FAUST remeshed and SCAPE-remeshed datasets .\n2. \"Neural Correspondence Prior\" : It experimentally shows that the \"Deep Image Prior\" holds for a shape correspondence problem.\n\nThe proposed method either outperforms or is on par with the sota methods on the KeyPointNet dataset, the SHREC20 dataset, the SMAL dataset and the PartNet dataset. ### Strengths\n\n1. Extending the \"Deep Image Prior\" to shape matching is an interesting idea.\n2. The paper is well written.\n3. The overall approach is simple.\n\n### Weaknesses\n\n#### 3.1 Neural bias for pointwise features\n\n1. This part of the paper experimentally shows that features extracted with a randomly initialized diffusionNet produce good matching performances on FAUST remeshed and SCAPE-remeshed datasets. I believe the results of a randomly initialized pointwise MLP should be added, otherwise the section title should be changed to \"diffusionNet bias for pointwise features\".\n2. The link between this neural bias (i.e the fact that an untrained network produces good matches) and the proposed method is unclear to me, since both the teacher and the student networks are trained.\n\n#### 4.1 NCP within a shape collection\n\n1. Why not using the standard terminology teacher network / student network ? I think it would make the whole paper easier to read.\n2. I was expecting the teacher network to be an untrained diffusionNet, especially after reading section 3.1. It seems to me that section 3.1 is not tightly connected to the rest of the paper.\n\n#### 5.1.1 Correspondences on Point Clouds\n\n1. The proposed method outperforms the sota methods but I could not find the performances of the teacher network (i.e unsupervised functional map method + PointMLP backbone).\n\n#### 5.1.2 Correspondences between non-rigid meshes\n\n1. Table 2 shows that the proposed method only slightly outperforms the DiffusionNet-based methods, for instance \"WSupFMNeT + DiffusionNet\" is an unsupervised method that is only slighly outperformed by the proposed method.\n2. Figure 4 shows the results of NeuroMorph which is the worst unsupervised method in Table 2. Why not showing the results of \"WSupFMNeT + DiffusionNet\" instead ?\n\nOverall the proposed method is probably interesting for the shape matching community but the novelty is limited. Moreover, it seems the proposed method only slightly outperforms Diffusion-based methods. Please see \"Weaknesses\" above. -" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 7, 7, 3 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4 ]

[ "3y5yTqJvioi", "x9coXOnGxD", "n0L6VJYeTZS", "n0L6VJYeTZS", "roJ5XXilQ3", "roJ5XXilQ3", "roJ5XXilQ3", "Sl_aXdWGuIL", "Sl_aXdWGuIL", "HA20apUD-XF", "nips_2022_ouXTjiP0ffV", "nips_2022_ouXTjiP0ffV", "nips_2022_ouXTjiP0ffV", "nips_2022_ouXTjiP0ffV", "nips_2022_ouXTjiP0ffV" ]

[ "_Ib2iTQC2iPt", "IVBO5IJSWe25", "9iXUj9Mm4UEj", "thiHwpDplIO", "cHKVbOSUywU", "Nr7zBhJa9-C", "3bu35i2dQ5E", "1ceJ_PWumHz", "YwzeHiThYN_", "x966UKTEVRE", "83pv1_ycmAZ", "xyZSjb7QBcp" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your insightful suggestions.\nThe distribution of selected attacks and other issues help a lot in further improving our paper.", " EOM", " We sincerely appreciate your time and efforts in reviewing our paper.\nWe truly thank you for the useful suggestions and the acknowledgment of $A^2$''s improvement.\nFor reproducibility, we will release the code on Github if it is accepted.\n\n", " I have read all reviewer comments as well as the author response. And I did not find a reason to reduce my original recommendation (7:accept). I agree that improving even 1% of adversarial robustness is already difficult enough at the current stage. It is highly suggested to release code for reproducing this work if it will be accepted.", " We sincerely appreciate your constructive comments. The comparison with CW and the design of the gradient-free version inspires us to explore $A^2$ in a more diverse attack space (e.g., CW and transfer-based black-box attack). As a plug-in, $A^2$ is used to boost various adversarial attack&training methods under the consideration of efficiency.", " Thanks for the additional experiments on the CW attack effect. I also appreciate the authors' insight about relating the choice of $\\nabla_{\\mathbf{x}^{(k-1)}} l(f_\\theta(\\mathbf{x}^{(k-1)}, y)$ to the reinforcement learning context. However, I'm not very convinced about this paper's \"high impact\" (compared to the existing cutting-edge methods, the improvement seems to be subtle), so I decided to stay at my initial evaluation of 6.", " We thank the reviewer for the valuable comments. The revised version has been uploaded. We have added experiments on transferable black-box attacks and a discussion of selected attacks in Appendix. Moreover, We have fixed the grammatical errors in the revised version. Next, we introduce the responses point by point.\n\n---\n\n> Q2: Did the authors investigate the efficacy of their adversarial training approach $A^2$ against transferable black box attacks?\n\nAccording to the suggestion, we further investigate the effectiveness of $A^2$ against transferable black-box attacks in Appendix B.4.\nThe transferable attacks are generated by **an ensemble of three transferable black-box attack methods (MI with momentum = 1[1], DI[2], and TI[3]) with 20 steps on three surrogate pre-trained models from [github](https://github.com/huyvnphan/PyTorch\\_CIFAR10): IncV3 (InceptionV3), VGG19, and DN201 (DenseNet201)**.\n\nThe following test robustness shows that AT boosts the robustness against transferable black-box attacks, and $A^2$ can further improve the adversarial robustness.\n\n|| IncV3\t| VGG19 |DN201| PGD20|\n|---|----|---|---|---|\n|ResNet-18|16.12|7.37|5.35| 0.02|\n|ResNet-18-AT\t|61.98\t|60.81\t|59.63\t|52.79|\n|ResNet-18-AT-$A^2$\t|**62.79**| **61.85**| **60.28** | **52.96** |\n\n\nMoreover, AutoAttack includes a query-efficient black-box attacker (i.e., Square Attack).\n\n\n\n---\n\n> Q3&Limitation1: Is there a combination of attack types or step sizes that are clearly selected a vast majority of the time? If so, does provide a considerable improvement over just using this combination of attack parameters? Or are there classes or datasets that are more vulnerable to certain attack combinations?\n\n\nThanks a lot for the comment.\n\nWe analyze the selected attacks from the perspective of blocks with different steps and datasets.\n\nThe first and final perturbation blocks of 10-step $A^2$ in CIFAR-10 are chosen for analysis.\nFigures in Appendix B.5 show the distribution of selected attacks of different perturbation blocks.\n\n- **Perturbation Block 1:** $A^2$ tends to choose FGM, FGSM, and partially random methods as initialization in the first step.\nThe momentum-based attack methods are quickly discarded as the gradient of the previous step is absent.\nFGSM is chosen more frequently due to its stronger attack on both foreground and background.\n- **Perturbation Block 10:** The optimization of the victim model leads to changes in the distribution of selected attacks in the last block.\nIn the early stage of training, the victim model is vulnerable.\n$A^2$ retains the diversity and plays the role of friendly attackers like FAT[5].\nAt the end of the training, $A^2$ prefers the momentum-based attacks (i.e., FGSMM and FGMM).\n\nFrom the perspective of datasets, SVHN and CIFAR-10 prefer different attack methods.\nSVHN discards FGSMM, which is most frequently used in CIFAR-10, and pays more attention to FGMM.\n\nIn summary, $A^2$'s preference for selecting attacks in blocks varies according to the block step, dataset, and victim model.\n\n\n---\n\n> Q1& Limitation2: Are the results from tables 2, 3, and 4 also run 5 times and averaged as well? \n\nYes. As details, we run 5 times for Table1&Table4. For Table2&Table3, limited by the huge resources that adversarial training consumes, we run the attack to test adversarial robustness 5 times. We have highlighted this in the table caption.\n\nFor reproducibility, we provide the source code and scripts with fixed random seeds in SupplementaryMaterial.\n\n\n> Limitation3: Emphasizing or explaining the significance of the relatively small performance improvements afforded by $A^2$.\n\nThank you for the suggestion.\nIn the revised version, we have emphasized the significance of performance improvements.\n\n- **Test Robustness:**\n$A^{2}$ generates stronger perturbations with low extra cost and improves the robustness of various AT methods against different attacks.\nCompared to the recent related works [4][5][6], the 1~2 percent robustness improvement on CW and AutoAttack introduced by $A^2$ is already non-trivial.\n- **Attack Effect:**\nConsidering generating perturbations on-the-fly during training, we balance the attack effect with the overhead.\nAt 1/5 cost, the 20-step $A^2$ finds better attacks than PGD100.\nThe results in Appendix B.3. \"Generality of $A^2$ in White-Box Attacks\" show that $A^2$ is general to improve the attack effects of PGD and CW.\n\n\n\n[1] Dong, et al. \"Boosting adversarial attacks with momentum.\" CVPR 2018.\n\n[2] Xie, et al. \"Improving transferability of adversarial examples with input diversity.\" CVPR 2019.\n\n[3] Dong, et al. \"Evading Defenses to Transferable Adversarial Examples by Translation-Invariant Attacks.\" CVPR 2020.\n\n[4] Wang, et al. \"Improving adversarial robustness requires revisiting misclassified examples.\" ICLR 2019.\n\n[5] Zhang, et al. \"Attacks which do not kill training make adversarial learning stronger.\" ICML 2020.\n\n[6] Wu, et al. \"Adversarial weight perturbation helps robust generalization.\" NeurIPS 2020.", " Thank you very much for the positive feedback and the useful comments.\nWe have addressed the issues in the revised version. The detailed response to each comment is as follows:\n\n\n> Weakness1: [important]Is the resulting adversarial perturbation clipped into the perturbation bound epsilon? The perturbation bound epsilon is required by Algorithm 1, but not explicitly used. Please clarify this and make it less confusing.\n\nYes, as shown in `SupplementaryMaterial/auto_adv/cell.py/Line77`, all perturbations have been clipped into $\\epsilon$-bound via `torch.clamp`.\nThank you for pointing out this issue.\nIn the revised version, we have highlighted this in `Algorithm1/Line7`.\n\n\n---\n\n> Weakness2: [minor suggestion.] It would be better to investigate whether the proposed method is still effective on larger-scale datasets like ImageNet.\n\nThank you for your suggestion.\nCurrently, we are unable to obtain results due to the expensive running time.\nThis will serve as our future work.", " We sincerely thank the positive feedback and useful suggestions from the reviewer. The revised version has been uploaded. Here is our response.\n\n\n\n> Question1: This paper specifically uses $\\nabla_{x^{(k-1)}} l$ to produce a query. Is it a necessary choice, or is your design flexible enough to take other values as input? To provide more context, I’m considering a gradient-free version of $A^2$ and expect the same design to work with a different attacker space and a different type of query.\n\n$A^2$ is flexible to take other values as input, as long as the input can be extracted as queries and the victim model back-propagates the loss in a white-box setting.\n\nIn fact, $\\nabla_{x^{(k-1)}}$ is an unnecessary but good choice during adversarial training, which contains the information of the model and sample.\nWe design such a query with reference to observable states and reward mechanisms in reinforcement learning.\nThe more information the state (i.e., $\\nabla_{x^{(k-1)}}$) and reward (i.e., backpropagation of loss) provide, the more efficient the automated attacker is.\n\nFurthermore, other black-box optimization algorithms need to be considered (e.g., Bayesian Optimization) in black-box settings where model gradients are not available.\n\n\n---\n\n> Weakness1: The authors can improve the experiment on the attack effectiveness by more comparisons to other attacks (other than PGD) such as CW and AutoAttack.\n\n\nMany thanks for the suggestion.\n\nAccording to the suggestion, we have added the attack effect of CW in Appendix B.3 and investigate whether $A^2$ is general to other white-box attacks.\nAs a more powerful attack method, $CW_{\\infty}$-based attacks stably outperform PGD-based attacks.\nFor comparison with $CW_{\\infty}$, we propose a variant of $A^2$ that uses $CW_{\\infty}$ loss $\\nabla_{x^{(k)}} l_{cw}$ as input to generate perturbations and denote it as $CW_{\\infty}$-$A^2$.\nThe results show that $A^2$ is general and can improve the attack effect of PGD and $CW_{\\infty}$ by combining attack methods and tuning the step size.\n\n\n| | MART | TRADES-AWP | MART-AWP | RST-AWP|\n|--|-----|-------|-----|----|\n|Natural|83.07|85.36|85.60|88.25|\n|$PGD^{20}$|53.76|59.64|59.52|64.14|\n|$PGD^{20}-A^{2}$ | 53.24 | 59.34 | 59.25 | 63.97|\n|$CW_{\\infty}$ | 49.97 | 57.07 | 56.44 | 61.82|\n|$CW_{\\infty}-A^{2}$ | **49.82** | **56.98** | **55.81** | **61.30** |", " - The authors propose a new approach for the adversarial training of deep neural networks using their $A^2$ automated attacker. By using an efficient and stronger attack algorithm, the adversarial perturbations can result in more robust models trained using adversarial training. Their inner attack algorithm is inspired by AutoML and can select the attack parameters that generate the worst-case perturbations. The authors’ attack incurs a small increase in runtime compared to PGD. Strengths\n\n- A new attack type that can be used to improve the robustness of models defended using adversarial training. The attack increases runtime by 5-7%, a rather acceptable trade-off.\n- The results and experiments show a consistent improvement over previous work in both attacking models and using $A^2$ for adversarial training.\n- Included analyses and explanations of certain results (e.g., natural vs. adversarial accuracy trade-off).\n\nWeaknesses\n\n- Most results only indicate small improvements of less than 2 percentage points.\n- It is unclear whether results from tables 2, 3, and 4 are also run and averaged 5 times.\n- Various minor typos and grammar issues: is developed -> was developed, PDG -> PGD, such linearization attack -> attacks tend, becompatible -> be compatible, etc. I would recommend the authors perform a thorough proofreading check.\n- No investigation of whether different datasets, classes, or samples actually require a significant amount of fine-tuning to find optimal attack parameters.\n - Are the results from tables 2, 3, and 4 also run 5 times and averaged as well? Can we be certain that the $A^2$ approach shows a consistent improvement over normal adversarial training (and were not cherry-picked results)?\n- Did the authors investigate the efficacy of their $A^2$ adversarial training approach against transferable black box attacks?\n- I’m curious how frequently each attacker parameter is selected. Is there a combination of attack types or step sizes which are clearly selected a vast majority of the time? If so, does $A^2$ provide a considerable improvement over just using this combination of attack parameters? Or are there classes or datasets that are more vulnerable to certain attack combinations?\n - The main limitations of this work can be addressed with the following suggestions:\n\t- I would suggest the authors log the distribution of selected attack parameters for each dataset and class.\n\t- The authors should ensure that the the results presented in tables 2-5 are reproducible. Though, it is understandable these experiments were run only once, given the expensive runtime of adversarial training.\n\t- Emphasizing or explaining the significance of the relatively small performance improvements afforded by $A^2$\n", " This paper proposes a novel attack method that efficiently generates strong adversarial perturbations. Specifically, based on the idea of AutoML, the authors design an automated attacker $A^2$ that finds the best perturbation for each iteration. The main idea is to use an attention mechanism to score possible attacks in the attacker space, then sample the attack to perform based on the assigned scores. The authors challenge the problem of training attention mechanism via reparameterization trick. By training both the model parameter and the automated attacker, the authors propose an improved adversarial training method using $A^2$.\n\nFrom a set of experiments, the paper answers three questions about $A^2$: the power of the attack method, its effect in adversarial training, and the robustness of $A^2$ training. The experimental results demonstrate that $A^2$ can increase the attack power and improve the adversarial training performance without too much overhead.\n Originality: To the best of my knowledge, the paper contains novel ideas.\n\nQuality: \n\n[[Strength]]\n1. The construction looks sound, and the reparametrization trick seems reasonable to handle similar situations in model training.\n2. The authors used various adversarial training methods, datasets, and attack methods for the adversarial training experiments, showing the proposed method's effectiveness.\n\n[[Weakness]]\n1. The authors can improve the experiment on the attack effectiveness by more comparisons to other attacks (other than PGD) such as CW and AutoAttack.\n\nClarity: The paper writing is clear, and there is no issue with the clarity of the paper.\n\nSignificance: \n\n[[Strength]]\n1. The result on the attack effectiveness shows that we can save the number of iterations by adapting $A^2$ in adversarial example generation.\n2. The experiments contain a practical overhead analysis for people adapting $A^2$ in practice. Considering the additional power of the attack, I believe the overhead is reasonably small.\n 1. This paper specifically uses $\\nabla_{\\mathbf{x}^{(k-1)}} l(f_\\theta(\\mathbf{x}^{(k-1)}, y)$ to produce a query. Is it a necessary choice, or is your design flexible enough to take other values as input? To provide more context, I’m considering a gradient-free version of $A^2$ and expect the same design to work with a different attacker space and a different type of query. The authors discussed limitations and potential negative societal impact in the paper appropriately.", " This paper presents a more efficient way for adversarial training – deciding attack algorithm parameter based on the idea of AutoML. In this framework, attack steps are split into step-wise cells, and the proposed method aims to predict the best parameter for each cell using attention mechanism. By fixing the parameters of each cell, the proposed framework degenrates into existing adversarial training method. The proposed method has been evaluated on three commonly used datasets: SVHN, CIFAR-10, CIFAR-100. Comprehensive experimental results demonstrate the effectiveness of the proposed method. # Strengths\n\n1. Traditional defense methods leverages multi-step PGD for creating adversarial examples to adversarially train a model. Such method is promising but poses very significant computational overhead. I've also gone through the pain of slow adversarial training. Hence, the motivation to create adversarial examples more effectively for training is valid and clear.\n\n2. The proposed method is novel – introducing ideas of automl into the manual parameter tuning of attack algorithms for better results. Meanwhile, the method is clearly described and is not difficult to understand.\n\n3. The proposed method is effective and clearly improves robust accuracy. Nowdays it's very hard to improve adversarial robustness on these standard benchmarks. Compared to the recent related works, the robustness improvement introduced by this method (such as Table 2) is already non-trivial.\n\n4. The proposed method is compatible with other state-of-the-art defense methods like AT, TRADES, and AWP.\n\n# Weaknesses\n\n1. [important] Is the resulting adversarial perturbation clipped into the perturbation bound epsilon? The perturbation bound epsilont is reuiqred by Algorithm 1, but not explicitly used. Please clarify this and make it less confusing.\n\n2. [minor suggestion.] It would be better to investigate wether the proposed method is still effective on larger scale datasets like ImageNet. My questions are listed in the weaknesses above. Generally this is a good paper and I did not find many questions. By searching the keyword \"limitation\" I found no result in the submission, but I consider this a minor issue.\nThis paper focuses on defense side, and hence negative impact is not of concern." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 4, 4 ]

[ "IVBO5IJSWe25", "3bu35i2dQ5E", "thiHwpDplIO", "1ceJ_PWumHz", "Nr7zBhJa9-C", "YwzeHiThYN_", "x966UKTEVRE", "xyZSjb7QBcp", "83pv1_ycmAZ", "nips_2022_SsA-0BZa7B_", "nips_2022_SsA-0BZa7B_", "nips_2022_SsA-0BZa7B_" ]

[ "R7cCUfAeCPc", "61vFPoLBYis", "r3DIuGN3vo-", "R4Hzibc1Qp", "aNC-uep6hO-", "QcKqi8-IvYea", "pvgjP5ppXRH", "3orR65qT7DJ", "zqBrSbkUnWy", "fXqVGJtGmYM", "VOuBf7pIWU8" ]

[ "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for answering my questions.\nThough I think there is still some space for making the paper more clear, I raised the score from 4 to 5.", " Dear reviewers and chairs, \n\nPlease let us know if there are any further clarifications needed concerning our paper after the rebuttal.\nWe would be happy to answer your questions.\n\nAuthors\n", " We thank LQNq for their insightful feedback!\n\n**From the title, it is not clear how much this manuscript differs from Karlsson et al. (2021)**\n\nThe key word in the title is *nonlinear*. The main contribution of our work is the generalization to prediction of nonlinear outcomes—this is not supported by Karlsson et al. In the original submission, we point out key differences on l.32–38, l.84–86, l.121–127. \n\nDifferences in theory are captured mainly in Theorem 1. The reviewer is correct that the main difference between theorems is that our result has different (less strict) conditions: the observed system is no longer assumed to be a linear-Gaussian Markov chain. As a result, the goal of learning, the mapping $E[Y \\mid X_1]$ from input to outcome can be nonlinear. Instead, we assume that observations can be mapped to such a chain using a (nonlinear) representation known up to linear transform. In Section 3.2 and Appendix B, we show that such a representation can be learned consistently using random feature maps.\n\nTo predict nonlinear outcomes, we also propose new learning algorithms based on kernels, random feature maps and representation learning using neural networks. Neither was previously used by Karlsson et al. The methods are then evaluated in a new set of experiments. \n\n**Are the latent states assumed to be from a stochastic process? Is $A$ stationary? I see some conditions of matrix A in Appendix, but I did not find the constraints of generating $A$. Why is $A$ designed to be like that.**\n\nYes, this is correct. The latent states form a stochastic process, with finite horizon T, assumed for Theorem 1 to be linear-Gaussian, see the definition of $Z_t$ in Assumption 1. The process is not assumed to be stationary, i.e., $A_t$ and $\\sigma_t$ can vary with $t$. We have updated the notation on l.82 slightly to clarify that $A_1, ..., A_{T-1}$ are (potentially) different matrices.\n\nThe choice of $A$ is not constrained in general. $A$ was chosen for synthetic experiments in order to create an interesting learning task (a similar procedure was used by Karlsson et al (2022)). It is not required by our theoretical results and we expect many choices of $A$ to produce similar empirical results. In the experiments on real-world datasets, we have no control over the data generating process.\n\n**What is the difference between OLS and the linear regression?**\n\nThey are the same. OLS (ordinary least squares) is the most common method for fitting a linear regression i.e., by minimizing the empirical average least squares error. The name OLS is well established in machine learning and statistics, see e.g., its uncommented use in [1]. \n\n**What is R^2 in Section 4?**\n\n$R^2$ is the “coefficient of determination”, as stated on l.200 in the original submission. It is one of the most commonly used metrics to evaluate regression models in statistics and machine learning. For this reason, we refrain from stating a mathematical definition. See, for example, https://en.wikipedia.org/wiki/Coefficient_of_determination (first definition of $R^2$) and https://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html, which is the implementation we used in our experiments.\n\n**The manuscript claims that the main goal is to improve learning efficiency. How \"learning efficiency\" is defined and estimated in the manuscript?**\n\nSample efficiency classically refers to the ability of a statistical estimator to achieve smaller error/risk than other estimators with the same number of samples [2, Chapter 20]. For unbiased estimators, this coincides with their variance. For learning algorithms, efficiency is typically measured by how the expected error of a learning algorithm varies with the number of training samples. This is the notion we adopt here and it can be precisely defined; a learner is more efficient if the expected risk $\\bar{R}_D$ is smaller for the same number of samples $m = |D|$. Theorem 1 shows that learning using privileged information is more efficient than non-privileged learning with empirical risk minimization in the same hypothesis class under appropriate conditions. We have clarified the connection between risk and sample efficiency on l.65–72 in the revision. Empirically, we estimate efficiency by comparing the prediction error for different estimators as we vary the number of training samples. \n\n**Minor suggestions**\n\nWe thank reviewer LQNq for these suggestions and will incorporate them in the final version of the paper. \n\n**References**\n\n[1] Hastie, T., Tibshirani, R., Friedman, J. H., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction (Vol. 2, pp. 1-758). New York: springer.\n\n[2] Dekking, F. M., Kraaikamp, C., Lopuhaä, H. P., & Meester, L. E. (2005). A Modern Introduction to Probability and Statistics: Understanding why and how (Vol. 488). London: Springer.\n", " We thank s32b for their insightful feedback!\n\n**Applications with a fixed time horizon**\n\nThe fixed-horizon setting is actually very common in applications. Other than the ADNI task (Section 4) to predict *2-year* progression of Alzheimer’s disease [1], important examples from healthcare include predicting *30-day* mortality, e.g., following surgery [2], and predicting *30 or 180-day* readmission of patients [3]. Outside of healthcare, examples include predicting user churn within a *fixed* interval [4], predicting *yearly* crop yields based on satellite imagery of farms [5] or predicting the *final cost* of a construction project at the end of planning [6]. Privileged time-series information is available in all of these examples (daily/hourly patient vitals; intermediate customer interactions, daily/monthly satellite imagery, construction events and changes).\n\n**Benefit of the approach for prediction beyond long term prediction**\n\nIn experiments, we demonstrate that there is a consistent benefit even if there is only a single privileged time point, where data comprises $X_1, X_2$ and $Y$ (see e.g., Fig 4a). The meaning of “long term” is domain dependent, but we see gains across varying horizons T (see comment below). More generally, the same approach could be used when the index t = 1, …, T does not even refer to time, but to, for example, a spatial coordinate.\n\n**Prediction using different prediction horizons**\n\nIn Appendix F, we give several examples of varying the horizon T (e.g., Figure 16a). We see that the benefit of privileged information remains for increasing T but note that the hardness of the prediction problem also changes with T ($R^2$ goes down for all methods in Figure 16a when T increases).\n\nIf the reviewer means predicting outcomes for different horizons using the same model, success would depend on the nature of the dynamical system. For our Theorem, we have not assumed that the system is stationary, but this would be required to use the same model for arbitrary horizons, without other assumptions. This is an interesting question for further study and we will include a comment about it in the discussion.\n\n**Significance beyond bias/variance analysis**\n\nOur main goal is to reduce variance in learning—to increase sample efficiency—so as to make more accurate predictions. Empirically, we see that this reduction is beneficial for reducing the prediction risk in almost all cases. In the experiments with neural networks applied to images, we also see that the approach has benefits in terms of recovering the underlying latent state space Z, both quantitatively (Fig 7a) and qualitatively (Fig 7b). \n\n**Which kind of non-linearity makes the proposed approach non-longer valid?**\n\nFor Theorem 1, we only require that the observation function is injective. For learning an unknown representation $\\Phi$, we must place further restrictions to get the same guarantee. The details will depend on the choice of estimator and the data generating process. For example, using Random Fourier Features (RFF) assumes that $\\Phi$ is continuous. Hence, this approach would not work well for discontinuous processes. In experiments, we see benefits even when we cannot guarantee that our assumptions hold. \nIt is important to note that this same limitation applies to classical learning—we use the same hypothesis class in both paradigms and if the hypothesis class cannot approximate the true function well, we cannot expect good results.\n\n**Algorithmic complexity**\n\nFor training the kernel and random feature estimators, the complexity will be (roughly) T times the complexity of the matching classical estimator; one fits T linear regressions and T random feature transformations. At test time, the complexities of classical and privileged estimators are equal. For the privileged neural network estimators, the complexity is equivalent to training a single recurrent neural network with T time points. We stress that algorithmic complexity is not a focus of this work. \n\n**References**\n\n[1] Beltran, J. F., Wahba, B. M., Hose, N., Shasha, D., Kline, R. P., & Alzheimer’s Disease Neuroimaging Initiative. (2020). PloS one, 15(7), e0235663.\n\n[2] Karhade, A. V., Thio, Q. C., Ogink, P. T., Shah, A. A., Bono, C. M., Oh, K. S., ... & Schwab, J. H. (2019). Neurosurgery, 85(1), E83-E91. \n\n[3] Mortazavi, B. J., Downing, N. S., Bucholz, E. M., Dharmarajan, K., Manhapra, A., Li, S. X., ... & Krumholz, H. M. (2016). Circulation: Cardiovascular Quality and Outcomes, 9(6), 629-640.\n\n[4] Huang, B., Kechadi, M. T., & Buckley, B. (2012). Expert Systems with Applications, 39(1), 1414-1425.\n\n[5] You, J., Li, X., Low, M., Lobell, D., & Ermon, S. (2017, February). Thirty-First AAAI conference on artificial intelligence.\n\n[6] Williams, Trefor P., and Jie Gong. Automation in Construction 43 (2014): 23-29.\n", " We thank gvbk for their insightful feedback!\n\n**An important correction**\n\nRegarding the summary by reviewer gvbk, we like to point out that $\\Psi$ is *not* generally a linear transformation. Our work precisely deals with generalizing to the case where this transformation is nonlinear (see comment on l.86 in the original submission).\n\n**Interesting but limited significance; Limitation for universal kernels; Importance for wider ML audience; The very model appears limited**\n\nWe appreciate the reviewer’s concern but argue that our setting is actually very general. Our method is applicable whenever predictions are made at a baseline time point about target outcomes at a fixed follow-up time and information is collected in between. Other than the ADNI task (Section 4) to predict 2-year progression of Alzheimer’s disease [1], important examples from healthcare include predicting 30-day mortality, e.g., following surgery [2], and predicting readmission of patients [3]. Outside of healthcare, examples include predicting user churn within a fixed interval [4], predicting yearly crop yields based on satellite imagery of farms [5] or predicting the final cost of a construction project at the end of planning [6]. Data that can be regarded as privileged time-series information is available in all of these examples (daily/hourly patient vitals; intermediate customer interactions, daily/monthly satellite imagery, construction events and changes). In addition we would like to highlight that the primary goal of our work is to make an accurate prediction of the outcome rather than learning the dynamical system.\n\nWe mention universal kernels as they are a popular choice in combination with linear models, not because of their importance in connection to our method. In real-world applications random feature methods often outperform universal kernels. Consequently, Proposition 1 is not a great limitation in terms of predictive accuracy. As the alternatives (random features and neural networks) show great benefits in empirical results, we do not view this as a key limitation of our approach. \n\nRegarding limitations, the model we learn is a combination of a representation $\\Phi$ and linear hypothesis. This is the most widely used model type in machine learning today. The only difference is that we make use of more than standard input-output pairs to learn it. In Theorem 1, we prove that doing so is more efficient when the data comes from a latent dynamical system as described in Assumption 1. It can be argued that, for the examples mentioned above (mortality, crop yield, construction cost), the causal mechanisms driving the system (e.g., disease progression) are not directly observed and therefore best represented as latent variables. Moreover, this does not rule out that our algorithm, or variants thereof, is more efficient than classical learning even when the assumptions are violated. We point out in l.262–265 of the original manuscript that we always observe a reduction in variance through the use of privileged time-series information. Indeed, in real-world experiments, we cannot guarantee that Assumption 1 holds, but nevertheless we witness consistent improvements using our method in all of them. This indicates that the model is not so limited after all. \n\n**Somewhat misleading title; Not what is usually meant by a time series; \"Dynamic systems\" would be better.**\n\nWe thank the reviewer for this suggestion. In the title, “time-series” refers to the type of data used for learning, which is certainly a time series, not to a particular learning problem. In our work, we reframe classical prediction problems (where observations of inputs and the target label are separated in time) as problems of learning from time series data. The reviewer is right that, in Theorem 1, we assume that the time series is generated by a (latent) dynamical system. However, in experiments, we show that the method works also when the data generating process for the time series is unknown and may not match the assumptions of Theorem 1. \n\n**References**\n\n[1] Beltran, J. F., Wahba, B. M., Hose, N., Shasha, D., Kline, R. P., & Alzheimer’s Disease Neuroimaging Initiative. (2020). PloS one, 15(7), e0235663.\n\n[2] Karhade, A. V., Thio, Q. C., Ogink, P. T., Shah, A. A., Bono, C. M., Oh, K. S., ... & Schwab, J. H. (2019). Neurosurgery, 85(1), E83-E91. \n\n[3] Mortazavi, B. J., Downing, N. S., Bucholz, E. M., Dharmarajan, K., Manhapra, A., Li, S. X., ... & Krumholz, H. M. (2016). Circulation: Cardiovascular Quality and Outcomes, 9(6), 629-640.\n\n[4] Huang, B., Kechadi, M. T., & Buckley, B. (2012). Expert Systems with Applications, 39(1), 1414-1425.\n\n[5] You, J., Li, X., Low, M., Lobell, D., & Ermon, S. (2017, February). Thirty-First AAAI conference on artificial intelligence.\n\n[6] Williams, Trefor P., and Jie Gong. Automation in Construction 43 (2014): 23-29.\n", " We thank oWQK for their insightful feedback!\n\n**Motivation and applicability**\n\nOur method is applicable when predictions are made at a baseline time point about target outcomes at a fixed follow-up time with data collected in between. The ADNI task (Sec 4) to predict 2-year progression of Alzheimer’s disease (AD), is an example of this [1]. Other examples from healthcare include predicting 30-day mortality, e.g., following surgery [2], and predicting readmission of patients [3]. Outside of healthcare, predicting user churn within a fixed interval [4], predicting yearly crop yields based on satellite imagery of farms [5] or predicting the final cost of a construction project at the end of planning [6]. Privileged time-series information is available in all of these examples (regular patient vitals; intermediate customer interactions, monthly satellite imagery, construction events). We believe it is a strength of our method that it is useful in many settings, as seen in our empirical results.\n\n**Defining sample efficiency; OLS in Fig 4(b)**\n\nSample efficiency classically refers to the ability of a statistical estimator to achieve smaller error/risk than other estimators with the same number of samples. For learning algorithms, this typically refers to how the expected error of a learning algorithm varies with the number of training samples [7, Chapter 20] — a learner is more efficient if the expected risk $\\bar{R}_D$ is smaller for the same number of samples $m = |D|$. Theorem 1 shows that privileged learning is more efficient than classical learning under appropriate conditions. We have clarified the connection between risk and sample efficiency on l.65–72 and l.125–128 in the revision. Empirically, we estimate efficiency by comparing the prediction error for different estimators as we vary the number of training samples. As the reviewer correctly points out, in Fig 4(b), OLS is more efficient than non-linear estimators *for very small sample sizes*, and the text (l.241–245 in the submission) acknowledges this, but it is less efficient at larger sample sizes due to large bias. Linear LuPTS has lower variance than OLS but higher bias here (see Fig 6). \n\n**Readability and conclusion of Fig 7(a)**\n\nWe agree that the readability of Fig 7(a) can be improved. The revision includes an updated version of the figure with the shaded marks removed, such that only mean values are displayed. We provide a clear conclusion about the content of Figure 7(a) in l.283 (original submission), by stating that the privileged learners are more accurate in their predictions (x-Axis) and also produce higher SVCCA coefficients (y-axis) on average.\n\n**Code availability**\n\nYes, the experiments will be made available in a code repository when the paper is made public; we have added a footnote on page 6. \n\n**I would recommend to spend much more time on the motivation; How does this setting connect to images?**\n\nIn the camera-ready version, we will use the additional space to make our motivating applications more visible (see answer to first question). The problem of predicting crop yields from satellite imagery is an example of how our setting is connected to images [5]. Here, both baseline inputs and privileged information are satellite images taken of the same farm and the target outcome is yearly crop yield. \n\n**Make the findings around L151 more precise instead of deferring to the appendix**\n\nWe thank Reviewer oWQK for recognizing the value of this result. Due to the page limit, we prioritized results concerning finite-sample properties (Theorem 1 and empirical results), since this is our main focus, over the asymptotic results discussed around l.151 in the original submission. Nevertheless, we believe that proving consistency of the random features method is an important step in justifying its use; we can trust the method to do the right thing as we increase $m$. We plan to expand the statements in the camera-ready version. \n\n**References**\n\n[1] Beltran, J. F., Wahba, B. M., Hose, N., Shasha, D., Kline, R. P., & Alzheimer’s Disease Neuroimaging Initiative. (2020). PloS one, 15(7), e0235663.\n\n[2] Karhade, A. V., Thio, Q. C., Ogink, P. T., Shah, A. A., Bono, C. M., Oh, K. S., ... & Schwab, J. H. (2019). Neurosurgery, 85(1), E83-E91. \n\n[3] Mortazavi, B. J., Downing, N. S., Bucholz, E. M., Dharmarajan, K., Manhapra, A., Li, S. X., ... & Krumholz, H. M. (2016). Circulation: Cardiovascular Quality and Outcomes, 9(6), 629-640.\n\n[4] Huang, B., Kechadi, M. T., & Buckley, B. (2012). Expert Systems with Applications, 39(1), 1414-1425.\n\n[5] You, J., Li, X., Low, M., Lobell, D., & Ermon, S. (2017, February). Thirty-First AAAI conference on artificial intelligence.\n\n[6] Williams, Trefor P., and Jie Gong. Automation in Construction 43 (2014): 23-29.\n\n[7] Dekking, F. M., Kraaikamp, C., Lopuhaä, H. P., & Meester, L. E. (2005). A Modern Introduction to Probability and Statistics: Understanding why and how (Vol. 488). London: Springer.\n", " We thank the reviewers for their insightful feedback and for recognizing the merits of our theoretical (as pointed out by reviewer oWQK, gvbk, s32b) and empirical contributions (oWQK, s32b) and the potential value of our method to the community (all reviewers).\n\nReviewers asked about the motivation and generality of our work and on the notion of efficiency. We respond to each reviewer in turn but would like to make the following general clarifications: \n\n* Our method is a tool for learning to make predictions of a single outcome at a fixed horizon. In addition to the applications mentioned in the paper, there are many more examples: predicting *30-day* mortality [1] or readmissions for patients [2]; predicting churn of users of an online service [3]; predicting *yearly* crop yields based on satellite imagery of farms [4]; predicting the *final* cost of a construction project at the end of planning [5]. Data that can be regarded as privileged time-series information is available for learning in all of these examples (daily/hourly patient vitals; intermediate user interactions, daily satellite imagery, construction events and changes), but not at the time of prediction. \n\n- For problems like this, classification and regression models are typically trained only on features that are available also at test time. Karlsson et al. (2022) showed that when privileged information is available and is related linearly to baseline features and the outcome, learning also from that reduces the expected error (increases efficiency). In this work, we derive methods which make use of this also in *nonlinear* prediction tasks, greatly extending the generality of the idea. We plan to include the examples mentioned above in the introduction of the camera-ready version of the manuscript.\n\n* Reviewers asked about the precise meaning of “efficiency”. Following tradition, see e.g., [6, chapter 20], we define an efficient estimator to be one that achieves the same error as another estimator using a smaller number of samples or, equivalently, a smaller error using the same number of samples. Our theoretical result proves that, in the right conditions, a learner using privileged information is at least as efficient (has at least as small a risk) as a comparable learner which does not use it—for any fixed training sample size. We have clarified the connection between risk (equation 2) and efficiency on l.65–72 and l.125–128 in the revision. \n\nAuthors\n\n**References**\n\n[1] Karhade, A. V., Thio, Q. C., Ogink, P. T., Shah, A. A., Bono, C. M., Oh, K. S., ... & Schwab, J. H. (2019). Neurosurgery, 85(1), E83-E91. \n\n[2] Mortazavi, B. J., Downing, N. S., Bucholz, E. M., Dharmarajan, K., Manhapra, A., Li, S. X., ... & Krumholz, H. M. (2016). Circulation: Cardiovascular Quality and Outcomes, 9(6), 629-640.\n\n[3] Huang, B., Kechadi, M. T., & Buckley, B. (2012). Expert Systems with Applications, 39(1), 1414-1425.\n\n[4] You, J., Li, X., Low, M., Lobell, D., & Ermon, S. (2017, February). Thirty-First AAAI conference on artificial intelligence.\n\n[5] Williams, Trefor P., and Jie Gong. Automation in Construction 43 (2014): 23-29.\n\n[6] Dekking, F. M., Kraaikamp, C., Lopuhaä, H. P., & Meester, L. E. (2005). A Modern Introduction to Probability and Statistics: Understanding why and how (Vol. 488). London: Springer.\n", " Through both rigorous theoretical analysis and empirical findings, this paper extends results on Learning using Privileged Information to general time series governed by linear latent dynamics and potentially nonlinear observation models. Under this general class of possible models, the authors demonstrate through learning theoretic analysis that learning with privileged (data that is available at training time but not at inference time) time series always leads to lower or equivalent risk, given that the nonlinear map from observations to latent variables is known up to a linear mapping. They then extend their results to the unknown mappings via an argument based on the use of random feature maps. Finally, the authors propose to approximate unknown mappings with deep learning architectures. In their empirical study, they demonstrate that the predicted learners with privileged information generally outperform baselines in terms of sample efficiency. The paper benefits both from strong theoretical analysis and rigorous empirical set-up. The results presented are relevant, and significantly expand understanding of learning using privileged time series (LuPTS) information. To the best of my knowledge, the paper proposes both novel theoretical findings and explores a set of new approaches for LuPTS. Finally, the paper is well-written, with clear and concise use of language.\n\nMy only concern about the paper is motivation. It is not clear to me, except some cases alluded to in the introduction to the paper, in which applications one would be interested in using privileged information. Unfortunately, the empirical study also does not motivate a single application but rather transforms existing time series applications such that the problem definition fits. I believe the readers would benefit greatly from a discussion of motivation and potential impact. - Sample efficiency is qualitative and subjective. In Fig 4(b) OLS seems to be outperforming all baselines in terms of \"sample-efficiency\" in contradiction to the text. So what precisely is meant by sample efficiency here? Could that be made more rigorous?\n- Figure 7(a) is not readable, and the conclusion is mostly not accessible. Could you please revise and explain?\n- Will the experiments be made available and reproducible? There is no mention of this in the paper. - I would recommend to spend much more time on the motivation, and amplify this in the experiments. For example, how does this setting connect to images (which is presented in the experiments)? \n- I would recommend to make the findings around L151 more precise instead of deferring to the appendix as I believe this is one of the key findings in the paper.\n\nMinor point:\n- L66 typo in \"respect\"", " The paper deals with the data generated by the following model.\n\nA vector $z_1$ comes from some distribution. Then it is subjected to a chain of linear transformations. The vector $z_2$ is obtained as a linear transformation of $z_1$ (plus some noise), $z_3$ is a linear transformation of $z_2$ etc. Finally we get to $z_T$. Then $z_T$ generates a label $y$ by a linear transformation of $a$ (finite dimensional) feature mapping.\n\nThe vectors $z_t$ are never visible directly. There are two modes of access to them. In the first, \"classical\" scenario we get to see $x_1 = \\Psi (x_1)$ where $\\Psi$ is a linear transformation. In the second, \"privileged\" scenario we get access to $x_2 = \\Psi(z_2), x_3 = \\Psi(z_3)$ etc.\n\nWe can have either classical or privileged information at the training stage, but only get classical information at the test stage. The paper compares two learning approaches.\n\nIn the first, classical approach we use Least Squares to regress y on a feature mapping of $x_1$. In the second, privileged approach we try reconstruct the whole model using least squares on the training set to find all transition linear transformations etc and get $y$. The paper shows that the variance of the later approach is lower than the variance of the former.\n\nThe advantage disappears if the feature mapping is infinite-dimensional and we get non-singular Gram matrices on the data.\n\nThe experimental results include reconstruction of the feature mapping using neural networks. I think this is an interesting result but its significance is somewhat limited. The authors very honestly show the key limitation for universal kernels. The result is certainly important for the dynamic systems community but I have doubts about wider ML audience. The very model appears limited (although it has important applications in neurophysiology).\n\nTypos/suggestions\n\nPage 3, line 93 on the form -> of the form ?\n\nI also find the title somewhat misleading. This is not what is usually meant by a time series. \"Dynamic systems\" would be better. None. The paper is clearly written. Yes.", " This paper proposes new insights into the analysis of Learning using privileged information 
(LuPI) learner with access to intermediate time series data and  generalizes it to nonlinear prediction tasks in latent dynamical systems. The authors extend theoretical guarantees to the case where the map connecting latent variables and observations is known up to a linear transform. In addition, the paper proposes algorithms based on random features, and representation learning for the case when the map is unknown. The paper is well written and theoretically sounds. The paper is clear easy to follow and bring to the fore an interesting contribution.\n\nParticularly, the fact that the authors extend the LuPTS framework to nonlinear models and prediction tasks in latent dynamical systems is an important step. \n\nFurthermore, the authors prove that learning with privileged information leads to lower risk when the nonlinear map connecting latent variables and observations is known up to a linear transform. This is also an important contribution.\n\nThe bias/variance analysis is also timely and important. Also, the experimentation with real data namely the prediction of traffic volume and Alzheimer progression is critical to validating the approach.\n\nHowever, the fact that the study is limited to predictions for a fixed time horizon given present observations limit the extend to which the approach could be validated and applied. What is the benefit of the approach for prediction if it is not experimented for long term prediction?\n\nHow would the approach fare for prediction using different prediction horizons?\n\nBeyond bias/variance analysis, what is the significance of this approach?\n\nWhich kind of non-linearity makes the proposed approach non-longer valid?\n\nWhat is the algorithmic complexity for its implementation and use in practical settings? It would be good if the authors could discuss the impact of their bias/variance analysis on societal applications?", " The manuscript proposes to predict nonlinear outputs using time series privileged information during training. The privileged information is not used for inference. The authors prove in Theorem 1 that under some conditions, \"the generalized LuPTS is never worse in expectation than the classical learner\". Experiments on both synthetic and real-world data sets show that using privileged information increases the sample efficiency and helps latent variable recovery. * Originality\n\nFrom the title, it is not clear how much this manuscript differs from [1] Karlsson et al. (2021) (https://proceedings.mlr.press/v151/k-a-karlsson22a/k-a-karlsson22a.pdf)\nWhile in the main text, the manuscript tackles the task by modeling with latent variables for each observation, which is a major difference.\nIf I understand correctly, Theorem 1 in the manuscript is similar to Theorem 1 in [1] with some changes of conditions.\nThe manuscript should better formulate the difference from [1] \n\n* Quality\n\nThe manuscript is technically sound. \n\n* Clarity\n\nThe manuscript is overall clearly written. Some (minor) suggestions are as follows.\n\n1. \"**Unobserved**\" applies to Figure 1 (b) but not Figure 1 (a).\n2. It is not clear what random variables the \"distribution $p$\" models in line 62.\n3. \"the matrix inverse $(\\cdot)^{-1}$\" in line 104 can not be found in the text. \n4. Figure 3 (b) is not informative enough. \n5. It is not clear what the metric in experimental evaluation is used. What is $R^2$ in Section 4?\n\n\n* Significance\n\nThe algorithm proposed in the manuscript would benefit the time series modeling community\n\n---\n\n[1] Karlsson, Rickard KA, et al. \"Using time-series privileged information for provably efficient learning of prediction models.\" International Conference on Artificial Intelligence and Statistics. PMLR, 2022. * Stochastic process\n\nIf I understand correctly, the latent states $Z_t$ are assumed to be from a stochastic process, is it?\nIt is yet not clear from the main paper whether $Z_t$ is stationary or not. \nI see some conditions of matrix $A$ in Appendix (line 659), but I did not find the constraints of generating $A$. That is, it is not clear why $A$ is designed to be like that. \n\n* OLS Linear estimator \n\nWhat is the difference between OLS (line 100) and the linear regression?\n$\\hat{\\theta}_C$ in eq(3) seems to be exactly the same as linear regression.\n\n* $R^2$\n\nWhat is $R^2$ in Section 4?\n\n* Efficiency\n\nThe manuscript claims in line 237 that the main goal is to improve learning efficiency. \nHow \"learning efficiency\" is defined and estimated in the manuscript?\n\n\n\n The authors addressed the limitations." ]

[ -1, -1, -1, -1, -1, -1, -1, 7, 6, 6, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, 3, 3, 5, 4 ]

[ "r3DIuGN3vo-", "nips_2022_V9ngeCMsZK3", "VOuBf7pIWU8", "fXqVGJtGmYM", "zqBrSbkUnWy", "3orR65qT7DJ", "nips_2022_V9ngeCMsZK3", "nips_2022_V9ngeCMsZK3", "nips_2022_V9ngeCMsZK3", "nips_2022_V9ngeCMsZK3", "nips_2022_V9ngeCMsZK3" ]

[ "IYszVERuDaZ", "qznqleJ0GEr", "CQNiqcQuhU7", "cwRdAV6kcF2", "i5b_NE7xXo5", "CRH_dtSyXZi", "OLgg5Frs1wp", "wby08EFaTx5", "QXPGDOiFp1K" ]

[ "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank all the reviewers for their thorough reviews and for appreciating the novelty of our method. We have highlighted the corresponding changes in the revised manuscript. We look forward to the discussion with all the reviewers. In the following, we will give our responses to the major issues mentioned by the reviewers.\n\n# 1. Reply for the major contribution\n## 1.1 Major contribution\nOur key contribution is a novel elastic part representation that builds the correlation between the latent space of the image representation and the scene space of the surface in a self-supervised way, which is different from the previous MVS or semantic learning methods that only focused on improving the prediction quality separately through supervised training. Besides, we demonstrate that building the correlation can guide patchmatch propagation and evaluation to get better reconstruction. **We believe that our representation will help the community to bridge the gap between the multi-view stereopsis in computer vision and the point cloud reconstruction in computer graphics.**\n\n## 1.2 The necessity of our part representation\nThe purpose of our part representation is to provide the inherent geometric correlations such as surface connectedness, smoothness and boundaries to guide the part-aware patchmatch and depth prediction. A heuristic geometric regularization is usually unavailable during predictions. For instance, there are no confident depth predictions in textureless regions. Therefore, directly applying geometric regularization often suffers from over-smoothed surfaces and rough boundary predictions. Besides, the part-level representation for reconstruction requires high-precision geometry, which can not be easily obtained in a self-supervised manner.\nSince it is important to learn a noise-robust part representation with clear boundaries and complete part segments, we have proposed several ways to robustly train the elastic part representation with the noise and error in the initialization.\n\n# 2. Reply for technical details\n## 2.1 Training robustness w.r.t initialization\n**During the training stage, we have properly dealt with the noise and error from the initialization.** Followed by COLMAP, the confidence map, a combination of photometric consistency and geometric regularization, is used to identify and diminish reconstruction artifacts. Regions with low confidence that contain noisy photometric predictions, textureless regions, and sudden changes in the surface normal are ignored from the contrastive learning process.\nOn the other hand, the contrastive (Eq. 6) and concentration loss (Eq. 7) are both designed to deal with training in low-confident regions. Therefore, there are three goals in the two loss functions: 1. In high-confident regions, we compact the representation in parts with close surface distance; 2. In high-confident regions, we separate the representation lies on different surface parts; 3. In low-confident regions, we encourage the representation to be as close as possible to nearby features from high-confident regions. Thus, the embedding distance trained in high-confident regions could be successfully passed to low-confident ones.\n## 2.2 Speed\nSince the whole optimization process during inference is inherited from the conventional patchmatch-based technical route, it has the potential to optimize efficiently by sampling a discrete set of hypotheses and choosing the best among them (see Patchmatchnet(Wang et al.)).\nBesides, the calculation of the feature distance, the confidence map and the normal map can be achieved by simple and efficient operations. However, the speed of ElasticMVS is majorly constrained by the iteratively time-consuming pixel-wise differentiable warping process. In the future, we plan to design a lightweight network architecture that incorporates the part correlation into the pixel-wise patch match process. Therefore, fewer computing iterations can be achieved while the superiority of part representation can be preserved.\n", " We sincerely thank you for recognizing our contribution and for your valuable comments. In the following, we address your concern in detail.\n\n## R4-1: Running time\nSince we inherit the conventional patchmatch-based technical route, the iterative propagation and evaluation process do have an inherent limitation in run time, which is due to the extremely time-consuming pixelwise differentiable warping process calculated multiple times. On the contrary, cost-volume-based methods only calculate homography once and then pass the warped features to the high-parral 3D CNN, they achieve a shorter run time. In the future, we plan to design a lightweight network architecture that uses an attention-based network that incorporates both the global structure correlation and the pixel-wise patchmatch process. Therefore, fewer computing iterations can be achieved while the superiority of part representation can be preserved.\n\nNevertheless, our key contribution is a novel elastic part representation that builds the correlation between the latent space of the image representation and the scene space of the surface in a self-supervised way. We believe that our representation will help the community to bridge the gap between the multi-view stereopsis in computer vision and the point cloud reconstruction in computer graphics.\n\n## R4-2: Robustness to the hyperparameters\nThanks for your valuable suggestion and we have added a subsection in Sec. 4.2 of the final manuscript to discuss the robustness of the parameters. **Overall, our method is robust to the hyperparameters within a proper range.**\nSpecifically, these hyperparameters can be categorized into scene-related (that is, depth range, image resolution) hyperparameters (i.e., $\\epsilon$) and scene-irrelevant hyperparameters (i.e., $\\xi$, $\\tau$ and $\\eta$). In our implementation, each scene-related hyperparameter should be modified according to the depth range of the dataset, while the non-geometry-related hyperparameters don’t need to be modified.\n\n\n## R4-3: Experimental details\n### R4-3-1: Missing unit\nThanks for pointing out the omissions in our experiment. We will add the metric and unit in our final manuscript.\n\n### R4-3-2: Meaning of the visualization in Figure 11\nSorry for the misleading description, we’ll modify the caption of Fig. 11 in our final manuscript. In fact, the six red points are manually selected only for visualization. The real case is that every pixel in the image has a bunch of corresponding blue points, which represents the hypotheses selected during the past three iterations of patchmatch. We will modify the caption as follows: Visualization of the candidates (blue) during 3 patchmatch iterations and their corresponding target points (red).\n", " ## R3-1: Contribution and main idea\nThanks for your in-deep review, but we disagree with the opinion that our idea of propagation is similar to “Adaptive propagation” in Patchmatchnet(Wang et al.) as follows:\n\n### Difference between PatchmatchNet\n**Although PatchmatchNet can propagate hypotheses to neighbors adaptively based on Deformable Convolution Networks, the method lacks reliable and geometric-intuitive indicators on how to train and select the propagation candidates on the same surface.** Instead, candidates in our part-aware propagation are sampled based on the distance of each representation in the latent space, correlated to the scene space of the surface with a clearly defined loss function (Eq. 1 and Eq. 6).\n\nMore specifically, propagation candidates in PatchmatchNet are directly predicted from a 2D CNN, a “black box”, on the reference feature map. **The network and the feature map are neither physically plausible nor geometrically intuitive to guarantee that the predicted candidates can lie on the same physically-connected surface.**\n\nMore importantly, there are no explicit geometric constraints on the deformable propagation network during training. It is reasonable to doubt whether the network has learned reliable deformation. Furthermore, the whole training process in PatchmatchNet is supervised by the ground-truth depth map, which **cannot be implemented in the self-supervised task**.\nWe have added the above description in the introduction and the related work of the final manuscript.\n\n### Our major contribution\nThe key idea of our work is actually a novel elastic part representation encoding physically-connected part segmentations, and we demonstrate that it can guide patchmatch propagation and evaluation to get better reconstruction.\n\n**Different from PatchmatchNet and all previous works in MVS, we aim to build the correlation between the latent space of the image representation and the scene space of the surface in a self-supervised way.** We designed a pixel-wise part representation that explicitly depicts surface correlations, i.e, the higher similarity between two representations directly denotes a higher probability they come from the same surface.\n**In fact, benefiting from the elastic part representation, the inherent geometric correlations can be effectively exploited by many other MVS methods.** \nFor example, in CasMVSNet (Gu et al 2019), we can sample hypotheses more efficiently during the coarse-to-fine cascade volume generation by only sampling hypotheses in the same surface part. Besides, we can improve the final depth regression layer in MVSNet (Yao et al 2018) by our part-aware correspondence.\n**Overall, our major contribution lies in a new image representation and a new self-supervised framework, rather than a specific propagation implementation.**\n\n### The effect of propagation\nAs illustrated in Sec. 3.2, there are three major parts during the inference: 1. propagation, 2. part-aware correspondence, and 3.part smoothness. All three components contribute equally to the final result of the part-aware patchmatch, as demonstrated in Table 3. From the dramatic performance drop w/o PC, we can conclude that even with the adaptive propagation scheme, evaluating hypotheses using only photometric consistency can not achieve comparative performance. **Therefore, it is part representation, rather than propagation, that crucially improves the experimental results of the reconstruction.**\n\n**Statement on initialization:** Our depth prediction does not rely on the initial depth estimation from Gipuma. Instead, the depth map is initialized randomly within the range of interest. We only need an initialized depth prediction during the training stage of the elastic part representation.\n\n\n## R3-2: Technical details\n### R3-2-1: Final loss function\nThe final loss function is the weighted sum of these two loss functions described as $L_{total}=L_c+\\alpha_s L_s$, where $\\alpha_s$ is a constant parameter which is set to 5*10^-3 in our implementation. We have added them to Sec. 3.4.\n### R3-2-2: Difference between Eq. 1 and Eq. 6 \nSince Eq.1 is the conceptual equation inherited from Soft-Nearest Neighbor Loss (Salakhutdinov and Hinton), which is the ideal equation used to describe the concept of our elastic part representation, it is not capable of the actual training process. Instead, Eq.6 describes a computable loss function with an efficient sampling strategy to approximate the property in Eq.1. \n### R3-2-3: Description of $Z_p$\nWe’ll modify them in the final manuscript. The two terms mean the same thing and we will replace “feature on pixel local p” with “per-pixel elastic part representation on p”.\n\n\n## R3-3: Detailed questions\nThanks for pointing out the omissions and mistakes, we have corrected them in the final manuscript. \n### Values reported for Gipuma\nOur values reported for Gipuma actually comes from the previous MVS paper such as MVSNet (Yao et. al) and Patchmatchnet (Wang et al.). \n", " We sincerely thank you for recognizing our contribution. In the following, we address your concern in detail.\n## R2-1: The connection between the part representation and the depth prediction\nSorry for the confusion and we have clarified their connection in the introduction and related work of the revised manuscript.\n\nWe aim to build the correlation between the latent space of the image representation and the scene space of the geometry in a self-supervised way, which also provides a neat solution to bridge the gap between the multi-view stereopsis and the point cloud reconstruction. Therefore, the purpose of our part representation is not to directly fix the wrong depth, but to provide the inherent geometric correlations such as surface connectedness, smoothness and boundaries to guide the part-aware patchmatch and depth prediction. We have demonstrated that it can guide patchmatch propagation and evaluation to get better reconstruction.\n**In R1-2, we have detailedly explained the strategy to learn a noise-robust part representation with clear boundaries and complete part segments given only incomplete and noisy depth maps.**\n### R2-1-1: How to fix the wrong depth?\n**Furthermore, given a part representation or propagation region estimation, there are several ways to estimate more accurate and complete depth predictions.** Previous work in MVS solved the problem by introducing pre-defined global structural priors such as planes to resolve the ambiguity (Romanoni and Matteucci, 2019; Bódis-Szomorú et al., 2014). For instance, TAPAMVS(Romanoni et al.) segments the whole image into a bunch of superpixels and assumes textureless areas piecewise planar. RANSAC is applied to estimate its corresponding plane parameters. Beyond that, a bunch of works in point cloud reconstruction [2] deal with reconstruction artifacts with outlier, noisy or missing data. For instance, implicit representation [3] is used to provide global surface smoothness prior given noisy data, and exterior visibility [4] is used to detect and eliminate redundant data. However, neither the handcrafted plane structure nor the complex smoothness prior can provide sufficiently diverse and accurate surface part modeling for real-world scenarios.\n\n**In ElasticMVS, we provide a novel solution, L1 median loss, to encourage a non-local piecewise smoothness surface prediction in each part segment.** Several works (Lipman et al.) have demonstrated that optimizing the L1 median loss is robust to the outliers and gives a piecewise second-order surface approximation if the underlying surfaces are physically connected. \n\n[2]Berger, Matthew et al. “State of the Art in Surface Reconstruction from Point Clouds.” Eurographics(2014).\n\n[3]Kazhdan, Michael M. et al. “Poisson surface reconstruction.” SGP(2006).\n\n[4]Katz S, et al. Direct visibility of point sets. SIGGRAPH 2007.\n\n## R2-2: Technical details\n### R2-2-1: Initialization\nAs described in Sec. 3.3, from the very beginning, the depth and normal are randomly initialized under the uniform distribution. After that, a depth map (using Gipuma) and a confidence map (using COLMAP) are passed to the contrastive training process. \nIn this paper, we did not repeat the training process using the improved depth map since we found that the part representation has achieved favorable results using only the initial depth estimation.\nIn future work, we consider building a lightweight network architecture that incorporates global part and local patch representations to replace the laborious and time-consuming patchmatch process. At that time, a refined part representation can be updated immediately once an improved depth map is obtained, without the need for depth map initializations.\n### R2-2-2: Depth hypotheses\nDifferent hypotheses choosing strategies are utilized before and after the training process. Before the training process, we inherit the strategy of Gipuma(Galliani et al.). After the training process, we choose hypotheses based on the feature correlation of nearby pixels as illustrated in Fig.3.\n### R2-2-3: Optimization\nIndeed, the function is not directly solved using optimization mechanisms such as gradient descent, but rather approximated using a discrete sampling strategy. This strategy has long been proposed in the field of stereo-matching (Schönberger et al., Galliani et al., Xu et al.).\n### R2-2-4: Runtime\nEvery calculation process has been counted. The calculation of feature distance is only an operation of the inner product, which is faster than calculating patch correspondence (which involves differentiable homography). Moreover, the optimization is solved by the efficient patchmatch, which is relatively a lightweight solution compared to cost-volume-based methods (Wang et al.). Besides, the confidence map is a simple \"loss function\" and the normal map can be obtained from a simple convolution layer. \n## R2-3: Teaser figure\nWe have added the illustration of the initialization step in the final manuscript.\n", " Dear reviewer, we sincerely thank you for your in-deep comments and for recognizing the novelty of our method. In the following, we address your concern in detail.\n\n## R1-1: Necessity of the representation\nThanks for your valuable comment and we have clarified it in the revised manuscript. In our opinion, there are three major reasons to learn the part representation z_p:\n\n**Firstly, the geometric cues are usually unavailable during predictions.** For instance, there are no confident depth predictions in textureless regions, where physically-connected boundaries have to be guessed during inference. Therefore, a heuristic geometric regularization suffers from over-smoothed surfaces and rough boundary predictions. As Table 3 demonstrated, a naive surface de-noising and completion implementation still suffer from low accuracy and noise.\n\nBesides, the part-level representation for reconstruction requires high-precision geometry, which is obtained from either coarse-to-fine refinement or several stages of propagation from random initialization. **These processes are time-consuming compared to a direct forward pass of a 2D ConvNet in ElasticMVS.**\n\nFurthermore, Since we are aiming at the self-supervised task, the only way to gain the geometry information is to utilize the cues from photometry. **However, the geometry recovered from pure photometric consistency always suffers from incomplete and inaccurate surface predictions.** We have proposed several ways to robustly train the elastic part representation z_p with the noise and error in the initial depth map, as described in Sec. 3.3 and R1-2. \n\nOverall, the necessity to learn the part representation instead of directly using geometry heuristics is as follows:\n\n• **Accessibility**: The geometry information gained from any photometric loss is usually missing in some areas of the image, especially in textureless regions. A heuristic geometry regularization is unavailable in these regions.\n\n• **Speed**: During inference, the scales, shapes and boundary information is obtained from a 2D ConvNet without laborious optimizations.\n\n• **Robustness**: The geometric-based heuristics from photometric loss such as the point-to-plane distance are unreliable, especially in textureless and illuminant regions. However, it can be solved during the training stage with proper training losses and strategies.\n\n\n## R1-2: Training robustness\n**During the training stage, we have properly dealt with the noise and error in the initial depth map using the confidence map.** Followed by COLMAP, the confidence map (line 137 and Fig. 13), a combination of photometric consistency and geometric regularization, is used to identify and diminish reconstruction artifacts. Regions with low confidence contain noisy photometric predictions, textureless regions and sudden changes in the surface normal.\n\n**More importantly, the contrastive (Eq. 6) and concentration loss (Eq. 7) are both designed to deal with training in low-confident regions.** Specifically, contrastive loss (Eq. 6) only acts on pixels with above-the-threshold confidence, which prevents the reconstruction artifacts from ruining the contrastive learning process, while concentration loss described in Eq.7 acts on all pixels, and encourages the spatially concentrated representation.\n\nTo take it a step further, the training process can be seen as a \"propagation scheme\" that propagates the correct representation distance from high confidence regions to low ones. Thus, the embedding distance trained in high-confident regions could be successfully passed to low-confident ones. \n\nAs shown in Fig. 6 and 8, embeddings from the same surface successfully gather together in the latent space in textureless regions.\n\nWe will clarify them in Sec.3.3 of the final manuscript.\n\n## R1-3: Abstract\nThanks for your valuable suggestion. To make it clearer, we will modify part of the abstract (line 6) in the final manuscript as follows:\nIn this paper, we show that geometric proximity such as surface connectedness and occlusion boundaries implicitly inferred from images could serve as reliable guidance for pixel-wise multi-view correspondences. \n\n## R1-4: Training spatially far apart pixels\nFig.6(b) shows that simply applying contrastive loss (Eq. 6) does lead to the spatially separated coplanar points being close in the latent space. Here's one reason why the concentration loss (Eq.7) comes in. The spatial concentration loss punishes the case when spatially far apart pixels have similar embeddings [1], therefore encouraging the embeddings of spatially distant points to be isolated.\n\n[1] Yang, Fengting et al. “Superpixel Segmentation With Fully Convolutional Networks.” _(CVPR) (2020)_.\n\n\n## R1-5: Minor questions\nThanks for pointing out the mistakes and we will correct them in the final manuscript. Specifically, $\\beta$ is a constant parameter that controls the weight of the feature similarity between p and q, which is set to 0.5 in our implementation. ", " This paper proposed a new self-supervised MVS method called ElasticMVS. Instead of relying on local photometric consistency as in existing methods, the proposed method utilizes geometric correlations parsed from images as guidance for pixel-wise multi-view correspondences. The paper first proposed a novel elastic part representation that encodes spatial proximity and surface connections, which is trained by a contrastive learning-based strategy. The paper then proposed a self-supervised MVS framework namely ElasticMVS that estimates per-view depth using a part-aware propagation and evaluation scheme. Experiments show that ElasticMVS archives significant performance gain over both the supervised and self-supervised approaches. Strengths:\n- Addressing the limitation of local photometric consistency is an important topic for self-supervised MVS. The insights and motivation of the proposed method are good.\n- The paper presents extensive and sufficient comparisons with baselines, and provides detailed and informative ablation studies.\n- The proposed method works very well and achieves state-of-the-art performance, supported by various qualititive and quantitative results. \n\nWeaknesses:\n\nI don't have major concerns about this paper but I have a few questions to ask for clarification.\n- It is not clear to me why it is necessary to learn the part representation $z_p$. $z_p$ is learned primarily using geometric cues such as the 3D point-to-plane geometric distance, which is also available during inference. Why can't we design some simpler similarity functions directly based on the supervision signal of $z_p$ which is the 3d distances between p and q? For propagation, the candidates for pixel p can just be its nearby pixels that satisfy line 113-117. What is the benefit of learning the part representation compared to directly using geometric based heuristics? \n- The quality of the elastic part representation relies on initial depth map. How robust is the elastic part representation to the noise and error in the initial depth map? Is the method still able to handle textureless regions if the initial depth map for these regions are already erroneous? \n- To me, the abstract is a bit overclaiming. In line 6 it says the method explores \"geometric correlations such as surface connectedness and occlusion boundaries\". This sets my expectation high but I found it does not really match the proposed method. The method does not reason about surface connectedness or occlusion boundaries explicitly, but rather implicitly. In my opinion the key part of the method is clustering points based on geometric proximity (both 3D point-to-plane and in full 3D), and use it to guide patchmatch propagation and evaluation. It is still a neat idea but the description in the abstract can be a little misleading. I think the sentence in line 6 can be replaced with a more proper description.\n- It is possible that two spatially far apart pixels can be coplanar and thus have a small 3D point-to-plane distance, but that is not desirable. What part of the method suppresses this kind of points? - What exactly is $\\beta$ in equation (7)? It is not mentioned in the implementation details. \n\nMinor:\nLine 94: \"sucn\" -> \"such\" Yes.", " This paper introduced elastic part representation into self-supervised MVS framework to achieve more accurate dense correspondences. The pixel-wise part representation is trained by a contrastive learning after a pre-training process. The proposed elastic part representation mainly identifies pixels of similar appearance for depth propagation. The proposed approach is evaluated on the DTU and T&T benchmark datasets and achieves promising results. # Strengths\n1)\tThis paper focuses on self-supervised learning for MVS. It adopts the contrast learning to identify pixels belonging to a connected surface or not based on learned features and guide the depth propagation\n2)\tIt achieves promising results on two benchmark datasets.\n3)\tComprehensive ablation studies are presented in the paper.\n\n# Weaknesses.\n1)\tThe figure 1 cannot accurately reflect the proposed algorithm. It is a multiple stage framework. Especially, the proposed framework relies Gipuma without part representation to obtain an initial depth which will be used to define the positive and negative set for contrastive learning for the start of the algorithm. It is missing from Fig.1.\n2)\tSome arguments in the paper are kind of misleading. Line 29-31 argues about the pixel-wise photometric regularisation is sensitive to textureless regions or illumination changes. It is not clear how the proposed elastic parts representation could overcome this. My understanding is the contrastive learning is based on the positive and negative samples obtained from an unsupervised learning framework which is already affected by the textureless and illumination changes. No depth information can be obtained from this initialisation. It is questionable the proposed representation can fix wrong depth estimation for the textureless regions. Line 32-35, It is not clear why these are related to the reconstruction.\n3)\tDepth estimation is obtained by traditional optimisation rather than learning based on the description between line 166-171.\n 1)\tHow was the initialisation of the depth map obtained for contrastive learning? Is this process repeated once an improved depth map is obtained?\n2)\tHow were the depth hypotheses chosen? Are they related to the initialisation without the pixel-wise part representation learning?\n3)\tPlease also clarify how the optimisation of the energy function in line 171 is solved. The reviewer interprets that no network learning is involved in the process listed in Figure.2.\n4)\tDoes the runtime reported in Table 5 include the calculation of feature distance, confidence map and the normal map?\n 1)\tThe method still cannot estimate accurate depth for textureless regions even with better propagation region estimation.\n2)\tIt is potentially time consuming because it requires iterative optimisation, calculation of the feature distance, confidence map, and solve the optimisation problem. Surprisingly, the reported run time is reasonable. \n", " The paper proposed an interesting idea to improve the pixel-wise multi-view correspondence matching using geometric correlations. \nAn elastic part representation is proposed to encode the surface connectedness. Specifically, the input image is passed through a convolutional neural network to get the per-pixel elastic part representation. Then based on the estimated depth and normal map, the authors proposed self-supervised contrastive learning to encourage the part representation to be similar on the same physical surface. \n Strengths:\n\nThe authors presented a novel elastic part representation and provided an ablation study to prove the effectiveness.\n\nA thorough experiment is conducted and the proposed method is compared to a large set of state-of-the-art methods, notable improvements are observed compared to other self-supervised methods.\n\nWeakness:\n\nAlthough contributions are presented in the paper, the core idea of the work is very close to PatchmatchNet (Wang et al. 2021a) and the resulting depth estimation relies on the initial depth estimation from Gipuma (Galliani et al. 2015). Especially the key idea of \"Propagation\" proposed in this paper is very similar to the \"Adaptive Propagation\" proposed in the PatchmatchNet (Wang et al. 2021a), more discussion on the differences in-between are expected.\n\nConfusing symbols. $z_p$ in Sections 3.1 and 3.2 is referred to as \"per-pixel elastic part representation\" and \"feature on pixel local p\". I assume these two terms mean the thing?\n\nThe second paragraph of Section 3.1 is better fitted in the Network Training section and Equations (1) and (6) are the same (almost). Not sure why the same equation is written twice in the text.\n\nThe authors talked about the two loss functions used in the training but didn't provide what is the final loss function. I assume it is a weighted sum of these two loss functions?\n\nIn the Experiment Section, the values reported for Gipuma (Galliani et al. 2015) on the DTU dataset seem different from the ones reported in the original paper. Also, since the reconstruction results of COLMAP on T&T dataset are provided in Figure 4, it seems strange to not provide the quantitative evaluation in Table 2.\n\nNitpicking:\n\nAbbreviations used without explanations, e.g. NCC\n\nThe supplementary document, Section C.3, first sentence:\n\"The depth map predicted in each iteration is not always unreliable ...\", shouldn't it be \"not always reliable\"? 1) Please clarify why the idea of \"propagation\" is very similar to the \"adaptive propagation\" in PatchmatchNet while the latter is not suitable cited. Also, discussions on the difference between these two should be discussed.\n\n2) Please clarify the usage of $z_p$ in the text.\n\n3) What is the final form of the loss function used to train the CNN. Well discussed.", " This paper proposes a self-supervised MVS framework that learns the representation and estimates depth following a part-aware propagation and evaluation scheme. To achieve this, this paper utilizes learns part-aware representation and optimizes a part-level consistency loss. The proposed method consists of part representation learning and part-aware matching. The part representation encodes geometric details to predict a piecewise-smooth depth map. The part-aware matching conducts the depth hypotheses propagation following the idea of patchmatch. Strength\n1. The proposed method achieves state-of-the-art performance. The proposed method even outperforms some of the supervised methods. \n2. In some datasets, the proposed methods show dramatic performance improvements w.r.t. the state-of-the-art methods in both supervised and self-supervised methods.\n2. The proposed method does not require a fixed number of labels for segmentations and a ground-truth segmentation map.\n3. The proposed method is geometrically reasonable and is quite novel.\n4. The visualization of the elastic part representation demonstrates the effectiveness of the proposed method.\n\nWeakness\n1. The evaluation metric and unit are missing in table 3. Because DTU and T&T use different evaluation metrics, table 3 can be confused without the evaluation metrics.\n2. The running time is not competitive compared to cost-volume-based methods.\n3. The proposed method has many hyperparameters for the threshold, such as \\epsilon, \\xi, \\eta, so I think it is quite vulnerable to the parameters. It would be better to show how robust the proposed method is w.r.t the hyperparameters. 1. How robust is the proposed method w.r.t. the threshold parameters? \n2. Does the authors use the same threshold values for all datasets? or find the best parameters for each dataset?\n3. Generally, how many seed points are obtained? (In figure 11 on supplementary materials, six pixels are provided.) Generally, six points are enough to cover all the images? Yes" ]

[ -1, -1, -1, -1, -1, 5, 5, 5, 7 ]

[ -1, -1, -1, -1, -1, 4, 5, 3, 5 ]

[ "nips_2022_lAN7mytwrIy", "QXPGDOiFp1K", "wby08EFaTx5", "OLgg5Frs1wp", "CRH_dtSyXZi", "nips_2022_lAN7mytwrIy", "nips_2022_lAN7mytwrIy", "nips_2022_lAN7mytwrIy", "nips_2022_lAN7mytwrIy" ]

[ "HvW5zssEWe", "TNdkWtXZ5-R", "WpOK0QhfLX4", "B9JvWvzBw9h", "nFksoTtOCgE", "2bjbm1e745b", "FTlXwwFaq0d", "f8ANnv2t0qr", "vVbQ6mNn7RC4", "LONqgVUAVu", "pueVCJBYumR", "CTbU5OATMR_", "LYdFRQ67ipB", "wb90dt9ubV3", "rRBXK81luln", "1B0rPRpbjHp", "pURzF73UVDk", "SxicR6ApZzo" ]

[ "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for the rebuttal. \nI understood your responses other than the third one. \nFor visualizing layers of relations, I saw Figures 10 and 11. I understood Figure 10, but I cannot interpret the second layer in Figure 11 (right bottom). \nTotally, my unclear points are clarified, but probably due to the combination of the methodological minor changes, I did not change the score. \n", " Thank you for taking the time and care to consider both our original manuscript and our responses. We will include a discussion of the limitations of our method in the revised version.", " Thank you for taking the time and care to consider both our original manuscript and our responses. This has certainly made the work stronger and clearer.", " Thank you very much for the detailed response. I have checked the comment as well as the other reviews and confirmed my rating (7: accept).\nI think the discussion of limitations posted above is very important and should be clearly stated in the paper with a sub-section. It will make it easier for the community to further extend this work.", " The rebuttal has addressed my main concerns and I'm happy to increase my rating to weak accept. I still encourage the authors to compare again traditional trajectory forecasting methods since the two fields, interaction modeling/relational inference & trajectory forecasting, are working on similar problems but often do not compare with each other. It would be helpful to integrate the efforts and measure the progress together.", " We thank the reviewer for their thorough reading of our work and insightful suggestions for improvement. We have updated the manuscript in reaction to these suggestions, which we hope considerably strengthens it. Here, we address the concerns point by point:\n\n- **Differences from factorized NRI**\n\nWe have now included fNRI (i.e., each layer-graph effectively only contains a single edge-type and sigmoid activation is used) as a baseline and have updated the manuscript with the new results. While fNRI is a competitive baseline, our model still outperforms in both trajectory prediction and relational inference.\n\nWith respect to factorized NRI (fNRI), our approach has a number of differences:\n\n(1) fNRI proposed use of a multiplex graph where each layer of the graph is a binary classification problem. They proposed to use sigmoid as an alternative to the formulation used in NRI. In our paper, we proposed to use attentional graphs (multi-class classification across agents) in the form of softmax, which we find to be important for modeling relative strengths in social dynamical environments. Please refer to the below question 'Motivation for soft-max across agents' for further explanation.\n\n(2) One of our innovations is to combine multiplex graph latent structure with progressive training. According to our ablation studies, this is a key component that makes our model excel (Table 3). We believe Progressive Layered Training is just as important of a contribution to our approach as the proposed model architecture.\n\n(3) fNRI only conducts experiments on spring datasets and has very limited results. We substantially expand the scope and application realm, and even if the fNRI work touches upon similar ideas, it should not preclude our contributions. \n\n- **Why did we not benchmark on ETH/UCY**\n\nPast literature [1] has pointed out that modeling interactions has an insignificant effect on trajectory prediction accuracy with ETH-UCY, in comparison to simply using the target agent's historical trajectories. More specifically, they evaluated ablated versions of multiple existing trajectory prediction models (i.e., Trajectron++, PECNet, Social-STGCNN) and found that incorporating the interaction modeling module does not meaningfully affect the trajectory prediction accuracy on pedestrian trajectory datasets such as ETH-UCY. However, substantial performance drops are observed on highly interactive datasets such as the NBA dataset when interactions are not modeled. Thus, in this paper, we focus on benchmarking our model on environments where interaction modeling is indispensable to making accurate future predictions. We compare IMMA with models that have demonstrated success in similar regimes. \n\n[1] Makansi, Osama, et al. \"You mostly walk alone: Analyzing feature attribution in trajectory prediction.\" arXiv preprint arXiv:2110.05304 (2021).", " - **Selection of baselines for comparison**\n\nWe chose to compare with NRI, RFM, and EvolveGraph because they are considered state-of-the-art in the line of works that explicitly learn an interaction graph as part of the trajectory prediction task. That is, our chosen baselines not only learn an interaction graph but also explicitly evaluate the interpretability of this graph, whereas many other trajectory prediction works [2,3,4] treat latent codes as a transient part of the computation. This difference is also discussed in the NRI paper [5]. Our paper falls into this line of research. \nWe prioritize comparing our model with EvolveGraph among the “SOTA models’’ because it is one of the few that has shown success in highly interactive environments such as the NBA dataset, that has been evaluated on relational inference, and that was also compared with trajectory prediction-focused models such as Trajectron++. Most other multi-agent trajectory forecasting works [2,3,4] mainly experiment with pedestrian prediction datasets (e.g., ETH/UCY) or autonomous vehicle trajectory datasets (e.g., nuScenes, drone datasets), for which modeling interactions is less important [1]. Thus, among the “SOTA methods” in the “traditional” multi-agent trajectory prediction works, we deem EvolveGraph the best method for us to compare with.\n\n- **Motivation for soft-max across agents**\n\nWe propose to use attention (i.e., softmax across agents) for each layered graph in the multiplex graph so that the relative strengths of interactions can be modeled more naturally. Note that we do not argue multiplex attention is the better formulation for all interactive systems, but our insight is that it is important for modeling relative strengths in social dynamical environments. Aside from yielding great performance, using attention provides the two following advantages: (1) increased interpretability (i.e., the ability to answer “what causes an agent to behave this way?”), as seen in table 2, and (2) the ability to be directly applicable to inductive learning problems as the softmax in the attention mechanism naturally normalizes the weights across all agents. This makes it more amenable to arbitrary agent counts, which is supported by our experimental results in table 4. Observe that our model with attention significantly outperforms other models in the zero-shot generalization experiment, where we incorporate twice the number of agents into the environment.\n\n- **Interpretation of latent codes, and Identification of codes for changing the leader**\n\nIn our method, latent codes are multiplex graphs, represented as adjacency matrices that describe interactions between agents. The primary graph is the first graph learned in Progressive Layered Training and should encode the primary interactive relationship that could reduce prediction loss the most. Leaders are identified by choosing the largest entry for each column agent of the primary graph. To change the leader of a specific agent, we go to the row index of the agent and simply assign 1 for the leader column and 0 for all other agents in the primary graph.\n\nIMMA learns these graphs purely based on the objective of minimizing prediction loss, and thus we do not know for certain the semantic meaning of each layer. However, we evaluate mainly the primary graph, through qualitative visualization (Figure 3 and Figure 5) and quantitative assessment (Table 2), because we have strong intuition as to what the first graph should encode, given the nature of the environment. For instance, in the Social Navigation Environment the primary graph should learn to encode the “leader-follower” relations since such knowledge would reduce prediction loss the most. As shown in Figure 3 and Figure 5, the primary graph learns the leader-follower relationship – which aligns with our understanding of the environment. \n\n- **Latent edges are directional**\n\nThe latent edges are directional, as $z_{ij}$ is different than $z_{ji}$. We have updated the manuscript to make this more clear.\n\n[1] Makansi, Osama, et al. \"You mostly walk alone: Analyzing feature attribution in trajectory prediction.\" arXiv preprint arXiv:2110.05304 (2021).\n\n[2] Mangalam, Karttikeya, et al. \"From goals, waypoints & paths to long term human trajectory forecasting.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.\n\n[3] Yuan, Ye, et al. \"Agentformer: Agent-aware transformers for socio-temporal multi-agent forecasting.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.\n\n[4] Wang, Chuhua, et al. \"Stepwise goal-driven networks for trajectory prediction.\" IEEE Robotics and Automation Letters 7.2 (2022): 2716-2\n\n[5] Kipf, Thomas, et al. \"Neural relational inference for interacting systems.\" International Conference on Machine Learning. PMLR, 2018.\n\n", " - **Relative zero-shot generalization performance**\n\nFurther analysis of our generalization results shows that when considering the variety of metrics (ADE/FDE/graph accuracy) and experiments (2x speed, 2x size, 2x agents), IMMA shows a better change in performance when averaged across the three generalization scenarios (Appendix Table 5). In particular, IMMA has a drop in ADE of 0.03 to 0.04, versus a baseline drop of 0.07 to 0.41. Similarly, IMMA has a drop in FDE of 0.06 to 0.08 versus a baseline drop of 0.15 to 0.71. With Graph Accuracy, where there was a large spread in the original (non-generalizing) performance of methods, if we disregard the two methods that performed very poorly on this metric in the original environment (fNRI and GAT_LSTM), we see that IMMA dropped less than the other high-performing baseline methods (NRI, EvolveGraph, RFM and RFM_skip1), with a drop of ~6 versus ~7 for the baseline methods. Similar results hold when using percent change in performance. Additionally, when averaged across generalization scenarios, IMMA also outperforms the other methods by a greater percentage, and a similar or greater percentage on each generalization scenario.We are grateful for the suggestion to represent the generalization experiment metrics in this way and have included a supplemental table that reports this directly.\n\nAdditionally, the fact that our model outperforms other models in absolute terms is meaningful: it implies that our model does not just find a way to overfit the current environment and that it learns to infer more accurate relations in a way that is translatable to moderately out-of-distribution scenarios.\n\n- **Relational inference from latent code**\n\nWe chose the largest entry for each column agent of the primary graph. The primary graph is the first graph trained according to our progressive training process.\n\n- **Discussion of limitations**\n\nWe believe our model would not be suitable for modeling dynamic systems where agents' relations are rapidly evolving. In our model, we use the same (multiplex) graph for all decoding steps, but that could be suboptimal when the underlying relations between agents change within the timespan of our forecasting horizon. We leave the incorporation of techniques available for dealing with this (e.g. [6, 7]) to future work.\n\nAdditionally, our model scales as N^2 in the number of agents, and thus may not be well-suited for scaling to large numbers of agents. Future work may be able to address this problem through incorporation of heuristics or priors about which interactions can be ignored from the beginning. \n\n[6] Graber, Colin, and Alexander Schwing. \"Dynamic neural relational inference for forecasting trajectories.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops. 2020.\n\n[7] Li, Jiachen, et al. \"Evolvegraph: Multi-agent trajectory prediction with dynamic relational reasoning.\" Advances in neural information processing systems 33 (2020): 19783-19794.\n\n", " We thank the reviewer for the time and effort to review our manuscript and provide insightful feedback. In the following, we address the raised concerns point by point:\n\n- **Difference from other multi-layer GNNs for trajectory prediction**\n\nAlthough there are similarities to related methods, our work is novel both in terms of the individual components of the method as well as the way in which we combine them.\n\nCompared to existing works that use multi-layer GNNs [3,4] our work is novel for the following reasons: \n\n(1) Existing works use different layers of graphs to explicitly model interactions of different scales [3,4], whereas we train our multiplex graphs with Progressive Layered Training to let the model automatically learn what to encode for each layer. \n\n(2) Existing works treat the graphs as a transient part of the computation and did not conduct quantitative analysis on the relations constructed. On the other hand, the graph is treated as an integral part of the computation in IMMA, and we go further by evaluating the learned relations quantitatively and qualitatively. This conceptual difference is also discussed in section 3 of the NRI paper [5].\n\n(3) Existing works simply use weighted graphs. We propose using attentional graphs as the latent structure because we believe it is essential to model relative strengths in social dynamical environments. Our experiments showed that using attentional graphs boosts trajectory prediction performance and interpretability. \n\n- **Difference from Progressive Learning (Li et al. 2020 ICLR)**\n\nThe proposed Progressive Layered Training (PLT), utilizing progressive training on a layered latent space as a curriculum learning technique, is novel to the best of our knowledge (progressive training [1] was first proposed to solve the problem of catastrophic forgetting). We conducted ablation studies (table 3) to provide insights as to why this training technique is crucial – finding that it helps with the disentanglement between different interaction types (i.e., graph layers).\n\nPLT is related to [2], but fundamentally different. They use progressive learning to learn hierarchical representations (i.e., lower-level latent codes are results of a function that takes in higher-level representations as input) to improve disentanglement. On the other hand, we can describe progressive layered training as modeling residuals by different neural networks, and each successive layer simply adds accuracy to an already-functional but less accurate predictor. Additionally, our main intention is to improve trajectory prediction performance, and improved disentanglement is a byproduct that appears to explain the effectiveness of PLT.\n\n- **Visualizing layers of relations**\n\nFor visualization, we did not merge the layers of relations. In the main text, we only visualized the primary graph (i.e., the first graph learned during progressive layered training) because we have strong intuitions about what the first layer should encode. \nTo further support our claim that different graph layers can indeed learn to encode different types of interactions (as schematized in Figure 1), we updated the supplementary materials to include two additional qualitative studies: (a) visualization of the second latent graph in the supplementary material, and (b) the predictions before and after learning the second graph. The results showed that incorporation of the second latent graph did help with modeling collision avoidance behaviors.\n\n- **Code availability**\n\nThe code of our model is available here: https://drive.google.com/file/d/1h7o6xJp6odsJ6RvZxzT30w0n_V-lDkGh/view?usp=sharing. We will release the entire repository upon publication.\n\n[1] Rusu, Andrei A., et al. \"Progressive neural networks.\" arXiv preprint arXiv:1606.04671 (2016).\n\n[2] Li, Zhiyuan, et al. \"Progressive learning and disentanglement of hierarchical representations.\" arXiv preprint arXiv:2002.10549 (2020). \nICLR version: https://openreview.net/forum?id=SJxpsxrYPS\n\n[3] Inhwan Bae and Hae-Gon Jeon, Disentangled Multi-Relational Graph Convolutional Network for Pedestrian Trajectory Prediction, AAAI, 2021\n\n[4] Rui Zhou et al. Grouptron: Dynamic Multi-Scale Graph Convolutional Networks for Group-Aware Dense Crowd Trajectory Forecasting, ICRA 2022\n\n[5] Kipf, Thomas, et al. \"Neural relational inference for interacting systems.\" International Conference on Machine Learning. PMLR, 2018.\n", " We thank the reviewer for the time and effort to review our manuscript and provide helpful feedback. In the following, we address the raised concerns point by point:\n\n- **Figure 1 as description of what the model learns**\n\nFigure 1 does describe our understanding of what the proposed method learns, in the context in which there is a dominant interaction (e.g. each follower wants to move towards a leader) and a local interaction (e.g. collision avoidance): who follows whom, as well as additional interactions like collision avoidance. We have added a figure (Appendix Figure 11) that visualizes multiple layers of the latent graph (as opposed to just the primary layer).\n\n- **What the multiplex graph has actually learned**\n\nIn our method, latent codes are multiplex graphs, represented as adjacency matrices that describe interactions between agents. The primary graph is the first graph learned in Progressive Layered Training and should encode the primary interactive relationship that could reduce prediction loss the most. In interpreting, leaders are identified by choosing the largest entry for each column agent of the primary graph. \n\nIMMA learns these graphs purely based on the objective of minimizing prediction loss, and thus we do not know for certain the semantic meaning of each layer. However, we mainly evaluate the primary graph, through qualitative visualization (Figure 3 and Figure 5) and quantitive assessment (Table 2), because we have strong intuition as to what the first graph should encode, given the nature of the environment. The primary graph is the first graph learned in the process of progressive layered training and should encode the primary interactive relationship that could reduce prediction loss the most. For instance, in the Social Navigation Environment and the PHASE dataset, the primary graph should learn to encode the “leader-follower” relations since such knowledge would reduce prediction loss the most. As shown in figure 3 and figure 5, the primary graph learns the leader-follower relationship – which aligns with our understanding of the environment. In the main text, we only visualized the primary graph (i.e., the first graph learned during progressive layered training) because we have strong intuitions about what the first layer should encode. \n\nTo further support our claim that different graph layers can indeed learn to encode different types of interactions, we updated the supplementary materials (Appendix Figures 10 and 11) to include two additional qualitative studies: (a) visualization of the second latent graph in the supplementary material, and (b) comparison of predictions before and after learning the second graph. The results showed that the second graph layer seems to learn collision-relevant interactions, and importantly, that incorporation of the second latent graph did help with modeling collision avoidance behaviors.\n- **Differences between RFM and Ours with conditional generation (Fig 5.)**\n\n \nRegarding analysis of the conditional generation experiments, achieved through latent graph manipulation, we want to preface our answer by saying that we do not have the ground truth for this analysis. This is a qualitative analysis, and we evaluate the predictions based on our understanding of the environment. We claim that the generated trajectories of the baseline are less optimal because (a) it consists of unnatural turns (i.e., when we change the leader of agent 0 to 1), and (b) other agents’ leaders remain the same, and thus their trajectories should not be affected when we only change the leader of agent 0. For example, agents 3 and 4 follow each other, and their behavior should not change throughout the process, yet the baseline method predicts that they would make a turn.\n\nTo quantify this evaluation, we ran a two-alternative forced (2AFC) choice human study with 20 subjects, using the trajectories shown in Fig. 5, in which subjects were asked to choose which model’s prediction is more reasonable (RFM vs. ours). In each of the three trials, the order of the predictions is randomized and the subjects do not have access to which prediction is generated by which model. The results show that our model’s prediction is judged as more reasonable than the RFM model’s in 76.67% of the trials. \n", " - **Limitations and failure cases**\n\nWe expect that our model would not be suitable for modeling dynamic systems where agents' relations are rapidly evolving. In our model, we use the same (multiplex) graph for all decoding steps, but that could be suboptimal when the underlying relations between agents change within the timespan of our forecasting horizon. We leave the incorporation of techniques available for dealing with this (e.g. [1,2]) to future work.\n\nAdditionally, our model scales as N^2 in the number of agents, and thus may not be well-suited for scaling to large numbers of agents. Future work may be able to address this problem through incorporation of heuristics or priors about which interactions can be ignored from the beginning.\n\n[1] Graber, Colin, and Alexander Schwing. \"Dynamic neural relational inference for forecasting trajectories.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops. 2020.\n\n[2] Li, Jiachen, et al. \"Evolvegraph: Multi-agent trajectory prediction with dynamic relational reasoning.\" Advances in neural information processing systems 33 (2020): 19783-19794.\n", " We thank the reviewer for their time and effort reading our work and providing detailed and insightful feedback. In the following, we address the concerns point by point:\n\n- **Formulation of IMMA as a CVAE**\n\nWe decided to frame our model as a CVAE because it allowed us to include a KL divergence term during training and to facilitate an understanding of how the proposed Multiplex Attention Graph might be thought of as an effective prior on the latent space. \nThe KL divergence term acts as a prior (i.e., regularization) on the latent variables. If we drop the KL divergence term in the standard (conditional) VAE formulation (Equation 1), it reduces to an autoencoder. In our experiments, we found that incorporating the KL divergence term does not improve the performance of our model. We believe the explanation is that using Multiplex Attention Graph for the latent structure imposes a prior on the latent space. We are happy to adjust our writing if this would be better grasped by another description.\n\n- **Implementation of EvolveGraph and NRI baselines**\n\nFor NRI, we used the official repository provided here (https://github.com/ethanfetaya/NRI). For EvolveGraph, we reached out to the authors and were able to use the official code for all our experiments.\n\n- **Selection of baselines for NBA dataset**\n\nWe chose to compare with NRI, RFM, and EvolveGraph because they are considered state-of-the-art in the line of works that explicitly learn an interaction graph as part of the trajectory prediction task. Moreover, our chosen baselines not only learn an interaction graph but also explicitly evaluate the interpretability of this graph, whereas many other trajectory prediction works treat latent codes as a transient part of the computation [1,2,3,4,5]. This difference is also discussed in the NRI paper [6]. \nFurthermore, many multi-agent trajectory forecasting works conduct experiments on pedestrian prediction datasets (e.g., ETH/UCY) or autonomous vehicle trajectory datasets (e.g., nuScenes, drone datasets), for which modeling interactions has been shown to be less important [7]. We prioritize comparing our model with EvolveGraph among the “SOTA models’’ because it has shown success in highly interactive environments such as the NBA dataset, has evaluated its model on relational inference, and has also been compared with many trajectory prediction-focused models such as Trajectron++ [8]. \nAdditionally, we included a new baseline fNRI [9], a model that also uses a multiplex latent graph structure (i.e., we consider the variant in which sigmoid activation is used) but does not use attention or progressive training.\n\n[1] Yuan, Ye, et al. \"Agentformer: Agent-aware transformers for socio-temporal multi-agent forecasting.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.\n\n[2] Yu, Cunjun, et al. \"Spatio-temporal graph transformer networks for pedestrian trajectory prediction.\" European Conference on Computer Vision. Springer, Cham, 2020.\n\n[3] Mangalam, K., Girase, H., Agarwal, S., Lee, K.H., Adeli, E., Malik, J. and Gaidon, A., 2020, August. It is not the journey but the destination: Endpoint conditioned trajectory prediction. In European conference on computer vision (pp. 759-776). Springer, Cham.\n\n[4] Hu, Y., Chen, S., Zhang, Y. and Gu, X., 2020. Collaborative motion prediction via neural motion message passing. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 6319-6328).\n\n[5] Wang, Chuhua, et al. \"Stepwise goal-driven networks for trajectory prediction.\" IEEE Robotics and Automation Letters 7.2 (2022): 2716-2\n\n[6] Kipf, Thomas, et al. \"Neural relational inference for interacting systems.\" International Conference on Machine Learning. PMLR, 2018.\n\n[7] Makansi, Osama, et al. \"You mostly walk alone: Analyzing feature attribution in trajectory prediction.\" arXiv preprint arXiv:2110.05304 (2021).\n\n[8] Salzmann, Tim, et al. \"Trajectron++: Dynamically-feasible trajectory forecasting with heterogeneous data.\" European Conference on Computer Vision. Springer, Cham, 2020.\n\n[9] Webb, Ezra, et al. \"Factorised neural relational inference for multi-interaction systems.\" arXiv preprint arXiv:1905.08721 (2019).\n", " - **Multiple modes of prediction by IMMA**\n\nThere are two ways for IMMA to produce multiple modes of prediction. The first method is to treat every row in the latent graph as a discrete latent variable and sample different categorical latent codes to produce different modes of prediction (i.e., consider Gumbel-Softmax VAE [10]). Figure 5 shows predictions of our models with different latent codes, except that the latent codes are not sampled but handcrafted. The second way to produce multiple modes of predictions is to adapt our model to predict the means and variances of a Gaussian mixture distribution and sample from this multi-modal distribution during test time, similar to what EvolveGraph did.\n\n- **Improved predictions by IMMA with latent graph manipulation**\n\nWe believe that the generated trajectories of the baseline are less realistic on two accounts: (a) they consist of unnatural turns (i.e., when we change the leader of agent 0 to 1), and (b) other agents’ leaders remain the same, and thus their trajectories should not be affected when we only change the leader of agent 0. For example, agents 3 and 4 follow each other, and their behavior should not change throughout the process, yet the baseline method predicts that they would make a turn.\nUsing the trajectories shown in Fig. 5, we ran a two-alternative forced (2AFC) choice human study with 20 subjects, in which subjects were asked to choose which model’s prediction is more reasonable (RFM vs. ours). In each of the three trials, the order of the predictions is randomized and the subjects do not have access to which prediction is generated by which model. The results show that our model’s prediction is judged as more reasonable than the RFM model’s in 76.67% of the trials. \n\n[10] Jang, Eric, Shixiang Gu, and Ben Poole. \"Categorical reparameterization with gumbel-softmax.\" arXiv preprint arXiv:1611.01144 (2016).", " We thank the reviewers for their thoughtful and constructive comments. We were encouraged that the reviewers agreed that multiplex attention with progressive layer training is a well-motivated and effective approach for modeling multiagent interactions. In response to excellent feedback, we provide an updated manuscript with a list of improvements and revisions made since the initial submission: \n\nHere we list some improvements and revisions made since the initial submission:\n- Inclusion of factorized NRI baseline (Tables 1, 2, 4)\n- Inclusion of the results of a newly conducted human experiment on the realism of Figure 5 conditional rollouts (Appendix Section C)\n- Table with a summary of relative zero-shot generalization performance (Appendix Table 5)\n- Qualitative analysis of the second latent graph layer (Appendix Figure 10, 11)\n", " This work tackles the problem of modeling multi-agent systems that contain a high degree of interaction between agents. To model such systems, this work proposes Interaction Modeling with Multiplex Attention (IMMA), which uses a multiplex graph latent structure to model different types of interactions in different layers of the multiplex. In addition, attention graph layers are used to capture the strength of the relations. Furthermore, thanks to the structure of the multiplex latent layers, this work proposes progressive layer training (PLT) where one can train different interaction layers separately, and iteratively adding different latent layers. The proposed approach is evaluated on three different datasets showcasing strong results on all. Furthermore, ablation studies show how having multiple latent layers and/or having PLT help the model’s prediction performance. Furthermore, the Social Navigation Environment provides the ground-truth interaction structure of each scene. This work shows that the predicted latent structure predicts ground truth more accurately than prior approaches. Strengths:\n- The paper is well organized and well-written.\n- I believe the application of multiplex attention in the “latent space” is novel to the problem of multi-agent motion forecasting with interaction modeling.\n- The results are strong and convincing on multiple datasets. The ablation studies provide further evidence of the utility of having multiple levels of attention. \n\nWeaknesses:\n- In the appendix, it is mentioned that training is performed with $q_\\phi(z|X^{1:T_h})$. This, combined with the footnote on page 3 (on which I have a question below), it seems like the proposed approach should not be formulated/classified as a CVAE, and is more of a model which has a specific hidden structure on the bottleneck that is not regularized by any external forces (e.g., KL divergence). - I’m wondering where the results of EvolveGraph and NRI are obtained. EvolveGraph reports minADE_20/minFDE_20, and use 5 historical timesteps (2.0s) to make the prediction over the next 4 seconds. Could the authors clarify if this was their own implementation?\n- Furthermore, there are multiple other works that report results on the NBA dataset, following the same configuration mentioned in my previous questions. These include STAR[1], PECNet[2], NMMP[3], GroupNet[4]. How come comparisons were not performed against these ones?\n- Related to my previous question, can IMMA produce multiple modes of predictions or is it always unimodal?\n- I’m confused about the footnote (2) on page 3 which states that one can ignore the KL divergence term. I have looked through the provided reference and could not find why it is possible to ignore this term. Can the authors clarify this?\n- Figure 5: it is not clear to me why the predictions produced by IMMA are better than the baseline when the latent graph is manipulated. - What makes the new generated turns unrealistic in the baseline when compared to IMMA’s predictions? I will say that it is an interesting feature that the predictions of the other agents do not change.\n\nReferences:\n\n[1] Yu, C., Ma, X., Ren, J., Zhao, H. and Yi, S., 2020, August. Spatio-temporal graph transformer networks for pedestrian trajectory prediction. In European Conference on Computer Vision (pp. 507-523). Springer, Cham.\n\n[2] Mangalam, K., Girase, H., Agarwal, S., Lee, K.H., Adeli, E., Malik, J. and Gaidon, A., 2020, August. It is not the journey but the destination: Endpoint conditioned trajectory prediction. In European conference on computer vision (pp. 759-776). Springer, Cham.\n\n[3] Hu, Y., Chen, S., Zhang, Y. and Gu, X., 2020. Collaborative motion prediction via neural motion message passing. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 6319-6328).\n\n[4] Xu, C., Li, M., Ni, Z., Zhang, Y. and Chen, S., 2022. GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 6498-6507).\n These are adequately addressed in the conclusion and the appendix.", " The paper proposes a multiplex attention method for multi-agent interaction modeling. The main motivation is that there can be more than one interaction type between agents. To address this, the paper proposes to use multiple latent graphs to encode the different interactions between agents and employs the VAE framework to infer the latent codes. To ease learning, the paper also proposes progressive layer training, which is a curriculum learning method that gradually adds latent graphs to the model. Evaluations are performed on multi-agent trajectory forecasting using one in-house simulated dataset and two public datasets, PHASE and NBA. The method outperforms prior methods in forecasting accuracy, relational inference accuracy, and sample efficiency. **Strength:**\n\n- The paper is generally well-written and ways to understand. The motivation is clear for encoding multiple types of interaction between agents and their relative strength.\n- The paper performed extensive experiments and analyses on three datasets. Both trajectory forecasting and relation inference are evaluated. The latent graph manipulation experiments are interesting which show the latent codes encode leader-follower behaviors.\n- The paper outperforms the baselines significantly.\n\n**Weakness:**\n\n- The main idea, multiplex attention, of this paper is quite **similar to factorized NRI [1]**, where multiple latent graphs are used in a variational inference framework. The technical novelty of this paper is limited. In some sense, the multiplex attention is not a big change from NRI since the latent code itself is multi-dimensional (therefore each dimension can be treated as a separate latent code) and the main difference of the proposed approach is to not share encoder weights.\n- The paper didn’t compare with strong multi-agent trajectory forecasting baselines on classic trajectory forecasting benchmarks such as ETH/UCY where a large number of agents are interacting with each other. The paper could compare with SOTA methods such as [2, 3, 4].\n- Some design choices are not well motivated. What is the motivation for soft-max across agents in Eq (2)? This constrains the interaction strength from $i$ to other agents to sum to 1 for interaction $k$. However, agent $i$ can have strong interaction strength with multiple different agents for interaction $k$. Therefore, I wonder why the method doesn’t just formulate inference of $z_{ij}^k$ as a binary classification (this interaction exists or not) instead of multi-class classification across other agents.\n\n[1] Webb, Ezra, et al. \"Factorised neural relational inference for multi-interaction systems.\" ICML 2019 Workshops.\n\n[2] Mangalam, Karttikeya, et al. \"From goals, waypoints & paths to long term human trajectory forecasting.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.\n\n[3] Yuan, Ye, et al. \"Agentformer: Agent-aware transformers for socio-temporal multi-agent forecasting.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.\n\n[4] Wang, Chuhua, et al. \"Stepwise goal-driven networks for trajectory prediction.\" IEEE Robotics and Automation Letters 7.2 (2022): 2716-2723. - In Fig. 3, how are the latent codes identified for changing the leader? If I understand correctly, there should be multiple latent codes. A more compelling experiment for interpretability is probably to show different latent codes can lead to different types of interactions (besides leader-follower). This also validates the key motivation of this paper better.\n- Are latent edges directional? i.e., is $z_{ij}$ different than $z_{ji}$? Eq (2) only makes sense if edges are directional, otherwise $i$ and $j$ are not symmetric when computing $z_{ij}$.\n- Zero-shot generalization experiments are not convincing in my opinion. The performance of all methods has dropped but in some cases the performance gap between the current method and the baselines becomes smaller. Normally, the method should outperform the baselines by a similar percentage in this new setting. Doesn’t this indicate the method actually generalizes worse than some of the baselines?\n- How are column agents selected for the relational inference in Table 2? Since the method has multiple latent graphs, do you choose the largest latent code as the latent code for each column agent?\n\n - The paper didn’t really talk about its limitation despite indicating in the form it has done so.\n- One clear limitation is that it cannot handle changing interaction types. As the multi-agent interaction evolves over time, their interaction could also evolve. For example, a follower passes a leader to become the new leader. Recent work on dynamic NRI [5, 6] has attempted to address this limitation.\n\n[5] Graber, Colin, and Alexander Schwing. \"Dynamic neural relational inference for forecasting trajectories.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops. 2020.\n\n[6] Xiao, Ruichao, Manish Kumar Singh, and Rose Yu. \"Dynamic Relational Inference in Multi-Agent Trajectories.\" ICLR 2021.", " The authors proposed a prediction model that uses a multiplex latent graph to represent multiple types of interactions and attention to account for different relations called Interaction Modeling with Multiplex Attention (IMMA). They also introduce a training strategy called Progressive Layer Training (PLT). The experimental results showed that their approach outperformed baseline models in trajectory forecasting and relation inference, spanning three multi-agent scenarios: social navigation, cooperative task achievement, and team sports. They also demonstrated better zero-shot generalization results in the social navigation environment.\n\n Stremgth:\n* They proposed a prediction model that combines multilayer graph neural networks and PLT for interpreting the multiplexed latent structure. \n* The experiments showed that their approach outperformed baseline models in trajectory forecasting and relation inference, spanning three multi-agent scenarios. They also demonstrated superior sample efficiency and better zero-shot generalization results.\n\nWeakness:\n* The novelty of this method seems to be combining multilayer graph neural networks and PLT, but the authors mentioned that each component has novelty, which may be exaggerated. I asked this question in the following “Questions”. \n* The result was clear but there was no code available (I saw “Checklist”) and there were some questions in the experiment description. \n\n 1. I don’t know all of the trajectory prediction studies, but multilayer graph neural networks in trajectory prediction may not be a new idea and the following studies were quickly found [1] [2]. \n2. The idea of PLT may seem to be a special case of the original paper (Li et al. 2020 ICLR, not arxiv). The authors can clarify the difference from the original idea.\n3. The strength of the method may be the decomposition of multilayer relations like Fig.1. However, the results including Fig 3 may show only one layer. How did the authors merge it? And I want to know whether each layer can extract multiple relations like Fig. 1 or not. \n\n[1] Inhwan Bae and Hae-Gon Jeon, Disentangled Multi-Relational Graph Convolutional Network for Pedestrian Trajectory Prediction, AAAI, 2021\n[2] Rui Zhou et al. Grouptron: Dynamic Multi-Scale Graph Convolutional Networks for Group-Aware Dense Crowd Trajectory Forecasting, ICRA 2022\n The authors addressed the limitations and potential negative societal impact of their work. ", " This paper presents a new method for modeling and predicting multi-agent interaction. Observing that such interactions could be affected by multiple factors such as target destinations and collision avoidance during crowd navigation tasks, the key idea was to model them using multiplex graphs. Specifically, rather than classifying types of edges of graphs as done in existing work, the proposed approach instead perform multi-class predictions for multiple edge types and construct multiplex attention matrices. To make latent graph layers diverse, the proposed work introduces a progressive learning scheme (progressive layer training) that gradually increases the number of graph layers to learn. Experimental results on multiple datasets show the effectiveness of the proposed approach over existing methods.\n ## Strengths\n- **Originality**: modeling multi-agent interaction using multiplex graphs seems novel, at least for trajectory forecasting tasks. It is well motivated by the observations that human interactions can be affected by multiple factors.\n- **Quality**: I agree that the proposed approach is well designed and technically sound. The questions that the paper addresses are clearly presented (Q1-Q4 in Section 4) and answered in the experimental results. Experiment details as well as potential societal impacts are clearly described in the appendix.\n- **Clarity**: Overall the paper is clearly written and easy to follow.\n- **Significance**: I believe that the proposed work is relatively significant mainly because it outperformed existing methods on multiple datasets. The zero-shot generalization experiment was interesting and showing the usefulness of the proposed approach.\n\n## Weaknesses\n- The motivating example for multiple factors affecting interactions, i.e., target friend and collision avoidance in Figure 1, may be a bit confusing. If I understand it correctly, multiplex graphs are built rather in a bottom-up fashion in the proposed method, where we cannot ensure that each graph layer has such semantic meaning. In fact, I'm still a bit confused what the multiplex graph actually learned. Is this just a leading agent as shown in Figure 5 or something beyond?\n- While it was great that the proposed method performs very well, I would also like to see typical failure cases. Are there some cases where interaction modeling or prediction are likely to fail? Some suggestions:\n\n- Figure 1 could be improved to precisely describe what the proposed method actually learns. Does it really learn to model collision avoidance, or does it just learn who follows whom?\n- Honestly, I can see few differences between RFM and Ours in Figure 5 or cannot tell which of results from RFM and those from Ours are more natural.\n- What are the limitations and failure cases for the proposed method? As also described above, the paper currently has few discussions on the limitations and typical failure cases for the proposed approach." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 4, 3, 3 ]

[ "vVbQ6mNn7RC4", "B9JvWvzBw9h", "nFksoTtOCgE", "pueVCJBYumR", "f8ANnv2t0qr", "1B0rPRpbjHp", "1B0rPRpbjHp", "1B0rPRpbjHp", "pURzF73UVDk", "SxicR6ApZzo", "SxicR6ApZzo", "rRBXK81luln", "rRBXK81luln", "nips_2022_SeHslYhFx5-", "nips_2022_SeHslYhFx5-", "nips_2022_SeHslYhFx5-", "nips_2022_SeHslYhFx5-", "nips_2022_SeHslYhFx5-" ]

[ "_CRUqiKIsuJ", "erFfooc0s8", "Xi48liWF6H", "LWUqKKrZf5B", "rHahkxLmZT0", "Zd1nOh380Ap", "_AKV1pv3x64", "QR6RBKAzCb0" ]

[ "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for the response and incorporating this important extra information in the revision. My questions have been adequately addressed", " We thank the reviewer for the valuable comment, pointing out that \"this paper addresses a very significant subject\", \"dataset construction is sound\" and \"the paper is easily understood\".\n\n> It's quite difficult to judge the results without looking at the appendix. Mostly I would at least add a conclusions derived from the results in the main paper.\n\nWe appreciate the reviewer's suggestion. Due to the page limit, lots of details went to the appendix in the submitted version of the paper. In camera ready, we will make use of the extra one page to add conclusions derived from the results in the main paper, and also add key implementation details into the main paper.\n\n> It's a well-known issue that LLMs are sensitive to prompt wording and even ordering ([1], [2]). Although the authors do mention they did an analysis on the sensitivity on the model to this and add it in the appendix, to make the claims that this paper makes I think this should be part of the main results (i.e. in the form of variance over prompt wording in Table 3). / How sensitive is the SOTA model (MoralCoT) to prompt wording and ordering?\n\nThanks for this suggestion! We will move the performance reported in the appendix to the main results in the form of standard deviation in the next version of the paper.\n\n> Information about the type of human annotators is missing (demographic, how were they recruited, etc.) / For human annotator demographic (seems like things could be cultural dependent, i.e. in some cultures it might be absolutely not OK to step on money when it is about to be blown away by the wind, whereas in others that's considered helpful)\n\nThanks so much for pointing this out. We completely agree that demographic information of our subjects/annotators is critical information for studying morality because at least some moral judgments may be culturally dependent. Here is a brief synopsis of the demographic features of our subjects. We will add this information into the supplementary.\n\nNovel rule study: Participation in the study was limited to MTurk workers located in the US. Mean age = 37.2 years, SD age = 11.9 years. Race/ethnicity: 68.5% white, 10.1% asian, 6.0% black, 5.7% Hispanic, Latino or Spanish Origin, 10.7% mixed race or other. Mean political leaning was 3.4 on a 5-point scale, anchored at 1 (extremely conservative) and 5 (extremely liberal).\n\nSnack study 1: Participation in the study was limited to MTURK workers located in the US. Mean age =38 years, SD age = 11.0 years. Race/ethnicity: 80.3% white, 4.2% Asian, 12.7% Black or African American, 7.0% Hispanic, Latino or Spanish Origin, 1.5% other (categories are not exclusive of one another; percents sum to more than 1). Mean political leaning was 3.1 on a 5-point scale, anchored at 1 (extremely conservative) and 5 (extremely liberal).\n\nSnack study 2: Participation in the study was limited to MTURK workers located in the US. Mean age = 37.1 years, SD age = 10.4 years. Race/ethnicity: 76.9% White, 5.0% Asian, 14.0% Black or African American, 6.6% Hispanic, Latino or Spanish Origin, 5.0% other (categories are not exclusive of one another; percents sum to more than 1). Mean political leaning was 3.6 on a 5-point scale, anchored at 1 (extremely conservative) and 5 (extremely liberal).\n\nProperty damage & deli line subjects: Participation in the study was limited to MTURK workers located in the US. No further demographic data was taken from participants, but average demographic information for MTURK participants is as follows (Difallah, Filatova, & Ipeirotis, 2018). Gender: 55 % Female. Age: 20% born after 1990, 60% born after 1980, and 80% born after 1970. Median household income: $47K/year.\n\n> Do you have any data on how much humans agree usually in the judgements, i.e. what is the distribution of percentages of permissibility?\n\nThe distribution of percentages is as follows: 0-10: 14.86% of the data, 10-20: 12.16% of the data, 20-30: 11.49%, 30-40: 9.46%, 40-50: 12.84%, 50-60: 4.73%, 60-70: 6.76% , 70-80: 9.46%, 80-90: 11.49% , 90-100: 6.76%\n\n### Writing Suggestions\n> - Consider also citing the following work for Chain-of-Thought prompting (scratchpad): https://arxiv.org/abs/2112.00114\n> - s/that/those line 74\n> - 131-133: I would rephrase this a bit less strong [...]\n> - typo line 206\n> - Reference to table 8 in line 312 should be table 4\n\nThanks for the careful suggestions. We have incorporated the suggested changes to the revised PDF.\n\n> I don't fully understand what's going on in the line 259 within the concat() operation\n\nThe concat() operation means natural language concatenation. The main goal is to elicit the model to answer subquestions and then combine all these answers to form a final query, so this concatenated query is like \"[Vignette] [subquestion 1] [answer to subquestion 1] [subquestion 2] [answer to subquestion 2] ... Taking all these into account, is it OK for that person to break the rule in this case?\"\n\n\n\n", " We thank the reviewer for their review, and the generally positive assessment of our work, -- “building AI systems that account for human moral judgment is a crucial need”, “The motivation related to AI safety is particularly strong”, and “RBQA is a new challenging task/dataset”.\n\n### Technical Details:\n> How is the sequence of questions q_1, ..., q_N chosen? Is it fixed (i.e., pre-determined) or adapted to each case?\n\nIn this study, the sequence of questions q_1, ..., q_N are a pre-determined list of questions, because adapting the questions to each case might require training data, which is not the scope for this work. (We encourage this direction of exploration in future work.)\n\nIn this work, the pre-determined set of questions (as shown in Figure 1) was chosen based on experiments that have been conducted with human subjects. The questions were based on factors that moral psychologists have found to be important predictors of the moral judgments that humans make. The questions from the psychology studies were themselves inspired by different schools of moral philosophy (e.g., the deontology question reflects whether there is a pre-existing rule, the contractualist question considers the purpose of the rule, and the consequentialist question evaluates the benefit and harm of breaking the rule).\n\n> Did you try other aggregation functions rather than concatenation to obtain the chained prompt c_i? / whether the authors tested a different aggregation function rather than concatenation (e.g., similarly to what happens with memory networks)\n\nThis work contributes a challenge set, but not a training set. So different aggregation functions as in the memory network can hardly be trained, as the technical realization of them is often to open up the large language model, and train their parameters, or the additional layer that process the aggregated embedding. For example, if the aggregation method is to add up the embeddings of the answers to the subquestions, then the model needs to learn an extra layer to map this aggregated embedding to the classification label.\n\n### Writing and formatting suggestions:\n\n> Other comments and typos: -- In Table 3, the last three columns are misleading: they represent an F1-score, but this becomes clear only after reading the caption. I would suggest either to split the table in two, or to move the three columns next to the initial F1 column, and include a supercolumn named F1 covering all the four cases (the average, plus the three single scenarios). \n\nThank you for the suggestion on more clear representation. We have reformatted Table 3 by adding a separator line and the super column names and revised the paper PDF. In the camera ready version, it will look nicer if splitting the table into two. We will do the split using the extra one page in the camera ready.\n\n> -- Line 255, \"to a multi-step prompt in Figure 1\" -> \"to a nulti-step prompt, as shown in Figure 1\" -- Line 344, \"that contradicts\" -> \"that contradict\"\n\nWe have also fixed both typos that the reviewer carefully pointed out.\n\n", " We thank the reviewer for pointing out the novelty of our work “authors' ideas are quite novel from the psycholinguistic view point”, and their generally positive assessment of our work.\n\n> Authors employed only 3 types of norms, which could be regarded as preliminary study. Therefore they need to prove the types are sufficient to cover the human morality. At least they should show how these 3 types of norms are important for dealing with human morality.\n\nThis work uses only three norms because our approach is to explore each individual norm thoroughly in order to understand the underlying structure of the way that these norms can be permissibly violated. We therefore chose a small number of norms but probed dozens of ways that the norm might be violated. \n\nIn addition, each rule acts as a case study of the broader category of rules that they represent. These categories are 1) rules that are found cross culturally (and therefore may be universal to human morality), 2) rules that vary cross culturally and are therefore constructed in social contexts, and 3) rules that are invented to adjudicate completely novel contexts. These three categories represent rules that need to be reasoned about using three distinct kinds of moral cognition -- that supported by socio-cultural evolution, that supported by social learning, and that supported by individual reasoning alone. So, if a model succeeds on RBQA, it would suggest that the model has achieved an important competence. We will elaborate on this idea in the final version (and cite another paper of ours in progress which draws out this distinction).\n\n> The proposed method fully relies on open AI's API, which leads to less reproducibility. / I think relying on InstructGPT is problematic for reproducibility, I'm wondering if InstructBERT can be compared? I would at least like to see the results of applying the same mechanism as MoralCOT to a pretrain model such as BERT.\n\nWe think maybe the reviewer is asking about \"generalizability\" rather than \"reproducibility\". For reproducibility, we release our codes, and use temperature=0 (i.e., argmax when decoding) so that InstructGPT's response is the same, thus reproducible, for anyone re-running our experiments.\n\nFor generalizability (about whether the MoralCoT mechanism can be effective when added to other models): The technical constraint here is that the chain-of-thought design is only compatible with autoregressive LMs that can do text generation. BERT is not a fit here (as it can only do \"masked token infilling\" for the classification to generate a direct result, but not free text generation for the chain-of-thought subquestion-answering function). \n\nAmong all the autoregressive LMs that can do text generation, most of them are not publicly accessible, such as many of Google's large models. Also those models are way too big for us to run in house, and thus we rely on APIs. The key here is that we are testing the limits of what the best/biggest models are capable of; this requires the largest models, which are impossible to run outside of industry without APIs. OpenAI's API is accessible to everyone, and the Bloom model too as of last month. We are taking some time to set them up, and will add the results in a following comment when that's ready, or directly add in our camera ready version.\n\n\n\n> For binary predictions of human moral judgment, how the inter-rater correlation would be? I'm wondering if each model could be comparable to individual's assessment.\n\nCould the reviewer elaborate a bit on the data they are interested in seeing? Are they interested in 1) the inter-rater reliability (e.g. a metric such as Cohen’s Kappa) for the ~50 subjects that gave judgments on each case? 2) Subject data from each study (for each of the ~150 vignettes, what percent of subjects judged it morally permissible) compared to the model responses for each vignette. 3) Something else. \n\nWe are happy to provide either of these measures and particularly agree that 2) could be valuable. (Another reviewer asked for something similar and we provide an initial set of data in response below.)\n\n\n\n", " We thank all reviewers for their valuable feedback and appreciating our work.\n\nWe summarize some of the main strengths of our work as summarized by the reviewers below. The reviewers point out that:\n(1) “authors' ideas are quite novel from the psycholinguistic view point” (Reviewer eUQ2), \n(2) “Building AI systems that account for human moral judgment is a crucial need”, “The motivation related to AI safety is particularly strong”, “RBQA is a new challenging task/dataset” (Reviewer P8j4), and \n(3) “This paper addresses a very significant subject”, “it's a clearly important and original addition”, “The clarity of writing is good” and “The dataset construction is sound and contains a lot of human judgements.” (Reviewer bKwH). \n\nThe reviewers have also posed several questions. We have addressed these questions in detail in replies to each comment.\n\nIn the revised PDF, we have also incorporated many suggestions about formatting and fixed all the typos. For additional experiments and moving contents from appendix to the main text, we will follow as many suggestions as we can and add them in the one extra page in the camera ready version.", " To achieve capturing the flexibility of the human moral mind, authors created a challenge set consisting of rule-breaking question answering.\nThey use the state of the art large language model (InstructGPT) and developed MoralCOT that is based on theories of moral reasoning, which outperformed other existing large language models, they say.\n [Strength]\nIn my opinion, authors' ideas (e.g., breaking down into a few decision processes and estimating costs) are quite novel from the psycholinguistic view point. They also provide detailed examples of input and output, which may be beneficial for the community.\n\n[Weaknesses]\nDealing with only 3 types of norms are not very sufficient. \nThe proposed method fully relies on open AI's API, which leads less reproducibility. \nDetails of human's responses are not shown, which results in less clarity. - I think relying on InstructGPT is problematic for reproducibility, I'm wondering if InstructBERT can be compared? \n I would at least like to see the results of applying the same mechanism as MoralCOT to a pretrain model such as BERT.\n\n- For binary predictions of human moral judgement, how the inter-rater correlation would be? I'm wondering if each model could be comparable to individual's assessment. Authors employed only 3 types of norms, which could be regarded as preliminary study Therefore they need to prove the types are sufficient to cover the human morality. At least they should show how these 3 types of norms are important for dealing with human morality.", " This paper addresses the problem of improving language models by taking into account human moral judgment: basically, the idea is to build AI systems that have to establish whether it is permissible to break a moral rule in several situations. This is a crucial task in AI safety, as it deals with the capability of understanding ethics in relation to heterogeneous contexts. The proposed approach consists in a prompting strategy that generates a sequence of questions and answers that can be exploited to predict human moral judgment.\n + Building AI systems that account for human moral judgment is a crucial need\n+ The motivation related to AI safety is particularly strong\n+ Rule-Breaking Question Answering (RBQA) is a new challenging task/dataset for NLP systems that aim to incorporate human moral judgment\n\n- The description of the model and of the proposed approach is too brief, and several details are lacking or just mention without a proper analysis.\n\n * How is the sequence of questions q_1, ..., q_N chosen? Is it fixed (i.e., pre-determined) or adapted to each case?\n\n* Did you try other aggregation functions rather than concatenation to obtain the chained prompt c_i? The main limitation of the paper is that the decription of the model is quite short. I would have liked to see more details on the cognivitely-inspired model: for example, whether the posed questions are fixed or not, or whether the authors tested a different aggregation function rather than concatenation (e.g., similarly to what happens with memory networks).\n\nOther comments and typos:\n-- In Table 3, the last three columns are misleading: they represent an F1-score, but this becomes clear only after reading the caption. I would suggest either to split the table in two, or to move the three columns next to the initial F1 column, and include a supercolumn named F1 covering all the four cases (the average, plus the three single scenarios).\n-- Line 255, \"to a multi-step prompt in Figure 1\" -> \"to a nulti-step prompt, as shown in Figure 1\"\n-- Line 344, \"that contradicts\" -> \"that contradict\"", " This paper addresses the important question whether LLMs understand human flexible moral judgements. Human moral judgements are based on rules (like \"don't cut the line\"), but most important are flexible. Depending on the situation, it might be morally OK to break the rule. Prior work (like MoralQA) doesn't address this important aspect of moral judgements.\nThis work proposes a challenge set that addresses precisely this. The set contains three different rules, each with a set of situations that either allow breaking them or not. The \"ground-truth\" is a large set of judgements made by humans. The situations are made such that novel scenarios occur that are unlikely to have occurred in training. This is important, because central to human morality is the ability to respond in a novel situation that is hasn't been exposed to in training. \nThe authors evaluate a set of language models on this challenge set, most notably of which Delphi (domain-specific, trained on moral judgements) and instructGPT (one of the SOTA LLMs). They show that most models don't achieve much better than random on this task, but that their proposed method called moral chain-of-thought prompting improves the SOTA by ~11% F1. The authors do an extensive error analysis and include high-stake wrong predictions in the appendix (e.g. when the model doesn't realise a life being at stake is important). **Strengths**\n- This paper addresses a very significant subject (to what extent do the LLM align with human moral judgements)\n- It does so by realising that this is not an objective task. The moral judgements are made by a large group of human annotators and not only binary accuracy by the models is reported (OK to break rule vs not OK), but also the % of people saying it's OK.\n- If it's true that a challenge set like this (flexible moral judgements) doesn't exist yet (reviewer can't judge because doesn't know the literature), then it's a clearly important and original addition.\n- The clarity of writing is good, the paper is easily understood in a single pass.\n- The dataset construction is sound and contains a lot of human judgements.\n\n**Weaknesses**\n- Information about the type of human annotators is missing (demographic, how were they recruited, etc.)\n- It's quite difficult to judge the results without looking at the appendix. E.g. in \"checking subquestion answers\" I have no idea what this accuracy means. Mostly I would at least add a conclusions derived from the results in the main paper.\n- It's a well-known issue that LLMs are sensitive to prompt wording and even ordering ([1], [2]). Although the authors do mention they did an analysis on the sensitivity on the model to this and add it in the appendix, to make the claims that this paper makes I think this should be part of the main results (i.e. in the form of variance over prompt wording in Table 3).\n\n[1] Ethan Perez, Douwe Kiela, and Kyunghyun Cho. True few-shot learning with language models. In A. Beygelzimer, Y. Dauphin, P. Liang, and J. Wortman Vaughan (eds.), Advances in Neural Information Processing Systems, 2021. URL https://openreview.net/forum?id=ShnM-rRh4T\n[2] Yao Lu, Max Bartolo, Alastair Moore, Sebastian Riedel, and Pontus Stenetorp. Fantastically ordered prompts and where to find them: Overcoming few-shot prompt order sensitivity. In ACL, 2022. Questions that could address limitations:\n- How sensitive is the SOTA model (MoralCoT) to prompt wording and ordering?\n- Would it be possible to add some conclusions from analyses that are part of the appendix in the main text?\n- Same but for human annotator demographic (seems like things could be cultural dependent, i.e. in some cultures it might be absolutely not OK to step on money when it is about to be blown away by the wind, whereas in others that's considered helpful)\n- Do you have any data on how much humans agree usually in the judgements, i.e. what is the distribution of percentages of permissibility?\n\nGeneral suggestions:\n- Consider also citing the following work for Chain-of-Thought prompting (scratchpad): https://arxiv.org/abs/2112.00114\n- s/that/those line 74\n- 131-133: I would rephrase this a bit less strong, it seems to me like the previous setup (moralQA + finetuning) can test flexibility (simply by having questions that reflect flexible judgement), but they don't currently, and your data is in a sense complementary; moralQA can test whether the model even has knowledge of the vast amount of norms out there, you test wether they understand the flexibility but with less data/norms.\n- typo line 206\n- I don't fully understand what's going on in the line 259 within the `concat()` operation\n- Reference to table 8 in line 312 should be table 4 Yes, the authors talk about the dataset size, the fact that there are different theories of moral judgement, the fact that models shouldn't be making moral decisions automatically." ]

[ -1, -1, -1, -1, -1, 5, 6, 7 ]

[ -1, -1, -1, -1, -1, 3, 4, 3 ]

[ "erFfooc0s8", "QR6RBKAzCb0", "_AKV1pv3x64", "Zd1nOh380Ap", "nips_2022_uP9RiC4uVcR", "nips_2022_uP9RiC4uVcR", "nips_2022_uP9RiC4uVcR", "nips_2022_uP9RiC4uVcR" ]

[ "mF7J2DpyDkh", "uRExL0Yg_w", "AC0-z2GG8ga", "Ud4y0RsSm6", "Hmbjc_42_vO", "LXf6a4SZ2k", "m-nKVapmyWA4", "hGOLsqpWTg7", "JFeMFthioB", "Pm7UdhvIjGv", "XbaARUESk8u", "uUmACsunpG7", "GauFpDsTQiN", "VSbOGeHZXsI", "QfDyZT6Va4c", "2zGRRWU9vn", "Of6FCavBFPp", "jyVSDZCGFKj" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank the reviewer for upgrading the score. ", " Thank you for your further clarification. I will upgrade my score.", " Dear reviewer,\n\nWe are grateful for your kind words and support. We are glad that the rebuttal and additional experiments adequately addressed your concerns. Finally, thanks for recognizing the value of our work -- ideas, empirical results, and insights -- and its potential impact both in research and real-world deployment. \n\nThank you,\n\nAuthors.", " I have read the rebuttal and the reviews from other reviewers. I really appreciate the explanations and additional experimental results provided in the rebuttal. The authors' response has adequately addressed all of my concerns. Just to reiterate my initial review, I do believe the empirical results and insights provided in this work are significant and will be of interest to the community. Therefore, I will be keeping my initial score.", " We thank the reviewer for their comments post our rebuttal. Following are some clarifications to their comments:\n\n**Technical Novelty:** We would like to stress that our work proposes the first nested representation learning framework that is scalable and general enough to be applied to a variety of applications. The key point of our paper is extremely simple, we can design a simple multi-headed loss function for matryoshka representation learning, that performs really well in practice which we establish via extensive experiments. For example, we show speed-ups of the order of 14x without significant loss in mAP for large-scale retrieval. \n\nIt would be great if the reviewer can clearly specify what they mean by \"*lack of technical novelty*\". To the best of our knowledge, no other work discusses such nested representations for significant impact on retrieval and classification metrics, and we have put our work in the context of the relevant literature. This would also help us in improving the paper further.\n\n**Insights:** We indeed agree that our paper establishes the utility of matryoshka representations empirically via extensive experiments across multiple applications on standard benchmarks. We also agree that more theoretical/grounded insights would be quite useful. But we would like to highlight that, in this area, generally theoretical insights are hard to derive, and a lot of progress has been made by more empirically established techniques (e.g., deep learning itself doesn't have a very strong theoretical basis or insights for a lot of the observations, similarly HNSW methods used extensively in retrieval still do not have compelling theoretical basis). \n\nWe strongly believe that empirical results and observations in this paper form a basis for interesting future work on explaining the insights and implications. Section 5 on further analysis and ablations in the paper does provide initial insights and some understanding of the proposed representations. Akin to a lot of empirical ML papers published in NeurIPS, MRL provides a simple algorithm with an extensive experimental evaluation which makes an extremely strong case for real-world usage.\n\n**Matching performance of higher dimension with lower dimensional representation:** We agree that our method's accuracy can at most match the original representation. But we would like to highlight that even at almost 20x lower-dimensional representations, we are able to get within 0.5% of accuracy of the original representation. Furthermore, this translates to 14x reduction in wall-clock time for retrieval of relevant items which is a significant gain and is critical for practical applications all while not losing anything on mAP@10 metric. Finally, this also allows us to train for larger representation sizes without worrying about deployment constraints, as we can leverage the improved accuracy through much more efficient (expected) lower dimensional representations which will make real-world deployment feasible.\n\nWe are still not sure as to what is the confusion here. The proposed representation matches the \"upper bound\" original representation accuracy at a much cheaper cost (*more efficient*). Improving the efficiency of retrieval that uses deep representations has been an important research direction with several papers being published in NeurIPS (Chen et al., NeurIPS 2021, Subramanya et al., NeurIPS 2019 etc.,) -- note that these methods are complementary to ours. We think bringing efficiency alongside similar accuracy of an existing method is a significant contribution to real-world deployment. Please do let us know if the proposed representation brings value to the table and makes sense.\n\n*We are happy to have further discussion in the next couple of days to clarify any other concerns and improve the manuscript.*\n", " I would like to thank authors for their response, but I can not recommend for acceptance due the following concerns.\n\n1. The limited technical novelty is a major issue which makes it below the acceptance bar of NeurIPS. I agree the idea of nested representation is interesting but still I do not anything technically novel. I do not see the application is novel either as claimed by the authors. \n\n2. The contribution of this work is merely empirical, lack of insights, for instance, the performance on OOD and long-tailed data can not be explained clearly. This again makes it not acceptable for a machine learning venue. \n\n3. The extensive experiments on different downstream tasks are appreciated, which unfortunately does not add any value to the technical novelty. \n\n4. Though being more efficient due to the lower dimensionality of the learned representations, while the performance does not always match the original representation. It seems to me the performance of the learned representation is actually bounded by the original representation. This make me doubt about if the proposed representation really makes sense or not. At least this is not clear.\n", " Dear reviewer,\n\nWe are glad to hear that most of your concerns have been addressed. We will add the random projection experiment in the appendix for the camera-ready. \n\n**Large-scale Impact:** Thanks for finding our work insightful. We agree that at web-scale (billion-trillion data points) often the speed and latency issues are solved by efficient pruning of search space through Approximate Nearest Neighbors Search (ANNS). However, despite that that there is still a linear dependence on the dimensionality of the representation (*d*) which MRL handles extremely well in expectation through adaptivity. \n\nAnother key thing to note is that ANNS does search space pruning on a compressed index that is built post-hoc and not learned. The lower dimensions of MRL also tackle this sub-optimality by providing an accurate, learned low-d index that is much easier to do search space pruning on. Finally, all of the techniques proposed in the paper are complementary to the current SOTA methods for search space pruning and ANNS -- while further improving efficiency with almost no accuracy drop. This was demonstrated in the real-world implementation of adaptive retrieval using ANNS for the initial shortlisting using lower dimensions (eg., 8 and 16) followed by exact reranking using the more informative dimensions. We show that this results in no accuracy drop whatsoever compared to an exact L2 search (brute-force k-NN). \n\n\n*Hope this further clarifies the last concern brought up by the reviewer, we thank them again for their time and constructive feedback*. ", " Yes, I did mean JL - thanks for the correction. Indeed surprised to see the abysmal results with JL, but I would add this experiment in the appendix for the final copy. \n\nMost of my concerns have been adequately satisfied. Although I have some concerns about the large scale impact especially in terms of application, since speed and latency issues are often solved by pruning the search space, instead of decreasing the dimensionality of the representation, I still think there is very solid insight in this work. Updating the score. ", " We thank the reviewer for the detailed and positive review. We are glad that the reviewer found the proposed solution simple and intuitive while being task and scale agnostic, the improved efficiency significant, adaptive methods interesting and improvement in long-tail continual learning promising. Following are the clarifications requested in the review:\n\n**Arbitrary granularities:** Thank you for the suggestion on arbitrary granularities. There 2 reasons for choosing logarithmic granularities over arbitrary granularities: a) The accuracy improvement vs representation size is not linear but is more logarithmic (as shown by the FF models) – This means, that optimizing for granularities increasing in a non-logarithmic fashion would be sub-optimal both for maximum performance and expected efficiency. b) If we have “m'' arbitrary granularities, the expected cost of the linear classifier to train MRL would scale O(L*(m^2)) while logarithmic granularities result in O(L*2log(d)) space and compute costs. These two reasons put together make logarithmic granularities a strong empirically driven design choice.\n\nHowever, we have run an experiment with uniform (*MRL-Uniform*) interval granularities [8, 212, 416, 620, 824, 1028, 1232, 1436, 1640, 1844, 2048] as shown in the table below. We have evaluated the interpolation at the usual (*MRL-log*) dimensions [16, 32, 64, 128, 256, 512, 1024, 2048] for ease of comparison to reported numbers using 1-NN accuracy (%).\n\nWe observe that the interpolation does happen, but is not strong as logarithmic granularities. The biggest difference is at the lowest dimensions as logarithmic spacing helps in tighter packing of information in the initial dimensions increasing the accuracy significantly. It is also evident that having granularities at higher dimensions does not help in significant accuracy improvement -- due to accuracy saturation which is often logarithmic w.r.t representation size as shown by FF models. Note that the slight improvement at higher dimensions for uniform beyond 512 is due to the multiple granularities around them compared to just 3 for the logarithmic -- which are not useful in practice for efficiency. \n\n| Representation Size | MRL-Uniform | MRL-log |\n|:-------------------:|:-----------:|:-------:|\n| 8 | 58.44 | 62.19 |\n| 16 (int) | 61.11 | 67.91 |\n| 32 (int) | 63.82 | 69.46 |\n| 64 (int) | 66.44 | 70.17 |\n| 128 (int) | 68.71 | 70.52 |\n| 212 | 69.95 | -- |\n| 256 (int) | 70.06 | 70.62 |\n| 416 | 70.84 | -- |\n| 512 (int) | 70.98 | 70.82 |\n| 620 | 71.16 | -- |\n| 824 | 71.30 | -- |\n| 1024 (int) | 71.37 | 70.89 |\n| 1028 | 71.39 | -- |\n| 1232 | 71.48 | -- |\n| 1436 | 71.49 | -- |\n| 1640 | 71.50 | -- |\n| 1844 | 71.48 | -- |\n| 2048 | 71.44 | 70.97 |\n\n**Lower than 8 dimensions:** Yes, we have tried working with lower than 8-dimensions. However, for ImageNet scale and beyond, we found that using lower than 8-dimensions in MRL does not affect the accuracies of other granularities significantly. However, lower than 8-dimension granularity have low accuracies which often can not be used during deployment meaningfully due to the hardness in the training of the lowest dimension. We also observe a small dip in accuracy at higher dimensions which we attribute to the joint loss that now also includes the harder optimization of lower than 8-dimensions. Lastly, we think the dimensionality of 8 is an empirically validated design choice due to the considerable accuracy it provides along with the ease of training. \n\nHere are the accuracy numbers for an experiment where we used MRL between 4-2048 (*MRL-4*) and 6-2048 (*MRL-8*) dimensions on ImageNet using ResNet50 compared to reported numbers (*MRL-8*) using linear classification (Top-1 accuracy(%)).\n\n| Representation Size | MRL-4 | MRL-6 | MRL-8 |\n|:-------------------:|:-----:|:-----:|-------|\n| 4 | 27.25 | -- | -- |\n| 6 | -- | 58.71 | -- |\n| 8 | 66.86 | 67.55 | 66.63 |\n| 16 | 73.36 | 73.10 | 73.53 |\n| 32 | 74.82 | 74.49 | 75.03 |\n| 64 | 75.51 | 75.32 | 75.82 |\n| 128 | 75.93 | 75.61 | 76.30 |\n| 256 | 76.08 | 75.82 | 76.47 |\n| 512 | 76.31 | 75.93 | 76.65 |\n| 1024 | 76.38 | 76.04 | 76.76 |\n| 2048 | 76.43 | 76.12 | 76.80 |\n\nRest of the clarifications in the comment below -- [Part 2/2](https://openreview.net/forum?id=9njZa1fm35&noteId=Pm7UdhvIjGv)", " Continuation of [Part 1/2](https://openreview.net/forum?id=9njZa1fm35&noteId=JFeMFthioB).\n\n**Performance improvement on next granularities based on tuning relative importance:** This is an interesting observation and we do not think we have a concrete insight into why this is happening. Our hypothesis is that this is highly dependent on hyperparameters and given that we use the same setting for every experiment (even the relative importance ablations), we might not be looking at the best possible outcome. We think that with the right hyperparameters and better training routines, the accuracy of the next granularity will benefit significantly from improving the lower representations. \n\n**Societal Impact:** This was an oversight on our end and completely missed explaining the potential social impact in the checklist. Our work does not have any additional negative societal impact on top of what representation learning already has. We will incorporate the societal impact into the next revision of the manuscript. We would also ask the reviewer to check the response on societal impact in [our rebuttal to reviewer HvJ7](https://openreview.net/forum?id=9njZa1fm35&noteId=uUmACsunpG7).\n\n*We hope that this rebuttal further solidifies your positive outlook on the paper and we are happy to discuss if you need any further clarifications to increase the score and facilitate acceptance of the paper.*\n\n", " We thank the reviewer for the detailed review. We are glad that the reviewer found the proposed solution simple and practical while being general, the paper to be well written, the experiments to be exhaustive and satisfying and the real-world improvements in retrieval to be significant. Following are the clarifications requested in the review: \n\n**Other Practical Applications of MRs:** We think increasing speed for retrieval tasks is a significant application, as you also agree in the strengths. MRs allow training/maintaining/inferring with *one* network and still allow for flexibility for downstream tasks powered through classification and retrieval. This is very critical in practice, because compute environments, latency requirements, and accuracy constraints for downstream tasks vary significantly. So MRL can allow maintaining one representation to serve multiple downstream tasks satisfactorily. In addition, MRs can be used for adaptive classification, quantifying the hardness of instances, and improved few-shot and long-tail performance all while maintaining the same robustness as the fixed feature baselines. \n\nAdditionally, MRs can also be used for adaptive latency-based transmission over computer networks. This would involve sending compressed representations of the data to be reconstructed depending on network bandwidth – MRs naturally solve this problem with the coarse-to-fine grained flexibility baked into them.\nWe are happy to discuss more practical applications of MRs and are looking forward to your feedback.\n\n**Anytime Neural Networks (ANNs):** As you mentioned, we are solving similar problems from different angles. ANNs aims at reducing the total inference cost by adaptive exiting at various depths. However, in the case of large-scale search and retrieval, this would involve storing multiple representations across depths in the database – which is prohibitively expensive for search and storage. But MRL is agnostic to any representation learning and can be combined with ANNs across all depths.\n\nHowever, the more interesting thing from the paper (https://arxiv.org/abs/1708.06832) is the aspect of the adaptive weight scheme for train losses – which is directly applicable to MRL’s own loss weightings. We thank the reviewer for this pointer (will cite in the next revision) and this would be very useful in future work involving the right weightings of loss functions in MRL and multi-objective MRL. \n\n**Performance improvement at higher dimensions:** We agree that improvement over FF is an interesting observation. We hypothesize it is due to multi-fold gradients of information that pass through the lower dimensions as they are shared across higher dimensions. For example, even 128 dims would get gradient feedback when we are also minimizing the losses for 256, 512, 1024 and 2048 dim. At the same time, accuracy is not saturated yet, resulting in slightly higher accuracy than the FF models. We find this to be interesting as well and are willing to have a longer discussion in this regard. \n\n**Variational Information Bottleneck (VIB):** VIB is a really interesting line of work – thanks for pointing us to it. It is a valid setup to have VIB adapted to a general representation learning setup and see if the bottleneck size is *much* lower than a vanilla neural network. Viewing VIB as a regularization, it can be easily combined with MRL making both the techniques complementary if need be. Lastly, training variational methods at large-scale are more expensive compared to usual training recipes; however, we think that VIB + MRL is an extremely interesting direction for empirically analyzing information bottlenecks. \n\n**Rest of the clarifications in the comment below** -- [Part 2/2](https://openreview.net/forum?id=9njZa1fm35&noteId=uUmACsunpG7)", " Continuation of [Part 1/2](https://openreview.net/forum?id=9njZa1fm35&noteId=XbaARUESk8u).\n\n**Random Projections:** We think you mean Johnson–Lindenstrauss (JL) when you mention Gram-Schmidt, as JL lemma suggests random projections to be a great way to reduce dimensionality while holding onto the similarity information. We did run random projections as a baseline but did not include them in the paper due to their abysmal performance compared to random feature selection and SVD – which is often the case for large-scale semantic search. However, please find the results of gaussian random projection with 1-NN accuracy (%) compared to SVD on FF - 2048 model in the table below and we will include random projection as a baseline in the next revision of the paper. We think SVD is a much better projection technique than random for dimensionality reduction.\n\n| Representation Size | Random Projection | SVD | \n| :-----------: | :-----------: | :-----------: |\n| 8 | 0.088 | 19.14|\n| 16 | 0.093 | 46.02|\n| 32 | 0.12 | 60.78|\n| 64 | 0.10 | 67.04|\n| 128 | 0.14 | 69.63|\n| 256 | 0.07 | 70.67|\n| 512 | 0.11 | 71.06|\n\n**Societal Impact:** This was an oversight on our end and completely missed explaining the potential social impact in the checklist. The reviewer is correct in stating that our work does not have any additional negative societal impact on top of what representation learning already has. We will incorporate the societal impact into the next revision of the manuscript.\n\nWe agree that the study on the tradeoff between representation size and the tendency to encode biases is an interesting direction. Along the lines of Hooker et al 2019, 2020 (https://arxiv.org/abs/1911.05248, https://arxiv.org/abs/2010.03058), we did some experiments to see the trends between the classes and their variance in accuracy with the change of dimensionality. A part of this was also presented as part of the “Disagreement across Dimensions” (Lines 334 - 342) which discusses superclass accuracy and hard instances. We will also include the per-class accuracy trends (some lose more than others) with dimensionality in the next revision of the paper. \n\nAll these tie well into the aspect of encoding biases and investigating them with the lens of information bottleneck capacities is an exciting future direction.\n\n*We hope that this rebuttal further solidifies your positive outlook on the paper and we are happy to discuss if you need any further clarifications to increase the score and facilitate acceptance of the paper.*", " We thank the reviewer for their time and feedback. We are glad that the reviewer found the idea interesting and the experiments to be thorough and comprehensive. Below, we answer the questions raised in the review: \n\n**“matryoshka representation can encode information at different granularities, which achieves the same level of performance while being of much smaller sizes.”:** We want to clarify that we achieve “same” performance up to minor drops (like .1% in mAP@10 for adaptive retrieval) using *adaptive* classification or retrieval, which means that for most of points we can get away with small MRL embeddings but for some points we might need to have larger embedding sizes. While it is true that smaller representation sizes (64 vs 2048) have similar accuracy (within 1%), the adaptive setups presented in the paper help in reducing the expected dimensionality even further for the same level of accuracy. This is an important distinction to note as we do not exactly match the accuracy of the highest dimensions by just using much lower dimensions – but is achievable when combined with adaptive methods.\n\n**Simplicity and Novelty:** We are glad that the reviewer found our idea to be simple and straightforward. We are unsure about the comment on technical novelty being weak. Through extensive literature review, we place MRL precisely in context of existing works and show that - to the best of our knowledge - MRL formulation and application is novel. We do agree that the idea is simple, as highlighted by the reviewer. But we view that as a significant strength of this work because the approach is generalizable to any standard architecture, domain, and loss function. Through comprehensive experiments, we do show the benefits of the approach in context of classification, retrieval, as well as for multiple domains like images, text, images-text at scale. We are happy to have a conversation on the technical novelty of the approach during the discussion phase.\n\n**Performance advantages at large representation sizes and SOTA performance:** We do not fully understand the reviewer’s concern here. There are two aspects to this question: a) We perform better than baselines for small dimensions. This is true because the lower dimensions get more gradient information due to the multiple losses attending to them compared to larger dimensions in MRL, b) We can achieve “nearly” the SOTA performance with much smaller dimensionality or at much smaller cost. That is, for ImageNet classification, we can get within 0.3% of SOTA with just 256 dimensional representations compared to 2048 dimensions required by the fixed feature baseline. We can in fact further reduce the expected dimensionality to 48 to achieve similar numbers by using adaptive classification. Similarly, for retrieval, we can get within 0.1% of the SOTA mAP@10 by using MRL+adaptive retrieval. \n\nThe adaptive methods slowly move up the granularities and eventually use the large representation size to achieve SOTA performance. However, the data points that require the highest dimension for any of the downstream tasks are extremely few. This makes the whole system at least an order of magnitude more efficient for deployment all while having the same performance as the strongest baseline. \nWe are happy to engage in a discussion and understand your concerns in this aspect to address them clearly and make the manuscript more accessible to a general audience. \n\n**Out-of-distribution and Long-tailed data:** This is an interesting question and honestly we don’t have a very good explanation as well and believe that this would be an interesting direction to explore for future work. We thought about it extensively while analyzing the OOD and FLUID results. We hypothesize that inducing coarse-to-fine grained structure (MRL) into representation learning results in tighter packing of information in the initial dimensions – which is a result of reinforced gradient feedback from higher dimensions to lower dimensions multiple times due the MRL loss. This leaves the higher dimensions to have more capacity and handle specific (rare) semantic information that is not already taken into account. This is often lost in fixed feature models due to the diffusion of information across dimensions which tends to mix rare semantics in a hard-to-leverage fashion. However, we agree that this aspect of MRL is an interesting future work.\n\n**Limitations:** Please refer to Sections 5.1 & 6 (Lines 343 - 358), where we have noted the limitations of MRL found through ablations and provided a discussion around it along with potential future directions. \n\n*We hope that the rebuttal clarifies questions raised by the reviewer. We would be very happy to discuss any further questions about the work, and would really appreciate an appropriate increase in score if reviewers’ concerns are adequately addressed to facilitate acceptance of the paper.*\n", " We thank the reviewer for the positive review. We are glad that the reviewer found the paper well-written, the principal ideas easy to follow, and the experiments exhaustive and impressive. Following are the clarifications requested in the review:\n\n**Switching between appendix and main paper:** Thank you for pointing this out. We will revisit the paper and its organization to minimize the back and forth. The current format of the paper tried to include all the plots in the main paper while their corresponding tables were pushed to the appendix. \n\n**Classification accuracies of the high dimensions:** The classification accuracies presented in Tables 1, 2, 4 all show that at high dimensions MRL sometimes does not have the same results as fixed feature models – MRL is at most 0.30% lower than FF models. We think this is an artifact of not having MRL-specific tuned hyperparameters. With better hyperparameters, slightly longer training, and reweighting of the MRL losses (as shown in Table 27), we can ensure that the highest dimensions of MRL models match the FF model accuracies. However, it should be noted that optimizing MRL is generally a harder problem than the baseline fixed feature models which could be a key reason for the slight dip in accuracy compared to FF at the highest dimensions.\n\n**Training difficulty of MRL:** We did not encounter any difficulties in training by introducing the nested loss for all the experiments presented in the paper. Notably, all the MRL experiments in the paper use the best hyperparameter setups of the fixed feature baselines – alleviating the need for extensive hyperparameter tuning. This makes training with MRL extremely straightforward in any existing representation learning pipeline.\n\n*We hope that this rebuttal further solidifies your positive outlook on the paper and we are happy to discuss if you need any further clarifications to increase the score and facilitate acceptance of the paper.*\n", " In this work, the authors propose Matryoshka Representations, a flexible coarse-to-fine representation that can be applied to multiple downstream tasks based on the computational budget. The authors demonstrate that utilizing the proposed Matryoshka Representations leads to a substantial reduction in embedding size for large-scale retrieval tasks. Finally, the authors have shown that the proposed representations can be incorporated into web-scale dataset experiments. Strengths:\n\n- The proposed solution is simple and intuitive.\n- The learned low-dimensional representations are as good as the models trained independently with that particular dimension without any additional computational overhead.\n- Significantly improves the efficiency of large-scale classification and retrieval tasks.\n- Allows for adaptive classification with variable embedding size.\n- Achieves promising improvement on long-tail continual learning experiments.\n- Matryoshka Representations can be easily extended to different modalities and even to web-scale datasets.\n\nWeaknesses:\n- No major weakness. The idea is simple and the results are compelling.\n\n - Have the authors experimented with arbitrary granularities? For instance, m random numbers can be generated up to the highest embedding size and these random numbers can be used for nesting dimensions. It will be interesting to see how the embeddings interpolate if the features are learned using such an arbitrary granularity. \n\n- Have the authors tried lower than 8 dimensions?\n\n- Any insight into why tuning the relative importance weight of dimension 16 did not lead to improvement of dimension 32 whereas only increasing the weight of dimension 8 led to a noticeable improvement of dimension 16. The limitations of the proposed work have been adequately addressed. However, no discussion about the potential negative soceital impact has been provided in the main text and supplementary materials. ", " The paper introduces \"Matryoshka Representations\" which are a way to encode dimensions over multiple scales such that for a chosen embedding dimension d, there are log(d) embeddings of increasingly smaller size that can encode the same information as the original d-dimensional vector, with minimal loss in performance of the downstream task. The paper thoroughly validates MRs on an impressively large variety of tasks spanning over challenging and large scale datasets, and different modalities (vision+language, vision, language). Strengths:\n- the main strength of the paper is that it proposes a simple and practical solution for the problem, which can be used in many downstream tasks\n- The paper is written very clearly.\n- 14 x faster retrieval is a very significant improvement\n- The experiments are exhaustive and satisfying, for an approach that offers a lot of generality. \n\nWeaknesses:\n- Outside of increasing the speed for retrieval tasks, I am not sure what other practical applications of MRs are there. \n- I would like to see the authors discuss the research done on anytime neural networks[1]. They are not similar in methodology, but try to solve a very similar problem.\n- The improvement over FF is impressive, albeit unclear to me, why there is still improvements are higher dimensions (~64+). I would think/hope that at around 64 dim, the amount of information starts to become noisy. I would also \n- I would be very interested in these two baselines on any task: \n - VIB [2] reformulated for this task, to see if its possible that there are any direct or indirect connections if the low-dim representations learned using VIB can be useful. \n - Taking the full d-dim embedding and projecting it to a lower dim space using a random projection and seeing if that works. According to Gram-Schmidt, the low-dim representations should be usefully informative, and it was tried in [3] to some success. It can be a useful baseline for the paper as well. \n\n\n[1] https://arxiv.org/abs/1708.06832\n[2] https://arxiv.org/abs/1612.00410\n[3] https://arxiv.org/abs/1910.13540 Please see strengths/ weaknesses. The authors do not explicitly discuss societal impacts of their work, but its unclear if the work has direct impacts. It would be useful for the community if the authors commented/showed if the lower dimensional representations are more or less susceptible of encoding biases in their representations, as its important to discuss such details. For practical purposes, is there a tradeoff between the dimensionality of the representations and the tendency to encode biases.", " This paper proposes the so-called matryoshka representation learning, which can learns coarse-to-fine representations by modifying the regular learning pipeline. The matryoshka representation can encode information at different granularities, which achieves the same level of performance while being of much smaller sizes. The authors show the effectiveness of the matryoshka representations for image classification and retrieval tasks. Extensive ablation studies demonstrates the robustness and the ability of learning with limited data (few shots) and long-tailed data settings. Strengths\n\n1. it is an interesting idea to learn representations that can encode information of different granularities. \n\n2. The learned representations are deployed to different downstream tasks, e.g., classification and retrieval.\n\n3. The experiments and ablation studies are thorough and comprehensive.\n\nWeakness\n\n1. The idea is simple and straightforward. The major weakness of this work is the technical novelty, which makes the contribution a bit weak.\n\n2. The proposed algorithm does not show performance advantages when the representation size is large although it performs much better when size is very small. It seems the proposed algorithm also relies on a large representations to produce SOTA performance. 1. It is unclear to me why the proposed algorithm can deal with out-of-distribution data and long-tailed data. I did not see any discussion about the limitations of this work.", " The authors propose a flexible representation learning approach MRL for an adaptive deployment on downstream tasks, where a single embedding can encode information at multiple granularities. An efficient variant MRL-E is also introduced with a set of common weights for nested dimensions. The coarse -to-fine representations are then applied to adaptive classification and retrieval tasks with various settings, where the method matches the performances of fixed-feature baselines. They provide as well further analysis in terms of robustness, few-shot learning and different dimensions. 1) The paper is well-written and quite easy for readers to follow the principal ideas, though switching between appendix and main paper from time to time troubles a bit.\n2) The author provides a surprising number of experiments, covering different aspects of modalities, datasets and applications, which is quite impressive and complete.\n3) Coming to the classification task, in Tables 1,2,4, for the high dimensions, it’s interesting to see that MRL sometimes cannot achieve the same results as FF. I am wondering if some explanations could be provided. I am wondering if there exist any difficulties in training by introducing the nested loss. I think the limitations mentioned in Section 6 are quite complete." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 6, 5, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 5, 3 ]

[ "uRExL0Yg_w", "GauFpDsTQiN", "Ud4y0RsSm6", "Pm7UdhvIjGv", "LXf6a4SZ2k", "GauFpDsTQiN", "hGOLsqpWTg7", "uUmACsunpG7", "QfDyZT6Va4c", "QfDyZT6Va4c", "2zGRRWU9vn", "2zGRRWU9vn", "Of6FCavBFPp", "jyVSDZCGFKj", "nips_2022_9njZa1fm35", "nips_2022_9njZa1fm35", "nips_2022_9njZa1fm35", "nips_2022_9njZa1fm35" ]

[ "VVZkAYxy2dX", "UdPfIAF5f0H", "o5dHr59CC60", "bUtQcQnoRBH", "WgPwAgXplLw", "yyPH-ZUUYMK", "fZciHkVkD2m", "Wr7xuKfcDQk", "6N7YResymnE", "kLsGvODxOaA", "DYlHzuuGNS9", "WuAC62jn_o7", "-_Xzwdn1fZ", "Bz7hsF4igaQ", "Gl95N6_2LfB", "DcZS8xHBqd" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your comment!\n\nI totally disagree with you. First, according to the spectral convolution theorem in Fourier theory, updating a single value in the spectral domain globally affects all original spatial data, which sheds light on design efficient neural architectures with non-local receptive field. Therefore, the proposed Fourier Up-sampling empowers the network the global information modeling ability in an effective manner. At the last count, in terms of Transposed convolution, it is the widely used up-sampling operator and not to be considered outdated. In addition, the pixel shuffle is not involved trainable parameters and coupled with pure convolution to perform the up-sampling action. However, the pure convolution and Transposed convolution is locally linear operator while our proposed Fourier Up-sampling is nonlinear, thus improving the model learning ability. Furthermore, in the line 39-42, we have claimed “However, the aforementioned methodologies only interact at a single resolution scale, and the spatial-Fourier interaction potential of multiple scales in the Fourier domain has not been investigated. The key to solving this problem lies in how to implement deep Fourier up-sampling for multi-scale Fourier pattern modeling.” To emphasize, our focus is to design the Fourier up-sampling for the multi-scale spatial-Fourier interaction.\n\nSecond, the selected baselines are the representative works in the related tasks. In addition, as a general operators, implementing the proposed Fourier Up-sampling in the standard benchmarks is more fair. Further, as you suggested, we implement the proposed Fourier Up-sampling into the state-of-the-art image de-raining method SGCN [1] to conduct experimental validation on Rain200L and Rain200H datasets. As can be seen in this table, with the proposed Fourier Up-sampling operators, the performance of original SGCN is improved in terms of PSNR and SSIM and the corresponding variant achieves the best de-raining results. \n\nFinally, we will insert our proposed Fourier Up-sampling into the state-of-the-art benchmarks of other reported tasks in revision.\n\n| | | Rain200L | | Rain200H | |\n|:------:|:-----------------:|:--------:|:-----:|:--------:|:-----:|\n| method | configuration | PSNR | SSIM | PSNR | SSIM |\n| | Original | 37.65 | 0.976 | 29.13 | 0.895 |\n| SGCN | Spatial-Up | 37.86 | 0.982 | 29.47 | 0.903 |\n| | FourierUp-AreaUp | 39.57 | 0.985 | 29.82 | 0.908 |\n| | FourierUp-Padding | 39.83 | 0.987 | 29.95 | 0.913 |\n\n[1] Xueyang Fu, et.al. Successive Graph Convolutional Network for Image De-raining. IJCV, 2022.\n\n", " I would like to thank the authors for their detailed response. However, I remain unconvinced about the overall significance of the work. \n\nIn their rebuttal, the authors clarify the main idea behind moving upsampling ot the Fourier domain is enabling a global receptive field for the operation under the assumption that this would be better than more or less localized operations in the spatial domain. This motivation seems questionable for a couple of reasons. First, it is not obvious that the frequency space with its total loss of spatial coordinates provides a more effective domain for interpolation. Indeed, it has been known since scale-space models and space-frequency transforms like wavelets that it is hard to exploit self-similarity in the Fourier domain. Second, the authors rightly point out the extreme locality (and linearity) of transpose convolution,but this operation is to be considered outdated and causing artifacting. The more popular current approach of pixel shuffling does not suffer from these limitations to the same extent due to the fact that pixels can be derived from features exploiting the entire receptive field of the network (which can be quite large). Moreover, thank to its use of an arbitrary feature space it effectively implements a non-linear polyphase decomposition of the signal.\n\nRelated to the issues of novelty and presentation, the derivation that takes most of page 4 is a standard result that can be found in any signal processing textbook. The result on page 5 is also a trivial property.\n\nRegarding, the experimental results, it seems that the authors use rather dated baselines (most are from 2018-2020). Even for the denoising experiment they graciously reported in the rebuttal, the VDN model from 2019 is currently outdated and outperformed by a number of methods. Due to this concern, there is no evidence that the proposed technique can work on actual state-of-the-art models and any gains observed in the paper might be due to the suboptimal designs of these older models.", " **1, Presentation and novelty.**\n\nIn terms of presentation, we are encouraged by other reviewers who recognize the good presentation of this paper. Specifically, Reviewer-1 admits “The paper writing and explanations are good. Reviewer-2 and Reviewer-3 comment “easy to follow and clear writing”. In addition, w also provide detailed proofs and illustrations that help one understand our method and the specific implementation in the main paper and supplementary material.\n\nIn terms of novelty, we wish to emphasize the contributions of our work again.\n\n1) We propose a novel Deep Fourier Up-Sampling, which enables the integration of the features of different resolutions in the Fourier domain. To the best of our knowledge, this is the first thorough effort to explore the Fourier up-sampling for multi-scale modeling. \n2) The proposed FourierUp is a generic operator that can be directly integrated with the existing networks, which provides flexible plug-and-play. \n3) Equipped with the theoretically feasible FourierUp, the networks achieve consistent performance improvement across multiple computer vision tasks, which suggests the potential of our method for refreshing the neural network designs in the Fourier domain.\n\nIn addition, other reviewers also confirm our novelty and contributions. To be specific, Reviewer-1 highly praises our work “I actually had this kind of idea but never tried this. It is refreshing to see that this paper has done this. This work will drive the community in a certain direction”. Reviewer-2 confirms our novelty: “Idea is interesting”. Reviewer-3 praises that “Interesting motivation: This work takes an interesting and challenging issue, and Theoretical proof: For the proposed Deep Fourier Up-Sampling, this work provides detailed and rigorous proof, making a theoretical sound solution. These proofs provide a new view to understand deep Fourier up-sampling and convince the readers.”\n\nFinally, in terms of the question “a more precise explanation of why we should expect gains with respect to existing techniques”, the underlying reasons why the FourierUp works better are summarized as follows:\n\n(a) First, our proposed “Fourier Up-Sampling” is performed in the frequency feature space where each factor connects with all the pixels in the spatial domain via Flourier transformation. In other words, learning in the frequency domain allows obtaining the image-wide receptive field that models the global contexts that are indispensable for vision tasks. Different from the existing spatial up-sampling strategies that only depend on local pixel attention for up-sampled reconstruction, our proposed “Fourier Up-Sampling” is performed in the frequency domain and thus fully explores the global dependency for up-sampling. \n\n(b) Second, the spatial up-sampling is implemented by Transposed convolution and various interpolation techniques and both of them are linear operators. Therefore, the spatial up-sampling also can be regarded as a linear transformation. Differently, our “Fourier Up-Sampling” is implemented in the Fourier space and the transposed components are processed by different convolutions. Therefore, it is non-linear, thus empowering the learning capability of deep models.\n \nIn a word, our proposed “Fourier Up-Sampling” empowers the network not only more powerful non-linear learning capability but also more global (image-wide) dependency modelling capability.\n\n\n\n\n", " **2, two very important problems.**\n\n(1) To our best knowledge, existing representative classification networks, e.g., VGG, ResNet, and InceptionNet, don not adopt the up-sampling operators. Therefore, we cannot report the experiments over the image classification task. \n\n(2) As a common sense, image de-raining and image de-noise follow the similar degradation formula:\n\nY= X+N\n\nwhere Y and X indicate the degraded image and the latent clear version. For image de-raining, N represents the rain effect. In terms of de-noise, N is the noise. Therefore, we only report the image de-raining task. \n\nAs suggested, we have added the experiments for image denoising. Due to the limited time, we only perform the image de-noising experiments with regards to the representative baseline VDN [1] using the commonly-used SIDD benchmark [2]. The results are presented in this table. As presented, the original baseline obtains the performance gain in terms of PSNR and SSIM when equipped with all the proposed “Fourier Up-sampling” variants. The results are consistent with other vision tasks presented in our main paper.\n\n| | | Original | Spatial-Up | FourierUp-AreaUp | FourierUp-Padding |\n|:------:|:-----:|:--------:|:----------:|:----------------:|:-----------------:|\n| VDN | PSNR | 39.23 | 39.31 | 39.55 | 39.67 |\n| | SSIM | 0.971 | 0.971 | 0.973 | 0.973 |\n\n[1] Zongsheng Yue, Hongwei Yong, Qian Zhao, Lei Zhang, Deyu Meng. Variational Denoising Network: Toward Blind Noise Modeling and Removal. NeurIPS, 2019.\n\n[2] Abdelrahman Abdelhamed, Stephen Lin, and Michael S. Brown. A high-quality denoising dataset for smartphone cameras. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2018.\n\n**3, Marginal improvements.**\n\nIn the manuscript, it can be found that our proposed Fourier Up-sampling achieves significant performance gain of different degrees over all the reported vision tasks. Compared with existing works, such improvements are significant, not marginal as these tasks are challenging. Therefore, according to previous studies, we would claim that these improvements are very important and meaningful when the computational burden introduced by our method is negligible. ", " We thank reviewer for the positive feedback. We are encouraged that the reviewer confirms the interesting motivation of our work, convincing theoretical proof, flexibility of the proposed operators, and sufficient experiments.", " We thank reviewer for the positive feedback. We are encouraged that the reviewer confirms the interesting idea of our work, easy to follow, and clear writing.", " **1, Figure 1.**\n\nFirst, Figure-1 aims to illustrate the motivation of our work. Unlike the spatial domain with local similarity property, up-sampling in the Fourier domain is more challenging as it does not follow such a local similarity property. Specifically, in Figure-1 (a), the input image is passed to the down-sampling and up-sampling in the spatial domain, and it still maintains the structure of the original input image. In other word, the resulting image can be added to the original input image because of the coordinate-aware pixel alignment. However, as shown in Figure-1 (b), directly employing the spatial up-sampling to process the down-sampled frequency information cannot restore the coordinate-aware structure alignment, thus incapable of integrating it with the original input image for multi-scale frequency modeling. Inspired by this issue, we attempt to design a more ingenious “Fourier Up-Sampling”. In Figure-1 (c), it can be seen that the proposed “Fourier Up-Sampling” can effectively restore the image of coordinate-aware structure alignment with the original input image. \n\nSecond, in terms of the question “reconstructions in the spatial domain are really bad after periodic padding or area-interpolation. Why does it still work?”, the reviewer may misunderstand our Figure-1. Figure-1 just aims to illustrate the motivation of our paper, but does not completely correspond to our detailed designs. \n\nTo be specific, (1) the reconstruction of Figure-1 (c) in the spatial domain is incompletely. It only employs the core step of periodic padding or area-interpolation of our proposed “Fourier Up-Sampling” for illustration and has not employed the following transformation coefficients with 4 and $\\frac{-4\\pi}{N}sin(\\frac{\\pi y}{N})(1+cos(\\frac{\\pi x}{M}))$ that are inferred in Theorem-1 and Theorem-2 of the main paper. When adding this step. i.e., complete reconstruction, our proposed method can produce visually pleasing reconstruction. \n\n(2) For visualization, Figure-1 shows the results in the image space and only adopts the fixed transformations. However, our proposed “Fourier Up-Sampling” is targeted at the feature space. In the feature space, we formulate our method as the learnable transformations for better flexibility and accuracy. Note that albeit being designed on the basis of strict theories, both constructed frequency up-sampling modules contain certain approximations, such as a learnable convolution operator instead of strictly 1/4 as described in Theorem-1 of the main manuscript, and an approximation cropping to preserve the map corners instead of accurate $\\frac{-4\\pi}{N}sin(\\frac{\\pi y}{N})(1+cos(\\frac{\\pi x}{M}))$ mapping as proved in Theorem-2 of the main manuscript and Theorem-3 of the supplementary materials. Such approximations make the proposed modules feasible and flexible when they are used to represent the frequency structures of real data. It is worth noting that this is the first attempt for constructing easy equitable frequency up-sampling modules. With our exploration, we wish this work could arouse more effective and rational designs for frequency up-sampling. \n\n(3) Compared with spatial up-sampling, our proposed “Fourier Up-Sampling” has the following advantages. In the feature space, the spatial up-sampling only depends on local pixel attention and can be regarded as a linear transformation. Instead, our proposed “Fourier Up-Sampling” is performed in the frequency domain and thus fully explores the global contexts via Fourier transformation, which achieves better up-sampling than simple linear transformation of spatial up-sampling. Furthermore, compared with the spatial up-sampling, our “Fourier Up-Sampling” is non-linear, thus empowering the learning capability of a deep model.\n\nIn summary, Figure-1 aims to illustrate the motivation of our paper not completely corresponds to our designed “Fourier Up-Sampling” solutions.", " **2, More recent SOTA competitors.**\n\nAs suggested, we have added the state-of-the-art cutting-edge methods as the baselines to validate the effectiveness of our proposed “Fourier Up-Sampling”. Due to limited time, we only select the latest image de-raining method SGCN [1] to conduct experimental validation on Rain200L and Rain200H datasets. As can be seen in this table, with the proposed Fourier Up-sampling operators, the performance of original SGCN is improved in terms of PSNR and SSIM. The results are consistent with other vision tasks presented in our main paper. We will add more baselines to further show the effectiveness of our method in the final version.\n\n| | | Rain200L | | Rain200H | |\n|:------:|:-----------------:|:--------:|:-----:|:--------:|:-----:|\n| method | configuration | PSNR | SSIM | PSNR | SSIM |\n| | Original | 37.65 | 0.976 | 29.13 | 0.895 |\n| SGCN | Spatial-Up | 37.86 | 0.982 | 29.47 | 0.903 |\n| | FourierUp-AreaUp | 39.57 | 0.985 | 29.82 | 0.908 |\n| | FourierUp-Padding | 39.83 | 0.987 | 29.95 | 0.913 |\n\n[1] Xueyang Fu, et.al. Successive Graph Convolutional Network for Image De-raining. IJCV, 2022.", " **3, Failures cases.**\n\nAs a general operator, our method needs to be integrated with networks, such as the baseline networks used in our paper. We validate the effectiveness of our operator via comparing the performance gain with and without the operator. Thus, as a general operator, it is inapplicable to show failure cases as we are not sure whether the failure cases are caused by the original baselines or our operator. Instead, in terms of failure case, our method may have limited application scenes. For example, our operator cannot be used in the networks that do not need the up-sampling operation, such as commonly used image classification networks, VGG, Resnet, and InceptionNet.\n\n**4, Complexity comparisons.**\n\nAs suggested, we have added the complexity comparisons against the competitors, including trainable parameters and FLOPs. Due to the limited time, we only report some representative baselines：image de-raining LPNet and pan-sharpening DCFNET in the manuscript.\n\n| | | Original | Spatial-Up | FourierUp-AreaUp | FourierUp-Padding |\n|:------:|:-----:|:--------:|:----------:|:----------------:|:-----------------:|\n| LPNet | #Params | 27055 | 27127 | 27127 | 27127 |\n| | FLOPs | 3.9621G | 3.9622G | 3.9622G | 3.9622G |\n| DCFNET | #Params | 2.7579M | 2.7988M | 2.7988M | 2.7988M |\n| | FLOPs | 13.7374G | 13.7376G | 13.7376G | 13.7376G |\n\nObserving this table, we can find that our proposed “Fourier Up-Sampling” introduces negligible parameter and FLOPs increment and achieves the significant performance gain as suggested in the experimental parts of the main manuscript when they are compared with the original models. Therefore, the comparison further validates the effectiveness and potentials of our proposed general operator.\n\n", " We thank the reviewer for the positive feedback. We are encouraged that the reviewer confirms the theoretical evidence provided in our work, the promising performance of our method, the good writing and explanations of our paper. We also happy to see the reviewer had this kind of idea before.", " **1, The parameter comparisons and more visual results.**\n\nAs suggested, we have added the complexity comparisons against the competitors, including trainable parameters and FLOPs. Due to the limited time, we only report some representative baselines: image de-raining LPNet and pan-sharpening DCFNET in the manuscript.\n\n| | | Original | Spatial-Up | FourierUp-AreaUp | FourierUp-Padding |\n|:----------------:|:----------------:|:----------------:|:----------------:|:----------------:|:-----------------:|\n| LPNet | #Params | 27055 | 27127 | 27127 | 27127 |\n| | FLOPs | 3.9621G | 3.9622G | 3.9622G | 3.9622G |\n| DCFNET | #Params | 2.7579M | 2.7988M | 2.7988M | 2.7988M |\n| | FLOPs | 13.7374G | 13.7376G | 13.7376G | 13.7376G |\n\nObserving this table, we can find that our proposed “Fourier Up-Sampling” introduces negligible parameter and FLOPs. Therefore, the comparison further validates the effectiveness and potentials of our proposed general operator. \n\nIn terms of the visual results, we will provide more results in the supplementary material.\n\n\n\n**2, The underlying reasons and whether each variant of the FourierUp prefers a specified vision task.**\n\n1) the underlying reasons why the FourierUp works better are summarized as follows:\n\nFirst, our proposed “Fourier Up-Sampling” is performed in the frequency feature space where each factor connects with all the pixels in the spatial domain via Flourier transformation. In other words, learning in the frequency domain allows obtaining the image-wide receptive field that models the global contexts that are indispensable for vision tasks. Different from the existing spatial up-sampling strategies that only depend on local pixel attention for up-sampled reconstruction, our proposed “Fourier Up-Sampling” is performed in the frequency domain and thus fully explores the global dependency for up-sampling. \n\nSecond, the spatial up-sampling is implemented by Transposed convolution and various interpolation techniques and both of them are linear operators. Therefore, the spatial up-sampling also can be regarded as a linear transformation. Differently, our “Fourier Up-Sampling” is implemented in the Fourier space and the transposed components are processed by different convolutions. Therefore, it is non-linear, thus empowering the learning capability of deep models.\n\nIn a word, our proposed “Fourier Up-Sampling” empowers the network not only more powerful non-linear learning capability but also more global (image-wide) dependency modelling capability.\n\n2) whether each variant of the FourierUp prefers a specified vision task?\n\nLike the spatial up-sampling techniques (e.g., transposed convolution, pixel shuffle, and various interpolation techniques), our proposed “Fourier Up-Sampling” is also the general strategy and each variant thus does not prefer a specified vision task. In addition, we have provided some insights on the use of different variants of the proposed “Fourier Up-Sampling” in Section 3.4 of the main paper. As well recognized, existing global dependency techniques like non-local and transformer both require a huge computational cost. Instead, our proposed “Fourier Up-Sampling” is capable of modeling global relationships with simple implementation and cheap computational resources. Thus, one can try our operators in different tasks without considering the introduced computational burden.\n\n**3. The flowchart of implementation details.** \n\nThank you for the suggestion. We will provide more results in the main paper and reorganize our layout. We will provide more details of our flowchart in the final version.\n", " **1, Figure 1.**\n\nFirst, Figure-1 aims to illustrate the motivation of our work. Unlike the spatial domain with local similarity property, up-sampling in the Fourier domain is more challenging as it does not follow such a local similarity property. Specifically, in Figure-1 (a), the input image is passed to the down-sampling and up-sampling in the spatial domain, and it still maintains the structure of the original input image. In other word, the resulting image can be added to the original input image because of the coordinate-aware pixel alignment. However, as shown in Figure-1 (b), directly employing the spatial up-sampling to process the down-sampled frequency information cannot restore the coordinate-aware structure alignment, thus incapable of integrating it with the original input image for multi-scale frequency modeling. Inspired by this issue, we attempt to design a more ingenious “Fourier Up-Sampling”. In Figure-1 (c), it can be seen that the proposed “Fourier Up-Sampling” can effectively restore the image of coordinate-aware structure alignment with the original input image. \n\nSecond, in terms of the question “reconstructions in the spatial domain are really bad after periodic padding or area-interpolation. Why does it still work?”, the reviewer may misunderstand our Figure-1. Figure-1 just aims to illustrate the motivation of our paper, but does not completely correspond to our detailed designs. \n\nTo be specific, (1) the reconstruction of Figure-1 (c) in the spatial domain is incompletely. It only employs the core step of periodic padding or area-interpolation of our proposed “Fourier Up-Sampling” for illustration and has not employed the following transformation coefficients with 4 and $\\frac{-4\\pi}{N}sin(\\frac{\\pi y}{N})(1+cos(\\frac{\\pi x}{M}))$ that are inferred in Theorem-1 and Theorem-2 of the main paper. When adding this step. i.e., complete reconstruction, our proposed method can produce visually pleasing reconstruction. \n\n(2) For visualization, Figure-1 shows the results in the image space and only adopts the fixed transformations. However, our proposed “Fourier Up-Sampling” is targeted at the feature space. In the feature space, we formulate our method as the learnable transformations for better flexibility and accuracy. Note that albeit being designed on the basis of strict theories, both constructed frequency up-sampling modules contain certain approximations, such as a learnable convolution operator instead of strictly 1/4 as described in Theorem-1 of the main manuscript, and an approximation cropping to preserve the map corners instead of accurate $\\frac{-4\\pi}{N}sin(\\frac{\\pi y}{N})(1+cos(\\frac{\\pi x}{M}))$ mapping as proved in Theorem-2 of the main manuscript and Theorem-3 of the supplementary materials. Such approximations make the proposed modules feasible and flexible when they are used to represent the frequency structures of real data. It is worth noting that this is the first attempt for constructing easy equitable frequency up-sampling modules. With our exploration, we wish this work could arouse more effective and rational designs for frequency up-sampling. \n\n(3) Compared with spatial up-sampling, our proposed “Fourier Up-Sampling” has the following advantages. In the feature space, the spatial up-sampling only depends on local pixel attention and can be regarded as a linear transformation. Instead, our proposed “Fourier Up-Sampling” is performed in the frequency domain and thus fully explores the global contexts via Fourier transformation, which achieves better up-sampling than simple linear transformation of spatial up-sampling. Furthermore, compared with the spatial up-sampling, our “Fourier Up-Sampling” is non-linear, thus empowering the learning capability of a deep model.\n\nIn summary, Figure-1 aims to illustrate the motivation of our paper not completely corresponds to our designed “Fourier Up-Sampling” solutions.\n\n\n**2，About frequency down-sampling.**\n\nThanks for your professional comments. As we illustrated in the manuscript, both the frequency down-sampling and up-sampling strategies contribute to multi-scale frequency modeling. Frequency down-sampling is also important. However, the frequency down-sampling has been studied in previous work [1] while the frequency up-sampling has never been explored. To this end, we are encouraged to fill this gap. The core of this work is frequency up-sampling.\n\nFurthermore, the core derivations between the down-sampling in [1] and our proposed up-sampling are significantly different. Specifically, the frequency down-sampling proposed in [1] is heuristic and only implemented by cropping the center-around frequency information as the expected down-sampled size. In contrast, our frequency up-sampling is on the basis of strict theories.\n\n[1] Oren Rippel, Jasper Snoek, and Ryan P. Adams. 2015. Spectral representations for convolutional neural networks. Neural Information Processing Systems (NIPS'15). ", " This paper proposes a novel up-scaling strategy to upscale the spatial features in an encoder-decoder-based spatial up-down sampling network. Upscaling is performed on the frequency domain to explore the global dependency. The upscaling module has been experimented with several computer vision tasks and experimental results show significant performance improvement in those tasks. This paper mainly proposes two different types of Fourier upscaling, namely periodic padding and area-interpolation. The main strengths are as follows.\n1. This paper explored the relationship between spatial and frequency domains. The theoretical evidence in support of upscaling module design is explained properly.\n2. The experiments in comparison with existing upscaling and different variants of Fourier upscaling are performed. The experimental outcome shows promising performance.\n3. The paper writing and explanations are good. I actually had this kind of idea but never tried this. It is refreshing to see that this paper has done this. This work will drive the community in a certain direction. \n\nThere is no such major weakness in this paper. I would like to know an explanation behind those results as we can see from Figure 1 that reconstructions in the spatial domain are really bad after periodic padding or area-interpolation. Why does it still work?\n Why did this paper not explore the frequency down-sampling strategies and experiments with different variants? Did frequency down-sampling not give satisfactory results? If so, why does only frequency upscaling work? N/A", " This paper proposes a theoretically feasible Deep Fourier Up-Sampling (FourierUp) to address up-sampling operators in Fourier domain. Extensive experiments across multiple computer vision tasks are conducted. Strengths:\n- Idea is interesting\n- Easy to follow\n- Clear writing\n\nWeaknesses:\n1. Sec. 3 introduces the details and theoretical evidences of the two kinds of FourierUp Modules, including Periodic Padding interpolation and Area Interpolation. However, it's not clear to me why the proposed FourierUp method is better. Even with the illustration in Fig. 1, the results of the two variants are not that good. Thus, deeper analysis on why and how FourierUp helps improve the performance should be discussed and illustrated.\n\n2. In experiments, more recent SOTA competitors are required to be compared. For example, PReNet is from CVPR'19, Aod-Net and PanNet are from ICCV'17. I think it's ok to adopt some classical methods as the baselines when proposing a novel framework for the existing task. It would be better if the proposed method is compared with the SOTA cutting-edge methods to provide some deeper understanding on the tasks, which may make the proposed method more insightful and convincing.\n\n3. I am curious about what kind of failure cases the proposed method may have. Sec. 5 actually avoids to show such cases.\n\n4. Complexity comparisons against the competitors are required. Please see [Weaknesses]. Yes, the authors discussed the limitations in Sec. 5. However, I am also curious about the failure cases that the proposed method cannot handle currently.", " This paper tries to solve a challenging issue in frequency related neural network designs, i.e., how to model the multi-scale frequency patterns. Unlike the simplex up-sampling operations in the spatial domain, up-sampling frequency information in a neural network is non-trivial because the local property of spatial up-sampling cannot be directly used in the frequency domain. According to the spectral convolution theorem, this work proposes an interesting and theoretically sound solution, called Deep Fourier Up-Sampling (DFU). DFU is the first work to consider the modeling of multi-scale frequency patterns and provides key insights for the frequency related network designs. Besides, the DFU can be implemented by different variants with different theoretical support. The DFU is also flexible in its compatibility with existing neural networks. Extensive experiments on multiple vision tasks demonstrate the effectiveness of the proposed DFU. Strengths:\n1. Interesting motivation: This work takes an interesting and challenging issue, multi-scale information modeling in the frequency domain, into account. Although there are some frequency-related neural networks, they cannot effectively and accurately model the relationship of multi-scale frequency information due to the Fourier transformation characteristics. However, the multi-scale frequency information is important for vision tasks. This key issue is the focus of this paper.\n2. Theoretical proof: For the proposed Deep Fourier Up-Sampling, this work provides detailed and rigorous proof, making a theoretical sound solution. These proofs provide a new view to understand deep Fourier up-sampling and convince the readers. \n3. Flexibility: The proposed Deep Fourier Up-sampling can be a generic operator, which can be compatibility with existing neural networks and boost their performance. \n4. This paper conducts sufficient experiments to demonstrate the effectiveness of the proposed Deep Fourier Up-sampling. To show the versatility of the proposed method, the experimental comparisons are carried out on diverse vision tasks, including object detection, image segmentation, image de-raining, image de-hazing, and guided image super-resolution. The experiments on multiple vision tasks provide strong supports for the advantages of the proposed multi-scale frequency information modeling.\n\n\nWeaknesses:\n1. Although this paper provides sufficient experimental results, it would be better if the parameter comparisons and more visual results could be provided. The reviewer understands that this paper has conducted extensive experiments, covering low-level and high-level vision takes in the limited space. More results could be provided in the supplementary material. \n2. In Section “Comparison and Analysis”, the underlying reasons why the FourierUp works better are insufficient. More explanations are expected. Furthermore, it is a little confusing that whether each variant of the FourierUp prefers a specified vision task? How to choose the variant when one uses the FourierUp for different vision tasks? Some insightful analysis or suggestion should be provided, which would guide the followers to make full use the capability of the proposed FourierUP. \n3. It would be better if more visual results could be provided in the main paper rather than the supplementary material. It is fine to shrink the sizes of figures for showing more cases. Current format is inconvenient to switch between the main paper and the supplementary material for checking the visual results. \n4. The flowchart of implementation details in supplementary materials are suggested to transfer to main manuscript. \n\n See the above weaknesses. The authors are suggested to give the detailed responses. The authors adequately addressed the limitations and potential negative societal impact of their work.", " The authors propose an upsampling layer based on the Fourier transform and properties of the frequency domain. The motivation behind the work is quite vague, only resorting to the fact that the Fourier transform is a global operator rather than local. The paper is generally poorly written, lacks a clear motivation, and the novelty is unclear. \n\nStrengths:\n- Frequency-based techniques for layer operations are an area of research that deserves more interest\n\nWeaknesses:\n- Poor presentation. Readability is very low, especially due to long derivations and proofs in the text rather than in the appendix. It is hard to grasp what the method does at a glance\n- Novelty unclear. It seems that the work just exploits well known properties of the Fourier transform of upsampled signals. It is also unclear why the scheme should outperform any other technique\n- Experiments show very marginal improvements and lack two very important problems: image classification and denoising I would like the authors to clarify where the novelty lies in the proposed method and a more precise explanation of why we should expect gains with respect to existing techniques. The authors addressed the limitation that two very important benchmarks (classification and denoising) are missing. Still, when proposing a very general technique, the body of proof required to demonstrate it is advantageous needs to be substantially larger than what is presented." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 5, 8, 3 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 5, 5, 4 ]

[ "UdPfIAF5f0H", "bUtQcQnoRBH", "DcZS8xHBqd", "DcZS8xHBqd", "Gl95N6_2LfB", "Bz7hsF4igaQ", "Bz7hsF4igaQ", "Bz7hsF4igaQ", "Bz7hsF4igaQ", "-_Xzwdn1fZ", "Gl95N6_2LfB", "-_Xzwdn1fZ", "nips_2022_NIrbtCdxfBl", "nips_2022_NIrbtCdxfBl", "nips_2022_NIrbtCdxfBl", "nips_2022_NIrbtCdxfBl" ]

[ "DQz-dUkVHn1", "IYoet_JYFh", "Gd_li4OW2ax", "hBUYRpH2t6", "FoBqzat1scU", "Zqg4v7reUMx", "EdiYctKNv-", "S9lgAihtW_", "zbqwxAqwhw" ]

[ "official_reviewer", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for answering my questions. It would have been interesting to check your hypotheses about Q 4) with extra experiments, but this is probably an unreasonable request given the limited time of the rebuttal period. I still believe this paper provides a solid theoretical contribution to tackle the considered problem therefore I am keeping my score unchanged.", " Thanks for the answers/clarifications. Based on them, I am willing to increase my score.", " Thank you for the detailed comments! Concerning your summary, let us stress that it was not obvious from [Lavenant et al.’20] that the optimization problem of Eq.(5) could be tackled with MFL. We needed to rework their formulation to have entropy terms appearing with the correct sign. We consider this reformulation -- which leads to an optimization method that was not obvious at first sight -- as our main conceptual contribution. Concerning the technical details, we’ll provide more details and clarification for the proofs.\n\n**Questions**\n\n(1) To quote from the paper, “The data model of Eq. (1) was introduced only to motivate the min-entropy estimator via Thm. 2.1 [quoted from [Lavenant et al.]], and plays no role in the rest of the paper.” So this assumption does not intervene in our theory or proofs: our only assumption about the data is that we observe discrete empirical measures $\\hat \\mu_{t_i}$ supported on $\\mathcal{X}$.\n\n(2) We’ll double check that all assumptions are clearly and correctly stated (did you have a specific theorem in mind with missing assumptions? Maybe this is about Thm. 2.1 which is quoted from another paper).\n\n(3) Yes we consider reflecting boundary conditions for SDE (10) (a.k.a. “Skorokhod problem”). We have now introduced explicitly the term of bounded variation that enforces the boundary condition in (10) for the sake of rigor.\n\n(4) Indeed, we need a formula that applies to reflected processes. Thank you for the correction. We have added an example of a precise reference where this derivation is proved using Ito-Tanaka’s formula.\n\n(5) We have added details about the part taken from [21]. As for the part coming from [23], it is a rather long proof by recursion and we use it exactly in the context of [23], so we prefer to cite the result.\n\n(6) In our original submission, we were providing a lower bound on $C$ (which gives the convergence rate of the form $e^{-Ct}$ in Thm.3.3) in terms of the parameters (including $D$). Unfortunately, with the corrected version of Thm. 3.3 it is a bit harder to track the constants and so we have decided to drop it. In any case, with our current approach, the lower bound cannot be better than $e^{-cst*D/\\epsilon}$. One direction for future work is to derive the convergence rate in the non-compact case which requires, we believe, a very different viewpoint and would better reflect the behavior of the algorithm.\n\n(7) We have expanded some of the proofs, and we will continue working on making Prop.D.1 and the rest of the proofs more clear and self-contained.\n\n", " Thank you for your detailed comments!\n\n**Questions**\n\n(1) The integral in l.156 is, in a measure-theoretic sense, the disintegration of $R^*$ by the evaluation map $e$ at times $(t_1,...,t_T)$ (i.e. $e(\\omega)=(\\omega(t_1),\\dots,\\omega(t_T))$). Probabilistically, it can be understood as saying that conditional on passing through $(x_1, …, x_T)$ at times $(t_1,...,t_T)$, the paths of $R^*$ are Brownian bridges with diffusivity $\\tau$. We have added this explanation.\n\n(2) [See our answer to Q3 of reviewer 2ZNK]\n\n(3) In the simulated experiments, the level of entropic regularization is determined by the ground truth diffusivity, i.e. $\\tau * (t_{i+1} - t_i)$ between a pair of time-points $t_i$ and $t_{i+1}$. For the reprogramming dataset, the regularization level was chosen to be effectively $0.1 * E [(X_{t+1} - X_t)^2/2] $ between time-points $t_i$ and $t_{i+1}$, as is described in Section H of the supplement. This works out to be almost equivalent to the default value of $0.05*\\text{median}[(X_{t+1} - X_t)^2]$ used in [Schiebinger et al., 2019]. In general for real data, the level of noise is not known and the problem of choosing the level of entropy regularization $\\tau$ (as well as the data-fitting parameter $\\sigma^2$) is related to that of bandwidth selection for kernel methods. For this, heuristics such as the mean and median criterion exist, see e.g. [Garreau et al. 2017].\n\n [Garreau et al. 2017]: Garreau, D., Jitkrittum, W. and Kanagawa, M., 2017. Large sample analysis of the median heuristic. arXiv preprint arXiv:1707.07269.\n\n(4) This is a good question: we believe that this trend indeed continues when $N$ gets larger because our method estimates the marginal $\\mu_t$ more diffused than they actually are. This is mainly owing to the data-fitting term which has a finite bandwidth parameter. Theory suggests that we should decrease the hyperparameter ($\\lambda$ and $\\sigma^2$) as $N$ increases, but in Fig. 1 only $\\lambda$ is varied and $\\sigma^2$ is kept fixed for simplicity (see supplement for details). In contrast, gWOT uses the same support as the input samples, which implicitly gives more strength to the data rather than the prior. If both $\\lambda$ and $\\sigma^2$ were allowed to vary with increasing $N$, we have reason to believe that this trend would not be observed.\n\n(5) Our method would work for any Markovian process as a reference (as long as its reversible measure has an explicit or tractable log-density). However, if the reference process is non-Markovian, then the “representer theorem” would not hold anymore and our approach would not apply; different ideas would be needed. \n\n(6) Thank you for the reference, we were not aware of such tools, which could be very useful indeed for this line of work! Note that in our case, the reconstructed stochastic process $R^*$ is characterized by the family of $T-1$ transport plans, which is a simpler object than a general stochastic process (SP). One point of difference between the provided reference and the present work is that [Salvi et al., 2021] consider a scenario where one has access directly to sample trajectories, whereas in our setting only population snapshots at fixed time-points are available; but their method could indeed be considered in synthetic experiments where the ground truth SP is known.\n", " Thank you for your detailed comments.\n\n**Weaknesses**\n\n(1) Although we do not study the challenging problem of particle discretization here, related results in the literature on mean-field Langevin dynamics suggest that that the method *does not* require an exponential number of particles. Instead we expect the error to decrease at a polynomial rate in the number of particles (independent of $d$) thanks to the stability of entropy regularized optimal transport (EOT) as discussed in Sec. 3.4. \n\n(2) Here, by guarantees, we mean consistency (i.e. non-quantitative) guarantees, e.g. as the number of particles goes to infinity. Such results are admittedly weak, but they are not even known for other nonconvex approaches. We would like to stress that the nearest-neighbor estimation of entropy *is not* needed to run the algorithm, it is only needed if one wants to plot the energy decrease.\n\n(3) A direct comparison to the approaches the reviewer mentions is difficult because we solve a different problem (those methods estimate a Waddington potential, and require $n_i>>1$). In contrast, gWOT solves the same estimation problem. Let us mention that optimal-transport-based approaches are compared to dozens of other approaches in the WOT paper [Schiebinger et al ‘19] and gWOT is compared to WOT in the gWOT paper.\n\n**Questions**\n\n(1) The (technical) proof of [1] would go through for Eq.(3) (the difference between the two objective functions is not important from a statistical viewpoint but our formulation is much more convenient for discretization/optimization). Rather than re-proving Thm. 2.1 with small changes, we are, in ongoing work, studying the sample complexity of (3) (i.e. a direct quantitative consistency result).\n\n(2) PDE (11) describes the evolution of the law of the marginals of the Mean-Field Langevin dynamics described by SDE (10), which we solve numerically by discretizing $\\mu$ to a family of discrete particle clouds, as explained in Eq. (13) (the Laplacian term in (11) is a consequence of the noise term (13)), as is standard in the Mean-Field Langevin dynamics literature.\n\n(3) A computational complexity result to reach $\\epsilon$-accuracy for the overall problem is beyond reach for the moment. With $1/\\Delta t$ marginals discretized each into $m$ particles, we carry out Sinkhorn iterations for each pair of timepoints until an $\\epsilon$ tolerance is reached in the dual Sinkhorn objective. We will expand the discussion in (Sec. 3.4) to mention that we have an *iteration* complexity of time $O(m^2/(\\tau(\\Delta t)^2\\epsilon))$ using [Dvurechensky et al’. 18] complexity bounds for Sinkhorn.\n\n(4) Quantifying the dimension dependence is an important open question. Note that the scrna-seq dataset related to Fig. 4 has ambient dimension $d=20,000$ and we reduce to a space of $d=10$ dimensions by PCA when preprocessing the data.\n\n(5) As mentioned, this unbalanced extension is only introduced as a heuristic and is motivated by the practical problem of accounting for growth. We do not claim that there is theoretical support for this extension for the moment.", " We thank the reviewers for their careful reading, comments and suggestions. We have replied to the specific comments of each reviewer separately. We have uploaded an updated version of the submission (and the supplementary material) with the important changes highlighted in red.\n\nShortly after submission, we have realized a mistake in the convergence theorem (Thm. 3.3) which is corrected in the new version. Our error was the following: the function $G$ from Eq.(7) is separately convex in each of its input $\\mu_i$ but it is *not* jointly convex while the proof of Thm 3.3 requires joint convexity. Our fix is the following: instead of using Mean Field Langevin (MFL) to minimize the function $F_0= G+\\tau H$, we apply it to $F_\\epsilon= G + ( \\tau + \\epsilon)H$ and we interpret $F_0=G+\\tau H$ as the convex term instead of $G$ ($F_0$ is indeed jointly convex, see Prop. D.1). This means that we need to add an additional entropic regularization term $\\epsilon H$ in order to have exponential convergence. The original problem (with $\\epsilon=0$) can be minimized using simulated annealing (see the new version of Thm. 3.3).\nNote that in practice, we were already using simulated annealing (SA) to speed-up convergence (App. F), so the change does not significantly impact our numerical experiments. We will add experiments to compare between our previous version of SA (where $\\tau$ decreases towards its final value and $\\epsilon=0$) versus the one recommended by the new theory (where $\\tau$ is fixed and $\\epsilon$ decreases). There is a difference between these two procedures because $G$ also depends on $\\tau$.\n\nWhile this update slightly weakens our results, it also points at the interesting fact that MFL to minimize $F=G+\\lambda H$ enjoys global convergence even when $G$ is non-convex, as long as $G+\\tilde{\\lambda}H$ is convex for some $\\tilde{\\lambda}<\\lambda$ (at least in the compact setting).\n", " The authors consider the problem of finding the dynamics of a population from snapshots of its temporal marginals. They introducing an estimator which which is the sum of the goodness of fit to data term and entropy-based term (a.k.a. prior/regularizer). Instead of minimization of the entropy-regularized functional over the space of all paths, they introduce the “reduced” functional for optimization that includes additional entropy-regularized Optimal Transport problems between intermediate positions. The reformulated problem turns out to be equivalent to the initial problem. This follows from Theorem 3.1 which the authors prove (they call it the Representer theorem as its idea is analogous the idea of the original representer theorem). The resulting “reduced” problem is practically more tractable as it considers only a finite amount of time moments. The authors use Mean-Field Langevin (MFL) dynamics to approach the functional and recover the trajectory of the stochastic process, finding the optimal corresponding marginal distributions simultaneously. In the experimental session, they compare proposed approach with Global Waddington-OT (gWOT) in the simulated and real data experiments in small dimensions. **Strengths**\n\n(1) While most other methods are based on recovering the Waddington potential directly, the current paper uses point of clouds (particles) to recover the desired dynamics.\n\n(2) The theoretical part of the paper is interesting, specifically I would like to highlight the Theorem 3.1 in the spirit of Representer which reduces optimization over paths to optimization over finite products of measure spaces at observation times. Additionally, the paper proves the result on the exponential convergence of the functional which they optimize (Theorem 3.3).\n \n**Weaknesses**\n \n(1) The method is point-cloud-based (particle-based) and it is presumably not very scalable for high dimensions as it would require exponential amount of particles.\n\n(2) The authors claim that existing approaches can be difficult to establish rigorous guarantees and establish guarantees for their method. However, when it comes to practice, it seems like in their method a large gap anyway appears between the theory and practice. For example, Thm. 3.3 is proved for measures, but in practice they are finitly approximated by particles (eq. (12)); entropy term is estimated by the nearest neighbor estimator (line 259); sinkhorn terms are also computed between discrete distributions – all these approximations introduce minor biases here-and-there which raises questions to which extent the proposed theory (Theorem 2.1, 3.3.) is still applicable and advantageous w.r.t. The other methods.\n\n(3) The comparisons are a little bit limited – only the gWOT method is included. What about (some) of the other related methods? Specifically, seems like [6] or [9] might be relevant.\n\n(4) The method has some hyperparameters which are not very clear how to choose.\n\n(5) There is not clear explanation of the final algorithm with description of all the inputs, outputs, parameters, etc. Seems like these details can be collected from the main text and appendix, but this is a negative factor for reproducibility and readability.\n (1) Consistency Theorem 2.1 seems to be formulated in [1] for a different than (3) functional (lines 110-111). Does the consistency hold for (3) which the authors use?\n\n(2) How do you solve numerically PDE (11)? \n\n(3) What is the computational complexity of the proposed method?\n\n(4) How well does the method scale to higher dimensions? It would be great to see the error dynamics on some simulated dataset with the increase of the dimension.\n\n(5) The unbalanced OT appears rapidly and out of nowhere. Is it true that all the theoretical results of the previous sections apply to formulation (14) instead of the original entropic balanced OT?\n The authors sufficiently fully describe the limitations.", " This paper tackles the challenge of recovering the law of a stochastic process from sample observations of its marginals. The authors propose to approximate an existing, continuou-time, consistent estimator minimising a given regularised functional by another reduced, discrete-time estimator defined as the sum of a functional G and an entropy term H. The functional G is built from solutions to Schrodinger bridge problems between consecutive marginals. To obtain the reduced estimator, the authors consider a Langevin SDE of Mc-Kean-Vlasov type and show that its dynamics converge to the unique minimiser of the reduced optimisation problem. Numerical experiments are performed on simulated data from a bifurcating SDE as well as on real-world RNA-sequencing data. Recovering the law of a stochastic process from sporadic observations of its marginals is an important and difficult task, both at a theoretical and practical level, and this work makes good contributions in this direction. I enjoyed reading the paper and found its material original, well-written and the mathematical claims thoroughly justified in the appendix.\n\nOne possible weakness is the scalability of the proposed algorithm to high-dimensional and long trajectories, as noted by the authors themselves in their conclusion.\n Is it possible to provide a more concrete interpretation of the integral in L. 156?\n\nCan you provide additional details or comment on the time- and space-complexities of the proposed algorithm? In particular, how does it scale in the length and dimensionality of the paths?\n\nHow are the regularising constants chosen in the experiments?\n\nIn Figure 1, for large values of N, gWOT seems to start outperforming MFL. Does this trend continue if N is chosen in the order of 10^3, 10^4...?\n\nWould the proposed methodology apply if one considered a different reference measure than Brownian motion (BM)? In particular, what would happen if one considered instead a non-Markovian reference process, for example fractional BM, or other processes with memory?\n\nRegarding benchmarking as well as assessment of the success for the proposed method, have you considered divergences for probability measures supported on pathspace, such as the families of MMD distances studied in [1]?\n\n[1] Salvi, C., Lemercier, M., Liu, C., Horvath, B., Damoulas, T., & Lyons, T. (2021). Higher order kernel mean embeddings to capture filtrations of stochastic processes. Advances in Neural Information Processing Systems, 34, 16635-16647. As the authors highlight in their conclusion, the proposed algorithm suffers from the typical drawbacks of min-entropy estimators which makes it not scalable to high-dimensional problems.", " In this work authors study the problem of fitting a law on the path space induced by gradient SDE with additive and reflective Brownian motion to the set of prescribed time marginals. This is similar to multi-marginal OT with a difference the transport plan is restricted the be the law induced by an SDE. The problem has been recently studied in Lavenant et al where, essentially, an estimator used in the current paper has been developed and analysed. Authors observed (which is not new) that one can translate entropic optimisation problem on the Wiener space (as in Lavenant et al.) to the optimisation problem on the product space of probability measures supported on the compact set \\mathcal X (the compactness being a technical condition). This reformulation then open the avenue for mean-filed langevin dynamics (MFLD) (or gradient flow on W_2 space) to be used as an optimisation ‘algorithm’ for which convergence along with the convergence speed can be deduced from recent works in the literature. Indeed mean-filed langevin dynamics has been recently studied by Mei et al (2018) and Hu et al (2019) where convergence has been proved rigorously. These result have been recently extended by Chizat 2022 and Nitanda et al 2022 that showed that under appropriate conditions convergence of MFLD is exponential. In the current paper authors showed, by assuming compactness of the space \\mathcal X, that results of Chizat and Nitanda et al apply. \n\nIt’s worth remarking that conceptually this work is related to ‘Mean-Field Neural ODEs via Relaxed Optimal Control’ by Jabir at al 2019 and \n‘Gradient Flows for Regularized Stochastic Control Problems’ by Siska et all 2020, where detailed analysis of coupled MFLD has been studied. In these works the cost function was slightly simpler and significant amount of regularisation was required to establish convergence. \n Strengths:\n- Very interesting contribution tackling difficult problem of proving convergence rates for gradient flow algorithms for the inference on the path space. \n- The paper is (mainly) well written making highly technical material accessible to broad audience \n- cell-RNA sequencing is a very promising area of applications for the ML models and I anticipate significant impact of this work on it\n\nWeaknesses:\n- The compactness of \\mathcal X is not a natural assumption but seem necessary for the analysis to go through \n- Some parts of the proofs are written in haste and I would appreciate more details (see comments bellow)\n- When citing other works, especially in the proofs, please give exact detail of the results used rather than just the name of the paper… - It wasn’t clear where in the proof you used the fact that only SDE with drift of grade it type are needed? I would appreciate more discussion on that in the appendix \n- When stating theorems please make sure assumptions are clearly stated \n- In eqn 10 reflected BM is used. How do I know X lives in \\mathcal X ? Don’t I need to consider Skorohod problem?\n- Similarly to derive 11 from 10 Ito formula is used. Please Don’t you need Ito-Tanaka formula here? \n- Proof of Lemma B.2 : for completes please provide more details rather then just citing [21] and [23]\n- In deriving LSI compactness of \\mathcal X is critical. Can you comment more about the constants how the diameter of D affects convergence ?\n- please provide more details in the proof of Proposition D.1 rather than just citing other’s people work. That will make the paper easier to read. \n Mathematically main limitation is the compactness of \\mathcal X, but the result is still very interesting." ]

[ -1, -1, -1, -1, -1, -1, 5, 7, 8 ]

[ -1, -1, -1, -1, -1, -1, 3, 4, 5 ]

[ "hBUYRpH2t6", "FoBqzat1scU", "zbqwxAqwhw", "S9lgAihtW_", "EdiYctKNv-", "nips_2022_Mftcm8i4sL", "nips_2022_Mftcm8i4sL", "nips_2022_Mftcm8i4sL", "nips_2022_Mftcm8i4sL" ]

[ "hx0NZ3PyTq2", "ziv4uBJfu3S", "VZRJF8UgfOD", "CiymgoahqJs", "eDftctIi9Lm", "Hp9FVPnvnJQ", "wq1fM92_-j1", "covoajdZpvR", "e8pLsN2czLx", "-vEU8AuO3M_", "LdZCnPe-EWs" ]

[ "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I highly value this work due to its novelty and promising improvements. I read other reviewers' comments and the rebuttal, and find that the authors have carefully and adequately addressed all my concerns. This work is the best tracking paper among ones that I have reviewed in NeurIPS. Thus, I keep my original rating as strong accept.", " We thank you for the precious review time and valuable comments. We have provided corresponding responses and results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.", " We appreciate your careful review and thoughtful comments. We are encouraged and grateful that the reviewer found our approach to be well-motivated, neat and inspiring. Below, we address the concerns that were raised.\n\n***\n***Q1: Why does not the pseudo language description generated by an image caption model show significant improvements?***\n\n**A1**: Thanks for this insightful comment. The reason lies in the domain gap between tracking datasets and existing image caption datasets, which results in poor quality of the generated language description by image caption model (e.g., [*1]) for tracking. For example, the official annotation for the first row in Fig. 7 of the supplementary material is \"black bird standing on the ground\", while the caption model [*1] generates the language description \"A blurry image of a person and a cat\", which is inaccurate in describing the scene. As a consequence, the usage of such inaccurate language description by the image caption model may introduce noise into training and testing of the tracker, leading to inferior performance. To make it clear, we will add clarification on this point in revision. Thanks, again.\n\n***\n***Q2: More examples such as conducting more experiments on additional pure CNN-based frameworks like SiamRPN++?***\n\n**A2**: Thanks for this constructive suggestion. As suggested, we apply our method on SiamRPN++ to develop the new VL tracker VLT_RPN++ and show the comparison in Tab. #1. As shown in Tab. #1, compared with the baseline SiamRPN++, the proposed VLT_RPN++ achieves considerable SUC gains of 9.4%/4.5% on LaSOT/TNL2K, respectively, which demonstrates the effectiveness and generalization of our multimodal VL representation in improving tracking. We will include the results and comparison in revision. Thanks.\n\n**Table #1**: Comparison bettwen VLT_RPN++ and its baseline SiamRPN++.\n| # | Method | LaSOT | LaSOT | TNL2K | TNL2K |\n| :-: | :-: | :-: | :-: | :-: | :-: |\n| | | SUC (%) | P (%) | SUC (%) | P (%) |\n| 1 | VLT_RPN++ | 59.0 | 62.6 | 45.8 | 47.4 |\n| 2 | SiamRPN++ | 49.6 | 49.1 | 41.3 | 41.2 |\n\n***\n***Q3: Add qualitative comparison with other sota methods.***\n\n**A3**: Thanks for this comment. As suggested, we update the supplementary material by adding qualitative results and comparison with other SOTA trackers in Fig. 6. Please kindly check the updated supplementary material for reference. Thank you.\n\n***\n***Q4: (1) For experiments with partial language (50% and 75%) in the supplementary material, how do you determine the which 50% or 75% should be used? (2) If you randomly generate it, it will be better to do multiple (e.g., 3) times of experiments.***\n\n**A4**: Sorry for the confusion. **(1)** For experiments with partial language, we generate the training date by sampling from each language-annotated datasets randomly based on the ratio setting. For example, for 50% language-annotated data, we randomly sample 50% of the data from each dataset. The procedure is the same for other settings. **(2)** Consider the randomness, the experiments are repeated for multiple times. We will clarify this in revision. Thanks.\n\n***\n\n***Q5: I don’t see the discussion related to the limitations and broader impact.***\n\n**A5**: Thanks for this helpful comment. One limitation of our work (also for other existing VL trackers) lies in the lack of language-annotated tracking datasets (only 1.7%), which is crucial to train an effective vision-language tracker. To remedy this issue, in our paper, we try to generate language descriptions for training videos with an image caption model [*1]. However, due to the large domain gap, the caption model shows unsatisfactory generation quality, which stops the step to enjoy benefits from huge scale multimodality training as in other VL tasks. In the follow-up work, we will address this problem.\n\n\n[*1] Radford et al. Learning transferable visual models from natural language supervision. In ICML 2021.\n***", " We thank the reviewer for providing valuable and thoughtful comments on our work. We provide our responses below to address the reviewer’s concerns, and remain committed to clarifying further questions that may arise during the discussion period.\n\n***\n***Q1: Different training data for the proposed trackers and baselines.***\n\n**A1**: Thanks for this helpful comment. As suggested, we retrain VLT_SCAR and VLT_TT and their baselines with the same data setting to ensure a fair comparison. The results are listed in Tab. #1:\n\n(1) We retrain SiamCAR with the same data setting of VLT_SCAR (#3 vs #5). Compared to the default setting (#1), double data volume and three more data sources contain different biases, which affect the trained model to produce biased outcomes, as illustrated in [*1-*3]. From the results (#3), the addition of TNL2K training set significantly improves the default #1 with 4.4% gains in SUC on TNL2K, whereas the performance on LaSOT slightly decreases. Compared to VLT_SCAR with the same setting (#5), #3 is still suppressed for 8.6%/7.4% of SUC and P on TNL2K, respectively. \n\n(2) We also retrain VLT_SCAR with the only LaSOT training set (#4), which keeps aligned with #2. The SUC scores on LaSOT and TNL2K degrade heavily to 57.0%/39.0% compared to the default #5, respectively. **This is caused by the great reduction of the language-annotated training data, i.e., from 1120(LaSOT)+1300(TNL2K)+9335(GOT-10k) to 1120(LaSOT).** Our model is hard to learn a good multimodal representation with the quite less language-annotated training data, which violates our intention. Even though, our VLT_SCAR (#4) still outperforms the baseline SiamCAR (#2) for 5.4%/4.0% of SUC scores on LaSOT/TNL2K.\n\n(3) TransT is also retrained with the same data setting as VLT_TT (#7 vs #8). More data sources bring similar biases and influence the performance as SiamCAR, compared to default TransT (#6). Our VLT_TT (#8) still achieves superior scores on both LaSOT and TNL2K.\n\nWe will include the results and comparison in revision. Thanks.\n\n**Table #1**: Comparison with different data volumes and sources.\n| # | Method | Data Volume | Data Source | LaSOT | LaSOT | TNL2K | TNL2K |\n| :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: |\n| | | | | SUC (%) | P (%) | SUC (%) | P (%) |\n| 1 | SiamCAR | 60W×20Epoch | VID, YTBB, DET, COCO | 50.7 | 51.0 | 35.3 | 38.4 |\n| 2 | SiamCAR | 60W×20Epoch | LaSOT | 51.6 | 52.3 | 35.0 | 36.4 |\n| 3 | SiamCAR | 120W×20Epoch | VID, YTBB, DET, COCO, GOT-10K, LaSOT, TNL2K | 48.7 | 46.6 | 39.7 | 39.2 |\n| 4 | VLT_SCAR | 60W×20Epoch | LaSOT | 57.0 | 58.6 | 39.0 | 39.8 |\n| 5 | VLT_SCAR | 120W×20Epoch | VID, YTBB, DET, COCO, GOT-10K, LaSOT, TNL2K | 63.9 | 67.9 | 48.3 | 46.6 |\n| |\n| 6 | TransT | 3.8W×1000Epoch | COCO, GOT-10K, LaSOT, TrackingNet | 64.9 | 69.0 | 50.7 | 51.7 |\n| 7 | TransT | 3.8W×1000Epoch | COCO, GOT-10K, LaSOT, TrackingNet, TNL2K | 62.2 | 65.2 | 51.2 | 52.3 |\n| 8 | VLT_TT | 3.8W×1000Epoch | COCO, GOT-10K, LaSOT, TrackingNet, TNL2K | 67.3 | 72.1 | 53.1 | 53.3 |\n\n[*1] Chang et al. Active bias: Training more accurate neural networks by emphasizing high variance samples. In NeurIPS 2017.\n\n[*2] Kim et al. Learning not to learn: Training deep neural networks with biased data. In CVPR 2019.\n\n[*3] Mehrabi et al. A survey on bias and fairness in machine learning. In CSUR 2021.\n\n***", " ***Q2: (1) Modality Mixer is too simple to be the main contribution. It’s cross-modal channel attention. The authors attempted to make the structure more complex by designing a residual connection. (2) Ablation analysis is required for the Modality Mixer.***\n\n**A2**: **(1)** We have somehow different opinions on the statement of \"Modality Mixer is too simple to be the main contribution\". First, it is not \"too simple\". Indeed, the Modality Mixer (ModaMixer) contains three components, including (i) cross-modal channel attention, (ii) asymmetrical searching strategy (ASS) and (iii) residual connection. The cross-modal channel attention is used to interact two modalities, the ASS to search adaptive structures for different modalities, and the residual connection to enhance fused representation. Although the implementations of these components seem simple, the idea or insight inside the ModaMixer is NOT simple, which is evidenced by its effectiveness in improving tracking performance.\n\nIn addition, the usage of \"residual connection\" is not intended to make the structure of ModaMixer more complex. Instead, it is designed to avoid losing informative vision details and mitigate the noise or bias that may exist in language description, with the goal of further improving performance. In fact, many well-known works such as Transform [*1] utilize the similar idea for the same purpose. \n\nWe thank the reviewer for this comment and will add clarification in revision to make it more clear.\n\n[*1] Vaswani et al. Attention is all you need. In NeurIPS 2017.\n\n**(2)** We appreciate this insightful comment. As suggested, we have conducted ablation experiments for the ModaMixer. In specific, we analyze the cross-modal channel attention and the residual connection in ModaMixer. The experiments are conducted with the \"template\" setting and results are shown in Tab. #2.\n\nFrom Tab. #2, we can see that, when using only cross-modal channel attention (i.e., VLT_SCAR w/o Residual Connection), the performance is increased by 9.0%/7.0% from 52.1%/40.7% to 61.1%/47.7% in SUC on LaSOT and TNL2K, showing the effectiveness of multimodal fusion. In addition, when adding residual connection (i.e., VLT_SCAT by default), the performance is further improved by 2.8%/2.1% from 61.1%/47.7% to 63.9%/49.8%, which verifies the importance of residual connection in ModaMixer. Based on this ablation analysis, we argue that final improvement by ModaMixes can be attributed to both multimodal fusion and the usage of residual connection, along with ASS (see ablation experiment in Tab. 3 of the manuscript). We will include the ablation experiments with analysis in revision. Again, thanks.\n\n\n**Table #2**: Ablation studies on ModaMixer.\n| # | Method | Setting | LaSOT | LaSOT | TNL2K | TNL2K |\n| :-: | :-: | :-: | :-: | :-: | :-: | :-: |\n| | | | SUC (%) | P (%) | SUC (%) | P (%) |\n| 1 | VLT_SCAR | w/o. Cross-modal Channel Attention and Residual Connection | 52.1 | 50.6 | 40.7 | 40.2 |\n| 2 | VLT_SCAR | w/o. Residual Connection | 61.1 | 63.6 | 47.7 | 48.1 |\n| 3 | VLT_SCAR | default | 63.9 | 67.9 | 49.8 | 51.1 |\n\n***", " ***Q3: Ablation experiments of using a 0-tensor or a visual pooling feature for inference are required.***\n\n**A3**: Thanks for this constructive comment. We agree that, in order to validate the effectiveness of modal fusion, it is crucial to conduct the ablation experiments of using a 0-tensor or a visual pooling feature for inference (as discussed in Tab. 5 (c) of the manuscript). As suggested by the reviewer, we conduct such an ablation as shown in Tab. #3. From Tab. #3, we can see that, when removing language from the tracking inference, the performance of VLT_SCAR heavily drops from 65.2%/48.3% to 50.8%/39.5% in SUC on LaSOT/TNL2K under 0-tensor setting, and 63.9%/49.8% to 53.4%/41.1 under template (i.e., visual pooling feature) setting. Likewise, without language for tracking, the performance of VLT_TT drops from 66.3%/52.2% to 60.7%/48.2% in SUC on LaSOT/TNL2K under 0-tensor setting, and 67.3%/53.1% to 61.0%/49.1% under template setting. All this reveals the importance of linguistic cues for tracking and shows that the learned representations are indeed multi-modal representations. \n\nWe thank the reviewer again and will include all the results with analysis in revision.\n\n**Table #3**: Ablation experiments of using a 0-tensor or a visual pooling feature (i.e., template in the table) for tracking.\n| # | Method | Setting | Language | LaSOT | LaSOT | TNL2K | TNL2K |\n| :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: |\n| | | | | SUC (%) | P (%) | SUC (%) | P (%) |\n| 1 | VLT_SCAR | 0-tensor | w/o. language (i.e., inference with 0-tensor only) | 50.8 | 52.6 | 39.5 | 41.2 |\n| 2 | VLT_SCAR | 0-tensor | w/. language | 65.2 | 69.1 | 48.3 | 46.6 |\n| 3 | VLT_SCAR | template | w/o. language (i.e., inference with template only) | 53.4 | 54.6 | 41.1 | 42.9 |\n| 4 | VLT_SCAR | template | w/. language | 63.9 | 67.9 | 49.8 | 51.1 |\n| |\n| 5 | VLT_TT | 0-tensor | w/o. language (i.e., inference with 0-tensor only) | 60.7 | 63.1 | 48.2 | 46.8 |\n| 6 | VLT_TT | 0-tensor | w/. language | 66.3 | 70.5 | 52.2 | 52.1 |\n| 7 | VLT_TT | template | w/o. language (i.e., inference with template only) | 61.0 | 63.4 | 49.1 | 48.3 |\n| 8 | VLT_TT | template | w/. language | 67.3 | 72.1 | 53.1 | 53.3 |\n\n***", " We appreciate the reviewer for the encouraging comments and constructive suggestions, and provide our responses below to address the reviewer's questions and concerns.\n\n***\n***Q1: The results of same algorithms should come from the exact same network structure, otherwise, they should be shown separately. For the same reason, the result of TNL2K in table 3(48.3/46.6) is different from it in Table 2(49.8/51.0).***\n\n**A1**: Thanks for this helpful comment. We show the detailed results of VLT_SCAR and VLT_TT under different settings (i.e., using \"0-tensor\" and \"template\", respectively), in Tab. #1. To make the results more comprehensive and consistent, as suggested, we will include the results in Tab. #1 into Tab. 2 of the manuscript in revision. Again, thanks.\n\n**Table #1:** Detailed results of VLT_SCAR and VLT_TT using \"0-tensor\" and \"template\", respectively.\n| # | Method | Setting | LaSOT | LaSOT | LaSOTExt | LaSOTExt | TNL2K | TNL2K | GOT | GOT | OTB99L | OTB99L |\n| :-:| :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: |\n| | | | SUC (%) | P (%) | SUC (%) | P (%) | SUC (%) | P (%) | AO (%) | SR0.5 (%) | SUC (%) | P (%) |\n| 1 | VLT_SCAR | 0-tensor | 65.2 | 69.1 | 41.2 | 47.5 | 48.3 | 46.6 | 61.4 | 72.4 | 72.7 | 88.8 |\n| 2 | VLT-SCAR | template | 63.9 | 67.9 | 44.7 | 51.6 | 49.8 | 51.1 | 61.0 | 70.8 | 73.9 | 89.8 |\n| |\n| 3 | VLT_TT | 0-tensor | 66.3 | 70.5 | 45.4 | 52.1 | 52.2 | 52.1 | 68.4 | 81.5 | 74.7 | 91.2 |\n| 4 | VLT_TT | template | 67.3 | 72.1 | 48.4 | 55.9 | 53.1 | 53.3 | 69.4 | 81.1 | 76.4 | 93.1 |\n\n\n***\n***Q2: This paper doesn't clearly state how to get the language description of a template during inference.***\n\n**A2**: Sorry about this. The language description of the template comes from the annotation of the benchmark, which is the same as in other vision-language trackers (e.g., [17, 18] in the manuscript). Please note, the language description is only given in the first frame of a video. For datasets without official language description, we have designed two strategies as discussed in Tab. 5 (c) of the manuscript (e.g., not using language description or generating the language description with a caption model [*1]). We will clarify this point in the revision by adding more explanation. Thanks.\n\n[*1] Radford et al. Learning transferable visual models from natural language supervision. In ICML 2021. \n\n***", " ***Q3: If the language description (in Q2) is from annotation or manual setting, it is not reasonable enough to compare results with algorithms that do not use language features.***\n\n**A3**: Thanks for this insightful comment. The goal of our work is to demonstrate the power of language description (given only in the first frame of a video) in improving video object tracking. For this purpose, we compare the proposed VLT with (1) its CNN (or Transformer)-based baseline, (2) other CNN (or Transformer)-based state-of-the-art (SOTA) trackers, and (3) other vision-language (VL) trackers, as in Tab. 2 of the manuscript. \n\nThe comparison with (1) is to show the performance improvement gained over the baseline method by leveraging linguistic information, which verifies the effectiveness of our method. The comparison with (2) is to demonstrate that our method can mitigate the huge gap between VL tracker and recent vision-only SOTAs, which shows its potential in further improving tracking. The comparison with (3) is to validate the effectiveness and superiority of our vision-language representation. Considering these reasons, we believe that it is necessary and reasonable to compare our method with various trackers, including its baseline, other vision-only and vision-language trackers, as in other VL trackers (e.g., SNLT [18]).\n\nWe thank the reviewer again and will include the above explanation in revision.\n\n***\n***Q4: The article does not include a discussion of solving common tracking problems such as target deformation and occlusion.***\n\n**A4**: Thanks for the thoughtful comments. Indeed, in Section A.12 (\"Attribute-based Performance Analysis\") of the supplementary material, we show the improvements of our method in various challenges (or the so-called attributes), including deformation, occlusion, background clutter, viewpoint change, etc, owing to the robust representation learned by our approach. The detailed SUC scores are listed in Tab. #2. With the proposed multimodal representation learning, VLT_SCAR significantly improves the baseline SiamCAR for 15.9%/15.8%/16% on the attributes of deformation, partial occlusion and full occlusion. VLT_TT also brings 1.7%/3.0%/2.8% gains compared to the baseline TransT. We will include the results and more quantitative and qualitative analysis in revision to discuss how our method solves common tracking challenges. Thanks, again.\n\n\n**Table #2:** SUC scores (%) on LaSOT under attributes of Aspect Ration Change (ARC), Low Resolution (LR), Our-of-View (OV), Fast Motion (FM), Full Occlusion (FO), Scale Variation (SV), Viewpoint Change (VC), Background Clutter (BC), Rotation (Rot), Camera Motion (CM), Motion Blur (MB), Deformation (Def), Partial Occlusion (PO) and Illumination Variation (IV).\n| # | Method | ARC | LR | OV | FM | FO | SV | VC | BC | Rot | CM | MB | Def | PO | IV |\n| :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: |\n| 1 | VLT_SCAR | 61.8 | 54.6 | 53.0 | 45.8 | 53.4 | 63.7 | 60.6 | 58.6 | 64.0 | 65.2 | 60.7 | 66.3 | 61.5 | 65.1 |\n| 2 | SiamCAR | 45.9 | 38.5 | 41.0 | 31.7 | 37.4 | 48.4 | 43.9 | 42.2 | 46.9 | 51.7 | 46.4 | 50.4 | 45.7 | 53.3 |\n| 3 | SNLT | 51.8 | 46.7 | 46.4 | 38.4 | 42.6 | 53.8 | 54.2 | 49.2 | 52.6 | 57.6 | 51.8 | 55.5 | 49.3 | 60.6 |\n| |\n| 4 | VLT_TT | 65.6 | 59.0 | 58.9 | 50.6 | 58.1 | 67.1 | 65.6 | 62.0 | 67.2 | 68.4 | 65.7 | 68.7 | 65.0 | 64.1 |\n| 5 | TransT | 63.2 | 56.4 | 58.2 | 51.0 | 55.3 | 64.6 | 61.7 | 57.9 | 64.3 | 67.2 | 63.0 | 67.0 | 62.0 | 65.2 |\n| 6 | TrDiMP | 62.6 | 58.8 | 61.0 | 54.0 | 56.7 | 63.6 | 62.6 | 59.9 | 62.5 | 68.5 | 62.9 | 64.7 | 61.5 | 67.5 |\n\n***\n***Q5: The introduction of the template update module may have better results on some samples.***\n\n**A5**: We agree with the reviewer and appreciate this constructive suggestion. Incorporation of temporal cues can further improve the adaption of the tracker in target localization. However, to ensure fair comparison with our baseline trackers SiamCAR and TransT and other VL tracker SNLT (these three trackers do not use the template update), this update mechanism is currently not applied in our method. We leave this as the future work. Thanks.\n\n***", " This paper proposes a tracking algorithm by designing a ModaMixer and asymmetrical networks to learn unified-adaptive VL representation. The combination of the two modules gives very good results. Applying language features to tracking tasks is a very reasonable and innovative multimodal learning algorithm. Strengths\n•\tThe paper is clearly written.\n•\tResults greatly improve the performance and seems achieve SOTA.\n•\tThe paper has adequate ablation experiments.\n\nWeaknesses\n•\tI noticed that the results in Table 2 used different settings(0-Tensor vs Template). The author just lists the best results, the results of same algorithms should come from the exact same network structure, otherwise, they should be shown separately. For the same reason, the result of TNL2K in table 3(48.3/46.6) is different from it in Table 2(49.8/51.0).\n This paper doesn't clearly state how to get the language description of a template during inference. If the language description is from annotation or manual setting, it is not reasonable enough to compare results with algorithms that do not use language features. The article does not include a discussion of solving common tracking problems such as target deformation and occlusion. The introduction of the template update module may have better results on some samples.", " This paper proposes an interesting solution to show how to achieve state-of-the-art (sota) tracking performance without relying on the complex Transformer architecture in visual tracking. Specifically, the authors explore a unified multimodal learning of vision and language under the simple ConvNets for tracking. The authors first give an in-depth analysis of the limitations of previous solutions and then introduce an innovative unified framework that learns better vision-language (VL) representation by proposing ModaMixer and asymmetrical searching strategy (ASS). The former well enhances the interaction inside vision-language for discriminative representation, while the later improves the adaption of the learned VL representation by ModaMixer. Extensive experiments on five challenging datasets demonstrates that, the proposed method improves a pure CNN-based baseline to be competitive and even better than recent Transformer-based counterparts. Moreover, the proposed method is general and can also be applied to improve Transformer tracking architecture, as shown by experiments. In addition, some theoretical analysis is given to explain the effectiveness of the proposed method. Strengths\n\nOverall, I am rather positive on this paper. In particular, I really like the motivation of this work that aims at finding alternative path, instead of relying on Transformer architecture (although it is shown to be powerful), to achieve sota tracking by exploring the almost ignored multimodal learning, which I believe can inspire many other works on tracking and facilitates this field. The strengths in this work include:\n\n(1) Novelty. This paper introduces an innovative framework of multimodal vision-language learning (VL) for object tracking. The proposed ModaMixer enables a good interaction between the two modalities throughout the whole network, which is completely different from other works that only interact two modalities at the result fusion stage. In addition, another novel point is the proposed ASS that adapts the representation of different branches and modalities in an asymmetrical way. Compared with the conventional symmetrical way, ASS is the first time to show the asymmetrical architecture may be more suitable for representation learning in tracking and may provide new insights to future research. I like these novel ideas in this work.\n\n(2) Good performance. This paper demonstrates excellent performance in improving the simple pure CNN-based tracking baselines. In specific on the challenging LaSOT, the proposed approach improves the baseline from 50.7% to 65.2% in SUC with absolute 14.5% gains, which is competitive and even better than recent Transformer-based trackers. Compared to previous best VL method with 54.0% SUC, this paper shows 11.2% improvement. The performance on other benchmarks is also sota. This excellent performance clearly shows the effectiveness and advantages of the proposed method.\n\n(3) Generality. The proposed method is general and not limited to CNN-based framework. The authors show this point by applying their methods on a Transformer-based tracking framework and show promising improvements on all the five challenging benchmarks, which is consistent with the improvements shown for CNN-based framework.\n\n(4) Rich experiments and analysis. The authors provide extensive experiments and analysis for the proposed method. I appreciate this. The experimental analysis with various ablation studies allows a better understanding of each module and overall performance, and the theoretical analysis gives an explanation why the proposed method works well in improving tracking performance.\n\n(5) Good writing and organization. This paper is well written and organized. Each section has a clear motivation. It’s easy to follow the ideas. I enjoy reading the paper.\n\nOverall, I believe this paper is significant to the visual tracking community because it shows new insights and directions in designing simple but effective tracking framework with sota performance.\n\nWeaknesses\n\nAlthough this paper is technically sound and novel, I have some minor concerns or questions.\n(1) In this work, language is crucial. I noticed that in the experiment the pseudo language description generated by an image caption model does not show significant improvements. What do you think are the reasons causing this?\n(2) The proposed method is shown to be general, which is nice. However, it will be great if the authors can show more examples such as conducting more experiments on additional pure CNN-based frameworks like SiamRPN++ (Li et al, CVPR, 2019).\n(3) The authors show many comparisons with other sota methods. But I don’t see qualitative comparison with other approaches. It will be nice to see these results and comparison to other sota methods.\n(4) For experiments with partial language (50% and 75%) in the supplementary material, how do you determine the which 50% or 75% should be used? Randomly generating? If you randomly generate it, it will be better to do multiple (e.g., 3) times of experiments. \n See Weaknesses. I don’t see the discussion related to the limitations and broader impact. I hope the author can provide a brief discuss on this part in the response and are encouraged to detail this part in the revision.", " This paper proposes a method to learn the vision-language representation for achieving SOTA tracking by using pure ConvNets. It proposes a modality mixer as the fusion module and uses it in both low-level ConvStages and high-level ConvStages to explore the complementarity of different modalities. It also uses NAS to search an asymmetrical siamese network to learn adaptive vision-language representations. The proposed method is also used to improve a Transformer-based tracker. Strengths: \n+The proposed method can make a CNN-based tracker and a Transformer-based tracker achieve SOTA performance on five benchmarks. The performance of vision-language tracking is improved largely.\n\n+This work uses NAS for tracking to search different model structures for template and search region respectively. This is a novel practice for siamese trackers.\n\n Weaknesses: \n-The proposed trackers and the baselines use different training data. The comparisons in this paper are unfair. For instance, both SiamCAR and TransT didn’t use TNL2K for model training, they shouldn’t be used as the baselines for comparison on TNL2K. SiamCAR only uses the LaSOT training set for model learning to achieve 50.7SUC. But the proposed trackers use lots of extra training sets. So the performance gains shown in Figure1 are debatable, and the current ablation study cannot show the effectiveness of the proposed method.\n\n-Modality Mixer is too simple to be the main contribution. It’s cross-modal channel attention. The authors attempted to make the structure more complex by designing a residual connection. But this modification brings some doubts about the effectiveness of the cross-modal channel attention. We don’t know whether the final improvements can be attributed to the modal-fusion or the pure vision feature. This paper didn’t provide any ablation analysis about it. The current experiments are not sufficient.\n\n-This paper proposes a VL representation learning method for object tracking. But half training pairs don’t have a language description, and the authors use the 0-tensor or the visual feature as the pseudo language description for training. It's doubtful that the learned representations are really multi-modal representations. The authors conducted an experiment by removing the description to prove the effectiveness of modal fusion. But how about using a 0-tensor or a visual pooling feature for inference? The current experiments are insufficient. -The proposed trackers and the baselines should be trained with the same training set.\n-More quantitative studies about the modality mixer should be supplemented.\n-During inference, using the 0-tensor or the visual pooling feature for further analysis.\n-See weaknesses. N/A" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 6, 8, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 5 ]

[ "VZRJF8UgfOD", "LdZCnPe-EWs", "-vEU8AuO3M_", "LdZCnPe-EWs", "LdZCnPe-EWs", "LdZCnPe-EWs", "e8pLsN2czLx", "e8pLsN2czLx", "nips_2022_NhrbIME2Ljl", "nips_2022_NhrbIME2Ljl", "nips_2022_NhrbIME2Ljl" ]

[ "oY4qxj0EmKv", "wlCPfY5CuCN", "clLgt4ykSVf", "BZLRkgAb-r0", "c6czX2E9hhp", "mfg7V2LxBi", "GbpUiXOW7B", "AH0VNcK4abc", "lo6A3sO6LI", "WiNyOfOwdLN", "K59pMKllt7S" ]

[ "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for the response. I do hope that the final text incorporates the additional explanations/results:\na) Includes the extended version of Tab2 reported above instead of only the MSN-H dataset\nb) has a more qualified statement on the speedup\n\nOverall, I would like to keep my current rating as I believe this paper presents a simple and sensible approach which the community should see.", " Thank you for the comments and visualizations, they explain the mismatch! I feel like FG-ARI might introduce some bias into the evaluation by explicitly ignoring background errors. But given its common use, it makes sense to report it. Even with slightly lower quality of the Slot-Mixer for some object boundaries (e.g. second example of the first linked image), the improved efficiency still makes the proposed approach valuable. Hence, I keep my rating of 7 after reading the other reviews and comments.", " We thank the reviewer for the positive feedback.\n\n**Related work on 3D object discovery**\n\nWe thank the reviewer for the references to additional related works. ROOTS [1*] and INFERNO [2*] are indeed closely related in that they address a similar problem, yet target significantly simpler experimental settings and datasets compared to our work. As such, we find that uORF [34] and ObSuRF [27] serve as better representatives for our setting: only they have been demonstrated on data of significantly higher visual complexity than CLEVR.\n\nWe will add these references and further update our literature review to include OCIG [3*] and other related methods from Sungjin Ahn’s lab.\n\n\n**Comparison to uORF and dataset complexity**\n\nWe would like to underline that the positive result of uORF on the visually more complex dataset in their paper is limited to using only a single class of objects (chairs). In this setting, the authors achieve strong results when limiting the data to a single model of a simple chair rendered in various colors, while segmentation quality already drops significantly when moving to multiple different chair shapes (see Tab. 2 in the uORF paper).\n\nIn terms of dataset complexity, we disagree with the statement that the MSN-H dataset is similar to datasets investigated in uORF. MSN-H is of substantially higher complexity even without considering the number of objects per scene: it contains diverse objects sampled from all ShapeNet classes (~51k unique objects, only novel objects in the test set) in random poses, 382 different realistic HD outdoor backgrounds (as opposed to 50 floor textures in uORF’s most complex dataset), and further contains significantly more challenging camera angles. We believe that this makes MSN-H a more suitable choice for studying the capabilities and limits of this class of models. To study model behavior in datasets with fewer objects per scene, we chose two representative datasets with varying levels of object complexity: CLEVR-3D and MSN-E.\n\n**Background handling in OSRT**\n\nSimilar to most methods utilizing Slot Attention (including the original paper [17] and ObSuRF [27]), we do not handle backgrounds in a special way: any slot can bind to (parts of) the background, and we typically find that it is captured by slots that do not bind to objects otherwise. Hence in practice, we choose to have at least 1 slot more than the maximum number of objects that we would like to model in a scene.\n\nuORF [34] assigns a specific slot to handle the background, but their approach requires additional supervision (e.g. in the form of the bounding box of the scene in which objects can appear). We found this solution to be unsatisfactory as it makes strong assumptions about the scene layout, but we agree that a general form of explicit background handling in slot-based models is an interesting avenue for future work.\n\n\n**Segmentation evaluation**\n\nAs the background itself can have compositional structure, we find that the full ARI score (i.e. ARI that is evaluated on all pixels including background pixels) is not an ideal metric for evaluation of object-centric models in our settings, as it strongly discounts discovered solutions that separate the background into meaningful parts. In line with prior work, we therefore choose FG-ARI as our main metric for evaluating unsupervised scene decomposition into objects. We will add (non-FG) ARI results to the paper if space permits, and otherwise to the appendix.\n\n\n**Learned vs. random slot initialization**\n\nThe question whether using learned (as opposed to random) slot initializations affects generalization to a different number of objects at test time in OSRT is indeed very interesting. Please note that the original Slot Attention paper already proposed both settings of using random vs. learned slot initializations, i.e. this is not one of our novel contributions. To analyze this in OSRT, we perform the following experiment: we trained OSRT either with 7 randomly initialized slots, or with 11 slots using a learned initialization, on CLEVR-3D scenes containing up to 6 objects.\nAt test time, we evaluate on scenes containing 7-10 objects by using 11 slots for both model variants. We find that in this setting, generalization performance in terms of PSNR and FG-ARI is similar for both models with a slight advantage for the model variant with random slot initialization. In terms of in-distribution performance, learned initialization appears to have an advantage in both metrics.\n\n\n|3-6 objects (iid)|PSNR|FG-ARI|\n|-------------------|-------|--------|\n|Learned init.|40.84|0.996|\n|Random init.|38.14|0.988|\n\n\n|7-10 objects (ood)|PSNR|FG-ARI|\n|--------------------|-------|--------|\n|Learned init.|33.03|0.955|\n|Random init.|33.36|0.968|\n\nWe generally found that learned slot initializations resulted in more stable training, especially on the more complex datasets, hence we opted for this as our default setting.\n", " We thank the reviewer for the positive feedback.\n\n**Qualitative vs. quantitative results for Slot Mixer and Spatial Broadcast decoders**\n\nWe understand the reviewer's concerns about the apparent mismatch between qualitative and quantitative results. When visualizing unsupervised scene decomposition results qualitatively, a balance has to be struck between accurately visualizing the quantity that the ARI metric evaluates, and more intuitive visualizations that can appear less misleading. In the draft, we have chosen to visualize hard masks, i.e. for each pixel, we identify the **single** most relevant slot and color it accordingly. Note that the ARI metric follows the same scheme by taking an argmax for evaluation, therefore assuming that each pixel can only belong to a single slot.\n\nAs to the apparent mismatch between qualitative results and the FG-ARI metric, we would like to emphasize that this commonly used metric only evaluates foreground objects, as background segmentation is ambiguous. Visualizing only the evaluated areas of the images by masking out the background areas leads to the following visualizations that are more in line with the quantity that FG-ARI measures (\"Masked Hard Seg.\" column):\n\nhttps://anopic.us/mM2Chkmpjifvc7TfYy70WkAxIw7K0vtUQXcis7qd.png\n\nhttps://anopic.us/92Buxt3gjXceYGHLHJEAFVLwN1YH1Y3ALmzfsNEj.png\n\nhttps://anopic.us/4aGAXPKkHfCzmSAcxBEGyPokVMfzVO85bNRRwWzT.png\n\nWe observe that the Spatial Broadcast decoder makes some mistakes along the object boundaries, leading to very slightly lower FG-ARI on this dataset.\n\nFurther, due to always using 32 slots for all MSN-H scenes, multiple slots are free to capture the background in scenes with fewer objects. In practice, we find that this results in background pixels being shared “softly” by multiple slots – a detail that is lost in our argmax-based visualization. In addition to the hard masks as in the paper (\"Paper Figure\" column), here we also visualize soft masks (\"Soft Segmentation\" column) by weighting the color of each slot according to its weight for each pixel. This reveals that the background is not necessarily oversegmented, but rather fully modeled by the union of multiple slots.\n", " We thank the reviewer for the positive feedback.\n\n**Reconstruction quality & Tab. 2 results on simpler datasets**\n\nWe thank the reviewer for the recommendation. We ran the suggested experiment and found the following results (MSN-H results copied from Tab. 2 for convenience):\n\n| CLEVR-3D | PSNR | FG-ARI |\n|-------------|-------|--------|\n| Slot Mixer | 39.98 | 0.976 |\n| SRT Decoder | 40.78 | 0.983 |\n\n| MSN-Easy | PSNR | FG-ARI |\n|-------------|-------|--------|\n| Slot Mixer | 29.74 | 0.954 |\n| SRT Decoder | 29.36 | 0.887 |\n\n| MSN-Hard | PSNR | FG-ARI |\n|-------------|-------|--------|\n| Slot Mixer | 23.54 | 0.812 |\n| SRT Decoder | 24.40 | 0.330 |\n\nWe did not find significant differences in reconstruction quality between the decoder variants on the simpler datasets, mostly as the quality is already very high with the Slot Mixer decoder. Interestingly, the SRT decoder achieves similar FG-ARI on CLEVR-3D and still reasonable FG-ARI on MSN-E, while it failed to decompose the scene meaningfully on the more realistic MSN-H dataset.\n\n**Speedup compared to baselines**\n\nWe agree that the >3000x speedup compared to the baseline is a result of both SRT and the novel Slot Mixer. As reported in Appendix Tab. 2, the real-world measured speedup of the Slot Mixer (32.47 fps) vs. Spatial Broadcast (1.39 fps) decoder is 23.4x which is a substantial difference in practice. Additionally, peak memory consumption is reduced by a similar factor which has a large impact on feasibility especially during model training.\n\nWe will improve the relevant sections in the manuscript to clarify how the speedup is a multiplicative result of these two largely independent factors. That said, we believe that one of our major empirical findings lies in demonstrating that the novel view synthesis task is crucial for better scene decomposition, not explicitly 3D volumetric rendering as in prior works.\n", " We thank the reviewer for the positive feedback and appreciate the comments from the representation learning point of view on inductive biases.\n\n**Role of inductive biases**\n\nWe agree that inductive biases should be used sparingly, especially when large amounts of data are available, as is often the case for unsupervised methods. Slot Attention makes use of a fairly minimal set of inductive biases: permutation equivariance of functions operating on the objects or slots, and softmax normalization across slots (instead of per slot), i.e. the scene has to be separated into the available slots, which is a direct implementation of scene-object decomposition principles.\n\nIn fact, our novel Slot Mixer relaxes the strong inductive bias of the RGB alpha blending in the popular Spatial Broadcast decoder, replacing it with a more powerful blending in feature space.\n\nCompared to prior art in 3D scene decomposition, OSRT makes fewer assumptions about the scene. Pixels are rendered directly instead of baking the physical volumetric rendering process into the model, or assuming a surface representation of the scene such as ObSuRF's depth supervision during training [27]. Furthermore, we do not explicitly address the background, for which several assumptions are made in uORF [34], e.g. the assumption that all slots should reside in a central scene bounding box.\n\n\n**Variance in synthetic datasets**\n\nWe agree that synthetic datasets often miss \"variance\" that is found in real-world datasets, such as outliers, biases, and overall variety. That said, we evaluate OSRT on the very challenging MSN-H dataset. For example, in contrast to datasets of prior works (uORF [34], ObSuRF [27]), objects and backgrounds have textures, and the cameras are sampled fully randomly instead of having fixed positions. Importantly, the dataset was not specifically designed for scene decomposition, but rather proposed by SRT [23] as a test bed for non-trivial novel view synthesis.\n", " We thank all the reviewers for their positive feedback and helpful comments. In particular, we appreciate that the reviewers find the paper to be well-written (jvub, VX3v, HAVj), our method to be technically sound and intuitive (jvub, 3uqV, HAVj), and that they agree our method is much more efficient and significantly outperforms prior art in both image quality and scene decomposition (jvub, VX3v, 3uqV, HAVj), without requiring further supervision such as depth maps (3uqV). The reviewers further welcome our extensive experimental evaluation (jvub, VX3v, 3uqV), highlighting in particular the importance of the role of novel-view synthesis for scene decomposition (VX3v, 3uqV).\n\nWe address comments below in direct replies to the reviews.\n", " The paper proposes Object Scene Representation Transformer, a framework for learning scene representation. The framework combines scene representation with the Slot Attention that constructs a bottleneck such that object-centric representation naturally emerges from learning. The proposed method is fast and achieves good performance. Let me start by honestly stating that my research background is in representation learning not in 3D understanding or rendering, therefore my comments should not serve as the key evidence for deciding the outcome of this submission.\n\nThe paper is well written and easy to understand even for someone who doesn’t work in the field. The technical details are sound and the claims are fair. The experimental evaluation seems comprehensive. The performance looks good.\n\nAs my background is in representation learning, I’d like to raise a few questions on its application in real-world and complex scenes. Object centric representation is mostly learned through adding inductive biases into a system, such as the Slot Attention adopted in the paper. A bottleneck stage can force a neural network to group pixels into a compact representation, and object *naturally emerges*. However, in my opinion and from my research experience, nothing naturally emerges in a neural network – it does what it does because we, the creators, told it so. In other words, we achieve this grouping by injecting inductive biases into the architecture.\n\nI have always been cautious about injecting inductive biases because doing so mostly helps *low data, low compute* regime, but many times harms a model’s capacity to scale to more data and more compute. Take the example of ViTs vs. CNNs – ViT models have much less inductive bias but they need more data to train and start outperforming CNNs (by a significant margin) as the model sizes grow. Inductive bias is a double-edged sword and any practice of adding inductive bias should be well motivated and examined with extreme caution. \n\nBack to the scope of this submission – I found that the datasets used here are rendered rather than from real-world. Naturally in these datasets object properties, such as numbers, lighting, materials, are randomized in a limited range. This setting seems to match the concerning low data, low compute criteria, therefore more inductive biases, especially dataset engineered ones, will unsurprisingly shine among baselines. It may not be the case for real-world data in which case the scalability and capacity of a model can truly be tested.\n\nI’d like to note the above comments are made without a comprehensive investigation of common practice in similar papers and domains. I plan to take all reviewers’ comments into consideration, and after reviewers’ discussion a further recommendation will be made.\n See above. N/A", " This work tackles the task of view-synthesis and extends a prior work “Scene Representation Transformer” by introducing a slot-based bottleneck representation. This allows the model to learn disentangled representations using only the standard view-synthesis objectives, and the learned disentanglement shown to be more accurate the prior unsupervised methods. Moreover, this representation also enables object removal (although not more general editing e.g. translation/scaling that prior NeRF based unsupervised disentanglement methods would allow).\n\nThe proposed approach is evaluated using the CLEVR and Multi-ShapeNet. (MSN) datasets where it outperforms a prior work ObSURF in both, view synthesis and scene decomposition accuracy. However, the bottleneck representation does limit the model expressivity and the learned model is less accurate at view-synthesis than the base SRT model. Strengths:\n+ The overall approach is simple and intuitive. The key idea of adding slots after the SRT encoder makes sense and it would be valuable for the community to see the results.\n\n+ The ablations performed regarding the decoder architecture choice are informative. In particular, the proposed ‘slot mixer’ solution seems like a good compromise in retaining slot properties while being more efficient than the ‘broadcast’ approach in prior work.\n\n+ The reported improvements ObSuRF are clearly significant and highlight the benefits of adding slots in the SRT network i.e. ability to handle variable views and more accurate results.\n\n+ The ablation highlighting the role of view synthesis for learning accurate decomposition was very interesting, and shows necessity of using novel views for learning as opposed to mere auto-encoding objectives.\n\n\nWeaknesses:\n- While the ‘slot mixer’ vs ‘broadcast’ decoder is a useful contribution, the overall approach rather straight-forwardly combines ideas from prior works like UORF and ObSuRF with the SRT approach, and I feel the technical contribution here is a bit limited. That said, I still think this maybe a valuable (if obvious) combination for the community to see.\n\n- As a downside of using the proposed slot representation, the quality of the synthesized views does suffer. While this is only highlighted in Table 2 on one dataset, it would be helpful. to see similar results across all datasets.\n\n- (minor point) I feel the claim of “3000x faster” rendering is a bit misleading as this mostly comes from the speedup obtained by SRT over volume-rendering based methods, and isn’t really a contribution of this work (the ‘slot mixer’ vs ‘broadcast’ speedup could be attributed to this work, but that is a much smaller factor).\n——\n\nOverall, I think this is simple but obvious paper. On the one hand, I am not sure this work makes any remarkable technical contributions or empirical findings. But on the other hand, it represents a well executed and sensible combination which the community would benefit from seeing, and I would therefore lean towards accepting it.\n\n N/A Yes", " - The paper addresses the problem of unsupervised decomposition of scenes into a discrete set of objects. The idea is that novel view synthesis requires reasoning about the geometry which should also be helpful for discovering objects without additional supervision. A novel transformer-based approach for object centric 3D representation learning is introduced which aims to overcome limitations of previous methods regarding generalization to complex scenes due to high computational costs.\n- The method uses a slot-attention mechanism in combination with a light-field rendering formulation using a transformer conditioned on a viewpoint-dependent latent representation derived from these slots. To avoid high computational costs, an early fusion scheme is presented that mixes slots early and thus has to run the decoder only once and not per slot.\n- Compared to [27], the proposed approach does not require depth supervision for efficiency as it relies on an SRT [23] based decoder for efficient rendering instead of volumetric rendering approaches. - Strengths\n - The introduction provides a good motivation towards the goal of learning about compositions and the geometry of scenes solely from observations. The related works section provides good context regarding neural rendering, object centric learning and specific differences to closest related works on object centric 3d learning.\n - Moving unsupervised 3d scene decomposition towards more complex and realistic scenes is an important goal with many applications. The proposed method demonstrates good performance on the more complex MSN-Hard dataset and could serve as a valuable baseline, especially in combination with the dataset's ground-truth instance labels.\n - The proposed approach is simple and reasonable. Its evaluation supports the stated claims regarding the presented model.\n - The experimental comparison to [27] (as well as the description of the attempts to train [5] in the supplementary) convincingly demonstrate the advantages of the proposed model in terms of accuracy and runtime, especially when going to more complex datasets.\n - The design of the ablations allows for a good analysis of the different components involved in the approach. The decoder analysis clearly demonstrates how the SM decoder improves decomposition over an SRT decoder [23] and runtime over an SB decoder. The experiments on the role of novel view synthesis for decomposition validate the hypothesis that novel view synthesis indeed helps object decomposition. Evaluating whether the approach is mainly segmenting by color cues is a good test for generalization capabilities of the approach. Scene editing experiments give a nice qualitative indication that slots indeed represent meaningful objects.\n- Weaknesses\n - The novelty of the proposed method is limited, as it is a rather straightforward adaptation of slot attention [17] to SRT [23] with an early fusion scheme for faster decoding.\n - Qualitatively (Fig. 3 of the supplementary), the SB decoder still looks better than the proposed SM decoder, although this comes at a large computational cost. The quantitative results suggest that the SM decoder performs better, which makes me question the metric a bit. - Fig. 3 in the supplementary seems to indicate that the Spatial Broadcast (SB) decoder suffers less from oversegmenting. Qualitatively it also seems to be more accurate around object boundaries but the quantitative results in Tab. 3 say the opposite. What could explain this discrepancy and could the proposed Slot Mixer (SM) decoder benefit from an explicit background modeling to avoid these problems? Limitations and potential negative societal impact have been addressed adequately.", " The paper presents a method to infer an object-centric scene representation aware of 3D geometry from multiple views of a scene. Similar to other works, it uses slot attention to segment scenes into slots, and it uses a ray-casting approach to rendering 2D views of the represented scene. However, the authors propose a novel decoder, based on Scene Representation Transformers (SRT), that only requires a single evaluation per ray query regardless of the number of objects in the representation. This makes the model faster than previous alternatives, while also achieving good quantitative metrics on different datasets. **Strengths:**\n\n+ Clear presentation:\n\nThe problem, method and results are presented clearly and it is easy to follow the paper.\n\n+ Fast approach to decoding 3D object-centric representations:\n\nThe model has much lower computational costs per iteration given that the number of evaluations per ray do not scale linearly with the number of objects. This makes the model fast and more scalable than other alternatives.\n \n+ Good performance compared to ObjSURF:\n\nThe model outperforms ObjSURF both quantitatively and qualitatively on different datasets.\n\n\n**Weaknesses:**\n\n- Missing references:\n\nThe paper is missing numerous relevant references. Specifically, it is missing the whole body of work of Sungjin Ahn's team, with ROOTS[1] being directly related to this paper, and relevant work by others [2,3].\n\n- Evaluation could be improved:\n\nWhile the paper compares in three datasets of increasing difficulty, the comparison is mostly to ObjSURF. The paper only compares to UORF on the harder dataset, in which it does not work well due to the high number of objects and computational costs associated. While this is a good comparison to highlight the better scaling capabilities of the proposed model (and this is an important point), it does not resolve the issue of how this model compares to competing approaches when they can actually compete. An easy way to solve this would be to train UORF and other previous methods on the simpler datasets, or compare on one of the proposed datasets in the UORF paper. In fact, there are experiments with different backgrounds and more complex objects in that paper, that are similar to the proposed datasets in this paper.\nIt would also be interesting to understand the quality of the segmentations by reporting regular ARI metrics, instead of just FG-ARI metrics, as these can be misleading when objects are not segmented tightly.\n\n\n**Detailed comments:**\n\nOverall this is a promising submission. While the idea of having an object-centric SRT model is relatively straightforward, the proposed decoder is novel and has clear advantages in terms of computational costs while still being interpretable. However, the paper could be improved with a more thorough literature review and a better comparison to previous approaches based on this literature review. There are a few questions to be answered, but overall I believe this can be a good submission with some modifications. I am currently arguing for its acceptance, and I would be happy to increase my score if the authors address my comments.\n\n**References:**\n[1] Chen, Chang, Fei Deng, and Sungjin Ahn. \"ROOTS: Object-Centric Representation and Rendering of 3D Scenes.\" J. Mach. Learn. Res. 22 (2021): 259-1.\n[2] Castrejon, Lluis, Nicolas Ballas, and Aaron Courville. \"INFERNO: Inferring Object-Centric 3D Scene Representations without Supervision.\" (2021).\n[3] Anciukevicius, Titas, Christoph H. Lampert, and Paul Henderson. \"Object-centric image generation with factored depths, locations, and appearances.\" arXiv preprint arXiv:2004.00642 (2020).\n - How is the background handled?\n- Differently from Slot Attention, it seems that the initial slot representation is learned. How does that affect the model performance and how does it affect its generalization capabilities to an a different number of objects from training/testing?\n- How does the model compare to UORF quantitatively on the simpler datasets proposed in that paper?\n- The segmentations compared on the FG-ARI metric do not take into account that some object segmentations might be covering the background. How do the metrics change when using the ARI metric The authors mention limitations of their work and ethical considerations. The limitations of their work could be better analyzed by conducting some of the experiments suggested in the Questions section." ]

[ -1, -1, -1, -1, -1, -1, -1, 5, 6, 7, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, 2, 4, 4, 4 ]

[ "c6czX2E9hhp", "BZLRkgAb-r0", "K59pMKllt7S", "WiNyOfOwdLN", "lo6A3sO6LI", "AH0VNcK4abc", "nips_2022_znNmsN_O7Sh", "nips_2022_znNmsN_O7Sh", "nips_2022_znNmsN_O7Sh", "nips_2022_znNmsN_O7Sh", "nips_2022_znNmsN_O7Sh" ]

[ "LNsI_b8PR3", "aNijtD_-nA0", "fBy0fVMNqp4", "erC6DtfYxJ2", "s-Icu9OyGsu", "_LvlM2tjCzi", "svBK6KNMD4y", "4Ql-cw5Kxj_", "KoRasQfxCk7", "_nV140U6ksR", "2Ssjl0ff_zJ", "73jmrkd9U-N", "w28xugoktA0", "HfHYPuuW1r", "LAyV9YSxvA_", "ATGI8cVL8Y2", "oVkjssIRrhg", "ZIN0S4yVz-a", "leWzAEVRrty" ]

[ "author", "author", "official_reviewer", "author", "author", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Because the $error_{dec}$ caused by partial observation is inevitable, this is the reason why $error_{dec}$ of time step t is left in Eq.(9). However, by comparing equation 7 and equation 9, we can see that error accumulation resulting from $error_{dec}$ can be avoided. ", " I am always glad to receive your reply. Eq.(9) analyzes the overall error in our framework. By replacing $q(\\tau,u)$ with $q(s,u)$, we can avoid the partial observation error $error_{dec}$ being accumulated in the Bellman iteration training process. However, in the end, our strategy needs to be applied to partially observed scenarios, which will still produce errors due to partial observation (of course, the error accumulation is avoided). You can refer to Figure 2 (a), in the second stage, we train the individual learner agent based on local observation by means of imitation learning.\n\nThis work focuses on addressing the error accumulation problem and proposes to introduce imitation learning into VD method.", " I think error accumulation is resulting from IGM decomposition error, so when we replace $q(\\tau, u)$ with $q(s, u)$, the error term will disappear, why the $error_{dec}$ of time step t is left in Eq.(9)?\n", " I look forward to your other questions and suggestions.", " I look forward to your other questions and suggestions.", " I look forward to your other questions and suggestions.", " Thank the authors for their responses. I tend to keep my score.", " According to your suggestion, we have plot curves showing Q differences (averaged over all timesteps and actions) over time. You can browse anonymous links to view the image (https://anonymous.4open.science/r/pymarl_HDA-5726/picture/Q%20Difference.png).\n\nMore experiments on sight view 9 are available in Appendix F. Moreover, we also extend simple experiment in the single agent environment in Appendix E, which also proves the advantages of our method.\n", " New Figure 3 shows Q functions at two time steps. The reviewer thinks it is not convincing. Why not plot curves showing Q differences (averaged over all timesteps and actions) over time.\n\nNew Figure 5(c) is quite interesting. DAgger with sight range 9 > DAgger with sight range 5 > DAgger with sight range 0. However, the proposed method is expected to address the problem of lossy decomposition, and these gaps between DAgger with different sight ranges need further elaborations.", " > 2. Proposition 5 indicates that when multiple samples satisfy the same local observation $\\tau$, imitation learning will take the average of these samples. The problem is that if the policies on these samples are completely different, imitation learning may lead to a bad policy, i.e., the policy distillation will fail due to insufficient information. The authors should discuss this case to justify the soundness of IGM-DA. \n\n> For example, there are two landmarks to the left and right of the agents. Agents should go to the winning landmark. The probability of whether the left and right landmarks are winning landmark is equal. The local observations of each agent cannot see the location of the winning landmark. In this case, local history does not have enough information to make the right decisions. IGM condition is a lossy decomposition due to partial observation and can IGM-DA address this problem?\n\nIn our teacher-student model, only the learners interact with the environment to generate trajectories. The experts evaluate the learners' trajectories and propose improvements, which are then absorbed by the learners in the form of Proposition 5. The new strategy of the learner is always based on the local information only. This new strategy then continues to interact with the environment. The whole training process is equivalent to a closed-loop control, which has two important components: global information-based reinforcement learning training and Dagger, a real-time strategy distillation. For the actual environment and a current strategy, we need to consider two questions: is the current strategy a locally optimal solution? Can this optimal strategy be distilled well? The current strategy will continue to improve or explore through ε greedy until convergence.\n- For problem: \nThe policy distillation will fail due to insufficient information. The authors should discuss this case to justify the soundness of IGM-DA.\n\nAnswer:\nIf the policy distillation fails due to insufficient information, learners will return the failed strategy to experts for further revision and experts will continue to adjust the strategy or explore through ε greedy until a suitable strategy is found.\n\nTake the scenario you mentioned as an example. For a single agent, because one does not know which side is the winning landmark, any left-to-right strategy is reasonable. In case two agents are cooperating, the optimal strategy is to explore both left and right. Because our method uses global information for reinforcement learning, this optimal strategy will be discovered without requiring any observations. Thus, tis optimal strategy can also be learned by the learners. \nConsider the traditional method, on the contrary, the agents try to iteratively learn an action value based on local observations through the Bellman equation. However, the local observation of the whole environment remains unchanged, leading to fluctuations in the iterative process. That is, the calculation of action value based on local information will become instable. This is also the reason why we use global information for value decomposition - to avoid unstable training (error accumulation) caused by local observations. Please refer to Appendix E, in which we present our simple experiments under a single agent, which also prove the advantages of our method against partial observations.\n\n- For problem: \nIGM condition is a lossy decomposition due to partial observation and can IGM-DA address this problem?\n\nAnswer:\nIGM condition is a lossy decomposition due to partial observation, which will lead to error accumulation during the bellman iterative training. IGM-DA avoids introducing partial observation into IGM decomposition, which is lossless and does not produce cumulative error in the training process.\n", " > 1. To address partial observation of IGM conditions, there is another way to enrich the observation of each agent using inter-agent communication. By discussing this branch of related work, the position of this paper would become clearer.\n\nThanks for drawing our attention to these relevant and interesting papers. Using extra communications is indeed an effective method to alleviate training instability caused by partial observations, provided that communication between agents is allowed. We briefly discussed these methods [1-3] in the newly added Section 5. Note, however, that the present work focuses on how to make agents learn a strategy more effectively in the presence of local observations without any communications between agents. In this regard, we found that IGM decomposition suffers from errors, and the training process will lead to error accumulation. To solve this problem, we integrated Dagger, an imitation learning technology, with IGM to construct a teacher-student model to reduce the overall error.\n\n[1] Wang T, Wang J, Zheng C, et al. Learning nearly decomposable value functions via communication minimization[J]. ICLR 2020.\n\\\n[2] Foerster J, Assael I A, De Freitas N, et al. Learning to communicate with deep multi-agent reinforcement learning[J]. Advances in neural information processing systems, 2016, 29.\n\\\n[3] Nguyen T T, Nguyen N D, Nahavandi S. Deep reinforcement learning for multiagent systems: A review of challenges, solutions, and applications[J]. IEEE transactions on cybernetics, 2020, 50(9): 3826-3839.\n\n\n\n\n\n", " > Minor: \\\n&#8194; Discount factor is missing in Eq.(7). \\\n&#8194; In Eq.(10), please use the indicator function to represent the one-hot probability.\n\nThank you very much for spotting the typos, which have been corrected.\n\n> Limitations: \\\nThe discussions on background literature and related work are limited. I do not penalize my evaluation by this point, but I strongly encourage authors to include a related work section in the paper.\n\nWe thank you for your constructive comments. According to your suggestion, we have added a new section (Section 5, “Related work”) discussing the most relevant work, including the following papers [1-3].\n\n[1] Castellini et al. \"The Representational Capacity of Action-Value Networks for Multi-Agent Reinforcement Learning\" AAMAS 2019. \\\n[2] Wang et al. \"Towards Understanding Cooperative Multi-Agent Q-Learning with Value Factorization\" NeurIPS 2021. \\\n[3] Huang et al. \"Multiagent Q-learning with Sub-Team Coordination\" AAMAS 2022.\n\n", " > 1. What is the formal definition of error-terms in proposition 2? Does it mean Bellman errors? What is $Error(Q)$? These error terms are the core concepts of this paper and should be defined in formal mathematical formulas.\n\nThis error term represents the current error in action values. Assuming that the real action value of the current strategy is $Q^\\pi$, and the calculated action value is $\\hat{Q}^\\pi$, then the error term is defined as $Error(Q^\\pi )=Q^\\pi -\\hat{Q}^\\pi$. We have added a definition of the error term before proposition 2 in the paper. Error accumulation discussed in the paper comes from the iterations of the bellman equation based on partial information. In this work, we avoid carrying out bellman equation iterations on the basis of partial information, thus avoiding error accumulation.\n\n> 2. There are no experiment results supporting the error accumulation is reduced from Eq.(7) to Eq.(9) in practice. It raises a concern that the performance improvement may come from any unmentioned implementation details.\n\nUnfortunately, it is difficult to experimentally show the errors in action values, which requires to know the real action value of a given strategy, and the calculation of the real correct action value relies on a complete understanding of the environment. Nevertheless, extensive empirical results demonstrated the robust performance of the proposed algorithm for scenarios with partial observations. The details of the proposed algorithm can be found in Appendix D. In addition, we also provide a simple implementation of the algorithm in a single agent environment with partial observation. The code has less than 100 lines, which is convenient for the reader to verify.\n\n> 3. The loss function of \"supervised imitation learning\" should be included in the main text. I even cannot find it in the appendix.\n\nApologies for the missing definition of the loss function. We have included the loss function of the supervised imitation learning (as shown below) in Proposition 5 of the revised manuscript. \n$loss = {q^i}({\\tau ^i},{\\mu ^i}) - 1/k\\sum\\nolimits_s {[{P_\\pi }({\\mu ^i}|s)]} $\n\n> 4. What is the purpose of proposition 5. I do not understand what \"satisfy local observation\" means in proposition 5 and what is \"the optimal action-value after imitation learning\".\n\nThis is an important part of our method. Assume we have obtained the individual action value provided by a group of experts. Our next task is to extract the action value of the learners from the action value of experts. According to the minimum risk Bayes decision rule, for a selected action, its risk can be defined as difference between the optimal action value of the expert and the currently selected action value. However, the individual action value has no practical significance because of the existence of IGM. The suboptimal individual action value of the experts does not necessarily mean the suboptimal individual action (IGM only guarantees that the maximum local action value corresponds to the maximum joint-action value. However, the secondary local action value does not necessarily correspond to the secondary joint-action value). Thus, a more practical definition of the risk is a penalty of 1 if the current action selection is inconsistent with the optimal action of the expert label, and no penalty if consistent. In other words, the minimum risk Bayes decision rule degenerates into the minimum error rate Bayes decision rule. Therefore, when we calculate the estimated risk of each action, the optimal action selection is the action with the minimum risk. \n - \"satisfy local observation\"\n\nBecause we need to estimate the risk term by sampling, “satisfy local observation $\\tau$” is the condition of selecting samples, see the proof of Proposition 5 in Appendix A.\n- \"the optimal action-value after imitation learning\"\n\nAccording to the minimum risk Bayes decision rule, we first define the expected loss and penalty functions. Because the action with the minimum expected risk (error) is the most popular one, we can define the action value after imitation learning as the negative expected risk. We recognize that 'best' here may be misleading, therefore, we have deleted it in the revised paper.\n\n", " > In CTDE, the decentralized execution is constrained with partial observation, the difference between global obs and local obs is determined by the partial obs environment, this problem can not be solved by imitating an expert. I'm not sure it's always good to imitate global state expert, especially, when the learner agent needs to execute independently.\n\nAs the reviewer correctly pointed out, CTDE is by far the most popular multi-agent reinforcement learning paradigm, and many empirical results have demonstrated its effectiveness. Although we agree that the issue of missing global observation cannot be completely resolved by imitating an expert, we show that learning from an expert is able to improve the performance. In particular, this work focuses on addressing the error accumulation problem, which has not been considered in the literature. In the proposed algorithm, Dagger is an important part that requires experts to evaluate and improve learner strategies rather than their own strategies. As a result, we can get a strategy depending on the local information, thereby avoiding error accumulation.\n\n> I think some previous works have proposed some methods like using a CTCE teacher and a CTDE student, what's the difference when comparing this paper to these works?\n\nTo the best of our knowledge, it is the first time that both IGM decomposition error and error accumulation have been considered. By seamlessly coupling IGM with the Dagger algorithm, we avoid error accumulation in IGM decomposition resulting from local observations without requiring human experts. \n\nRegarding similar previous work, we found one article using CTCE and distillation learning [1]. The research, however, assumes that communications between agents are allowed. The main focus of that paper introduced completely centralized training to address the low efficiency of sampling resulting from frequent changing communication topology. Compared with our research, the motivations are completely different. We provided a brief discussion of this work in a newly added Section 5 (“Related work”).\n\n> Limitations:\nThis paper analyses the value decomposition error problem, but the method of this paper is of limited help in solving this problem.\n\nWe have achieved an average improvement of 20 % over the state-of-the-art algorithms in the SC2 experiment with a sight view of 0. And we have conducted new experiments when the sight view is 5 and 9, respectively, to prove the robustness of our method. We also extended our structure to partially observed single-agent environments (Appendix E), which also showed promising performance. The code of the single agent experiment has less than 100 lines, which is also fairly convenient for the reader to verify.\n\n\n[1] Chen G. A New Framework for Multi-Agent Reinforcement Learning–Centralized Training and Exploration with Decentralized Execution via Policy Distillation[C]//Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems. 2020: 1801-1803.\n", " > (1) It is not surprising that local Q functions conditioned on local information are not accurate enough. Can the authors give a bound to $Error_{dec}$? Perhaps by quantifying the ratio of lossy information in $\\tau$. (It is fine if this is too difficult, but the reviewer will fight for the acceptance of this paper if the author can make it and change Figure 3.)\n\nThanks for your appreciation of our work and your insightful comments. We fully agree that providing a bound of the error is of particular interest. Although your suggestion to quantifying the ratio of lossy information is an attractive idea, we are not able to provide a theoretic bound of the error. It is interesting to note that, in reinforcement learning, the calculation of action value (strategy generation) depends on the reward function and Markov property of the environment. The dependence of the reward function and Markov property on global information will seriously affect the calculation of action value (strategy generation). However, the obtained strategy does not necessarily have such strong dependence on global information. Taking the maze as an example, a simple strategy is to walk right, which does not depend on any position information. In short, the quantitative analysis of action value error is a complex problem. If the quantitative analysis of action value error can be realized, it is expected to provide reference for the number of sensors in practical engineering.\n\n> (2) Figure 3 does not give many insights. It should be replaced. Please demonstrate the gap between Q functions depending on local and global information.\n\nIn proposition 1, we only prove that if the observation is incomplete, the performance of some complex strategies (Q function) will be affected. For a real environment, we still need to carry out experiments to empirically verify this, which is the purpose of the experimental results presented in Figure 3 in the previous manuscript. Of course, as the reviewer pointed out, comparing the winning rate only may be insufficient to demonstrate the gap between the Q functions when global information is available or not. Consequently, we conducted new experiments to illustrate the differences. \n\nIn the presence of partial observations, different global states may correspond to the same local observations, and the action value of the learner under a local observation is the weighted average of the action value of the expert under different global observations. Figure 3 (b) in the revised manuscript shows the distribution of the action values. The discrepancies in the action distribution may eventually lead to wrong action choices of the learners.\n\n> Please show the influence of the sight range (changing from 0 to, say, 5). For now, a zero sight range may be too extreme.\n\nFollowing your suggestion, we added an experiment with an additional sight view of 5 for the Qmix algorithm and the scene of 5 m _ vs _ 6 m. As shown in Fig. 5 (c), our algorithm is more robust to partial observations. ", " This paper provides a new perspective on the study of Q-value decomposition methods in the field of multi-agent reinforcement learning. In order to maintain decentralized execution while avoiding learning non-stationarity during the training phase, centralized training with decentralized execution paradigm is widely studied. The authors pinpoint a gap between local and global observation, which leads to the fact that local action-value functions cannot represent the right Q values. Such a representational error may accumulate temporally. The authors use a supervised learning method (with the \"label\" being action values conditioned on global observations) to solve this problem and found it can improve the performance of multiple MARL methods. ### Significance\n\nThe paper discusses an interesting issue in CTDE value-based multi-agent learning methods that are ignored in the previous literature. As far as the reviewer is concerned, the paper is interesting, and the contribution may inspire many MARL researchers.\n\n### Quality\n(1) The major concern of the reviewer is that the experimental results cannot fully support the analysis in the previous sections. Figure 3 does not make sense. A smaller sight range must hurt the performance, but it may simply be because they have little information about the other agents and enemies. It cannot be guaranteed that the discussed issue in this paper leads to this performance gap.\n\n(2) Another drawback of the paper is that some results are not surprising. For example, it is well-known that Q functions conditioned on local observations are less accurate than those based on global information. And such an error will certainly accumulate temporally. It would be much more interesting if the authors could bound this error.\n (1) It is not surprising that local Q functions conditioned on local information are not accurate enough. Can the authors give a bound to $Error_{dec}$? Perhaps by quantifying the ratio of lossy information in $\\tau$. (It is fine if this is too difficult, but the reviewer will fight for the acceptance of this paper if the author can make it and change Figure 3.)\n\n(2) Figure 3 does not give many insights. It should be replaced. Please demonstrate the gap between Q functions depending on local and global information. \n\n(3) Please show the influence of the sight range (changing from 0 to, say, 5). For now, a zero sight range may be too extreme. The reviewer thinks the paper has made many interesting findings and does not see obvious negative societal impacts", " This work analyzes the current IGM decomposition framework in CTDE problem, especially the lossy in value decomposition and the accumulation of lossy in the training process. Based on the analysis, this work proposes a method combined with imitation learning to solve the lossy between global observation and local observation of Q (s, U) = \\sum Q(s_i, u_i) in value decomposition.\nThe method part includes an expert agent trained using off-policy algorithm with global observation and a learner agent trained using supervised algorithm with local observation, through alternately training, the training lossy of learner is alleviated.\n Strength:\nThe paper is well organized and well written and the analysis/method part is very detailed, and the definition is more formal.\nIt is a relatively novel perspective to integrate imitation learning into the framework of CTDE to alleviate value decomposition error.\n\nWeakness:\nThe flaws of IQM-based method is widely studied. This paper has spent a lot of space on analysis, but most of the analysis is not deep enough and I think the analysis result is not innovative enough.\nThe experiment part is insufficient. The setting of the experiment is zero sight SMAC, which is obviously more conducive to the setting of this method, I think adding some experiments with normal sight in SMAC will be better. In CTDE, the decentralized execution is constrained with partial observation, the difference between global obs and local obs is determined by the partial obs environment, this problem can not be solved by imitating an expert. I'm not sure it's always good to imitate global state expert, especially, when the learner agent needs to execute independently.\n\nI think some previous works have proposed some methods like using a CTCE teacher and a CTDE student, what's the difference when comparing this paper to these works? This paper analyses the value decomposition error problem, but the method of this paper is of limited help in solving this problem.", " This paper analyzes the error accumulation in multi-agent Q-learning and focuses on the error caused by partial observability. Regarding this problem, this paper integrates a DAgger module to distill the full-observability policy to the partial-observability policy. Strength: This paper studies an important problem and the idea is novel and makes sense.\n\nWeakness: Although I can roughly capture the main idea of this paper, the notation and definition of many core concepts are not clear (see questions). The writing quality is far from a conference publication. Major concerns:\n\n1. What is the **formal definition** of $error$-terms in proposition 2? Does it mean Bellman errors? What is $Error(Q)$? These error terms are the core concepts of this paper and should be defined in formal mathematical formulas.\n\n2. There are no experiment results supporting the error accumulation is reduced from Eq.(7) to Eq.(9) in practice. It raises a concern that the performance improvement may come from any unmentioned implementation details.\n\n3. The loss function of \"supervised imitation learning\" should be included in the main text. I even cannot find it in the appendix.\n\n4. What is the purpose of proposition 5. I do not understand what \"satisfy local observation\" means in proposition 5 and what is \"the optimal action-value after imitation learning\".\n\nMinor:\n\n1. Discount factor is missing in Eq.(7).\n\n2. In Eq.(10), please use the indicator function to represent the one-hot probability. The discussions on background literature and related work are limited. I do not penalize my evaluation by this point, but I strongly encourage authors to include a related work section in the paper.\n\nAs this paper is titled by \"rethinking IGM\", it would be better to connect with other papers studying the algorithmic property of VD methods (maybe in other aspects), e.g., [1-3].\n\n[1] Castellini et al. \"The Representational Capacity of Action-Value Networks for Multi-Agent Reinforcement Learning\" AAMAS 2019.\n\n[2] Wang et al. \"Towards Understanding Cooperative Multi-Agent Q-Learning with Value Factorization\" NeurIPS 2021.\n\n[3] Huang et al. \"Multiagent Q-learning with Sub-Team Coordination\" AAMAS 2022.", " This paper rethinks a popular principle in cooperative MARL called Individual Global Max (IGM) decomposition, discovers the limitation of the IGM condition, and proposes an imitation learning strategy (IGM-DA) to address this problem. Due to partial observation, local observation may not provide enough information. Thus, the IGM condition will be a lossy decomposition. This paper trains an expert using a global state during centralized training and distils a decentralized agent using imitation learning. Empirical results show that IGM-DA can outperform state-of-the-art IGM-based approaches with zero sight view. The reviewer will list the main strengths and weaknesses as follows:\n\nSTRENGTHS\n\nIGM is a very popular principle in the value-based MARL algorithm. This paper rethinks the limitation of the IGM principle, which is very interesting and novel. Due to the partial observation, IGM is hard to keep the consistency between local and global greedy action selection. This paper proposes a teacher-student model to utilize the global information during centralized training to address this problem, which is an appropriate way to handle it.\n\nWEAKNESSES\n\n1) To address partial observation of IGM conditions, there is another way to enrich the observation of each agent using inter-agent communication [1]. By discussing this branch of related work, the position of this paper would become clearer.\n\n2) Proposition 5 indicates that when multiple samples satisfy the same local observation $\\tau$, imitation learning will take the average of these samples. The problem is that if the policies on these samples are completely different, imitation learning may lead to a bad policy, i.e., the policy distillation will fail due to insufficient information. The authors should discuss this case to justify the soundness of IGM-DA.\n\n[1] Wang T, Wang J, Zheng C, et al. Learning nearly decomposable value functions via communication minimization[J]. ICLR 2020. For example, there are two landmarks to the left and right of the agents. Agents should go to the winning landmark. The probability of whether the left and right landmarks are winning landmark is equal. The local observations of each agent cannot see the location of the winning landmark. In this case, local history does not have enough information to make the right decisions. IGM condition is a lossy decomposition due to partial observation and can IGM-DA address this problem? The main concerns are listed in the WEAKNESSES. The authors should discuss the examples presented in the reviewer's Question to justify IGM-DA." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 5, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4 ]

[ "fBy0fVMNqp4", "fBy0fVMNqp4", "HfHYPuuW1r", "_nV140U6ksR", "73jmrkd9U-N", "HfHYPuuW1r", "4Ql-cw5Kxj_", "KoRasQfxCk7", "LAyV9YSxvA_", "2Ssjl0ff_zJ", "leWzAEVRrty", "w28xugoktA0", "ZIN0S4yVz-a", "oVkjssIRrhg", "ATGI8cVL8Y2", "nips_2022_xs9Sia9J_O", "nips_2022_xs9Sia9J_O", "nips_2022_xs9Sia9J_O", "nips_2022_xs9Sia9J_O" ]

[ "_irYiAOF6xP", "pqjsKgz7dF3", "_aCjNLtXm-", "gmoXgeiHOM", "oscVwJw6XQF", "LcbZc8Qk2L", "4BjR6vUUuk6" ]

[ "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your response and for running this experiment! I think it helps to see the contribution in this work as giving an extended and tighter analysis of this warm-starting approach.", " We appreciate the reviewer's thoughtful comments and questions on the worst-case bounds.\n\n&nbsp;\n> What is the reason that your approach is unable to recover optimal worst-case bounds? Is this inherent to the approach, or can it be alleviated?\n\nOur approach based on discrete convex analysis (DCA) can sometimes enjoy worst-case bounds, which, however, require instance-specific discussions and are often weaker than those of the standard algorithms without warm-starts (hence we should resort to the parallel execution in practice, as described in Section 6). Since our main focus is to develop a general framework for warm-starting algorithms with predictions, we did not go into the details of the worst-case bounds to avoid complications. In response to subsequent questions, we will detail the worst-case bounds of our DCA-based approach for bipartite matching, matroid intersection, and discrete energy minimization.\n\nWe agree that an additional mention of the worst-case bounds and the applicability of our DCA framework will be instructive to the readers. We will add discussions on them to the final version if accepted.\n\n&nbsp;\n>You discuss in Section 6 that the issue above can be mitigated by running a standard algorithm in parallel. It seems as if the time complexity of such an approach would, compared to alternatives, never be worse by more than a constant factor 2. Is this a correct interpretation?\n\nThe interpretation is correct. Please note that we can independently execute our algorithm with warm-starts and a standard algorithm. Therefore, if two computational environments are available, the parallel execution takes at most the same time as the standard algorithm.\n\n&nbsp;\n>What is the worst case? Can similar lower bounds be shown for the time complexity?\n\nWe can derive the worst-case bounds for bipartite matching and matroid intersection as follows, although they are weaker than those of standard algorithms.\n\nIt is known that the long-step steepest descent algorithm for an L-convex function $g: \\mathbb{Z}^V \\to \\mathbb{Z} \\cup \\\\{+\\infty\\\\}$ converges in $n\\max\\\\{g(p)-g(p+d):p\\in\\mathbb{Z}^V,d\\in\\mathcal{N}\\_+\\\\}$ iterations if the minimum minimizer $d\\in\\mathcal{N}\\_+$ is chosen in every local optimization [46, Theorem 4.17]. Thus, our warm-starting algorithm for bipartite matching (resp. matroid intersection) terminates in $O(n^2)$ (resp. $O(nr)$) iterations. Since a single iteration takes $O(m\\sqrt{n})$ (resp. $O(\\tau nr^{1.5})$) time, the total worst-case time complexity is $O(mn^{2.5})$ (resp. $O(\\tau n^2 r^{2.5})$).\n\nWe can also obtain a similar worst-case bound for discrete energy minimization when the derivatives of $\\phi_i$ and $\\psi_{ij}$ are bounded. We, however, do not know whether those bounds are tight, i.e., whether there is a worst-case instance of bipartite matching, for example, such that our algorithm incurs $\\Theta(mn^{2.5})$ time.\n\n&nbsp;\n### On bipartite matching\nWe would like to mention why our DCA approach cannot immediately recover the $\\tilde{O}(mn)$-time bound for bipartite matching ($\\tilde{O}$ hides logarithmic factors).\nIn a nutshell, this is because our algorithm is subtly different from the standard $\\tilde{O}(mn)$-time Hungarian method as follows (see [44, Section 18.5b] for more details). \n\nLet $G=(L\\cup R,E)$ be a bipartite graph with edge weights $w\\in\\mathbb{Z}^E$. Keeping a dual solution $p = (s,t)\\in\\mathbb{R}^{L\\cup R}$, our DCA-based algorithm alternately computes a maximum matching of the tight subgraph $G^*=(L\\cup R,E^*)$ with respect to $(s,t)$ from scratch with the Hopcroft--Karp algorithm and updates $(s,t)$. This results in the $O(mn^{2.5})$ time complexity bound, as discussed above.\nBy contrast, the standard Hungarian method keeps a maximum matching $M$ of $G^*$ and a dual solution $(s,t)$.\nIn every iteration, it augments $M$ or updates $(s,t)$ by searching an augmenting path in an orientation $D^\\*\\_M$ of $G^\\*$ defined from $M$. Moreover, the sequence of dual updates between two augmentations of $M$ can be aggregated into the single shortest-path searching on $D_M$, the orientation of $G$ by $M$ defined similarly to $D_M^*$, with respect to edge length $l_{ij}\\coloneqq s_i-t_j-w_{ij}$ for $ij\\in E$. Since the edge lengths are non-negative, we can use Dijkstra's $\\tilde{O}(m)$-time algorithm, thus achieving the $\\tilde{O}(mn)$ time.\n\nSince the above difference is too involved, we omitted the details in the manuscript.\nTo recover the $\\tilde{O}(mn)$-time bound, we need to convert our algorithm into the above standard Hungarian method.\nThis modification, however, is specific to bipartite matching and is not covered by the general DCA theory. \nMoreover, the modification may worsen the prediction-dependent bound. This is because, while our DCA-based algorithm always updates the dual solution in every iteration, the standard Hungarian method does not when $M$ is augmented, implying that the bound based on $\\\\|p^*-\\hat p\\\\|_\\infty$ does not follow immediately.", " We appreciate the reviewer's careful reading and thoughtful comments.\n\n> How does the proposed approach for weighted bipartite matching compare experimentally to Dinitz et al. 2021?\n\nWe conducted a preliminary experiment on synthetic data. We observed that the method of Dinitz et al. and ours exhibited similar performances, and both outperformed the baseline without warm-starts. For details of the experiment, please see the [response to Reviewer TRn1](https://openreview.net/forum?id=-GgDBzwZ-e7&noteId=gmoXgeiHOM).\n\n&nbsp;\n### Minor comment\nPerhaps the \"Ethics Flag\" is marked \"Yes\" mistakenly. Please change it to \"No\" if you have no ethical concerns.", " We are grateful to the reviewer for providing valuable comments and questions.\n\n> Do you think that the DCA-based algorithms actually improve on the work of Dinitz et al in practice, or is it rather the case that you can give a tighter analysis of these algorithm than they could?\n\nWe think our practical improvement from Dinitz et al. is not very large. Indeed, reading the comment, we conducted a preliminary experiment to compare the two methods and observed that their performances are similar. We will detail the experiment later.\n\nTheoretically, however, we believe our work has significantly improved Dinitz et al. in two aspects.\n\n1. As mentioned in the comment, our bound depending on the $\\ell_\\infty$-distance offers a tighter result than the previous $\\ell_1$-dependent one, which yields up to $n$ times improvement of the time complexity bound.\n\n2. More importantly, our discrete-convex-analysis-based framework has revealed a broad class of discrete optimization problems (i.e., $\\text{L}$/$\\text{L}^\\natural$-convex minimization problems) that accepts a geometric understanding of why learning of warm-starts is effective.\n\nIn summary, our main improvement from Dinitz et al. is the theoretical results, i.e., tighter analysis and extension of the class of problems.\n\n&nbsp;\n## Preliminary experiment\nWe here present preliminary experimental results. We will work more on the experiments and, if accepted, add the results to the supplementary.\n\nFirst, we summarize the differences between Dinitz et al. and ours. Once a feasible dual solution $p^\\circ \\in \\mathbb{R}^V$ is given, both methods solve a bipartite matching instance by iteratively calling the Hopcroft-Karp algorithm. Thus, the bipartite-matching solvers used in Dinitz et al. and our DCA-based framework are identical. The differences between Dinitz et al. and our method lie in how to learn (infeasible) predictions $\\hat p$ and obtain feasible solutions $p^\\circ$.\n\n- **Learning predictions.** Dinitz et al. learned predictions to minimize the empirical $\\ell_1$-loss, while we have replaced the $\\ell_1$-loss with the $\\ell_\\infty$-loss. In the following experiment, we learn predictions using the online gradient descent method (OGD), as described in Section 4 and [31], where the loss functions are $\\ell_1$- and $\\ell_\\infty$-losses for Dinitz et al. and ours, respectively.\n\n- **Obtaining feasible solutions.** Dinitz et al. converted an infeasible prediction $\\hat p$ into a feasible initial solution $p^\\circ$ with a greedy approximation algorithm tailored to the $\\ell_1$-loss. By contrast, we obtain feasible solutions $p^\\circ$ by minimally shifting $\\hat p$ in the all-one direction as in lines 198--200 and rounding the resulting vector to the nearest integer point.\n\nDue to the above differences, the method of Dinitz et al. and ours yield different feasible initial solutions $p^\\circ$, which are fed to the common bipartite-matching solver.\nThe following experiment examines how this difference affects the number of iterations taken by the bipartite-matching solver.\n\n### Settings\nWe generated a random bipartite graph $(V, E)$ such that $V = L \\cup R$, $|L| = |R| = 5$, and each $(i, j) \\in L \\times R$ has an edge with a probability of $0.8$.\nFixing this graph, we generated $1000$ sets $\\\\{w_e\\\\}_{e\\in E}$ of random edge weights by setting $w_e = 5 + \\lfloor u \\rceil$ for each $e \\in E$, where $u$ is drawn from the standard normal distribution. We thus created $1000$ bipartite-matching instances with various edge weights. For each of these instances, we iteratively predicted a dual solution $\\hat p$ with OGD, converted $\\hat p$ into a feasible solution $p^\\circ$, and solved the instance by warm-starting the bipartite-matching solver with $p^\\circ$.\n\n### Results\nWe solved the $1000$ instances using the method of Dinitz et al. and ours and computed the average number of iterations for each method.\nOur method took $3.458$ iterations on average, while the method of Dinitz et al. took $3.614$ iterations.\nWe also solved the $1000$ instances using the solver without warm-starts and observed that it took $5.122$ iterations on average.\nTo conclude, both methods successfully took advantage of learned predictions, and their empirical performances were similar.", " This paper considers using predictions to improve algorithm running time via warm start as in the recent work due to Dinitz et al. 2021. The authors propose a framework based on discrete convex analysis which applies a discrete steepest decent approach to go from an initial feasible solution to a global optimum. Each iteration requires solving a local optimization problem to find a descent direction and the number of iterations can be bounded by $O(||p-p^*||_{\\infty})$, where $p$ is the initial solution and $p^*$ is an optimal solution. Algorithms for projecting infeasible predicted solutions onto the feasible set (with respect to the $\\ell_\\infty$) norm and efficiently learning an initial predicted solution are also given to complete the framework.\n\nUsing this framework the authors give warm-start-with-predictions algorithms for:\n- weighted bipartite matching (improving the result of Dinitz et al. 2021)\n- weighted matroid intersection\n- Discrete energy minimization\n- The more general class of L/L♮-convex functions.\n\n This paper gives a nice improvement over Dinitz et al 2021 for weighted bipartite matching and also extends the ideas to other problems. The writing is a bit dense, but overall well explained. An experimental evaluation may be interesting, but is probably not necessary for the current submission. - How does the proposed approach for weighted bipartite matching compare experimentally to Dinitz et al. 2021? N/A", " This paper extends recent work by Dinitz et al. on using the learning-augmented algorithms model to speed up graph algorithms by warm-starting the dual solutions (in particular, they focused on the Hungarian algorithm for minimum-cost bipartite matching). In this paper, the authors interpret this idea of warm-starting in the context of discrete convex analysis, inspired by the idea that warm-starting is a well studied concept in convex optimization. Through this lens, they give an improvement in the min-cost matching problem, reducing the dependence on the prediction error from linear in the $\\ell_1$ error to linear in the $\\ell_\\infty$ error. Their framework is rather general and the authors apply it to get learning-augmented algorithms and bounds for weighted matroid intersection and discrete energy minimization as well. The authors also provide PAC bounds on learning predictions for these problems under the $\\ell_\\infty$ norm. Strengths\n- The connection between warm-starting in Dinitz et al and in the framework of discrete convex analysis is interesting and general.\n- The improvements in the bounds from prior work are significant, changing the error dependence from $\\ell_1$ to $\\ell_\\infty$.\n- I thought the discussion of learning primal vs. dual solutions in Section 5 was very interesting. It is worthwhile to consider what factors make some predictions useful or not for algorithms with predictions.\n\nWeaknesses\n- For large graphs, the PAC bounds require many samples. In particular, if we set $C=n\\|w\\|_\\infty$, we need at least $\\frac{n^2 \\|w\\|_\\infty^2}{\\epsilon^2}$ sample instances which for large graphs seems extreme. The bounds are a significant improvement over the bounds given in prior work but I'm not sure how informative they actually are.\n- It seems that many of the techniques used in this paper come almost directly from prior work. Nonetheless, I think the application and combination of these ideas makes for some interesting insights and results on learning-augmented algorithms.\n- Perhaps most importantly, seeing as both this and the prior work are in some sense not comparing themselves to the best theoretical algorithms for matching (even if the predictions are near-perfect, the theoretical bounds will be worse), it would be more compelling if some experiments were done to show that the this discrete convex analysis approach is actually a better way to approach the problem than Dinitz et al. Do you think that the DCA-based algorithms actually improve on the work of Dinitz et al in practice, or is it rather the case that you can give a tighter analysis of these algorithm than they could? I found the discussion of limitations to be adequate. I do not foresee any specific negative impacts of this work as it is quite theoretical and abstracted away from applications.", " This paper presents results illustrating the possible benefits of initializing learning algorithms based on predictions. By using a discrete convex analysis framework, the results indicate improved bounds for the sample and time complexity. The usefulness of the framework is shown by applications to weighted perfect bipartite matching, weighted matroid intersection, and discrete energy minimization. Finally, whereas the choice whether to learn primal or dual solutions has typically been made somewhat heuristically, the paper uses the proposed framework to give principled guidelines. The paper is clearly written and structured, addresses a pertinent issue, and seems to provide novel improvements on prior work. The presentation is neat. \nThe improvements over prior results are significant; for instance, the time complexity of some algorithms is improved by up to a factor $n$, where $n$ is the number of vertices.\n\nOne weakness of the results is that, unlike many previous analyses where the possible performance of learning algorithms due to the use of predictions, the analysis is unable to recover optimal worst-case bounds. \nA more extensive discussion of the applicability of the given convexity assumptions and how these contrast with other notions of convexity could be beneficial in order to more clearly motivate the work and clarify the benefits and limitations. What is the reason that your approach is unable to recover optimal worst-case bounds? Is this inherent to the approach, or can it be alleviated? (I understand that this is not crucial, as discussed in the end of the paper) \nYou discuss in Section 6 that the issue above can be mitigated by running a standard algorithm in parallel. It seems as if the time complexity of such an approach would, compared to alternatives, never be worse by more than a constant factor 2. Is this a correct interpretation? What is the worst case? \nCan similar lower bounds be shown for the time complexity? \n\nMinor things: \nline 28: worse->worst \nline 113: \"the the\" The authors clearly state the limitations, but an extended discussion on what classes of problems enjoy the different convexity notions could be beneficial." ]

[ -1, -1, -1, -1, 7, 6, 6 ]

[ -1, -1, -1, -1, 3, 4, 1 ]

[ "gmoXgeiHOM", "4BjR6vUUuk6", "oscVwJw6XQF", "LcbZc8Qk2L", "nips_2022_-GgDBzwZ-e7", "nips_2022_-GgDBzwZ-e7", "nips_2022_-GgDBzwZ-e7" ]

[ "aWr-TEBWcyq", "sT3wKtNWDxt", "iXHD21a0pId", "Plck1DfDKAO", "jO3fWBcTWgx", "OfEszt74USL", "oA4jHF1--5t", "Ue4Cx1uq0H6", "i-wWVRkHOKs", "XRAoXJR3HDH", "4svVX8ETKTR", "tP02CGWOE7", "yjrei3MTm1y", "22deXEFa6Jv" ]

[ "author", "author", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your comments.\n\n---\n**1. Handle unmatched expressions by adding a background class to ReferFormer and other methods.**\n\nWe provide a further discussion to address that adding a naïve classification model that treats negative samples as an additional class is limited, while our method exploiting the nature of the problem with cycle consistency could handle the unmatched expressions. \n\nThe principal difference is that between **implicit** and **explicit** classes. In the absence of negative samples, a \"none of the above\" (background class) is effectively an **implicit** class. Being implicit, there are no training data provided for it, so you are correct, we end up handling it as a problem of trying to identify OOD through thresholding criteria. There is a key feature here. In OOD determination, there is no **discriminative** component of the model assigned to the class -- the rejection is effectively performed based entirely on low likelihood as computed from the distributions of the known classes, and as a consequence heuristics must be imposed.\n\nWhen we convert \"none of the above\" to an **explicit** class, as we have, it converts this to a discriminative modeling problem. The challenge is that, given the vast scope of the \"none of the above\" class, it is generally infeasible to obtain sufficient training data to model all possibilities. This is a known problem. \n\nThis has also been noticed in the ReferFormer and MTTR, where, when we introduce the none-of-the-above as an explicit class through a classification head, it provides no benefit -- the ReferFormer is unable to model it well.\n\nOur cyclic consistency approach provides us a way to capture this class using just a limited number of training samples from this now-explicit class, and we are able to do this because of the specific nature of the R-VOS problem. This, in fact, is a **novelty** of our approach -- we are exploiting the nature of the problem to be able to model this very diverse class effectively using a limited number of training samples. This also clearly shows up in the performance numbers.\n\nAs such, our approach is not a trivial increment. We have proposed a solution that exploits the structure of the problem to achieve what a naive inclusion of negative samples in techniques such as ReferFormer would not.\n\nThe reviewer is, unfortunately, dismissing our feature -- the introduction of an **explicit** class and a mechanism that allows us to handle its diversity as a solution that could hypothetically also have been achieved by other models, had they too introduced it as an explicit class. While this may or may not be true (given that there is no evidence for or against it), it should ideally not be held as a criterion for evaluation. Otherwise, similar hypothetical criteria could be applied against most innovations.\n\nWe thank the reviewer in advance for consideration of this fact.\n\n---\n**2. Clarification of the novelty**\n\nWe agree that cycle consistency is commonly used and has many variants. However, the novelty of our work is not only proposing the relational cycle consistency. We summarize our key novelty as follows.\n\n- Given the fact that referring expression is not always paired with the video in practice, we introduce the $\\mathrm{R}^2$-VOS problem, which extends the R-VOS task to accept unpaired video and text as inputs, and propose a proper metric $\\mathcal{R}$ to measure the false-positive objects.\n- We propose a pipeline that jointly optimizes the primary referring segmentation and dual expression reconstruction task. A early grounding module is introduced which serves as an intermediate proxy for both problems.\n- We introduce relational cycle consistency constraint to enhance the semantic alignment between visual and textual modalities. In particular, the constraint is applied in the embedding space to avoid decoding the textual embedding to expression (always biased by pretrained language model).\n- The proposed components not only help suppress false positives but also improve the segmentation ability. Our method achieves state-of-the-art performance on two common R-VOS dataset (Ref-Youtube-VOS, Ref-DAVIS), and our proposed $\\mathrm{R}^2$-Youtube-VOS", " Thank you for your further suggestions! We will revise the paper to reveal those changes.", " Thanks for the detailed response.\n\n**1. Handle unmatched experssions by adding a background class to ReferFormer and other methods.**\n\nAs you pointed out, ReferFormer and other methods, _e.g._, MTTR, only train with positive samples, _i.e._, matched experssions. I agree with you that this is the reason why they do not work well on your dataset even if they have a background class. However, to me, this shows they have great potential to work well if trained with negative samples, _i.e._, unmatched experssions in the same way that your method is trained. In other words, your method is trained with samples that are not used to train ReferFormer and MTTR, thus making the comparison somewhat unfair.\n\nIf you do not use any negative samples during training, they are OOD samples. However, if the negative samples are used during training, they are not OOD samples anymore. The negative samples could be handled by the background class of ReferFormer and MTTR, if you use them during training. This further validates my point that the comparison is not fair.\n\n**2. Novelty of the relational cycle consistency.**\n\nI agree that the proposed relational cycle consistency is not the same as existing ones. However, to me, a variant of the cycle consistency is not novel enough for me to change my rating.\n\n ", " Thank you for clarifying the differences between your work and Referformer. Points 3 and 4 are particularly useful in clarifying the difference in the method architecture which is most useful.\n\nThe part of the rebuttal response to reviewer Gh1L, \"As the positive video evaluation of $\\mathcal{R}^{2}$-VOS is the same as Ref-Youtube-VOS, the numbers of J & F do not change [...]\" would be useful to include in the main paper as well since this also clarifies how $\\mathcal{R}^{2}$-VOS is different from Ref-Youtube-VOS.", " Thanks for your further suggestions! Our answers to the questions are as follows.\n\n---\n**1. The ablation study is too simple by removing each component independently.**\n\nSorry for the misleading notions in Table 3. Our ablation study is conducted by adding each component step by step (Line 302-303 in the revised paper). The **gains** reported in Table 3 are based on the baseline setting. The **relative gain** for FT is 0.4 $\\mathcal{J}$\\&$\\mathcal{F}$ and 0.1 $\\mathcal{R}$. The contribution of FT is not significant. We have revised the notion of Table 3 to clarify the underlying relation between each experiment.\n\nTable3: Impact of different components in our method:\n\n| Components | $\\mathcal{J}$\\&$\\mathcal{F}$ | $\\mathcal{J}$ | $\\mathcal{F}$ | $\\mathcal{R}$ |\n| ---- | ---- | ---- | ---- | ---- |\n| Baseline | 52.4 | 51.9 | 52.8 | 34.9 |\n| +EG | 55.5$_{\\rm{\\bf{+3.1}}}$ | 54.4 | 56.5 | 32.9$_{\\rm{\\bf{-2.0}}}$ |\n| +EG+CC | 56.9$_{\\rm{\\bf{+4.5}}}$ | 55.7 | 58.1 | 94.0$_{\\rm{\\bf{+59.1}}}$ |\n| +EG+CC+FT | 57.3$_{\\rm{\\bf{+4.9}}}$ | 56.1 | 58.4 | 94.1$_{\\rm{\\bf{+59.2}}}$ |\n\n---\n**2. The difference between this work and ReferFormer.**\n\nWe have clarified the differences between our paper and ReferFormer in Response to Reviewer fwGH, and also added the Appendix.A in the revised paper. Here we list the discussion: \n\nWe summarize differences between our work and ReferFormer, and will add the discussion in the revision. \n\n- Different from all the existing R-VOS methods, including ReferFormer, using all positive text-video pairs for training, we use both positive and negative pairs, which help the learning of differentiating semantic consensus between different pairs.\n\n- We leverage the relational text-video-text cycle consistency to better correspond the text embedding space to the video embedding space. Positive pairs are constrained with the cycle consistency for better embedding learning, while negative pairs unconstrained with the cycle constraint could be identified. \n\n- We utilize the early-grounding module, which modulates the video feature with the video-aware text embedding. Thus, irrelevant video features are suppressed in an early stage, while ReferFormer only uses dynamic convolution in the final mask decoding stage, easier to involve irrelevant objects, as shown in the results of positive pairs Figure 6.\n\n- Our instance query is composed of both the original sentence embedding and the reconstructed one. Different from ReferFormer that only utilizes original sentence embedding as queries, the reconstructed embedding can encode visual information to facilitate the instance query to decode the objects from visual features.\nWe have already shown more qualitative results in the video demo of the supplemental material, and will add some samples in the main paper.\n\n- Our method achieves superior performance than Referformer. Under the same ResNet-50 backbone, our method achieves 57.3 $\\mathcal{J}$\\&$\\mathcal{F}$, 94.1 $\\mathcal{R}$ and 30 FPS compared to the 55.6 $\\mathcal{J}$\\&$\\mathcal{F}$, 30.6 $\\mathcal{R}$ and 22 FPS of ReferFormer (more analysis to improvements on each metric is available in Appendix.A). \n\n", " Thanks for reporting more experimental results. I still have several issues after reading the rebuttal.\n1. For Table3 Impact of different components, the ablation study is too simple by removing each component independently. The underlying contribution between CC and FF is not clear. More in-depth analysis about these two components should be discussed, such as adding them step-by-step.\n2. As Reviewer Fhve pointed out, the difference between this work and RefFormer should be further clarified.", " Dear AC and all reviewers:\n\nThanks again for all of your constructive suggestions, which have helped us improve the quality and clarity of the paper!\n\nSince the discussion phase is over half, we have not heard any post-rebuttal response yet.\n\nPlease don’t hesitate to let us know if there are any additional clarifications or experiments that we can offer, as we would love to introduce you to the merits of the paper. We appreciate your suggestions.\n\nBest regards,\n\nAuthors of NeurIPS 2021 Submission #746", " We thank the reviewer for the valuable comments. Our answers are split into two parts: Part 1 for weakness and Part 2 for Questions.\n\n---\n**1. Some R-VOS methods overcome the problem that unpaired video and text as inputs so that $\\mathrm{R}^2$-VOS does not need to be studied separately.**\n\nWe argue that studying the $\\mathrm{R}^2$-VOS problem is necessary.\nTo the best of our knowledge, there are no existing R-VOS methods that can overcome the false positives caused by unpaired inputs. Please be aware of the robustness $\\mathcal{R}$ evaluation in Table 2 and qualitative results in Figure 6 (negative pairs), the previous state-of-the-art methods, ReferFormer and MTTR, can not handle such cases well.\nAlthough existing R-VOS methods align multi-modal semantic information by learning with positive text-video pairs, they didn't consider the negative pairs. Negative pairs are demonstrated helpful to learn correspondences between two feature spaces [1]. Our model exploits the negative pairs in training and achieve better robustness.\n\nIn summary, we propose the new $\\mathrm{R}^2$-VOS problem to generalize and refine the original R-VOS problem from the data, methodology and evaluation aspects: augment both the training and validation datasets with negative pairs; enhance or verify multi-modal consistency according to (object-level) semantic consensus with cycle consistency; introduce a new metric of robustness $\\mathcal{R}$ against unpaired inputs for practical scenarios.\n\n[1] Learning transferable visual models from natural language supervision, ICML 2021\n\n---\n**2. This paper proposed a new task and proposed a new dataset while makes the ablation study based on the Ref-Youtube-VOS.**\n\nAblation study on the $\\mathrm{R}^2$-VOS dataset is a very constructive suggestion, and we update new $\\mathcal{R}$ metrics on $\\mathrm{R}^2$-VOS in the following tables (also marked in blue in the revised submission). As the positive video evaluation of $\\mathrm{R}^2$-VOS is the same as Ref-Youtube-VOS, the numbers of $\\mathcal{J}$\\&$\\mathcal{F}$ do not change. \n\nTable3 Impact of different components (note that components are added step by step):\n\n| Components | $\\mathcal{J}$\\&$\\mathcal{F}$ | $\\mathcal{J}$ | $\\mathcal{F}$ | $\\mathcal{R}$ |\n| ---- | ---- | ---- | ---- | ---- |\n| Baseline | 52.4 | 51.9 | 52.8 | 34.9 |\n| +EG | 55.5$_{\\rm{\\bf{+3.1}}}$ | 54.4 | 56.5 | 32.9$_{\\rm{\\bf{-2.0}}}$ |\n| +CC | 56.9$_{\\rm{\\bf{+4.5}}}$ | 55.7 | 58.1 | 94.0$_{\\rm{\\bf{+59.1}}}$ |\n| +FT | 57.3$_{\\rm{\\bf{+4.9}}}$ | 56.1 | 58.4 | 94.1$_{\\rm{\\bf{+59.2}}}$ |\n\n\nTable 4 Impact of cycle consistency constraint:\n\n| Constraint | $\\mathcal{J}$\\&$\\mathcal{F}$ | $\\mathcal{J}$ | $\\mathcal{F}$ | $\\mathcal{R}$ |\n| ---- | ---- | ---- | ---- | ---- |\n| None | 55.5 | 54.4 | 56.5 | 32.9 |\n| PW | 54.4$_{\\rm{\\bf{-1.1}}}$ | 53.3 | 55.5 | 88.7$_{\\rm{\\bf{+55.8}}}$ | \n| RA | 56.7$_{\\rm{\\bf{+1.2}}}$ | 55.5 | 57.9 | 93.6$_{\\rm{\\bf{+60.7}}}$ |\n| RD | 56.4$_{\\rm{\\bf{+0.9}}}$ | 55.2 | 57.6 | 90.4$_{\\rm{\\bf{+57.5}}}$ |\n| RD+RA | 56.9$_{\\rm{\\bf{+1.4}}}$ | 55.7 | 58.1 | 94.0$_{\\rm{\\bf{+61.1}}}$ |\n\nTable 5 Impact of the query number:\n\n| Query Number | $\\mathcal{J}$\\&$\\mathcal{F}$ | $\\mathcal{J}$ | $\\mathcal{F}$ | $\\mathcal{R}$ |\n| :----: | ---- | ---- | ---- | ---- |\n| 1 | 54.9 | 54.2 | 55.6 | 94.7 |\n| 5 | 57.3 | 56.1 | 58.4 | 94.1 |\n| 9 | 57.0 | 56.8 | 57.2 | 93.5 |\n\nTable 6 Impact of the window size:\n| Window Size | $\\mathcal{J}$\\&$\\mathcal{F}$ | $\\mathcal{J}$ | $\\mathcal{F}$ | $\\mathcal{R}$ |\n| :----: | ---- | ---- | ---- | ---- |\n| 1 | 53.5 | 53.0 | 54.0 | 89.2 |\n| 3 | 56.8 | 56.5 | 57.1 | 92.1 | \n| 5 | 57.3 | 56.1 | 58.4 | 94.1 |\n\n---\n**3. Text reconstruction to reconstruct the text feature to measure semantic consensus is commonly used for Video-Language tasks.**\n\nWe agree that utilizing text reconstruction in Video-Language tasks is common, but our work is very different from the previously used text-vision-text cycle consistency, also stated in Line 97-124.\n* (1) We use **relational** cycle consistency instead of the previous **point-wise** counterpart, making the cycle constraint feasible between two feature spaces that do not have strict bijective mapping (Figure 2 (d)). In particular, the mapping from visual objects to textual expressions is not necessarily bijective, as there could be multiple textual descriptions for the same object (about 5 for Ref-Youtube-VOS). Thus, naively adding point-wise consistency may make the feature space collapse (Line 116-119). Our ablation study in **Table 4** demonstrates the effectiveness of our relational cycle consistency. The point-wise cycle consistency even decreases the accuracy.\n* (2) We apply the cycle consistency on the text embedding space instead of the text expression space, which avoids the dataset bias of the pretrained linguistic model from other datasets. Also, we enable the joint optimization of the primary and dual problem efficiently without decoding text embeddings into expressions, as illustrated in Figure 2 (b).\n", " Here are answers to the raised questions.\n\n---\n**4. Detailed explanation for $1(\\hat{A})$ in Equ 8.**\n\nIn Equation 8, $\\hat{A}$ denotes the ground-truth semantic alignment degree, i.e., the probability indicating whether the text expression corresponds to the visual object in the video, which equals to 1 for paired input and 0 for unpaired ones. $1(\\hat{A})$ aims to filter out the text reconstruction loss $\\mathcal{L}_{text}$ for unpaired inputs, since text-video-text cycle is meaningless. \nIn addition, we note that $A \\in [0,1]$ is the predicted alignment degree. The indicator function 1(A) equals to 1 when $A>0.5$, else 0.\n\n\n---\n**5. Is the model trained on the Ref-Youtube-VOS dataset and directly evaluated on the $\\mathrm{R}^2$-VOS dataset?**\n\nYes. We train all the models based on the original Ref-Youtube-VOS dataset. $\\mathrm{R}^2$-VOS dataset is an evaluation set.\n\n* Although using the same Ref-Youtube-VOS dataset in training, we augment it with both positive and negative text-video pairs, which is different from previous R-VOS methods. We construct negative pairs in each batch. After each iteration of positive pairs, we shuffle the video set in the batch to create negative pairs and feed them into the network again. The ground-truth semantic alignment $\\hat{A}$ is set to 1 for positive pairs and 0 for negative pairs. We will elaborate detailed training in the revision.\n\n* The evaulation dataset $\\mathrm{R}^2$-VOS can be assumed as an augmented Ref-Youtube-VOS val set containing two parts: Ref-Youtube-VOS val set (for positive videos, evaluated by $\\mathcal{J}$\\&$\\mathcal{F}$) and shuffled Ref-Youtube-VOS val set (for negative videos, evaluated by $\\mathcal{R}$). \n\n---\n**6. The source of the negative sample videos in the dataset. Video that do not correspond to text information in the entire dataset should be added.**\n\nFor negative pairs in $\\mathrm{R}^2$-VOS dataset, the videos and texts are still selected from the Ref-Youtube-VOS validation set, while the order of videos is shuffled to make sure that each text queries to a different video.\n\nTo evaluate on videos that are not in Ref-Youtube-VOS, we collect **new negative videos** by adding videos in Ref-DAVIS val set into the original Ref-Youtube-VOS val set. We report the $\\mathcal{R}$ metric in the table below. This evaluation indicates that the source of negative videos does not have high impact on the robustness of our model. \n\n|Negative Video Source|ReferFormer ($\\mathcal{R}$)|Ours ($\\mathcal{R}$)|\n| ---- | ---- | ---- |\n|Ref-Youtube-VOS|30.6|94.1|\n|Ref-Youtube-VOS + Ref-DAVIS|33.1|92.2|", " \nWe thank the reviewer for the time and effort to review our paper. Our answers to the questions are as follows.\n\n---\n**1. False positives can be easily handled by adding a background class to ReferFormer and other methods.**\n\nWe would like to argue that simply adding a background class in existing methods, like ReferFormer, cannot handle the cases of an expression that does not correspond to any objects in the video well. \nIn fact, ReferFormer has already involved a background (empty) class to indicate the object existence at the frame level (in the Section 3.4 of the ReferFormer paper, represented as $p_i^t$). Similarly, MTTR also has a background class. However, the robustness evaluation in Table 2 indicates that the background class with a simple classification head cannot effectively discriminate semantic consensus between input pairs.\n\n\nHere are the reasons.\nExisting R-VOS methods only use positive text-video pairs in training, while none of negative pairs are sampled. Modeling negative correspondences between textual expressions and visual object is an out-of-distribution (OOD) problem as any unrelated expressions to the video can be regarded as a negative sample. Existing methods only consider positive pairs, and it is known that a naive classification head cannot solve the OOD problem well. Thus, modeled correspondences between unpaired textual expressions and videos by these methods could be uncertain, usually resulting in false positives, as Figure 6 shown.\nUnlike some previous methods (ReferFormer, MTTR) directly applying a classification head on the output of text-to-video queries, our model exploit the consistency in the text-to-video-to-text cycle and enable the discrimination by assessing the cycle consistency, which smartly circumvent difficulties in the classification for OOD problem. We also add negative pairs in training for learning better discrimination.\n\n\n---\n**2. Researchers have already used cycle consistency (text reconstruction) to help referring expression segmentation in images. It is an extension to videos.**\n\nOur method is exactly not an extension of the conventional cycle consistency used in previous referring image segmentation methods [1,2].\nAs stated in Line 97-124, our method is very different from the previously used cycle consistency: \n* (1) We use **relational** cycle consistency instead of the previous **point-wise** counterpart, which makes the cycle constraint feasible between two feature spaces that do not have strict bijective mapping, as illustrated in Figure 2 (d). In particular, the mapping from visual objects to textual expressions is not necessarily bijective, as there could be multiple textual descriptions for the same object (about 5 for Ref-Youtube-VOS). Thus, naively adding point-wise consistency may make the feature space collapse (Line 116-119). Our ablation study in **Table 4** demonstrates the effectiveness of our relational cycle consistency. The point-wise cycle consistency even decreases the accuracy.\n* (2) We apply the cycle consistency in the text embedding space instead of the original text expression space [1,2], which avoids the dataset bias of the pretrained linguistic model from other datasets. Also, we enable the joint optimization of the primary and dual problem efficiently without decoding text embeddings into expressions, as illustrated in Figure 2 (b).\n\n\n[1] Query reconstruction network for referring expression image segmentation, TMM 2020\n\n[2] Referring Expression Object Segmentation with Caption-Aware Consistency, arXiv 2019\n\n---\n**3. What is the range of A? When does the indicator function 1(A) equal to 1?**\n\nThe predicted alignment degree $A \\in [0,1]$ is the probability indicating whether the textual expression corresponds to the visual object in the video. The indicator function $1(A)$ equals to 1 when $A>0.5$, else 0.\n", " \nWe thank the reviewer for the particularly insightful feedback. \nThe detailed comments have been incorporated in the revised version to improve the readability of the paper. \nOur answers to the questions are as follows.\n\n---\n**1. Details in $\\textrm{R}^2$-Youtube-VOS dataset. How many negative text-video pairs are created?**\n\nWe describe the $\\textrm{R}^2$-Youtube-VOS dataset construction in Line 239-243. Here we supplement with details. The $\\textrm{R}^2$-Youtube-VOS is an evaluation dataset that contains two parts, i.e., positive pairs and negative pairs. For positive pairs, the text-video pairs are exactly the same as the Ref-Youtube-VOS validation set. For negative pairs, the videos and texts are still selected from the Ref-Youtube-VOS validation set, while the order of videos is shuffled to make sure that each text queries to a different video. The number of negative pairs is the **same as positive pairs**. In this way, each text queries to **one** positive and **one** negative video.\n\n---\n**2. In the sentence in lines 242-243, can you clarify what \"constrain all negative text-video pair unrelated\" means?**\n\nThis sentence aims to emphasize that the text is ensured to query to a different video after shuffling the original video set. Thus, the text is not related to the queried video. We will clarify the expression in the revised paper.\n\n---\n**3. Suggestions**\n\nThanks for your constructive suggestions. We will revise the paper for the following items.\nWe have revised the submission. The revised parts are marked in **blue for easy tracking. Here we list the changes. \n\n* We will add related reference on vision-language representation learning in Section 2.\n\n* We will correct the typos and adjust the unclear sentence according to the suggestions. \n\n* We summarize four differences between our work and ReferFormer, and will add the discussion in the revision. \n(1) Different from all the existing R-VOS methods, including ReferFormer, using all positive text-video pairs for training, we use both positive and negative pairs, which help the learning of differentiating semantic consensus between different pairs.\n(2) We leverage the relational text-video-text cycle consistency to better correspond the text embedding space to the video embedding space. Positive pairs are constrained with the cycle consistency for better embedding learning, while negative pairs unconstrained with the cycle constraint could be identified. \n(3) We utilize the early-grounding module, which modulate the video feature with the video-aware text embedding. Thus, irrelevant video features are suppressed in an early stage, while ReferFormer only uses dynamic convolution in the final mask decoding stage, easier to involve irrelevant objects, as shown in the results of positive pairs Figure 6.\n(4) Our instance query is composed of both the original sentence embedding and the reconstructed one. Different from ReferFormer that only utilizes original sentence embedding as queries, the reconstructed embedding can encode visual information to facilitate the instance query to decode the objects from visual features.\nWe have already shown more qualitative results in the video demo of the supplemental material, and will add some samples in the main paper.\n\n---\n**4. Limitation**\n\nWe agree on the point that \"per-frame false positive when object disappeared\" can be a limitation of the current method. As the reviewer said, this is because the ground-truth label of RVOS is in the video-level, semantic alignment cannot be measured in a per-frame manner. We will add the limitation discussion to reveal this point for our future research.\n", " This paper presents a new method for referring video object segmentation (R-VOS). It points out an assumption that current R-VOS datasets make: that the object referred to in the text is present in the video. This assumption is not true in real-world text-video query applications. Current models rely on the assumption which results in false positives when the referred object is not in the video. The paper addresses this in two ways: by introducing a dataset $R^{2}$-YouTube-VOS and evaluation metric that measures the false positives made by a model, and by creating a method that enforces the semantic matching of visual and text features. The authors demonstrate that their method outperforms current methods on Ref-YouTube-VOS and Ref-DAVIS and has fewer false positives than previous methods on the proposed $R^{2}$-YouTube-VOS. Strengths:\n\n- The paper points out an important limitation of current R-VOS datasets and evaluation metrics and takes the proper steps to address it by creating the metric R and augmenting Ref-YouTube-VOS with negative video-text alignment pairs.\n- The idea to enforce semantic consistency of the embedded textual space and generated embeddings is novel and interesting.\n- The experiments are carefully designed. They clearly show that the model improves upon the state of the art. The ablation results show the benefit of the proposed relational cycle consistency losses.\n\nWeaknesses:\n\n- The paper is missing some details on the $R^{2}$-YouTube-VOS dataset including how many negative text-video pairs are created. Questions:\n- In the sentence in lines 242-243 can you clarify what \"constrain all negative text-video pair unrelated\" means?\n\nSuggestions:\n- There are many works on vision-language representation learning and it would be useful to the reader if the authors could include more of this background in Section 2.\n- Line 58 a better word instead of \"medium\" would be \"proxy\"\n- It would be more clear to call $f_{m}$ an intermediate feature rather than a medium in line 112.\n- Typo in line 109 \"textural\" -> \"textual\"\n- Figure 2c caption is a run-on sentence and would sound better split into two.\n- When discussing the window size in line 259 mention that Swin or VideoSwin is used as a backbone.\n- Refer to Figure 4 somewhere in the text.\n- Line 320 \"temporal-consistent\" -> \"temporally-consistent\"\n- The discussion of quantitative results is currently limited. It would benefit from more details on how the proposed method differs from the ReferFormer architecture and why the ReferFormer is not able to learn the necessary information to avoid false positives. - The paper does not include a section on limitations/negative societal impact.\n- An important challenge for segmentation in videos is temporary object disappearance due to occlusion, which results in false positives on a per-frame level. Since the semantic alignment ground truth is per-video rather than per-frame the method would not able to address this challenge, but if the ground truth were collected per-frame then perhaps it would.\n", " The authors introduce a \"new\" variant of referring video object segmentation. This variant considers the possiblity that the given referring expression does not correspond to any object in the given video. A method based on relational cycle consistency is introduced as well. The proposed method has an additional head that predicts whether there is an object that corresponds to the given expression or not. Experiments are mainly conducted on two standard benchmarks to validate the effectiveness of the proposed method. Strengths:\n(1) The paper is well written is easy to understand. Notations and symbols are well defined.\n(2) The authors propose a method that can handle expression that does not correspond to any objects in the given video via a simple head, which is likely a simple fully connected layer.\n(3) The proposed method is evaluated on two standard benchmarks and achieves good performance on both datasets.\n\nWeakness:\n(1) While existing methods do not explicitly consider the possiblilty of being given an expression that does not correspond to any objects in the video, it is likely that this can be easily handled by adding a background class to ReferFormer [1] and other methods.\n(2) Researchers have already used cycle consistency (text reconstruction) to help referring expersion segmentation in images. To me, this work is mainly an extension of existing ideas to video.\n\n[1] Language as Queries for Referring Video Object Segmentation, CVPR'22 What is the range of A? When does the indicator function 1(A) equal to 1? N.A.", " This paper introduces the Robust R-VOS task that accepts unpaired video and text as inputs. In addition, a pipeline is proposed to optimize the primary referring and dual expression reconstruction task. A relational cycle consistency constraint is proposed to enhance the semantic alignment between different modalities. The proposed approach achieves state-of-the-art results on three datasets. Strengths:\n1)This paper proposed the Robust R-Youtube-VOS dataset, is collected to measure the robustness of R-VOS models.\n2)The relational cycle consistency is applied to preserve the structure of the feature space rather than point-wise consistency. Through the experience, the cycle consistency achieves better results than point-wise consistency.\n3)The proposed approach achieves state-of-the-art on three datasets, and some ablation studies are conducted to validate the effectiveness of each component.\n4)The paper is generally well written. \n\nWeaknesses:\n1) My main concern is that the main novelty. In this paper, for negative videos\nM_o is empty. For some R-VOS methods, they are able to align the semantic information of different modalities, and they also overcome the problem that unpaired video and text as inputs so that Robust R-VOS does not need to be studied separately.\n2) This paper proposed a new task and proposed a new dataset. However, the paper makes the ablation study based on the Ref-DAVIS17, and Ref-Youtube-VOS.\n3) This paper leverages text reconstruction to reconstruct the text feature to measure semantic consensus. It is commonly used for Video-Language tasks.\n 1 In formula 8, l(A ̂) is used to measure semantic consensus between Reconstructed text feature and text feature, it should be explained clearly.\n2 It is not clearly stated in the article how to evaluate this model on the Robust R-VOS dataset. Is the model trained on the Ref-Youtube-VOS dataset and directly evaluated on the Robust R-VOS dataset?\n3 The ablation experiments in this paper are performed on the Ref-Youtube-VOS dataset, which does not need to consider this problem that unpaired video and text as inputs, so different modules need be used separately to verify their effectiveness.\n4 The authors should clearly introduce the source of the negative sample videos in the dataset. If these videos are also from the Ref-Youtube-VOS dataset, each video in the entire dataset will correspond to a positive text message. In order to better verify the robustness of the model, video that do not correspond to text information in the entire dataset should be added.\n Yes" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 4, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 4 ]

[ "iXHD21a0pId", "Plck1DfDKAO", "XRAoXJR3HDH", "4svVX8ETKTR", "OfEszt74USL", "Ue4Cx1uq0H6", "nips_2022_vExdPu73R2z", "22deXEFa6Jv", "22deXEFa6Jv", "yjrei3MTm1y", "tP02CGWOE7", "nips_2022_vExdPu73R2z", "nips_2022_vExdPu73R2z", "nips_2022_vExdPu73R2z" ]

[ "jv1ek0VuWDJ", "Gs0EZrtbyWi", "OpNRQF0g4dP", "mG-Wt7fN9Lr", "7yBACbxzGW3", "mAHcA0LSyj", "3a4uNgp51UC", "EisE-2-remd", "NPmZQqZfD9L", "0YeHvlOws3a", "BrwRVd52tvO", "ETqf1_tlUgG", "jGTmZb1lJCM", "D452RkQ30d3", "vlt0HF_VcSr", "s2x1OqNETKI", "mDYZ2tlZUvI" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank your for your valuable suggestions! \n\n> I would advise to replace \"Finished Accuracy\" by \"Final Accuracy\" since it is supposed to be the same thing and \"Final Accuracy\" is mostly used in the literature.\n\n**Response:** Thank you for your suggestion. We have changed the 'finished acc' to 'final acc' in the paper.\n\n> \"the validation set is randomly sampled from memory buffer and all examples in memory are used for training. \"\nusing a validation set for training could lead to overfitting, it should be only for model / HPs selection.\n\n**Response:** Sorry for the confusion. About the validation set, \n1. Our validation sets are sampled from the training set or memory, and are used to compute the example influences in training set instead of selecting models or hyperparameters. \n2. The validation sampling is dynamic at each step in order to approach the dataset or memory distributions.\n3. We did not split an independent validation set because the memory buffer is too small, where any split will damage the continual learning and lead to more serious catastrophic forgetting. \n\n> \"this is an verification contribution.\" write it then! :)\n\n**Response:** Thank you for your suggestion. We have added this to the paper.", " I think the authors provided a good answer to my questions and comments and I will increase my rating to accept. \n\nSome comments:\n\n- I would advise to replace \"Finished Accuracy\" by \"Final Accuracy\" since it is supposed to be the same thing and \"Final Accuracy\" is mostly used in the literature.\n\n> \"the validation set is randomly sampled from memory buffer and all examples in memory are used for training. \"\n\nusing a validation set for training could lead to overfitting, it should be only for model / HPs selection.\n\n> \"this is an verification contribution.\"\n\nwrite it then! :)", " > I appreciate this experiment -- was it added to the paper as well? Also, one more comment -- the diff metrics you show by themselves are not easily interpretable as it is hard to say whether a difference of magnitude 1e-4 is small or big. I would recommend focusing on the second table (True Positives, etc) or adding some kind of baseline so that the numbers are easier to compare.\n\n**Response:** Thanks for your suggestion. We follow the comments to focus on the second table. In detail, we evaluate on the above toy experiments (1000 training data influence 500 test data) with three extra baselines. The three baselines use different ways to approximate inverse Hessian, and the results are shown in the following table and the Appendix. The results show the proposed method has better approximation rate compared with other inverse Hessian approximation methods.\n\n\n\n|Method|Total examples|true positive|true negative|false positive|false negative| \n|----|----|----|----|----|----|\n|Larsen [1]|1000|552|304|26|118|\n|Luketina [2]|1000|533|313|17|137|\n|Neumann Series [3]|1000|642|282|48|28|\n|Ours|1000|650|315|15|20|\n\n[1] Larsen J, Hansen L K, Svarer C, et al. Design and regularization of neural networks: the optimal use of a validation set[C]//Neural Networks for Signal Processing VI. Proceedings of the 1996 IEEE Signal Processing Society Workshop. IEEE, 1996: 62-71.\n\n[2] Luketina J, Berglund M, Greff K, et al. Scalable gradient-based tuning of continuous regularization hyperparameters[C]//ICML, 2016\n\n[3] Lorraine J, Vicol P, Duvenaud D. Optimizing millions of hyperparameters by implicit differentiation[C]//AISTATS. 2020.\n\n> Another minor comment, Figure 3 (bottom) was definitely improved in the paper, but I still don't get the colorbar/equal proportion part. Could you explain in a little more detail, e.g. in the Figure caption?\n\n**Response:** Sorry for the confusion, we have revised Figure 3 and the caption to clarify the confused colorbar and proportion.", " Thank you for the thorough response and modifications made to the paper. Overall, I'm satisfied by the response and I decided to increase my score to \"Accept\". \n\nI don't have any comments for most of the points made by the authors in the reply except for the Hessian approximation experiment (the first response). I appreciate this experiment -- was it added to the paper as well? Also, one more comment -- the diff metrics you show by themselves are not easily interpretable as it is hard to say whether a difference of magnitude 1e-4 is small or big. I would recommend focusing on the second table (True Positives, etc) or adding some kind of baseline so that the numbers are easier to compare.\n\nAnother minor comment, Figure 3 (bottom) was definitely improved in the paper, but I still don't get the colorbar/equal proportion part. Could you explain in a little more detail, e.g. in the Figure caption?", " Dear reviewer, we have revised the manuscript and reuploaded the revised version, where contents in cyan are revised. Please download the revised manuscript and appendix. \n\n## Response to Weakness\n\n> The major weakness of the paper from my perspective is that in the end, I'm not sure how well the Importance Function motivation connects with the final MetaSP algorithm. Intuitively, these two seem connected, but a theoretical or empirical argument confirming that would be very useful. In particular, do you know how well the MetaSP approach approximates the gradient from Equation (6)? Can we show their equivalence, either theoretically or by running some experiments on toy problems? The authors hint at this kind of result in Section 4.1, but no hard proof is given. \n\n**Reponse:** Sorry for the confusion. \n\n- Eq.(6) shows the chain rule in influence function, that the derivation on the small perturbation can be computed by the product of test gradient, Hessian inverse and the training gradient. The detail can be seen in the Appendix A.2. \n- To evaluate the example influence approximation from our meta method to Hessian Influence Function (Eq. (6)), we build a toy experiment. We use 1000 FMNIST training data and 500 test data. We design a simple fc network with a single hidden layer. The results is the influence from the 1000 training data to 500 test data. We have the following observation: (1) The influence difference of two ways are small; (2) Most examples (965/1000) have the true influence property of compared with Hessian Influence Function.\n\n|Total examples|diff<0.1|diff<0.01|diff<0.001|diff<0.0001|\n|----|----|----|----|----|\n|1000|1000|1000|1000|670|\n\n|Total examples|true positive|true negative|false positive|false negative| \n|----|----|----|----|----|\n|1000|650|315|15|20|\n\n> The fact that the algorithm is actually applied only on the last 5 epochs out of 50 should be highlighted. This is only mentioned in a single subsection near the end of the paper but seems quite crucial. Have you checked how well the other methods perform in this scenario? For example, what happens if we use fine-tuning for 45 epochs and then ER for 5 epochs? \n\n**Reponse:** Thank you for your suggestion. We evaluate the \"45 finetune + 5 rehearsal epochs\" trick on other rehearsal methods in the following table. The table shows that other rehearsal methods can hardly benifit from the trick, i.e., the performances may got drops compared to training on full 50 epochs. For example, ER achieves better performance in class-incremental learning but gets worse performance in task-incremental learning. We think the performance increase is maybe the less gradient conflict between old and new tasks after 45 epochs. More results about our trick is shown in the Appendix Fig 3(a). \n\n\n(**CI: Class increment, TI: Task increment**)\n|Method |CIFAR10-TI-50epoch |CIFAR10-TI-45+5epoch|CIFAR10-CI-50epoch |CIFAR10-CI-45+5epoch|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|\n|GEM |96.62/89.34/92.49 |96.64/89.04/91.41\t|93.90/37.51/55.43|95.18/35.91/52.54|\n|AGEM |96.78/85.52/90.16|96.62/66.83/79.11\t|96.57/20.02/45.57|96.62/19.65/44.10|\n|MIR |96.76/88.50/90.87|96.87/86.04/88.95\t|96.70/38.53/56.96|96.03/36.90/55.67|\n|GSS |96.56/88.05/90.60|96.96/86.42/89.13 |96.53/35.89/54.33|96.75/36.78/54.32|\n|GMED |96.73/88.91/91.20|96.72/89.20/91.66\t |96.65/38.12/58.92|96.73/38.12/58.89|\n|ER |96.93/88.97/91.12|96.92/85.46/88.78\t|96.73/34.19/53.72|96.82/36.95/55.07|\n|Ours ||97.10/89.40/92.54 ||96.87/42.42/63.52|\n|Ours+RehSel||97.11/89.91/92.66| |96.85/43.76/63.69|", " > The presentation could be improved, as the paper is hard to read at times. There are some minor mistakes (see the Minor comments section below) and in general I think the paper could be more self-contained. In particular, checking the previous works was necessary for me to understand Section 5.1 (SP Pareto Optimal), as the authors do not list the KKT conditions and do not really explain what the result of Eq (10) is. Grammar could also be improved, but for the most part, the mistakes do not make it harder to understand the paper so this is not an important issue. \n\n\n**Reponse:** Sorry for the confusion.\n- We have revised the miner mistakes in our revised manuscript. The details can be seen the response belows.\n- We have described more about the KKT conditions of MGDA [1] in our Appendix.\n\n*Refer to MGDA*:\n\nWe first introduce the Steepest Gradient Method (SGM) [2] in dual-objective optimization. Given two tasks 1 and 2, the objective of SGM\nis \n$$\nd^*, \\alpha^*=\\arg\\min\\_{d,\\alpha}\\quad\\alpha+\\frac{1}{2} ||d||^2,\\quad \\text{s.t.}\\quad g\\_1^\\top d\\le \\alpha, g\\_2^\\top d\\le \\alpha,\n$$\nwhere $g\\_1$ and $g\\_2$ are the gradients for task 1 and 2 specifically. \nThe two constraints can be seen as the difference between task gradients and the optimal gradients.\n\nConsidering the Lagrange multipliers $\\lambda\\_1$ and $\\lambda\\_2$ for the two constraints, we have the dual problem of the above problem as\n$$\n\\lambda\\_1^*, \\lambda\\_2^*=-\\max\\_{\\lambda\\_1,\\lambda\\_2}||\\lambda\\_1 g\\_1+\\lambda\\_2 g\\_2||^2,\\quad\\text{s.t.}\\quad \\lambda\\_1+\\lambda\\_2=1,\\lambda\\_1\\ge0,\\lambda\\_2\\ge 0,\n$$\nThis is the objective of Eq.(10) of the paper.\nIn SGM, the KKT conditions can be writen as\n\n$$\\lambda\\_1^*(g\\_1^\\top d^*- \\alpha^*)=0$$\n$$\\lambda\\_2^*(g\\_2^\\top d^*- \\alpha^*)=0$$\n$$\\lambda\\_1^* \\ge 0, \\lambda\\_2^* \\ge 0$$\n$$\\lambda\\_1^* + \\lambda\\_2^* = 1$$\n$$\\lambda\\_1^* g\\_1+\\lambda\\_2^* g\\_2=d^*$$\n\nThe solution of the dual problem is \n$$\n\\lambda\\_1^*=1-\\lambda\\_2^*=\\min\\left(\\max\\left(\n\\frac{(g\\_2-g\\_1)^\\top g\\_2}{\\|g\\_2-g\\_1\\|\\_2^2},0\\right),1\\right)\n$$\nThis is the objective of Eq.(11) of the paper.\n\n- [1] Ozan Sener and Vladlen Koltun. Multi-task learning as multi-objective optimization. In NeurIPS, 2018.\n- [2] Jörg Fliege and Benar Fux Svaiter. Steepest descent methods for multicriteria optimization. Mathematical methods of operations research, 2000.\n\n> I'm a bit skeptical whether K-Means on the input space learns anything more than just basic background colors. Have you checked how the examples get clustered? What happens if you do not perform clustering at all (i.e. 1 cluster) or just cluster the examples randomly? \n\n**Reponse:** \n\n- Our K-Means is based on the color. Images with similar color appearance are more like to be clustered.\n- In the Appendix (Table 5), we have evaluated if we do not perform clustering (1 cluster, named RehSel w/o Cluster) or random selection in rehearsal (named Random). The proposed method with both clustering and influence obtains superior performance.\n\n> The paper does not list limitations although in the checklist the authors claim that it does. \n\n**Reponse:** In the revised paper, we discussed the limitation of the method.\n\n- The proposed method relies on the rehearsal selection. Like most previous rehearsal, storing the raw data may afftect the privacy to some extent and extra storage is needed. \n- The proposed method is not fast enough in online continual learning (only one epoch). In most situation, however, we can leverage our training tricks (finetune + our method) to reduce the time.\n- Our method is limited in the extreme small memory size. Large memory size means better remembering and accurate validation set (sampled from training set). The proposed method does not perform well when the memory size is extreme small. To prove this, we give an extra experiment as follows. When the buffer size is set to 50, our method outperforms ER. However when the buffer size is set to 20, our method has worse performance than ER.\n\n\n\n(**CI: Class increment, TI: Task increment**)\n|Method|CIFAR10-CI-buffer20|CIFAR10-CI-buffer50|CIFAR10-TI-buffer20|CIFAR10-TI-buffer50|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|\n|ER|97.02/21.87/45.93|97.02/23.37/48.64|97.02/78.60/85.55|97.03/82.63/87.11|\n|Ours|96.80/20.56/45.96|97.24/25.14/50.26|96.99/79.31/86.02|97.32/84.40/89.69|\n\n\n|Method|CIFAR100-CI-buffer20|CIFAR100-CI-buffer50|CIFAR100-TI-buffer20|CIFAR100-TI-buffer50|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|\n|ER|87.87/9.38/25.76|87.99/9.55/25.91|87.87/42.86/52.99|87.99/48.36/57.84|\n|Ours|89.17/9.46/25.90|89.19/10.33/27.34|89.19/42.83/53.07|89.24/49.19/58.62|", " ### Minor comments: \n\n> Line 22: \"robust CL system should achieve outstanding S while keeping a stable P\" - that statement might be a bit controversial as it depends on your desiderata - you might want a model that is plastic but can remember the past moderately well. \n\n**Reponse:** Yes, it is. We have revised the confused representation.\n\n> Line 96: What do you mean by performance? You are using the $p$ symbol which suggests probability, but that's a bit confusing. \n\n**Reponse:** $p$ means the performance (accuracy in classification), this can be seen in Definition 1 of paper.\n\n> Line 120: \"Hessian [...] assumed as positive definite\" - that's a pretty strong assumption if we're not close to the minimum (i.e. during the training). \n\n**Reponse:** Sorry for the confusion, we recheck the IF [1] and remove the assumption. We miswrote the assumption in [1] where the problem is convex. In general, in a non-convex model, the Hessian may be not positive definite. \n\n[1] Pang Wei Koh and Percy Liang. Understanding black-box predictions via influence functions. In ICML, 2017.\n\n\n> Line 121: \"Always out-of-memory\" - that's a bit informal, given enough storage or a small number of parameters I think this operation should be tractable. Of course, I agree that in most cases this statement is true, but I would suggest using more precise wording. \n\n**Reponse:** Sorry for the confusion. We have revised the confused representation to \"maybe out-of-memory\".\n\n> Line 168: might be useful to state those KKT conditions \n\n**Reponse:** Thank you. The detail can be seen in the response above.\n\n> Line 225: I would suggest, when possible, reusing metrics from previous CL papers, as introducing new metrics make it difficult to compare between papers. \n\n**Reponse:** We have reused previous metrics Backward Transfer (evaluate the performance drop, i.e., forgetting), Finished Accuracy and Mean Average Accuracy in Table 1 of the revised manuscript.\n\n> Figure 3: At what point is each of these plots generated? I.e. these metrics are dependent on the parameters $θ$, so which $θ$ are we using? The one from the end of the current task? \n\n**Reponse:** We plot the figure using the updating $θ$, i.e., the $θ$ is changing. Each example got multiple influence in different mini-batchs. And the final influence is the average of all corresponding batchs and epochs.\n\n\n> Figure 4: I don't quite understand this figure. Why are there three bars per task and why there are two separate plots? \n\n**Reponse:** Sorry for the confusion. We have revised the confusion in the manuscript.\n- Left plot: example influence of old task (memory buffer 500); Right plot: example influence of new task (10000 for Split-CIFAR-10)\n- Three bars: influence to stability, influence to plasticity and influence to both stability and plasticity.\n\n> Figure 5: How was the Pareto front plotted? \n\n**Reponse:** The front is plotted by the fitting of 15 points (5 differnt seeds * 3 ablation types).\n\n> Table 2: I assume you mean \"training time\" rather than \"implementation time\"?\n\n**Reponse:** We have revised the confused representation to \"training time\".", " ## Answer to Question\n\n> I would like to ask the authors about the issues mentioned in the \"weaknesses\" section above. In particular, I'd like to highlight he first one: do you have theoretical or empirical proof of how well your approach approximates the results obtained from the Importance Function?\n\n**Answer:** See the responese in weakness.\n\n---\n\n## Response to Limitations\n\n> I don't think a discussion on potential negative societal impact is needed. The authors do not list the limitations of their method and in my opinion, a section like that should be added. \n> - The method relies on experience replay, so it cannot be applied in settings where data privacy is crucial.\n> - The proposed approach is rather slow (2x slower than ER even with the \"use MetaSP only in the last 5-epoch\" trick), so it might be an issue in some settings.\n> - The method was implemented only for classification tasks. How hard would it be to extend it to other problems?\n\n**Reponse:** We have discussed the limitation of the method in the above weakness.\n\n- Beyond classification task: \nOur method is not related to the network structure and output head or design specific loss function. Our methods can be implemented to any other tasks such as semantic segmentation, detection... by modifying these parts. ", " Dear reviewer, we have revised the manuscript and reuploaded the revised version, where contents in cyan are revised. Please download the revised manuscript and appendix. \n\n## Response to Weakness\n\n> The definition of the metrics is not very clear. \"Finished Accuracy\" seems to be the classical \"Final Accuracy\". \"First Accuracy\" and its relationship with plasticity is not very clear. Is it the average best performance realized on each task? Maybe, \"backward transfer\" from \"Gradient Episodic Memory for Continual Learning\" Lopez-Paz et al would be more precise in measuring stability. And \"Final performance\" would measure the mixture between S and P. I am not sure about what \"Mean Average Accuracy\" brings here. \n\n**Response:** Sorry for the confusion.\n\nLet us review the metrics and the mentioned BWT metrics.\n- Finished Accuracy ($A\\_\\infty=\\frac{1}{T}\\sum\\_{t}\\sum\\_{(x,y)\\in\\mathcal{D}^\\text{tst}\\_t}\\mathbf{1}(y,{\\theta}\\_T(x))$): The Finished Accuracy is equivalent to the classical Final Accuracy. Most works used this metrics to evaluate all tasks after all tasks have their training finished. Many previous methods use this metric, such as [1-5].\n- First Accuracy ($A\\_1=\\frac{1}{T}\\sum\\_{t}\\sum\\_{(x,y)\\in\\mathcal{D}^\\text{tst}\\_t}\\mathbf{1}(y,{\\theta}\\_t(x))$): This metric is used to evaluate the performance of each task when it was first trained done (Evaluate each new task immediately). \n- Mean Average Accuracy ($A\\_\\text{m}=\\frac{1}{T}\\sum\\_{t}\\left(\\frac{1}{t}\\sum\\_{k\\le t}\\sum\\_{(x,y)\\in\\mathcal{D}^\\text{tst}\\_k}\\mathbf{1}(y,{\\theta}\\_t(x))\\right)$): This metric computes along CL process, indicating the SP performance after each task trained done. Many previous methods use this metric in the form of line figure, such as [6-8].\n- Backward Transfer (BWT from GEM): ($BWT=\\frac{1}{T-1}\\sum^{T-1}\\_{t=1}\\sum\\_{(x,y)\\in\\mathcal{D}^\\text{tst}\\_t}\\left(\\mathbf{1}(y,{\\theta}\\_T(x))-\\mathbf{1}(y,{\\theta}\\_t(x))\\right)=\\frac{T}{T-1}(A\\_\\infty-A\\_1)$) This metric is the performance drop from their first accuracy to the final accuracy of each task.\n\n[1] Jin X, Sadhu A, Du J, et al. Gradient-based Editing of Memory Examples for Online Task-free Continual Learning[J]. Advances in Neural Information Processing Systems, 2021, 34: 29193-29205.\n\n[2] Prabhu A, Torr P H S, Dokania P K. Gdumb: A simple approach that questions our progress in continual learning[C]//European conference on computer vision. Springer, Cham, 2020: 524-540.\n\n[3] Buzzega P, Boschini M, Porrello A, et al. Rethinking experience replay: a bag of tricks for continual learning[C]//2020 25th International Conference on Pattern Recognition (ICPR). IEEE, 2021: 2180-2187. \n\n[4] Lopez-Paz D, Ranzato M A. Gradient episodic memory for continual learning[J]. Advances in neural information processing systems, 2017, 30.\n\n[5] Chaudhry A, Ranzato M A, Rohrbach M, et al. Efficient Lifelong Learning with A-GEM[C]//International Conference on Learning Representations. 2018.\n\n[6] van de Ven G M, Siegelmann H T, Tolias A S. Brain-inspired replay for continual learning with artificial neural networks[J]. Nature communications, 2020, 11(1): 1-14.\n\n[7] Dhar P, Singh R V, Peng K C, et al. Learning without memorizing[C]//Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2019: 5138-5146.\n\n[8] Rahaf Aljundi, Lucas Caccia, Eugene Belilovsky, Massimo Caccia, Min Lin, Laurent Charlin, Tinne Tuytelaars[C]. NeurIPS. 2019.\n\nWe give an example to show the necessarity of the metric $A\\_m$. \n\n|Table 1|After task 1|After task 2| After task 3|\n|--|--|--|--|\n|Task 1|90|85|70|\n|Task 2||85|80|\n|Task 2|||90|\n\n|Table 2|After task 1|After task 2| After task 3|\n|--|--|--|--|\n|Task 1|90|80|70|\n|Task 2||85|80|\n|Task 2|||90|\n\nWith the definition, we have\n- Table 1: $A\\_1=88.3$, $A\\_\\infty=80$, $A\\_m=83.3$, $BWT=-12.5$ \n- Table 2: $A\\_1=88.3$, $A\\_\\infty=80$, $A\\_m=82.5$, $BWT=-12.5$ \n\nIn the two tables, we have same $A\\_1$, $A\\_\\infty$ and BWT but different $A\\_m$. Obviously, Table 1 outperforms Table 2. Because an CL model will be deployed at any time, for example right after task 2 instead task 3. $A\\_m$ fits this situation because this metric considers all starting, end value of all tasks at any step. As a result, to evaluate the comprehensive ability on both S and P, we suggest $A\\_m$. \n", " In the revised manuscript, we also add the metric BWT in Table 1 to show the forgetting. The results is also shown in the folowing table. The results of BWT can also show the superivority of the proposed method.\n\n|Method|CIFAR10-CI-buffer300|CIFAR10-CI-buffer500|CIFAR10-TI-buffer300|CIFAR10-TI-buffer300|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/BWT/A\\_m$ |$A\\_1/A\\_\\infty/BWT/A\\_m$|$A\\_1/A\\_\\infty/BWT/A\\_m$|$A\\_1/A\\_\\infty/BWT/A\\_m$|\n|GDUMB |- / 36.92 / - / - | - / 44.27 - / - / -|- / 73.22 / - / -| - / 78.06 / - / -|\n|GEM |93.90/37.51/-70.48/55.43 |92.76/36.95/-69.76/57.36 |96.62/89.34/-9.10/92.49 |96.73/90.42/-7.89/92.93|\n|AGEM |96.57/20.02/-95.69/45.57 |96.56/20.01/-95.70/46.52 |96.78/85.52/-14.07/90.16 |96.71/86.45/-12.83/90.90|\n|HAL |91.30/24.45/-83.57/46.34 |91.96/27.94/-80.02/49.05 |91.41/79.90/-14.39/83.78 |92.03/81.84/-12.73/84.19|\n|MIR |96.70/38.53/-72.72/56.96 |96.65/42.65/-67.50/59.99 |96.76/88.50/-10.33/90.87 |96.73/90.63/-7.62/91.99|\n|GSS |96.53/35.89/-75.80/54.33 |96.55/41.96/-68.25/58.16 |96.56/88.05/-10.63/90.60 |96.57/90.38/-7.74/92.19|\n|GMED |96.65/38.12/-73.17/58.92 |96.65/43.68/-66.22/62.56 |96.73/88.91/-9.77/91.20 |96.72/89.72/-8.75/92.10|\n|ER |96.73/34.19/-78.18/53.72 |96.74/40.45/-70.36/57.69 |96.93/88.97/-9.95/91.12 |96.79/90.60/-7.75/92.28|\n|Ours |96.87/42.42/-68.07/63.52 |96.82/49.16/-59.58/67.88 |97.10/89.40/-9.63/92.54 |97.30/90.91/-7.99/93.38|\n|Ours+RehSel|96.85/43.76/-66.37/63.69|96.81/50.10/-58.39/68.28 |97.11/89.91/-9.00/92.66 |97.30/91.41/-7.36/93.28|\n\n|Method|CIFAR100-CI-buffer500|CIFAR100-CI-buffer1000|CIFAR100-TI-buffer500|CIFAR100-TI-buffer1000|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/BWT/A\\_m$ |$A\\_1/A\\_\\infty/BWT/A\\_m$|$A\\_1/A\\_\\infty/BWT/A\\_m$|$A\\_1/A\\_\\infty/BWT/A\\_m$|\n|GDUMB |- / 11.11 / - / - |/15.75 / - / -|- /36.40 / - / -|- / 43.25 / - / -|\n|GEM |85.28/15.91/-77.07/29.38 |84.28/22.79/-68.32/34.09 |85.53/68.68/-18.72/68.49 |85.24/73.71/-12.81/72.59|\n|AGEM |85.97/9.31/-85.18/24.60 |85.66/9.27/-84.88/24.67 |85.97/55.28/-34.10/58.23 |85.66/55.95/-33.02/59.96|\n|HAL |67.33/8.20/-65.70/22.72 |68.06/10.59/-63.86/24.74 |67.64/44.98/-25.17/50.79 |68.62/50.07/-20.62/54.01|\n|MIR |87.38/13.49/-82.10/28.88 |87.39/17.56/-77.60/32.48 |87.42/66.18/-23.60/67.43 |87.50/71.20/-18.11/71.42|\n|GSS |86.03/14.01/-80.03/28.00 |86.31/17.87/-76.04/31.82 |86.10/66.80/-21.45/66.55 |86.44/71.98/-16.07/71.00|\n|GMED |87.18/14.56/-80.69/33.41 |87.29/18.67/-76.24/38.69 |87.30/68.82/-20.53/72.66 |87.49/73.91/-15.10/76.36|\n|ER |87.23/13.75/-81.65/28.88 |87.33/17.56/-77.52/32.45 |87.29/66.82/-22.74/67.56 |87.40/71.74/-17.40/71.60|\n|Ours |88.13/18.96/-76.85/38.62 |87.58/24.78/-69.77/45.20 |88.94/70.03/-21.01/74.07 |88.94/75.32/-15.14/78.09|\n|Ours+RehSel|87.81/19.28/-76.14/39.23|87.55/25.72/-68.70/45.48 |88.58/70.81/-19.75/74.24 |89.03/76.14/-14.33/78.27|\n\n|Method|MiniImagenet-CI-buffer500|MiniImagenet-CI-buffer1000|MiniImagenet-TI-buffer500|MiniImagenet-TI-buffer1000|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/BWT/A\\_m$ |$A\\_1/A\\_\\infty/BWT/A\\_m$|$A\\_1/A\\_\\infty/BWT/A\\_m$|$A\\_1/A\\_\\infty/BWT/A\\_m$|\n|GDUMB |- / 6.22 / - / - |- / 7.15 / - / - |- / 16.37 / - / -|- / 17.69 / - / -|\n|AGEM |50.06/10.69/-49.22/22.29 |50.03/10.69/-49.17/22.28 |50.06/18.34/-39.66/28.05 |50.03/18.78/-39.06/28.12|\n|MIR |51.44/11.07/-50.46/23.65 |51.25/11.32/-49.92/24.09 |51.47/29.10/-27.96/35.20 |51.31/31.39/-24.90/37.24|\n|GSS |51.63/11.09/-50.67/23.62 |51.35/11.42/-49.91/24.05 |51.64/28.67/-28.72/35.22 |51.40/31.75/-24.56/37.23|\n|GMED |51.21/11.03/-50.24/24.47 |50.87/11.73/-48.93/25.50 |51.29/30.47/-26.03/37.64 |51.00/32.85/-22.69/39.66|\n|ER |51.68/11.00/-50.84/23.71 |51.41/11.35/-50.08/24.08 |51.70/28.97/-28.41/35.30 |51.55/31.59/-24.95/37.36|\n|Ours |51.76/12.48/-49.10/26.50 |50.91/14.43/-45.59/28.47 |52.44/32.59/-24.82/39.38 |52.27/36.25/-20.03/41.59|\n|Ours+RehSel|51.81/12.74/-48.85/26.43|50.96/14.54/-45.52/28.44 |51.73/34.36/-21.71/40.48 |51.47/37.20/-17.83/42.19|\n", " ## Answer to Question\n\n> Table 1: \"ours\" method use random sampling selection? Maybe comparing the sampling selection to another example from the literature would make sense to assess the method better. (cf. eg \"An Investigation of Replay-based Approaches for Continual Learning\" Bagus et al)\n\n**Answer:** Yes, \"ours\" method use random sampling selection. Referring to the suggested work [1], we compare the proposed rehearsal selection. The results are shown in the Appendix, and we have cited the missing suggested paper. We also show the comparison as following table. The results show the superviorty of the proposed rehearsal selection method that using example influence.\n\n[1] Bagus B, Gepperth A. An investigation of replay-based approaches for continual learning[C]//IJCNN, 2021.\n\n\n(**CI: Class increment, TI: Task increment**)\n||CIFAR10-CI-buffer500 |CIFAR10-TI-buffer500|\n|----|:----:|:----:|\n| |$A\\_1 / A\\_\\infty / A\\_m$|$A\\_1 / A\\_\\infty / A\\_m$ |\n|NSR Random(Ours) |96.82 / 49.16 / 67.88 |97.30 / 90.91 / 93.38|\n|NSR+ Random |96.82 / 49.49 / 67.58\t|97.20 / 90.94 / 93.22|\n|NSR Mean |96.60 / 40.63 / 63.90 |97.18 / 89.18 / 92.18|\n|NSR Intensity(lowest) |96.70 / 26.07 / 52.64 |96.98 / 85.10 / 89.60|\n|NSR Intensity(highest)\t|96.39 / 34.79 / 56.39\t|96.92 / 85.79 / 87.60|\n|Ours RehSel w/o Influence |96.82 / 47.55 / 67.49\t|97.15 / 90.33 / 93.07|\n|Ours RehSel w/o Cluster |96.60 / 38.50 / 62.38\t|97.27 / 85.55 / 91.22|\n|Ours RehSel |96.81 / 50.10 / 68.28 |97.30 / 91.41 / 93.28|\n\n> What does that mean that a sample increases plasticity or stability? Beyond the definition provided in sec. 3, I miss the high-level idea.... \n\n**Answer:** In this paper, we study the example influence in continual learning. The two significant ability of continual learning is the Plasticity and Stability. Inspired by previous work [1], we propose to explore the example influence on Plasticity and Stability. With the proposed MetaSP, we can ontain the example influence on S and P. Strengthening the training of examples with both positive S and P, SP can be improved.\n\n[1] Pang Wei Koh and Percy Liang. Understanding black-box predictions via influence functions. In ICML, 2017.\n\n> l266 \"We divide all example influence equally to 5 groups from the minimum to the maximum.\" how does this division is realized exactly? \n\n**Answer:** We first obtain the maximum (MAX) and minimum (MIN) of all example influences, and divide the value range into $\\{[\\text{MIN}, \\text{MIN} + \\cfrac{1}{5}(\\text{MAX}-\\text{MIN})], [\\text{MIN}+\\cfrac{1}{5}(\\text{MAX}-\\text{MIN}), \\text{MIN} + \\cfrac{2}{5}(\\text{MAX}-\\text{MIN})],\\cdots,[\\text{MIN}+\\cfrac{4}{5}(\\text{MAX}-\\text{MIN}), \\text{MAX}]\\}$. We count the number of examples grounding each range and plot Fig.4.\n\n> l269 \"The two observations suggest we should consider the example difference to improve model training.\" but you do not do it, right? So what is the point of this figure in the paper? \n\n**Answer:** We do use the example difference to improve the CL training. \n- This can be seen in Sec 5. We use the influence form differnt examples to rehearsal selection and model update. To improve the model training, we use the example influence to weight the training in example-level. \n- We use Fig.4 to show the example influence distributions in the CL process. We think this is an important insight of the example differnce in CL. As shown in Fig.4, example influences are not in a similar degree, we need to consider the influence difference from examples to improve the training as mentioned in Sec 5. \n\n> Fig.3: left is the evaluation of the data stored in the memory, and the left is the new data? I think the legend could be more detailed to make it clear from the beginning. \n\n**Answer:** The left subfig is the statistics on the 500 memory data and the right subfig is the statisctics on the 10000 new task data. We have revised the legend of Fig.3 and Fig.4 in the revised manuscript.\n\n> Tab 1: code color is not defined. \n\n**Answer:** We have defined the code color of Table 1 in the revised manuscript. The blue values means the best of compared methods and the red values means the best of our methods.\n\n> Is the data used for validation in the memory buffer used at some point for training? \n\n**Answer:** Sure, the validataion set is randomly sampled from memory buffer and all examples in memory are used for training. \n\n> Table 2: how many seeds lead to those results? \n\n**Answer:** We use 5 seeds in all our experiments.\n\n> l.69 \"4) By considering the example influence, in our experiments on both task- and class-incremental, better S and more stable P can be observed\" I do not understand what this contribution is... \n\n**Answer:** In our view, this is an verification contribution. We evaluate our methods on both task- and class-incremental continual learning and demonstrate that the S and P influence of an example can be obtained and used to improve continual learning.", " ### Comments\n\n> \"KKT\" is never defined. \n\n**Response:** We have revised the manuscript to highlihgt the \"KKT conditions\" is the abbreviation for \"Karush–Kuhn–Tucker conditions\". We have described more details about the KKT conditions of MGDA [1] in our Appendix.\n\n*Refer to MGDA*:\n\nWe first introduce the Steepest Gradient Method (SGM) [2] in dual-objective optimization. Given two tasks 1 and 2, the objective of SGM\nis \n\n$$\nd^*, \\alpha^*=\\arg\\min\\_{d,\\alpha}\\quad\\alpha+\\frac{1}{2} ||d||^2,\\quad \\text{s.t.}\\quad g\\_1^\\top d\\le \\alpha, g\\_2^\\top d\\le \\alpha,\n$$\n\nwhere $g\\_1$ and $g\\_2$ are the gradients for task 1 and 2 specifically. \nThe two constraints can be seen as the difference between task gradients and the optimal gradients.\n\nConsidering the Lagrange multipliers $\\lambda\\_1$ and $\\lambda\\_2$ for the two constraints, we have the dual problem of the above problem as\n$$\n\\lambda_1^*, \\lambda_2^*=\\arg\\max_{\\lambda_1,\\lambda_2}\\quad -||\\lambda_1 g_1+\\lambda_2 g_2||^2,\\quad\\text{s.t.}\\quad \\lambda_1+\\lambda_2=1,\\lambda_1\\ge0,\\lambda_2\\ge 0,\n$$\n\nThis is the objective of Eq.(10) of the paper.\nIn SGM, the KKT conditions can be writen as\n\n$\\lambda\\_1^*(g\\_1^\\top d^*- \\alpha^*)=0$\n \n$\\lambda\\_2^*(g\\_2^\\top d^*- \\alpha^*)=0$\n\n$\\lambda\\_1^* \\ge 0, \\lambda\\_2^* \\ge 0$\n\n$\\lambda\\_1^* + \\lambda\\_2^* = 1$\n\n$\\lambda\\_1^* g\\_1+\\lambda\\_2^* g\\_2=d^*$\n\n\nThe solution of the dual problem is \n$$\n\\lambda_1^*=1-\\lambda_2^*=\\min\\left(\\max\\left(\n\\frac{(g\\_2-g\\_1)^\\top g\\_2}{\\|g\\_2-g\\_1\\|\\_2^2},0\\right),1\\right)\n$$\nThis is the objective of Eq.(11) of the paper.\n\n- [1] Ozan Sener and Vladlen Koltun. Multi-task learning as multi-objective optimization. In NeurIPS, 2018.\n- [2] Jörg Fliege and Benar Fux Svaiter. Steepest descent methods for multicriteria optimization. Mathematical methods of operations research, 2000.\n\n> I would move the task-incremental results in the appendix (task incremental is not very classical to study when using replay, but this is not problematic) and add std of results in the main body. \n\n**Response:** Thank you for your suggestion.\n\n> It would be better to group figures 3 and 4 or to modify figure 4, such as the legend is not in figure 3. \n\n**Response:** We have revised the legend of Fig.3 and Fig.4 in the revised manuscript.\n\n\n## Response to Limitations\n\n> It would be nice to see in the table which results are statistically significant. \n\n**Response:** To show the statistically sigificant of our experiments, we use T-test (Student's t-test) [1] to evaluate that if the means of two methods' results are significantly different from each other. The detail can be seen in Table 1 of the revised manuscript.\n\n[1] Semenick D. Tests and measurements: The T-test[J]. Strength & Conditioning Journal, 1990, 12(1): 36-37.\n\n\n\n> The legend of several figures could be improved. \n\n**Response:** We have revised the legend of Fig.3 and Fig.4 in the revised manuscript.", " Dear reviewer, we have revised the manuscript and reuploaded the revised version, where contents in cyan are revised. Please download the revised manuscript and appendix. \n\n## Response to Weakness\n\n> However, I feel that the paper’s presentation can benefit from another iteration. There are many sentences which need to be improved and that at the moment hinder the readability of the paper. E.g. lines 44, 52, 190, and 203.\n\n**Reponse:** Sorry for the confusion, we have revised the mentioned sentences in the revised manuscript.\n\n> Moreover, I was not left with the impression that the presentation of the background material, in particular on influence functions, was satisfactory. For instance, I am confused by eq. (6) and the use of iff. Apart from the presentation, it’d be good if the experiments also introduced baselines which represent other CL directions, s.a. regularisation-based methods. \n\n**Reponse:** Sorry for the confusion.\n- Background on influence function: Referring to [1], influence function is a classic technique from robust statistics to trace a model’s prediction through the learning algorithm and back to its training data, thereby identifying the training data most responsible for a given prediction.\n- Eq.(6): This equation indicates that the example influence $ I(\\mathcal{D}^\\mathrm{tst},\\mathcal{B})$ is reflected in the derivative $\\nabla\\_{\\mathbf{E}}\\ell(\\mathcal{D}^\\mathrm{tst},\\hat{{\\theta}}\\_{\\mathbf{E}, x})\\big|\\_{\\mathbf{E}=\\mathbf{0}}$. In detail\n$$\n\\mathbf{I}(\\mathcal{D}^\\mathrm{tst},\\mathcal{B})= \\frac{\\partial l(\\mathcal{D}^\\mathrm{tst},\\hat{ {\\theta}}\\_{\\mathbf{E}, \\mathcal{B}})}{\\partial \\mathbf{E}}\\bigg|\\_{\\mathbf{E}=\\mathbf{\\mathbf{0}}}\n=\\frac{\\partial l(\\mathcal{D}^\\mathrm{tst},\\hat{{ {\\theta}}})}{\\partial{ {\\theta}}}\\cdot\\frac{\\partial\\hat{{ {\\theta}}}\\_{\\mathbf{E}, \\mathcal{B}}}{\\partial \\mathbf{E}}\\bigg|\\_{\\mathbf{E}=\\mathbf{\\mathbf{0}}}- \\nabla\\_{{ {\\theta}}}l(\\mathcal{D}^\\mathrm{tst},\\hat{{ {\\theta}}})\\mathbf{H}^{-1}\\nabla^\\top\\_{{ {\\theta}}}\\mathbf{L}(\\mathcal{B},\\hat{{ {\\theta}}}),\n$$\nwhere\n$$\n\\mathbf{H}=\\frac{1}{|\\mathcal{B}|}\\sum\\_{x\\_i\\in\\mathcal{B}}\\nabla\\_{ {\\theta}}^2\\ell(x\\_i,\\hat{ {\\theta}}\\_{\\epsilon\\_i}),\n\\quad\n\\frac{\\partial\\hat{{ {\\theta}}}\\_{\\mathbf{E}, \\mathcal{B}}}{\\partial \\mathbf{E}}\\bigg|\\_{\\mathbf{E}=\\mathbf{0}}=-\\mathbf{H}^{-1}\\left[ \\frac{\\partial \\mathbf{L}}{\\partial {\\theta}} \\right]^\\top.\n$$\nMore details can be seen in Appendix A.2.\n- The use of $\\iff$ in Eq.(6): We have modified $\\iff$ to $\\stackrel{\\text{def}}{=}$ to represent the meaning of \"define\". We have added the description in the revised manuscript.\n- We compare other regularization-based methods including EWC, SI, and LwF, the results (average in 5 seeds) are shown in the following table. The results show that regularization-based methods perform not well in class-incremental CL, but have comparable performance to other rehearsal methods in task-incremental CL.\n\n|Method|CIFAR10-ClassIncrement|CIFAR10-TaskIncrement|\n|----|----|----|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|\n|EWC|93.89/18.99/43.12|93.89/73.01/76.20|\n|SI|96.41/19.59/44.10|96.53/68.63/77.41|\n|LwF|96.61/19.61/44.03|96.71/74.03/81.20|\n|Ours(buffer 500)|96.82/49.16/67.88|97.31/90.91/93.38|\n|Ours+RehSel(buffer 500)|96.81/50.10/68.28|97.30/91.41/93.28|\n\n|Method|CIFAR100-ClassIncrement|CIFAR100-TaskIncrement|\n|----|----|----|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|\n|EWC|80.48/8.43/23.46|80.25/35.96/39.20|\n|SI|82.34/9.20/22.92|82.34/36.96/44.63|\n|LwF|83.23/9.27/22.91|83.23/50.53/56.27|\n|Ours(buffer 500)|88.13/18.96/38.62|88.94/70.03/74.07|\n|Ours+RehSel(buffer 500)|87.81/19.28/39.23|88.58/70.81/74.24|\n\n|Method|Mini-Imagenet-ClassIncrement|Mini-Imagenet-TaskIncrement|\n|----|----|----|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|\n|EWC|46.07/10.00/21.41|46.27/21.22/30.01|\n|SI|36.80/6.02/19.15|36.80/27.90/33.54|\n|LwF|52.05/11.13/23.05|52.05/31.74/37.29|\n|Ours(buffer 500)|51.76/12.48/26.50|52.44/32.59/39.38|\n|Ours+RehSel(buffer 500)|51.81/12.74/26.43|51.73/34.36/40.48|\n\n[1] Pang Wei Koh and Percy Liang. Understanding black-box predictions via influence functions. In ICML, 2017.\n", " ## Answer to Question\n\n> Do you anticipate that your method would work on sequences of tasks with different input domains? For instance, if you had FMNIST classification mixed with CIFAR10. \n\n**Answer:** We evaluate the results of mixed FMNIST and CIFAR-10, and treat them as two tasks (10 + 10 classes for class increment and 1 + 1 tasks for task increment). The comparisons with SOTA can be seen in the following Table, and the results show the superiority of the proposed on the mixed-domain.\n\n(**CI: Class increment, TI: Task increment**)\n|Method|FMNIST-CIFAR10-CI-buffer100|FMINST-CIFAR10-TI-buffer100|\n|----|:----:|:----:|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|\n|gdumb\t |-/27.74/-\t |-/29.44/-|\n|agem\t |90.39/67.88/80.98 |90.39/77.51/85.80|\n|hal\t |67.98/25.96/58.90 |67.98/43.58/67.71|\n|mir\t |91.32/64.02/79.05 |91.32/72.57/83.33|\n|gss\t |91.89/61.20/77.70 |91.89/74.78/84.49|\n|gmed\t |91.46/66.15/80.12 |91.46/78.22/86.15|\n|ER |91.42/60.77/77.43 |91.42/73.17/83.63|\n|Ours |92.57/75.17/84.63 |92.57/80.72/87.41|\n|Ours+RehSel|92.90/75.85/85.13 |92.90/81.25/87.84|\n\n---\n\n## Response to Limitation\n\n> I did not see a discussion on the limitations of the method. \n\n**Reponse:** In the revised paper, we discussed the limitation of the method.\n\n- The proposed method relies on the rehearsal selection. Like most previous rehearsal, storing the raw data may affect the privacy to some extent and extra storage is needed. \n- The proposed method is not fast enough in online continual learning (only one epoch). In most situation, however, we can leverage our training tricks (finetune + our method) to reduce the time.\n- Our method is limited in the extreme small memory size. Large memory size means better remembering and accurate validation set (sampled from training set). The proposed method does not perform well when the memory size is extreme small. To prove this, we give an extra experiment as follows. When the buffer size is set to 50, our method outperforms ER. However when the buffer size is set to 20, our method has worse performance than ER.\n\n\n(**CI: Class increment, TI: Task increment**)\n|Method|CIFAR10-CI-buffer20|CIFAR10-CI-buffer50|CIFAR10-TI-buffer20|CIFAR10-TI-buffer50|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|\n|ER|97.02/21.87/45.93|97.02/23.37/48.64|97.02/78.60/85.55|97.03/82.63/87.11|\n|Ours|96.80/20.56/45.96|97.24/25.14/50.26|96.99/79.31/86.02|97.32/84.40/89.69|\n\n\n|Method|CIFAR100-CI-buffer20|CIFAR100-CI-buffer50|CIFAR100-TI-buffer20|CIFAR100-TI-buffer50|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|\n|ER|87.87/9.38/25.76|87.99/9.55/25.91|87.87/42.86/52.99|87.99/48.36/57.84|\n|Ours|89.17/9.46/25.90|89.19/10.33/27.34|89.19/42.83/53.07|89.24/49.19/58.62|\n\n\n> I’d be curious to better understand the number of tasks the method can handle before it breaks, possibly as a function of the memory size.\n\n**Response:** We enlarge the task number of CIFAR-100, i.e., we split it into 50 tasks (2 classes per task). The results are shown in the following table. We observe the performance of our method still outperfoms ER especially in class-incremental CL.\n\n(**CI: Class increment, TI: Task increment**)\n|Method|CIFAR100-CI-buffer500|CIFAR100-CI-buffer1000|CIFAR100-TI-buffer500|CIFAR100-TI-buffer1000|\n|----|:----:|:----:|:----:|:----:|\n||$A\\_1/A\\_\\infty/A\\_m$ |$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|$A\\_1/A\\_\\infty/A\\_m$|\n|ER|95.66/3.90/10.53|95.58/4.92/12.18|95.20/77.48/78.75|95.72/81.67/81.66|\n|Ours|96.80/20.56/45.96|97.24/25.14/50.26|96.99/79.31/86.02|97.32/84.40/89.69|\n", " The method augments rehearsal-based methods for continual learning. At the heart of the method is a measurement of the influence of each example on the stability and the plasticity of the algorithm. First, the authors introduce a method for estimating said influence. Second, they present a method for using the influence to regularise the parameter updates. Third, they show how to use the influence in order to select which examples of past tasks to store in memory. The paper introduced an interesting direction of combining research on Example Influence with Continual Learning. It appears that the methods they introduce are novel and well motivated. Finally, the experiments show good improvement over the many rehearsal-based baselines.\n\nHowever, I feel that the paper’s presentation can benefit from another iteration. There are many sentences which need to be improved and that at the moment hinder the readability of the paper. E.g. lines 44, 52, 190, and 203. Moreover, I was not left with the impression that the presentation of the background material, in particular on influence functions, was satisfactory. For instance, I am confused by eq. (6) and the use of iff. \nApart from the presentation, it’d be good if the experiments also introduced baselines which represent other CL directions, s.a. regularisation-based methods.\n Do you anticipate that your method would work on sequences of tasks with different input domains? For instance, if you had FMNIST classification mixed with CIFAR10. I did not see a discussion on the limitations of the method. I’d be curious to better understand the number of tasks the method can handle before it breaks, possibly as a function of the memory size.", " The paper investigates the question of how important each example is for plasticity and stability in continual learning. The authors motivate their approach from the perspective of the Influence Function which was previously used as an explainability method. However, since computing the actual Influence Function requires computing an inverse of the Hessian, the authors decide to instead propose MetaSP, a two-level optimization technique, which aims to approximate the Influence Function. Equipped with this, one can find a loss balancing factor $\\gamma$ which is Pareto optimal with respect to stability and plasticity, and then use this balanced loss for training as well as choosing which examples to keep in the buffer. Finally, the authors show an empirical evaluation on multiple datasets and perform additional analysis of the method. Strengths:\n- The idea of disentangling plasticity and stability through IF-like approach and then using this information to get better performance seems novel and intriguing.\n- The empirical evaluation is quite thorough and the proposed method performs well. In particular, I appreciate including the training time as the algorithm seems to be computationally complex. \n- The ablation studies are useful and give a deeper insight into the method. It's interesting to see how the number of examples with a positive impact on plasticity and stability changes with time. \n\nWeaknesses:\n- The major weakness of the paper from my perspective is that in the end, I'm not sure how well the Importance Function motivation connects with the final MetaSP algorithm. Intuitively, these two seem connected, but a theoretical or empirical argument confirming that would be very useful. In particular, do you know how well the MetaSP approach approximates the gradient from Equation (6)? Can we show their equivalence, either theoretically or by running some experiments on toy problems? The authors hint at this kind of result in Section 4.1, but no hard proof is given.\n- The fact that the algorithm is actually applied only on the last 5 epochs out of 50 should be highlighted. This is only mentioned in a single subsection near the end of the paper but seems quite crucial. Have you checked how well the other methods perform in this scenario? For example, what happens if we use fine-tuning for 45 epochs and then ER for 5 epochs? \n- The presentation could be improved, as the paper is hard to read at times. There are some minor mistakes (see the Minor comments section below) and in general I think the paper could be more self-contained. In particular, checking the previous works was necessary for me to understand Section 5.1 (SP Pareto Optimal), as the authors do not list the KKT conditions and do not really explain what the result of Eq (10) is. Grammar could also be improved, but for the most part, the mistakes do not make it harder to understand the paper so this is not an important issue.\n- I'm a bit skeptical whether K-Means on the input space learns anything more than just basic background colors. Have you checked how the examples get clustered? What happens if you do not perform clustering at all (i.e. 1 cluster) or just cluster the examples randomly?\n- The paper does not list limitations although in the checklist the authors claim that it does.\n\n\nMinor comments:\nLine 22: \"robust CL system should achieve outstanding S while keeping a stable P\" - that statement might be a bit controversial as it depends on your desiderata - you might want a model that is plastic but can remember the past moderately well.\nLine 96: What do you mean by performance? You are using the $p$ symbol which suggests probability, but that's a bit confusing.\nLine 120: \"Hessian [...] assumed as positive definite\" - that's a pretty strong assumption if we're not close to the minimum (i.e. during the training).\nLine 121: \"Always out-of-memory\" - that's a bit informal, given enough storage or a small number of parameters I think this operation should be tractable. Of course, I agree that in most cases this statement is true, but I would suggest using more precise wording.\nLine 168: might be useful to state those KKT conditions\nLine 225: I would suggest, when possible, reusing metrics from previous CL papers, as introducing new metrics make it difficult to compare between papers.\nFigure 3: At what point is each of these plots generated? I.e. these metrics are dependent on the parameters $\\theta$, so which $\\theta$ are we using? The one from the end of the current task?\nFigure 4: I don't quite understand this figure. Why are there three bars per task and why there are two separate plots? \nFigure 5: How was the Pareto front plotted?\nTable 2: I assume you mean \"training time\" rather than \"implementation time\"?\n\n\n**EDIT:** Authors' responses and improvements made to the paper convinced me to increase my score to Accept. I would like to ask the authors about the issues mentioned in the \"weaknesses\" section above. In particular, I'd like to highlight he first one:\ndo you have theoretical or empirical proof of how well your approach approximates the results obtained from the Importance Function? I don't think a discussion on potential negative societal impact is needed. \nThe authors do not list the limitations of their method and in my opinion, a section like that should be added. Just to name a few: \n- The method relies on experience replay, so it cannot be applied in settings where data privacy is crucial.\n- The proposed approach is rather slow (2x slower than ER even with the \"use MetaSP only in the last 5-epoch\" trick), so it might be an issue in some settings.\n- The method was implemented only for classification tasks. How hard would it be to extend it to other problems? ", " The authors investigate the stability dilemma through the lens of the training data and the selection for the replay buffer.\nThey evaluate the influence of data points on stability and plasticity using small perturbation to data instead of computing hessian (for computation sake).\nThe authors use the stability and plasticity influence to optimize the gradient update and the sample selection.\nThe algorithm is evaluated on CIFAR10, CIFAR100, and Mini-Imagenet and compared with several state-of-the-art algorithms.\n\nOverall I like the paper and the idea. I think, however, that the authors could realize some improvements to make the paper clearer and better. Strengths:\nThe paper is well written and organized, with a detailed description of the method.\nSample selection is a crucial problem to study to improve replay methods.\nthe method is interesting and looks well-performing.\n\nWeaknesses:\nThe definition of the metrics is not very clear. \"Finished Accuracy\" seems to be the classical \"Final Accuracy\". \"First Accuracy\" and its relationship with plasticity is not very clear.\nIs it the average best performance realized on each task?\nMaybe, \"backward transfer\" from \"Gradient Episodic Memory for Continual Learning\" Lopez-Paz et al would be more precise in measuring stability.\nAnd \"Final performance\" would measure the mixture between S and P. I am not sure about what \"Mean Average Accuracy\" brings here.\n Table 1: \"ours\" method use random sampling selection? Maybe comparing the sampling selection to another example from the literature would make sense to assess the method better. \n(cf. eg \"An Investigation of Replay-based Approaches for Continual Learning\" Bagus et al)\n\nWhat does that mean that a sample increases plasticity or stability? Beyond the definition provided in section 3, I miss the high-level idea....\n\nl266 \"We divide all example influence equally to 5 groups from the minimum to the maximum.\" how does this division is realized exactly?\n\nl269 \"The two observations suggest we should consider the example difference to improve model training.\" but you do not do it, right? So what is the point of this figure in the paper?\n\nFig.3: left is the evaluation of the data stored in the memory, and the left is the new data? I think the legend could be more detailed to make it clear from the beginning.\n\nTab 1: code color is not defined.\n\nIs the data used for validation in the memory buffer used at some point for training?\n\nTable 2: how many seeds lead to those results?\n\nl.69 \"4) By considering the example influence, in our experiments on both task- and class-incremental, better S and more stable P can be observed\" I do not understand what this contribution is...\n\n\n********\nSome Comments:\n**************\n\n\"KKT\" is never defined.\n\nI would move the task-incremental results in the appendix (task incremental is not very classical to study when using replay, but this is not problematic) and add std of results in the main body.\n\nIt would be better to group figures 3 and 4 or to modify figure 4, such as the legend is not in figure 3. It would be nice to see in the table which results are statistically significant.\n\nThe legend of several figures could be improved." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 4, 4 ]

[ "Gs0EZrtbyWi", "ETqf1_tlUgG", "mG-Wt7fN9Lr", "7yBACbxzGW3", "s2x1OqNETKI", "s2x1OqNETKI", "s2x1OqNETKI", "s2x1OqNETKI", "mDYZ2tlZUvI", "mDYZ2tlZUvI", "mDYZ2tlZUvI", "mDYZ2tlZUvI", "vlt0HF_VcSr", "vlt0HF_VcSr", "nips_2022_u4dXcUEsN7B", "nips_2022_u4dXcUEsN7B", "nips_2022_u4dXcUEsN7B" ]

[ "wTRg0zr3rQL", "eiBdVTXcXw", "JPSSfkJw-ej", "pHJep_s_0ve", "bttcmk1hJ3l", "1IqDjqswtbc", "dmddg2xzGbB", "wWgrosHNLjz", "mKp53-kA82z", "2sw1vrXSIJd", "trULltT-lIl6", "swAsmsa16D3", "iy6N46x13dd", "miAW_MP8fEc", "EsAEXZmp7gn", "nI_-TLdMHRL", "MIuRPHkh6rJ" ]

[ "author", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you very much for acknowledging our additional experiments and providing positive feedback! \n\nYour constructive comments and suggestions are very helpful in improving our paper quality. Thanks!\n\n", " Thank you for uploading the revised paper. It's a great work and I increased my score to 7.", " Thanks for the detailed explanation and additional results and clarification.\n\nThe additional experiments to ablate the query setting is critical to demonstrate the efficiency of the proposed method given it is entangled with multiple components. I also read your responses to other reviewers and recognize the contribution made in this work. Most of my concerns are well addressed.\n\nI maintain my positive rating to this work. And will make more discussion in the next stage with other reviewers to calibrate my final rating. ", " Thank you very much for the positive feedback! \n\nAccording to your valuable suggestions, we have revised and uploaded the paper and appendix. \nWe will continue to polish the paper for better readability. \nThanks! ", " Thank you very much for the positive feedback! \n\nAccording to your valuable suggestions, we have revised and uploaded the paper and appendix. \nWe are happy to further update the paper / appendix if there are any other suggestions. \nThanks!", " Thank you for the detailed feedback. I understand the 2nd contribution better now. Please do improve the readability of the paper itself. \n\nI'll recommend accept. Thank you!", " Thank you for your answers. Most of my concerns are well-addressed.\n\nI am planning to increase the score. Once the revised paper is uploaded, I will increase.", " We sincerely thank the reviewer for providing thoughtful review and constructive suggestions. We answer the questions as follows. \n\n****\n\n**Q1**: \"I assume it is the initial version of the final 1st place work [1], sharing very similar methods and almost the same framework, thus I would encourage authors to update the paper with [1].\"\n\n**A1**: \nThanks for the valuable suggestion. We will follow the reviewer's suggestion and update the paper in the revised version.\n\n****\n\n**Q2**: \"The most concern is that all the strategies are well-studied in this community\" and \"It would be better if more insights could be included for model design, and highlight the differences/contributions.\"\n\n**A2**: \nThanks for the constructive suggestion. We discuss more insights about the model design and highlight our differences and contributions in the following, which will be included in the revised version:\n\n* Our key contribution lies in the design of the motion decoder network. Indeed, we agree with the reviewer that there are already some works focusing on exploring the transformer idea, scene context and interaction modeling (*e.g.*, SceneTransformer [30], MultiPath++ [40], etc.). However, most of existing works focus on the model design of scene context encoding and agent interaction modeling, and how to design a better motion decoder for multimodal motion prediction is still underexplored. \n* Hence, we propose a transformer-based motion decoder network with a novel concept of motion query pair, where each motion query pair is bound with a fixed intention point and takes charge of generating the future trajectory of a specific motion mode. \nThe insight is that modeling different motion modes with different motion query pairs facilitates better multimodal motion prediction and makes the predictions more explainable, since each motion query pair has explicit correspondence with a specific motion mode and predicts their own confidence/trajectory respectively.\nMoreover, our approach can predict very different motion modes of multiple categories (*e.g.*, vehicle, pedestrian and cyclist, etc.) in a single model, because the motion query pair utilizes shared MLP to encode the intention points, so that we just need to set different sets of prior intention points for different categories to get their corresponding motion query pairs. \n* We propose to iteratively refine the predicted trajectory in motion decoder network by continually probing trajectory-specific features in different decoder layers, which is novel and hasn't been explored in motion prediction field (also endorsed by Reviewer 3fr6). The insight is that the predicted future trajectory should be consistent with its local context environment, especially the HD map context. Hence we introduce dynamic map collection module to force the model to constantly focus on the latest context environment around the predicted trajectories, so as to refine them with fine-grained features. \n* Compared with previous goal-based methods [51,18], our approach eliminates the dependence of dense goal candidates (*e.g.*, about $10k$ in Waymo dataset) by introducing a small set of learnable motion query pairs (*e.g.*, 64 in Waymo dataset), which makes our approach more efficient than these methods. \nCompared with other state-of-the-art methods (*e.g.*, SceneTransformer [30], MultiPath++ [40]), our approach introduces intention priors through motion query pairs, which can predict better multimodal motion by separately considering each explicit motion mode. In contrast, SceneTransformer [30] predicts various motion modes from the same agent feature and MultiPath++ uses implicit and latent anchor embeddings. \n\n****\n\n**Q3**: \"In Line 134-135, how to pad zeros for trajectories that have less than frames?\" \n\n**A3**: We apologize for the confusion. The history motion state $A_{in}$ is represented with full $t$ frames according to their frame positions, where the zeros are padded at the position of the missing frames, since these invalid frames may be intermediate frames of $t$ frames due to temporary occlusion. We will clarify this in the revised version. \n\n****\n\n\n**Q4**: \"Some missing references when referring to future interactions, some works [2-4] have been proposed to argue the future interaction point and to consider such future interactions.\"\n\n**A4**: \nThanks for pointing out these valuable references. We will cite and discuss these works in the revised version. \n\n****\n\n**Q5**: \"Line 56, I believe it is 'empirical' instead of 'experimentally'.\"\n\n**A5**:\nThanks for pointing out this. We will revise it according to the reviewer's suggestion. \n\n****\n\n**Q6**: \"In References, the names of conferences or journals, i.e. abbreviation or full name, are not consistent.\"\n\n**A6**: Thanks for pointing out this issue. We will revise the reference to make it consistent. ", " **Q4**: \"line 73: Why not also using ensemble to boost the accuracy a bit to achieve top results?\"\n\n**A4**: Because different ensemble strategies may lead to very different performance gains, causing unfair comparison of different models. Therefore, in the introduction section, we only report the ensemble-free performance to demonstrate the effectiveness of the model itself.\nActually, Table 1 shows that our ensemble-free performance already outperforms the state-of-the-art model ensemble performance of MultiPath++ [40] in terms of mAP.\nMoreover, we have also provided a model ensemble performance (*i.e.* MTR-ens) in Table 1 by utilizing a simple ensemble strategy, which achieves much better performance than our default setting (43.23\\% vs. 41.64\\% in terms of mAP). \n\n****\n\n**Q5**: \"Figure 1: The figure is far from self-explaining.\" \n\n**A5**: Thanks for pointing out this issue. We will revise the figure and caption to make it self-explaining. The caption will be updated as something like: \n\n``The architecture of MTR framework for multimodal motion prediction. $K$ is the number of motion query pairs, $T$ is the number of future frames to be predicted, $D$ is the hidden feature dimension and $N$ is the number of transformer decoder layers. The predicted trajectories, motion query pairs, and query content features are the outputs from last decoder layer and will be taken as input to current decoder layer. For the first decoder layer, both two components of motion query pair are initialized as predefined intention points, the predicted trajectories are replaced with the intention points for initial map collection, and query content features are initialized as zeros.''\n\n****\n\n**Q6**: Some confusion about \"Eq 2, ln 164\", and \"please use subscripts to make it clear that the variable in LHS and RHS are not the same.\"\n\n**A6**: We apologize for the confusion and thank the reviewer for the valuable suggestion. We will follow the suggestion to use subscript to make LHS and RHS clear. \n\n****\n\n**Q7**: \"ln 237: where does the auxiliary loss $L_a$ come from?\" and \"if it's just an L1 loss against the GT. I don't understand the intuition why it helps with interaction.\" \n\n**A7**: We apologize for the confusion and provide the following clarifications:\n\n* **Auxiliary loss**: $L_a$ is calculated by L1 regression loss, which only optimizes the prediction of each agent to predict a single future trajectory as in Eq.(3) and does not enable the interaction of the agents. We will add the loss equation and clarify this in the revised version.\n* **How dense prediction task helps interaction**: \nThe dense future prediction task can predict future trajectories of all agents within the same scene, which are encoded and then taken as input to the transformer decoder network for providing additional future context information. \nThis future context information helps the interaction between the interested agent (*i.e.*, the agent at the center of the normalized input coordinate) and other agents, and facilitates the model to predict more scene-compliant future trajectories for the interested agent. \nFor example, if the interested agent has interactions with one or multiple surrounding agents, the dense future prediction module can predict potential future trajectories of these surrounding agents as additional future context information, which is input to the transformer decoder network, so that the model can predict better future trajectories for the interested agent by considering the consistency between its predicted trajectories and these potential future trajectories of the surrounding agents. \nThe experiments in Table 3 demonstrate that the dense future prediction module can effectively improve the performance from 32.84\\% to 34.37\\% in terms of mAP. \n\n****\n\n**Q8**: \"The limitation section is about high-level limitation.\"\n\n**A8**: We will revise the limitation section and add more discussion as follows:\n\n\"The proposed framework adopts an agent-centric strategy to predict multimodal future trajectories for one interested agent, which leads to redundant context encoding if there are multiple interested agents in the same scene. Although the dense future prediction module partially compensates for this limitation, it can only predict a single future trajectory for each agent. Hence, how to develop a joint motion prediction framework that can simultaneously predict multimodal motion for multiple agents is one important future work. \nBesides, the rule-based NMS post-processing can result in suboptimal predictions for minADE and minFDE metrics, and how to develop a learning-based module to produce a required number of future trajectories (*e.g.*, 6 trajectory) from full multimodal predictions (*e.g.*, 64 predictions) is also worth exploring for a more robust framework.\"\n", " We sincerely thank the reviewer for providing thoughtful review and constructive suggestions. We answer the questions as follows. \n\n****\n\n**Q1**: \"Somewhat novelty: Using DETR for motion forecasting is not that new anymore. I reviewed several papers for CVPR'22 and ECCV'22 that contained similar ideas. But those should be considered concurrent work. Additionally, the hierarchical separation of intent vs. fine control adds an additional hint of novelty, though the hierarchical separation by itself is not novel either [9, 51].\"\n\n**A1**: \nWe appreciate the reviewer's acknowledgement and recognition of some novelties of the proposed framework. \nHere we would like to highlight our core contributions and differences compared to existing works: \n\n* The key contribution of our approach lies in the design of motion decoder network. \nTo model multimodal motion modes of the agent, we propose a novel concept of motion query pair in the decoder network, where each motion query pair is bound with a fixed intention point and takes charge of generating the future trajectory of a specific motion mode. \nThis independent modeling of different motion modes facilitates better multimodal motion prediction. The major differences compared to existing works are discussed below: \n * Compared with other DETR related motion predictors like MultiPath++ [40]: they generally consider queries as latent anchor embeddings while our motion query pair has explicit meaning and is more explainable. For example, in our framework, each motion query pair corresponds to a specific local region around its prior intention point, and the position of this intention point can jointly consider both the motion direction (*e.g.*, turn left, turn right and go straight, etc.) and moving distance (*e.g.*, velocity) by considering this local region as agent's destination.\n * Compared with TNT/DenseTNT [51,18]: they generally depend on a very large number of goal candidates (*e.g.*, about 10k for Waymo dataset) to achieve good performance, while our approach is much more efficient by only adopting a small set of motion query pair (*e.g.*, 64 for Waymo dataset).\n * Compared with MultiPath [9]: Unlike MultiPath which uses anchor trajectories, our intention point modeling can better handle various possible trajectories for the same intention, since our learnable motion query pairs can dynamically predict different feasible trajectories based on the context information.\n* We propose to iteratively refine the predicted trajectory by continually probing trajectory-specific features with stacked transformer decoder layers, which is novel and hasn't been explored in motion prediction field (also endorsed by Reviewer 3fr6).\n\n\nWe are happy to compare and discuss more related works in the revised version, and we are also happy to answer any further questions. \n\n****\n\n**Q2**: \"Unclear writing: Abused notations, missing descriptions of variables, figures that are not self-contained.\"\n\n**A2**: We apologize for the confusion. We will follow the reviewer's suggestions to utilize different notations for LHS and RHS of Eq.(2) / line-164, revise the figure and add more descriptions to the caption to make it self-explaining. \n\n**** \n\n**Q3**: \"Insufficient experiments (minor)\" and \"Having strong results on a secondary dataset would make the representation a lot stronger.\"\n\n**A3**: \nThanks for the valuable suggestion. As suggested by the reviewer, \nwe further evaluate our approach on the latest large-scale Argoverse2 dataset. \nGiven the limited time and resources during the rebuttal period, we directly train our approach with the same hyper-parameters as in Waymo dataset. \nAs shown in the following table, we compare our approach with the top-10 submissions on the leaderboard of Argoverse2 dataset [A] (note that these submissions are highly competitive since most of them are tailored submissions for this year's Argoverse2 competition in June).\nThe experiments show that our preliminary results already achieve new state-of-the-art performance with remarkable gains on two miss rate related metrics, demonstrating the great generalizability and robustness of our approach. \nWe will follow the reviewer's suggestion and add the evaluation of this secondary dataset in the revised version. \n\n| Method | Miss Rate (K=6) | Miss Rate (K=1) | brier-minFDE (K=6) |\n|:---|:---:|:-----:|:--:|\n| MTR (Ours)| **0.15** | **0.58** | 1.98| \n| TENET| 0.19 | 0.61 | **1.90**| \n| OPPred| 0.19 |0.60 | 1.92 |\n| Qml| 0.19 | 0.62 |1.95| \n| GANet| 0.17 |0.60 |1.97 |\n| VI LaneIter| 0.19 | 0.61 | 2.00 |\n| QCNet |0.21 | 0.60| 2.14 |\n| GOHOME Scalar | 0.20 | 0.64 |2.16|\n| HDGT | 0.21\t| 0.66 | 2.24|\n| GNA | 0.29 | 0.71 | 2.45|\n| vilab | 0.29\t| 0.71 | 2.47 |\nThe performance comparison on the test set leaderboard of Argoverse2 dataset. Note that K is the number of predicted trajectories for calculating the evaluation metrics. \n\n\\[A\\]: https://eval.ai/web/challenges/challenge-page/1719/leaderboard/4098\n\n****", " **Q3**: \"In the field of motion prediction, the feature itself includes the postion information (coordinate). I am wondering why the proposed method uses the PE + MLP instead of just MLP. Is there any experiments about its effectiveness?\"\n\n**A3**:\nThanks for the valuable question. \nThe PE module has been utilized in three components of the proposed framework, which are ablated in the following to investigate their individual effectiveness:\n\n* Using PE + MLP to encode motion query pair in Eq.(4,5): Here the PE module aims to map raw point coordinate to a sinusoidal positional embedding space, so as to be consistent with the sinusoidal positional embedding of keys. The experiments ($1^{st}$ and $2^{nd}$ rows) show that removing PE and applying MLP directly on raw coordinate lead to a slight performance decrease.\n* Using PE in cross attention as in Eq.(5,7): The experiments ($1^{st}$ and $3^{rd}$ rows) show that the performance drops a lot if we remove all the positional embeddings in cross attention module. It demonstrates that although all features naturally contain position information, the key/value and query are still not well aligned since they are deeply encoded by different sub-networks (*i.e.*, context encoder for key/value and transformer decoder for query). Hence, the positional embedding plays an important role in cross attention to associate the input key/value and query. \n* Using PE in self attention of transformer encoder as in Eq.(2): The experiments ($1^{st}$ and $4^{th}$ rows) show that removing the positional embedding in transformer encoder just slightly decreases the performance. \nIt is in line with the reviewer's argument: the positional embedding is not important in self attention since the input feature is the same for key/value/query and it already includes position information. However, the slight performance decrease also implies that adding the positional embedding to self attention can constantly augment the positional information and benefit the performance. \n\n\n| Setting | Miss Rate (low) | mAP (high) |\n|:--|:--:|:--:|\n| MTR | **0.1668** | **0.3437** | \n| Remove PE in Motion Query Pair - Eq.(4,5) | 0.1730 | 0.3328| \n| Remove PE in Cross Attention - Eq.(5,7) | 0.3304 | 0.2075 |\n| Remove PE in Encoder - Eq.(2) | 0.1707 | 0.3424|\n\n\n****\n\n**Q4**: \"In equation (6), it uses $C^{j-1}$. How to initialize it in the first layer is not described.\"\n\n**A4**: Thanks for pointing out this. We follow the common setting in DETR related works to initialize $C^0$ as a zero tensor. We will clarify it in the revised version. \n\n****\n\n**Q5**: \"I noticed that Waymo Motion Challenge 2022 recently finished. Authors may discuss about those top-ranked methods including golfer, MPA, HDGT, etc, which could make the paper more up-to-date.\"\n\n**A6**: \nThanks for the constructive suggestion. We will compare and discuss these latest references in the revised version. ", " We sincerely thank the reviewer for providing thoughtful review and constructive suggestions. We answer the questions as follows. \n\n****\n\n**Q1**: \n\"It would be more convincing if the experiments could be done on other large scale datasets.\" and \"it is okay if there is no enough time/resource to try other datasets.\" \n\n**A1**: \nThanks for the valuable suggestion. \nWe evaluate our proposed approach on the latest Argoverse2 dataset, which is another large-scale dataset for motion prediction. \nGiven the limited time and resources during the rebuttal period, we directly train our framework with the same hyper-parameters as in Waymo dataset. \nAs shown in the following table, we compare our approach with the top-10 submissions on the leaderboard of Argoverse2 dataset [A] (note that these submissions are highly competitive since most of them are tailored submissions for this year's Argoverse2 competition in June).\nThe experiments show that our preliminary results already achieve new state-of-the-art performance with remarkable gains on the miss-rate related metrics, demonstrating the great generalizability and robustness of our approach. \nWe will include the evaluation of our approach on this new dataset in the revised version.\n\n| Method | Miss Rate (K=6) | Miss Rate (K=1) | brier-minFDE (K=6) |\n|:---|:---:|:-----:|:--:|\n| MTR (Ours)| **0.15** | **0.58** | 1.98 | \n| TENET | 0.19 | 0.61 | **1.90** | \n| OPPred | 0.19 |\t0.60 | 1.92 |\n| Qml | 0.19 | 0.62 | 1.95 | \n| GANet | \t0.17 |\t0.60 | 1.97 |\n| VI LaneIter | \t0.19 | 0.61 | 2.00 |\n| QCNet | 0.21 | 0.60\t| 2.14 |\n| GOHOME Scalar | \t0.20 | 0.64 | 2.16 |\n| HDGT | 0.21\t| 0.66 | 2.24 |\n| GNA | 0.29 | 0.71 | 2.45 |\n| vilab | 0.29\t| 0.71 | 2.47 |\nThe performance comparison on the test set leaderboard of Argoverse2 dataset. Note that K is the number of predicted trajectories for calculating the evaluation metrics. \n\n\\[A\\]: https://eval.ai/web/challenges/challenge-page/1719/leaderboard/4098\n\n****\n\n**Q2**: \"It would better position this work if the authors could discuss about the proposed method's relation with recent DETR related works.\"\n\n**A2**: \nThanks for the constructive suggestion. We will add a discussion section about this in the revised version. \nHere we discuss the relation and differences between DETR related works and our approach to better demonstrate our specific model design for motion prediction task:\n\n* Indeed, as mentioned in L109, our work is inspired by DETR [4] and its follow-up works like DAB-DETR [23]. \nSpecifically, both DAB-DETR [23] and our work utilize sinusoidal positional encoding and MLP to explicitly encode a spatial anchor point as positional query in transformer decoder layer. \nHowever, we adopt different definition and usage of the positional query to make our model more explainable for multimodal motion prediction. Concretely, instead of using dynamic learnable query as in DETR related works, we propose to use motion query pair as positional query, where each motion query pair is bound with a fixed intention point, taking charge of predicting the future trajectory of a specific motion mode (*e.g.*, turn left, turn right and go straight, etc.) towards this intention point.\nThis independent modeling of different motion modes enables our framework to predict better multimodal trajectories. \nIn contrast, the positional query in DETR related works may be dynamically associated with different ground-truth objects and does not have explicit and stable correspondence. \n* Besides, during the iterative refinement with transformer decoder layers, we propose dynamic map collection to constrain the input map to a deformable region along the predicted trajectory for fine-grained trajectory refinement. This explicit attention constraint is novel and hasn't been explored in DETR related works.\n\n****", " We sincerely thank the reviewer for providing thoughtful review and constructive suggestions. We answer the questions as follows. \n\n****\n\n**Q1**: \"The implementation of MTR-e2e is hard to follow given limited illustration.\" \n\n**A1**: We apologize for the confusion. Here we provide more implementation details of MTR-e2e by clarifying its two differences compared with the default setting MTR: \n\n* **Different numbers of motion query pairs**: MTR-e2e uses 6 motion query pairs (the required trajectory number in most benchmarks) so as to remove NMS post-processing, while MTR has 64 motion query pairs. \n* **Different training strategies for selecting positive motion query pair**: During the training process, we need to assign one motion query pair as the positive query, and its predicted trajectory is utilized for calculating the regression loss to cover the given ground-truth trajectory. MTR and MTR-e2e adopt different training strategies: \n * MTR adopts a static assignment strategy that depends on 64 fixed intention points. As each motion query pair corresponds to one intention point, the motion query pair, whose intention point is closest to the endpoint of ground-truth trajectory, is selected as the positive query. \n * MTR-e2e adopts a dynamic assignment strategy that depends on the predictions of 6 motion query pairs. As each motion query pair predicts a single future trajectory, we select the positive motion query pair by dynamically checking these 6 predictions whose endpoint is closest to the endpoint of the ground-truth trajectory. The reason for using such strategy is that the above static assignment strategy may assign a ground-truth trajectory to some faraway intention points and increase the burden of model optimization, since MTR-e2e only has 6 intention points that can not well cover all potential ground-truth future trajectories in a large region. \n\nNote that we ablate the effects of these two training strategies with different numbers of motion query pairs in Figure 4 and Section 4.3. \n\n****\n\n**Q2**: \"It would be helpful to ablate the choice of query pair number for end-to-end version.\" \n\n**A2**: Thanks for the valuable suggestion. As discussed in **A1**, the end-to-end version indicates using the dynamic assignment strategy to select positive motion query pair, which has been ablated in Figure 4 and Section 4.3. Specifically, the green lines in Figure 4 ablate the choice of query pair number under the dynamic assignment strategy, where we can see that 6 motion query pairs achieve the best performance for MTR-e2e. \n\n****\n\n**Q3**: \"It would be helpful for us to better understand the efficiency of this by making an ablation study of using only one type of query or both.\"\n\n**A3**: \nThanks for the constructive suggestion. We ablate the individual effects of the motion query pair by removing one of its two components. The results and discussions are listed below: \n\n| Intention Points | Static Intention Query | Dynamic Searching Query | Miss Rate (low) | mAP (high) | \n|:---------------:|:---------:|:---------:|:---------------:|:---------:|\n| Y | Y | Y | **0.1668** | **0.3437** | \n| Y | Y | | 0.1706 | 0.3284 |\n| Y | | Y | 0.1734 | 0.3379 | \n| | | Y | 0.2150 | 0.2202 | \n\n* $1^{st}$ row: The default setting with complete motion query pair. \n* $2^{nd}$ row: Dynamic searching query in Eq.(7) is replaced with static intention query $Q_I$. The performance drops from 0.3437 to 0.3284 in terms of mAP. \n* $3^{rd}$ row: Static intention query in Eq.(6) is replaced with dynamic searching query $Q_S^j$, while intention points are still used to initialize dynamic searching query and select positive motion query pair for optimization. The performance slightly drops from 0.3437 to 0.3379 in terms of mAP.\n* $4^{th}$ row: The intention points are also removed. Hence, dynamic searching queries need to be set as learnable embeddings, and the dynamic assignment strategy is adopted to select positive motion query pair since we do not have any intention points. The performance drops dramatically from 0.3437 to 0.2202 in terms of mAP. \n \n\nThe above experiments demonstrate that both two components of the motion query pair benefit the final performance, where static intention query is responsible for learning interaction among different motion modes (as in Eq.(6)) while dynamic searching query is able to probe trajectory-specific features for motion refinement (as in Eq.(7)). \nNotably, the intention points are critical for MTR framework since each motion query pair is bound with one specific intention point to better model multimodal motion prediction, and removing the intention points will greatly decrease the performance.\nBesides, all these settings have similar inference latency (33ms per scene as provided in L35 of supplementary material) since their basic frameworks remain unchanged. ", " This paper proposes a transformer-based method for vehicle trajectory forecasting. It proposes to combine the tasks of global localization and local refinement for more accurate trajectory forecasting. On the structure side, the authors design a mechanism of motion query pair to model motion prediction as the joint optimization of the two tasks. Moreover, the interaction among agents is considered in the proposed method and collaborates to make the dense future prediction. The proposed method is demonstrated to be efficient on the large-scale Waymo Open Dataset. And an end-to-end variant of the proposed method is also provided for a broader study. Strengths:\n1. The proposed method is well elaborated and the implementation details are necessarily provided to help understand the model design.\n2. The performance of the proposed MTR on the Waymo Open Motion Dataset is good, advancing the SoTA under the setting further.\n3. The paper is mostly well written that I can understand the motivation, high-level intuition, and model design quickly.\n\nWeaknesses:\n1. Some details are not clear, for example, the implementation of MTR-e2e is hard to follow for me given the limited illustration at L273. \n2. Though it may not be necessary, it would be helpful to ablate the choice of query pair number for end-to-end version as well as there is a claim that \"since 6 intention points are too sparse to well cover all potential future motions.\" may need some experiment backup.\n3. Given the proposed method stresses on the design of query pair, it would be helpful for us to better understand the efficiency of this by making an ablation study of using only one type of query or both.\n I can understand the technical design of the proposed method while I have some concerns as mentioned in the \"Weaknesses\" part above. It would be helpful if the authors can address them with more clarification, with which I can more confidently assess the significance of this paper and adjust my rating. Some technical design of the proposed method is explained at the end of the draft. I don't recognize more potential negative societal impact or limitations of this paper.", " This paper proposes an decoder method for motion prediction task, which refines different modes with the static prior and dynamic attention. Its performance on the Waymo Open Motion Dataset is impressive, which demonstrates the effectiveness of iteratively refine the prediction (similar to DETR/DAB-DETR). Strengths\n* The idea of iteratively refining the prediction by Transformer is novel in the motion prediction area.\n* The performance on Waymo Motion Dataset is great.\n* The ablation experiments is well-organized and convincing\n\nWeakness\n* The proposed method is only evaluated on one dataset. It would be more convincing if the experiments could be done on other large scale datasets. However, considering the Waymo Open Motion is fairly large, I think it is okay if there is no enough time/resource to try other datasets.\n* Some parts of the proposed methods is not clearly described in the manuscript, which is understandable considering the space limit. \n* The proposed method has similarities with the DAB-DETR in the objection detection area. I think it would better position this work if the authors could discuss about the proposed method's relation with recent DETR related works. #### Question\n* The PE module is first introduced in the NLP field so that tokens' position information could be considered (Transformer is a set operator which ignores the postion information). However, in the field of motion prediction, the feature itself includes the postion information (coordinate). I am wondering why the proposed method uses the PE + MLP instead of just MLP. Is there any experiments about its effectiveness?\n* In equation (6), it uses C^{j-1}. How to initialize it in the first layer is not described.\n* I noticed that Waymo Motion Challenge 2022 recently finished. Authors may discuss about those top-ranked methods including golfer, MPA, HDGT, etc, which could mkae the paper more up-to-date. The limitation part is ok.", " The work addresses the motion forecasting problem for autonomous driving. The authors introduce a transformer-based framework (MTR) that works in the following ways, as highlighted in the contribution section of the paper:\n\n- Separates the modeling of the global intention from local movement refinement in the trajectories in the transformer framework. The predictor is inspired by DETR. \n- Interaction modeling between agents via an auxiliary dense prediction task, essentially letting the model to predict the future directly (I didn't fully understand that part... see below)\n- SOTA results on the Waymo dataset. Ranked #1 among results without using ensembles. \n\nSince I don't understand the 2nd contribution, I cannot recommend accept at this point. Looking forward to understanding it post-rebuttal!\n\nPOST REBUTTAL UPDATE: I understand the contribution better now. In line with other reviews' feedback, I'll change the rating from 4 -> 7, and recommend an accept.\n Strengths:\n\nStrong results: Significant improvement over the SOTA. I checked the leaderboard on Waymo Open Dataset, and verified the claims. \n\nSomewhat novelty: Using DETR for motion forecasting is not that new anymore. I reviewed several papers for CVPR'22 and ECCV'22 that contained similar ideas. But those should be considered concurrent work. Additionally, the hierarchical separation of intent vs. fine control adds an additional hint of novelty, though the hierarchical separation by itself is not novel either [9, 51]. \n\nGood ablation: The paper contains ablation for all the contributions and novelties in their methods. This is great!\n\nWeaknesses:\n\n- Unclear writing: Abused notations, missing descriptions of variables, figures that are not self-contained. See below under \"questions\".\n\n- Insufficient experiments (minor): The only results are on the Waymo dataset. There are other popular datasets such as Argoverse and nuScenes. Having strong results on a secondary dataset would make the representation a lot stronger. line 73: Why not also using ensemble to boost the accuracy a bit to achieve top results? \n\nFigure 1: The figure is far from self explaining. What do the small road illustrations above the dense future prediction and dynamic map construction say? What are K, T, N and D (I know its in the text, but it doesn't hurt to say it here)? Where do the input \"predicted trajectories\", \"map query\" and \"query content feature\" come from? The figure is way too complicated, and I don't feel rewarded for looking closely....\n\nEq 2, ln 164: There are equations like X = f(X), e.g. A = MLP([A, A_t]) what does this even mean? please use subscripts to make it clear that the variable in LHS and RHS are not the same. \n\nln 237: where does the auxiliary loss L_a come from? just write equations and not words. And if its just an L1 loss against the GT. I don't understand the intuition why it helps with interaction. It seems like its just like a multi-head network where you supply the GT at several layers of the network. Yes, but it didn't hit the mark. \n\nThe limitation section is about high-level limitation, like \"the method is not great for long tail behaviors\", not a wish list of future works. ", " In this paper, a Motion TRansformer (MTR) framework is proposed for the motion prediction task, including marginal and joint motion prediction. Specifically, motion query pairs are designed for global intention localization and local movement refinement, which takes advantage of both goal-based methods and the regression methods. Experiments on Waymo Open Dataset indicate the effectiveness of the proposed method. Strengths: \n- Strong motivation and well-organized.\n- Promising results.\n\n\nWeaknesses: (See Questions for details) \n- Some insights/details are not clear.\n- Lack of some experiments.\n Concerns: \n1. Overall, it is a paper for motion prediction challenge with promising results and clear presentations. I assume it is the initial version of the final 1st place work [1], sharing very similar methods and almost the same framework, thus I would encourage authors to update the paper with [1]. \n2. The most concern is that all the strategies are well-studied in this community, i.e., the transformer idea, scene context and interaction modeling, etc. It would be better if more insights could be included for model design, and highlight the differences/contributions.\n3. In Line 134-135, how to pad zeros for trajectories that have less than $t$ frames? In the front/back? Some details are missing here.\n4. Some missing references when referring to future interactions, some works [2-4] have been proposed to argue the future interaction point and to consider such future interactions.\n\nMinors: \n1. Line 56, I believe it is 'empirical' instead of 'experimentally'.\n2. In References, the names of conferences or journals, i.e. abbreviation or full name, are not consistent. \n\nI am happy to improve my rating if these concerns could be addressed.\n\n\n[1] https://storage.googleapis.com/waymo-uploads/files/research/MotionPred/MotionPrediction_MTRA.pdf \n[2] EvolveGraph: Multi-Agent Trajectory Prediction with Dynamic Relational Reasoning. NeurIPS 2020 \n[3] Tra2Tra: Trajectory-to-Trajectory Prediction With a Global Social Spatial-Temporal Attentive Neural Network. ICRA 2021 \n[4] StarNet: Pedestrian Trajectory Prediction using Deep Neural Network in Star Topology. IROS 2019 \n\n There is a limitation section in the main body of the paper." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 8, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 4, 5 ]

[ "JPSSfkJw-ej", "bttcmk1hJ3l", "iy6N46x13dd", "1IqDjqswtbc", "dmddg2xzGbB", "mKp53-kA82z", "wWgrosHNLjz", "MIuRPHkh6rJ", "2sw1vrXSIJd", "nI_-TLdMHRL", "swAsmsa16D3", "EsAEXZmp7gn", "miAW_MP8fEc", "nips_2022_9t-j3xDm7_Q", "nips_2022_9t-j3xDm7_Q", "nips_2022_9t-j3xDm7_Q", "nips_2022_9t-j3xDm7_Q" ]

[ "eA3OVdS5TJk", "uF_SodZGbO9", "NmK6yZsCFkJ", "mn84fgpbbis", "XyMjKmOmMlv", "Kbiak1N698i", "HlF9duuyGfE-", "XiTkxlFKyKY", "16Kg5maX2nL", "sxo0QsVu9l9", "knlAr3X4Nz3", "UUS25ObYcl-", "XjwqiiC4bSd", "uePzSrnxwir", "gy9MKU7SI_Z" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank all the reviewers for going through our response and providing support. As suggested by the reviewers, we will update the numbers which are obtained after exclusion of all novel/rare classes. Our response shows that the benefit of our approach in comparison to state-of-the-art methods ViLD (ICLR'22) and Detic (ECCV'22) holds under the new setting. We believe that all the queries have been answered and we welcome any further feedback from the reviewers.", " Thanks for the response, and the additional experiments. I've also read the comments from other reviewers (SdFN and wmjL) and agree with adding/replacing experiment results about MViT. I'll keep my current rating at this moment.", " Thank you for the suggestion. We will update our results accordingly. As noted from our updated results, the MViT trained after excluding novel class box annotations performs well and our final model still provides performance gain compared to existing state of the art approaches, ViLD (ICLR 2022) and Detic (ECCV 2022).\n\nRegarding the details about what exactly is trained and what is frozen in the phases of training, we follow a three stage training strategy. Specifically, in stage-1, the base model is first trained for 1x schedule using only base class annotations using a simple linear projection layer. In stage-2, the model is fine-tuned for another 1x schedule using Region-based Knowledge Distillation (RKD), where it adapts the projection layer in stage-1 to align the local region representations to the language representations. We refer to this adapted projection layer as $W_D$. Finally in stage-3, the model is further fine-tuned to learn from weak image-level supervision with pseudo-box labels (PIS) by learning the VL projection layer $W_P$. During this stage, the weight transfer function explicitly conditions $W_P$ on the mapping learned from distillation, $W_D$. Here VL projection layer $W_D$ is kept frozen. All the losses in L229 are used during the last stage of the training. The above details were also provided under \"Method Clarifications\" (point viii) of our previous response.\n\nWe will further clarify above details in section 4.2 (implementation details) of the paper.", " Thank you for your answers.\n\nI agree with Reviewer wmjL that it is absolutely crucial to update the numbers in the paper with the MViT that has not been trained on images containing bounding box annotations from the \"novel classes\". \n\n\nBy the way I think that question was omitted in your response:\n\n> Related to the previous 2 questions, please provide details about what exactly is trained and what is frozen in the phases of training.\n\nIt would be great if you could provide an answer to this and clarify in the paper. \n\nThank you.", " Thank you for the suggestion and we will update our results accordingly.", " > We also train our LVIS model in a stricter open-vocabulary setting by only using LVIS base categories for image-level supervision. We achieve an overall 21.71 AP in this experiment which is similar to the model trained using image-level supervision from 997 categories (22.75 AP).\n\nThank you for providing these results. The results obtained by using only LVIS base categories should be used in the paper. That way, APr actually measures open-vocabulary performance, rather than some mixture of known and unknown-class performance.\n\nThe same goes for the MViT pretraining: Please only show results obtained with the MViT that was not trained on novel classes.", " ## Open-vocabulary setting\n\nThank you for the suggestion. Due to time limitation in rebuttal phase, ImageNet-21K pretraining was not possible however we are attempting it and will include in the final version.\n\n**Weak image-level supervision:**\n\nInspired from Detic, we define our work under the **weakly-supervised open-vocabulary** setting as it uses image-level labels for expanding the detector's vocabulary. However, the complete target vocabulary set is not known (e.g., in our LVIS experiments see Table 4 in the main paper). This way, the generalization and OVD capability of the proposed model is assessed.\n\nPrior works such as OVR-CNN and ViLD use different forms of weak-supervision to enlarge the vocabulary, such as COCO captions for pretraining or large-scale pretrained CLIP as the classifier head can have an overlap of target vocabulary, $C_{B} ∪ C_{N}$.\n\n**Generalization to cross-datasets:**\n\nOur LVIS model when evaluated on cross-datasets (OpenImages and Objects365) shows better performance compared to previous methods which indicates the generalization of our approach beyond the LVIS common, frequent and rare classes. Specifically, we ablate on the performance of cross-data evaluation by comparing overlapping categories with LVIS. In OpenImages our LVIS model attains 55.8 AP on seen classes, and 36.3 AP on unseen. In case of Objecs365, our model attains 31.3 on seen and 13.1 on unseen categories.\n\nWe provide details about our experimental setup along with some additional experiment results as follows.\n\n> **COCO Split:** Our COCO model does not selectively filter any categories specific to novel categories and instead considers all COCO categories seen in the captions during the image-level supervision, consistent with OVR-CNN.\n\n> **LVIS Split:** Our LVIS model uses images from 997 overlapping ImageNet categories. However not all 337 rare categories are included in this which is a desired property for an open-vocabulary setting. Specifically, 157 rare categories do not have any overlap with image-level labels from ImageNet.\n\nWe also train our LVIS model in a *stricter open-vocabulary setting* by only using LVIS base categories for image-level supervision. We achieve an overall 21.71 AP in this experiment which is similar to the model trained using image-level supervision from 997 categories (22.75 AP).\n\n## MViT pretaining\nThough the MViT training dataset has no overlap with the evaluation data, some novel classes are exposed during MViT training. To this end, we train MViT again using the author's provided code by entirely restricting any exposure to the novel classes. The results in Tables A-2 and A-3 show that even with the exclusion of novel classes in MViT training, our approach consistently maintains a significant advantage over Detic and ViLD on COCO and LVIS datasets.\n\n|Method|AP$_r$|AP$_c$|AP$_f$|AP|\n|-|-|-|-|-|\n|ViLD (384 epochs)|16.1|20.0|**28.3**|22.5|\n|Ours (36 epochs)|**17.1**|**21.4**|26.7|**22.8**|\nTable A-2: Our LVIS results after excluding rare classes from MViT training\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Detic|28.4| 53.8| 47.2| \n|Ours|**36.6**|**54.0**|**49.4**|\nTable A-3: Our COCO results after excluding novel classes from MViT training\n\n## IRM Loss \nThe IRM loss is computed for regions from single images and average over all the images in a mini-batch. We will clarify this in the final version.\n\n## Typos\nIt will be corrected in the final version.", " ## Use of MViT in our pipeline\nThe previous works inline with weakly-supervised and OVD uses off the shelf pretrained models, to enhance the performance. For example, WSDNN uses proposals from selective search and edge boxes. Similarly Detic and ViLD use a pretrained Faster-RCNN to generate proposals. In a similar way, we enhance our proposal quality by incorporating MViT in our pipeline without any significant overhead. The approach of using detectors to produce quality proposals is consistent in literature.\n\nThough the MViT training dataset has no overlap with the evaluation data, some novel classes are exposed during MViT training. To this end, we train MViT again using the author's provided code by entirely restricting any exposure to the novel classes. The results in Tables A-2 and A-3 show that even with the exclusion of novel classes in MViT training, our approach consistently maintains a significant advantage over Detic and ViLD on COCO and LVIS datasets.\n\n|Method|AP$_r$|AP$_c$|AP$_f$|AP|\n|-|-|-|-|-|\n|ViLD (384 epochs)|16.1|20.0|**28.3**|22.5|\n|Ours (36 epochs)|**17.1**|**21.4**|26.7|**22.8**|\nTable A-2: Our LVIS results after excluding rare classes from MViT training\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Detic|28.4| 53.8| 47.2| \n|Ours|**36.6**|**54.0**|**49.4**|\nTable A-3: Our COCO results after excluding novel classes from MViT training\n## MViT direct evaluation in OVD setting\nWe evaluate the performance of MViT directly on the OVD setting. From Table A-4, we observe that naively using and evaluating MViT for OVD task results in lower performance (row-2). However class-agnostic are relatively higher (row-3) suggesting that the classification performance of MViT is originally very low.\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Supervised (Base)|1.7|53.2|39.6|\n|MViT (Class-specific)|5.6|4.1|4.5|\n|MViT (Class-agnostic)|18.5|28.0|25.5|\n|Ours|**40.3**|**54.1**|50.5|\nTable A4: Evaluating MViT directly on OVD COCO\n\nMViT class-specific and class-agnostic proposals can provide better results over supervised base model for novel classes. However it significantly lags over our final results as our other contributions like RKD (Region-based Knowledge Distillation), PIS (Pseudo-labeling for Image-level Supervision) and Weight-transfer ensure the synergy between complementary components, leading to best performance.\n## Overall pipeline is complex\nAlthough the method is complex, the proposed multi-phase training pipeline is effective to ensure the synergies between different proposed methods including RKD, PIS and weight transfer. An important contribution of our approach is a careful design for unifying the advantages of generic object detector (MViT), knowledge distillation and pseudo-labeling. It performs well on the cross-dataset evaluation (Table 5 main paper) which indicates the generalization of our model. Our code and pretrained models will be publicly released.\n## Combining different approaches from literature\nWe are the first to simultaneously integrate object-centric visual and language alignment within a single architecture for OVD. This combination is not trivial and combining both techniques naively results in inferior performance as the RKD and PIS objectives compete. Our approach of using RKD along with PIS using weight transfer function mitigates competition and provides complementary benefits. Overall, our proposed approach requires meticulous design to ensure synergy between complementary components existing in the literature leading to good performance improvements.\n## Training epochs\nFor a fair comparison with Detic, we train Detic for 3x schedule (36 epochs).\n## Small improvements \nOur approach consistently improves over SoTA for all datasets. In comparison to COCO, the gains on LVIS and Objects365 may seem relatively less, however it should be noted that these large-scale datasets are challenging and even small improvements here demonstrate the scalability of our approach.\n\n## Too many abbreviations\nIt will be clarified in the final version.\n\n## Comparison with Detic (without MViT)\n\nFor stricter comparison with Detic, we train our models using RPN proposals instead of MViT proposals (Table A-4). In row-2, we use RPN proposals for RKD. For ILS, we compare max-size proposal (same as Detic) on RPN (row-3) with MViT proposals (row-4). With $\\mathcal{Q}_{\\text{pseudo}}$, the multi-modal nature of MViTs are be exploited for pseudo-labelling using intuitive text queries (row-5). Finally we combine our proposed RKD and weight-transfer on RPN proposals (row-6) instead of MViT proposals plus Q_pseudo. These elements still show improvement over performance of Detic.\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Detic (3x schedule)|28.4|53.8|47.2|\n|RKD on RPN|12.3|53.9|43.1|\n|Max-size ILS on RPN|25.9| 51.1|44.5|\n|Max-size ILS on MViT|28.9| 50.7|45.4|\n|RKD+ILS+Weight transfer on RPN|31.1|54.0|48.0| \nTable A-4: Comparison with Detic (without MViT) using only RPN", " ## Whether MViT training Datasets Contain Box Annotations for Novel Classes?\n\nThough the MViT training dataset has no overlap with the evaluation data, some novel classes are exposed during MViT training. To this end, we train MViT again using the author's provided code by entirely restricting any exposure to the novel classes. The results in Tables A-2 and A-3 show that even with the exclusion of novel classes in MViT training, our approach consistently maintains a significant advantage over Detic and ViLD on COCO and LVIS datasets.\n\n|Method|AP$_r$|AP$_c$|AP$_f$|AP|\n|-|-|-|-|-|\n|ViLD (384 epochs)|16.1|20.0|**28.3**|22.5|\n|Ours (36 epochs)|**17.1**|**21.4**|26.7|**22.8**|\nTable A-2: Our LVIS results after excluding rare classes from MViT training\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Detic|28.4| 53.8| 47.2| \n|Ours|**36.6**|**54.0**|**49.4**|\nTable A-3: Our COCO results after excluding novel classes from MViT training\n\n## Direct evaluation of MViT on COCO OVD splits\nWe evaluate the performance of MViT directly on the OVD setting. From Table A-4, we observe that naively using and evaluating MViT for OVD task results in lower performance (row-2). However, class-agnostic results are relatively higher (row-3) suggesting that the classification performance of MViT is originally quite low.\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Supervised (Base)|1.7|53.2|39.6|\n|MViT (Class-specific)|5.6|4.1|4.5|\n|MViT (Class-agnostic)|18.5|28.0|25.5|\n|Ours|**40.3**|**54.1**|**50.5**|\nTable A-4: Evaluating MViT directly on OVD COCO\n\nMViT class-specific and class-agnostic proposals can provide better results over supervised base model for novel classes. However, it significantly lags over our final results as our other contributions like RKD (Region-based Knowledge Distillation), PIS (Pseudo-labeling for Image-level Supervision) and Weight-transfer ensure the synergy between complementary components, leading to better performance.\n\n## Method clarifications\n**i)** $\\mathcal{R}$ represents embeddings of all regions, while $\\mathcal{R}(r)$ represent the region embeddings of a region $r$.\n\n**ii \\& iii)** We have all zeros for the background embeddings as it makes dot product zero and its exponential to 1, avoiding pushing non-foreground bounding boxes, which may contain target/novel classes, to an arbitrary region of the embedding space.\n\n**iv)** The CLIP embeddings used for RKD are obtained by feeding the cropped image region to CLIP image encoder.\n\n**v)** In Fig. 2, the similarity matrices are computed for 17 COCO novel classes and tSNE plots are shown for 10 classes for visualization simplicity.\n\n**vi)** Here $N$ varies for each COCO caption image. The words in a caption are compared heuristically with every category name to generate a list of categories for each image ($N$), which is used as labels for PIS.\n\n**vii)** Given that we have $C_B$ total classes and $N$ positive image-level labels in an image $i$, then the negative classes would be $C_B-N$.\n\n**viii)** Our pipeline has three stages. The base model is fine-tuned for 1x schedule using RKD, where the model learns the VL projection layer $W_D$. The model is further fine-tuned to learn from PIS by adapting the VL projection layer $W_P$. During this stage, the weight transfer function explicitly conditions $W_P$ on $W_D$. Here, $W_D$ is kept frozen. This explicit conditioning is achieved as the weight transfer function transforms $W_D$ to $W_P$, via our weight transfer function $\\mathcal{W_T}$. \n\n## Optimization details\nIn Table 2 (main paper), we show that naively using RKD and PIS in a single training phase is inferior to using our proposed stage-wise training setting (row 4 vs 5). This is because the RKD and PIS objectives compete with each other and our weight transfer function helps obtain complementary benefits from both.\n\nFurther, we provide results of training our model with a common projection layer between RKD and PIS ($W_P$ = $W_D$), by freezing $W_D$ from second stage (Table A-5). This shows the importance of separate linear projections for individual methods and weight transfer function to mitigate competition.\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Ours|40.3|54.1|50.5| \n|$W_D$ $=$ $W_P$|33.5|54.1|48.7| \nTable A-5: COCO model trained with a common projection layer\n\n## Datasets details in Table 3\nOVR-CNN uses COCO captions for pretraining. Detic uses COCO Captions and ImageNet-21k datasets while uses a pretrained RPN for proposal generation. Our approach uses COCO Captions and ImageNet-21k datasets and MViT pretrained on GQA, Visual Genome & Flickr for proposal generation. We will clarify these details in our main paper table.\n\n## Limitations and societal impacts\nThese are discussed in supplementary material (Appendix F-H). Regarding limitation, our detailed analysis shows that the model struggles to detect small objects that have rare occurrences in the training. We will further elaborate on this in the final version.", " The main question posed by Reviewer LKon is to assess how much the distillation from MViT contributes to our performance improvement. To answer this question, we report below ablation studies as well as new experimental results on refined data splits. Our conclusion is that although MViT is an important component of our approach, other contributions of this work including RKD (Region-based Knowledge Distillation), PIS (Pseudo-labeling for Image-level Supervision) and Weight Transfer are important towards developing an integrated framework for OVD. An important contribution of our approach is a careful design for unifying the advantages of generic object detector (MViT), knowledge distillation and pseudo-labeling. This is also highlighted by Reviewers wmjL, SdFN and dzUw, e.g., by mentioning \n>It is the first paper in attempt to combine the advantages of both knowledge distillation and self-training.\n\n## Ablation study replacing RPN proposals with proposals from MViT\n\nWe refer to the Table A-1 where we use max-size strategy from Detic with RPN proposals (rows 2-3) in comparison with MViT proposals (row-4). We show that using MViT proposals provides improvements, indicating the suitability of proposals from MViT. However, an equally important question is *how to effectively use these proposals from MViT*, which we solve using our proposed pseudo-labeling strategy, $\\mathcal{Q}_{\\text{pseudo}}$ (row-5). In addition to MViT proposals, our other proposed components including RKD and Weight Transfer proves to be equally valuable (row-6).\n\n| Method| AP$_{novel}$ | AP$_{base}$ |AP|\n|-|-|-|-|\n|1: Supervised (Base)|1.7|53.2|39.6| \n|2: Detic with RPN (Max-Score loss)|15.9|48.2|39.7| \n|3: Detic with RPN (Max-Size loss)|25.9|51.1|44.5| \n|4: Detic with MViT (Max-Size loss)|28.9|50.7|45.0|\n|5: Pseudo-box on MViT (Ours)|34.2|52.0|47.4|\n|6: Ours (RKD + PIS + Weight-transfer)|**40.3**|**54.1**|**50.5**| \nTable A-1: An ablation study on replacing RPN in Detic with MViT on COCO dataset\n\n## Exclusion of novel classes in MViT training\n\nThough the MViT training dataset has no overlap with the evaluation data, some novel classes are exposed during MViT training. To this end, we perform the following additional experiments.\n\n1. We train MViT again using the author's provided code by entirely restricting any exposure to the novel/rare classes. The results in Tables A-2 and A-3 show that even with the exclusion of novel classes in MViT training, our approach consistently maintains a significant advantage over Detic and ViLD on COCO and LVIS datasets.\n\n|Method|AP$_r$|AP$_c$|AP$_f$|AP|\n|-|-|-|-|-|\n|ViLD (384 epochs)|16.1|20.0|**28.3**|22.5|\n|Ours (36 epochs)|**17.1**|**21.4**|26.7|**22.8**|\nTable A-2: Our LVIS results after excluding rare classes from MViT training\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Detic|28.4| 53.8| 47.2| \n|Ours|**36.6**|**54.0**|**49.4**|\nTable A-3: Our COCO results after excluding novel classes from MViT training\n\n2. We evaluate the performance of MViT directly on the OVD setting. From Table A-4, we observe that naively using and evaluating MViT for OVD task results in lower performance (row-2). However, class-agnostic results are relatively higher (row-3) suggesting that the classification performance of MViT is originally very low.\n\n|Method|AP$_{novel}$|AP$_{base}$|AP|\n|-|-|-|-|\n|Supervised (Base)|1.7|53.2|39.6|\n|MViT (Class-specific)|5.6|4.1|4.5|\n|MViT (Class-agnostic)|18.5|28.0|25.5|\n|Ours|**40.3**|**54.1**|50.5|\nTable A4: Evaluating MViT directly on OVD COCO\n\nMViT class-specific and class-agnostic proposals can provide better results over supervised base model for novel classes. However, it significantly lags over our final results as our other contributions like RKD, PIS and Weight-transfer ensure the synergy between complementary components, leading to best performance.\n\n## Training using weight transfer function \nOur proposed pipeline has three stages. The base model is fine-tuned for 1x schedule using RKD, where the model learns the VL projection layer $W_D$. The model is further fine-tuned to learn from PIS by adapting the VL projection layer $W_P$. During this stage, the weight transfer function explicitly conditions $W_P$ on $W_D$. All the losses in L229 are used during this stage. This explicit conditioning is achieved as the weight transfer function transforms $W_D$ to $W_P$, via our weight transfer function $\\mathcal{W_T}$. Further, in Table 2 (main paper), we show that naively using RKD and PIS in a single training phase is inferior to using our proposed stage-wise training setting (row 4 vs 5). This is because the RKD and PIS objectives compete with each other and our proposed weight transfer function helps obtain complementary benefits from both.\n\n## Limitations and societal impacts \nThese are discussed in supplementary material (Appendix F-H).", " We sincerely thank all the reviewers (LKon, SdFN, wmjL, dzUw) for their detailed and constructive feedback. All reviewers appreciate the technical soundness and innovations of the proposed components in our open-vocabulary object detection (OVD) pipeline. Specifically, the proposed approach used for combining different components (dzUw) and improving their synergies (wmjL) may inspire other ensembling/multi-component fusion systems (LKon). The proposed approach results in better performance on OVD benchmark datasets (LKon, SdFN) and the ablation studies have been noted to be thorough and well conducted (SdFN, dzUw). The reviewers also appreciate the clear writing and presentation of the paper (LKon, wmjL, dzUw).\n\nOur code and pretrained models will be publicly released. ", " This paper proposed a training pipeline for better dealing with open-vocabulary object detection. Specifically, it incorporates CLIP as a pre-trained vision-language embedding to significantly expand the potential object detection vocabulary and mitigated performance degradation due to the gap between image-centric and object-centric representation. In this paper three important components are proposed to enhance the system, including (1) region-based knowledge distillation to match the CLIP embedding for image patch (instead of full image) with text, thus the replaced text classification head can better fit the region detection; (2) image-level supervision with pseudo box labels which benefit from a recent multi-modal ViT (MViT) class-agnostic object detector; (3) a weight transfer function which combines (1) and (2) more effectively in a trainable approach. The overall system is validated on multiple benchmarks and achieves state-of-the-art performance, especially for novel object classes. Strengths:\n\n- The assumption for the performance degradation from CLIP to object detection is reasonable and the authors propose a solid solution to mitigate the gap. The image-centric and object-centric nature may lead to incompatibility of the visual encoder and textual embedding, thus introducing the $L1$ and $L2$ regularization objectives is intuitively helpful to bridge the gap.\n- The weight transfer function seems interesting and shows great potential for merging two components in a more harmonized way. The performance boost is quite significant and similar ideas may inspire other ensembling/multi-component fusion systems.\n- The details of the training and evaluation are provided and the paper is easy to follow.\n\nWeaknesses:\n\n- The model did demonstrate significant improvements over other approaches, although it doesn't seem clear to me how much of the distillation from MViT is involved in these improvements. See my Questions. 1. Although the authors perform detailed ablation studies to validate each component in their system, one critical aspect is not covered which is the performance of MViT on \"novel\" object proposal/detection. Specifically, since the region proposal is generated from MViT for both class-agnostic and class-specific approaches, one possibility is that the pre-training of MViT may have some leaked information to the student model. The authors did mention that \"we ensure that MViT pretraining dataset has no overlap with any of the evaluation datasets in our work.\" but I'm curious about details about the exclusion -- does it mean the eval images are never included in the pre-training or even the novel object classes are not exposed? Probably an even more careful ablation study would be replacing RPN in the baseline object detection with MViT so the effect of the enhanced proposal can be analyzed. Essentially I'm feeling that the quality of the system is heavily dependent on the $\\mathcal{Q}_{pseudo}$ but this paper did not provide sufficient ablations about it.\n\n2. Regarding the weight transfer function, I'm curious how this is trained -- is it being trained in an end-to-end fashion (I presume) together with the full system using loss defined in L229? Does it mean $W_P$ in the weight transfer function is now replaced by $W_\\tau$ and $W_D$? Probably it's better to explicitly show this relation in the equation below L229. This author does not provide explicit explanations of limitations and societal impacts but I presume this system has similar issues with other systems (e.g. potential societal bias when trained with large-scale automatic collected datasets).", " This paper proposes a method for open-vocabulary detection where the goal is to train an object detector able to detect objects in an image given a text description of the desired object category. The method is evaluated by its ability to detect novel classes for which no bounding box supervision is provided during train time. In more details, during training, one has access to a dataset containing bounding box annotation (e.g. COCO detection) along with a dataset that has only image level annotation (e.g. COCO captioning). The proposed approach relies on 3 core ideas: (1) a region-based knowledge distillation (RKD) approach which aims at enforcing that the features extracted from the detection vision backbone (the student) match the ones of a multimodal CLIP visual encoder (the teacher), (2) A pseudo labelling technique to extract candidate bounding boxes on the dataset containing image level annotation and (3) a method to enforce better combination of the two previous techniques by tying parameters. They report performance on COCO and LVIS and show stronger performance compared to previous approaches. **Strengths**\n\n- The paper obtains good results on LVIS and COCO that outperform the state-of-the-art (Detic),\n- The ideas are overall well motivated and the method is technically sound \n- The ablation study is overall well conducted (see more suggestions in the Questions section) \n\n**Weaknesses**\n\n- An important aspect of the method seems to be that it relies on the MViT approach to obtain region proposals (used both in RKD with class agnostic proposals as well as for the pseudo labeling approach, see for Example Table 6 and Table 7 which shows the importance of MViT especially for the AP on novel classes. However MViT is trained on 3 datasets, some of which have bounding box annotation (GQA, VisualGenome and Flickr). The authors should discuss whether or not these datasets contain bounding box annotation for classes that are considered \"novel\" in the evaluation. If yes then I believe this would be unfair compared to previous approaches. See Questions for more details about this. \n\n- Related to the previous point, it would be good to list in Table 3, what are the datasets that are used by each methods (e.g. what is the source image-text pairs for all methods etc etc). I encourage the authors to provide this information in the rebuttal as well. This will help to better compare against past work such as Detic.\n\n- The description of the approach is not always clear (see Questions section for a detailed list of those questions). It is important that the authors clarify this during the rebuttal.\n\n- Some additional experiments could be conducted (see suggestions in Questions) \n\n=== POST REBUTTAL\n\nAfter reading the rebuttal and other reviews, I am raising my score from 5 to 6. The authors have adequately addressed the important concerns I had about the novel class results. To the best of my knowledge, I believe that the results are now legit. \n **About MViT**\n\nAs discussed above, it is unclear if using MViT is coherent with the idea of trying to generalize the method to novel classes. The authors should reply to the following questions:\n\n- Among the datasets used to train MViT, what are the ones that are annotated with bounding box annotations? Among those, are there classes that overlap with the \"novel classes\" of COCO or LVIS?\n- Is it possible to say how much MViT alone is getting on the novel classes of COCO (it seems that it should be possible to evaluate MViT on it)?\n\n\n**Method clarifications**\n\nThere are various things that are not very clear from reading the method section. Questions are listed below:\n\n- L140: what is the difference between $\\mathcal{R}$ and $\\mathcal{R}(r)$?\n- L143: how do you take the cosine similarity against the background vector since it consists of a vector of all zeros (how does the normalization works in that case)?\n- L143: related, isnt it bad to assign boxes to background even when they could be from another class which is simply not annotated in the dataset? (e.g. a COCO images could contain objects that are not in the regular 80 COCO classes and therefore not annotated). \n- L 167: How do you obtain the CLIP embedding used for RKD? Do you extract them by cropping the input images and feeding the crop to the CLIP model or do you instead extract a ROI pooled feature from a feature grid computed over the whole image? \n- Figure 2: please add the total number of categories used here. From the matrix it sounds like there are 16 categories (16 * 100 images total) but I could only count 10 colors in the TSNE plot).\n- L205: what is N in practice for ImageNet21K and COCO captions? In particular how do you obtain image-level category label from coco captions? I might have missed this but I could not find those details.\n- Equation (4): what are the negative classes used in this equation? \n- About the weight transfer function: it is unclear to me why one needs to have 2 different set of weights $W_P$ and $W_D$. The section 3.4. would benefit from better details on what exactly the architecture is and why those weights are different? The notation $f$ is used for the projection function but I found it confusing as I could not exaclty relate what $f$ precisely was with respect to the different weights $W_P$ and $W_D$. See related questions in the experiment section below.\n\n**Question about experiment choices and details**\n\n- Optimization details (beginning of section 4.2). Why does the method consists of multiple phases of training? Isn't it possible to train everything at once with all the additional losses?\n- Related to the previous question, if everything was trained together, isnt it possible in theory to completely tie together $W_P$ and $W_D$ so that to have the exact same of weights for going from the visual feature space to the joint text-image CLIP embedding space?\n- Related to the previous 2 questions, please provide details about what exactly is trained and what is frozen in the phases of training. \n- Alternative to weight transfer (Table 2): it would be good to add the following two approaches:\n * $W_P=W_D$ by freezing it from the second phase of training \n * Cotraining with all the losses of L 229\n\n**Minor requests/typos**\n\n- Table 6 does not bold the right numbers. Table 7 is also missing a bold number (Supervised Base on AP_base) The limitations are not discussed in the main paper. It would be good to do so: are there novel classes that suffer more than others? If yes, why? What are the important pieces of the method and how robust is the method to failure in those pieces? (e.g. the MViT component etc etc). Potential negative societal impact is also not discussed despite the method potentially being trained on large scale image and text datasets. ", " This paper proposes an approach for training open-vocabulary object detection models, i.e. models that can detect objects based on a list of object categories that is given at test time, potentially including novel categories not seen during training.\n\nThe paper starts from what has become the standard open-vocabulary approach: A Faster-RCNN detection architecture that is combined with a CLIP image/text model to allow open-vocabulary classification. The paper points out that the CLIP model is trained using only image-level supervision, and proposes a two-stage training approach to adapt it for the object-level detection task:\n\n**First training stage: Region-based knowledge distillation:** In this stage, a pre-trained object detector is used to predict class-agnostic boxes on some dataset. A vision/language model (CLIP) is then used to extract image embeddings for the regions defined by the predicted boxes. These embeddings are then used as distillation targets for the region embeddings of the detection model. This approach closely follows the ViLD paper, although the present paper uses a different object detection model for the pseudo-labeling. One innovation is to add an “inter-embedding relationship matching loss”, which minimizes the difference between the similarity matrices of the CLIP (teacher) embeddings and the region embeddings of the student detector.\n\n**Second training stage: Image-level supervision with pseudo-box labels:** In this stage, a pre-trained open-vocabulary detector is used to add box annotations to images from a classification dataset, by using the image-level (classification) labels as queries for the detector. These pseudo-labels are then used to train the classification loss of the detection models. This approach follows the Detic paper, but the present paper adds a new component called \"weight transfer function\". The weight transfer function conditions the model in the second stage on the embedding projection learned in the first stage, which is supposed to prevent the image-level supervision from destroying the representations learned in the first training stage.\n \nThe method is evaluated on the COCO and LVIS open-vocabulary benchmarks and compared to relevant prior work. All proposed components are ablated in experiments.\n\n ### Strengths\n1. The paper is written very clearly. Even though the proposed methods are quite complex, they are motivated and explained well. It was a pleasure to read.\n\n2. While the method primarily combines existing approaches from ViLD and DETIC, it it contributes important innovations that improve the synergy between these approaches (the weight transfer function and IRM loss).\n\n### Weaknesses\n1. In their current form, the presented results are **not open-vocabulary**, in contrast to the claims in the paper: the paper restricts the training data to the target vocabulary (_“Following [2, 1], we use a subset of ImageNet-21K having 997 overlapping LVIS categories and COCO captions dataset for ILS in LVIS and COCO experiments respectively.”_). This vocabulary restriction means that the method is in fact not open-vocabulary, but closed-vocabulary, since the target vocabularies (LVIS and COCO) must be known at training time for this filtering. Please either use a non-restricted training vocabulary that is not specifically tailored to the test data (e.g. all ImageNet-21k labels) for all main results, or explicitly and prominently state that the results are not open-vocabulary. For a method to be “open-vocabulary”, no part of the training pipeline should have knowledge of the label space used during testing. I emphasize that the fact that prior work (Detic) does the same is not a reason to repeat this practice. If knowledge of the test label space is required to reach good results, then these results are not \"open-vocabulary\", and if such restriction becomes accepted in the literature, then the term \"open-vocabulary\" becomes meaningless.\n\n2. It is not clear how the MViT model used for pseudo-box prediction is trained. Does this model see any bounding box annotations during training? Is it ensured that none of these bounding box annotations include any of the \"novel\" classes used for evaluation?\n\nThe validity of the paper critically depends on the soundness of the evaluation. If the results hold for rigorous open-vocabulary evaluation, then the work represents and significant contribution to the field. 1. See \"Weakness 1\": Provide true open-vocabulary results.\n2. See \"Weakness 2\": Clarify MViT pretraining. If box annotations for \"novel\" classes were not held out for MViT training, this may inflate results. In this case, please provide results with novel-class annotations removed from all training stages.\n3. Is the IRM loss computed for regions from single images, or all regions within a batch?\n4. \"Complimentary\" --> \"complementary\" Currently, the evaluation is not truly open-vocabulary, this needs to be addressed.\n\nSocietal implications are sufficiently addressed in the appendix.", " This work aims at training open-vocabulary object detectors by leveraging CLIP and pretrained multi-modal ViT. This work propose RKD to align the region representations from the RPN and that of CLIP image encoder. In order to better make use of external images (like ImageNet) which only provide image-level annotations, this work proposes to use MViT to generate pseudo boxes and labels and use them to self-train the detector. In addition, this work proposes to adopt a weight transfer function to alleviate the competition between the two losses. The results on COCO has a significant improvement over previous works. Pros\n1. The technical contents of the paper are quite a lot. I can tell that the authors put many efforts on the paper. It includes improvements on both knowledge distillation side (as in ViLD) and pseudo boxes labeling side (as in Detic). It is the first paper in attempt to combine the advantages of both knowledge distillation and self-training.\n2. The experiments are throughout, including results on different dataset and the ablation study.\n3. The use of weight transfer in this task is interesting and shown to help.\n\nCons\n1. My major concern is the use of MViT that makes the comparison against ViLD and Detic unfair. Because (1) model perspective: MViT can already detect objects, so using MViT in this task is like supervising a detector using another trained detector; (2) data perspective: MViT is pretrained on LMDet dataset, which is very large with human annotations. If the authors can address this concern of mine, I may consider raising the rating.\n2. The overall pipeline is quite complex, including the three training stages and how different losses/components work together. Moreover, the hyper-parameters need to be searched for different datasets, which makes me concern about the generalization of the proposed method.\n3. It feels like the authors combines many existing methods/models in order to achieve good performance. For example, the IRM loss is just the loss proposed in Similarity-Preserving Knowledge Distillation [39]. Without IRM, the proposed RKD degrades to the knowledge distillation proposed in ViLD. Besides, the weight transfer function is proposed in [41]. \n4. The total training on COCO takes 36 epochs, which is longer than Detic.\n5. The advantage of the proposed method on large scale datasets seems insignificant. Although the performance gain on COCO is significant, but the gap between the proposed method and Detic on LVIS and Object365 is marginal (ie. less than 1AP).\n6. There are too many abbreviations in the paper, such as RKD, ILS, PIS, IRM loss, which to some extent makes the paper less easy to read. 1. What is the performance on MViT on COCO or LVIS in the open-vocabulary setting?\n2. Do the author have some results without the use of MViT? I would like to see a fair comparison to Detic. Yes." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 5, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 5, 5 ]

[ "nips_2022_aKXBrj0DHm", "sxo0QsVu9l9", "mn84fgpbbis", "16Kg5maX2nL", "Kbiak1N698i", "HlF9duuyGfE-", "uePzSrnxwir", "gy9MKU7SI_Z", "XjwqiiC4bSd", "UUS25ObYcl-", "nips_2022_aKXBrj0DHm", "nips_2022_aKXBrj0DHm", "nips_2022_aKXBrj0DHm", "nips_2022_aKXBrj0DHm", "nips_2022_aKXBrj0DHm" ]

[ "zHGgnRqcdF", "h193_rVJfgV", "8qF-zRm7kmt", "HfpXweNZQnM", "v2s5FD7SaZ-", "Bih03GkXgJ", "FcRnURGdvxj", "Bclvdf7t0in", "PbGsE8syp3n", "iHArleH0vaB", "UvkEOgN_wL_", "3FirgJ3JgqI", "Z_8rDY7S41k", "eUlJSSudJK", "a-R3Y-7Pp0a", "YrO73iAT3Gq", "1ac2y7awZZL", "Mh6MOKvbiqs", "VBKKZa2NR23", "WECmLYG0VOr", "-8CRRf8v38i", "ChYL5CEV0Xo", "0tPoRCfEnw", "eaVXVhySeUk", "ClNwppdtx6z", "jZtCYAS3H9" ]

[ "author", "official_reviewer", "author", "author", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you *so much* for generously raising the score! Your suggestions are well-taken. We *promise* to materialize the 3 conditional changes in our revised version. Thanks again!", " **Edited review**\n\nIn light of the authors _active discussion and contributions_ during this phase, as well as their addressal of my own concerns, I will tentatively raise my score from 4 to 7. Obviously this is conditional on some changes to the manuscript, namely:\n- Making the math more digestible (we already discussed this in great detail)\n- Preferring plots to large tables where applicable, or having plots supplement them. I leave this to the authors' discretion since space constraints will mean decisions will have to be made as to what should be a table vs what should be a plot, and what should be relegated to the appendix.\n- Further work on plotting Equation 8 vs its approximation vs both 'bad' and 'good' students. The authors have acknowledged this and even provided preliminary results.\n\nThanks.", " Dear Reviewer n9FN,\n\nThank you for pointing out the derivation mistakes in our original manuscript. Also, thank you for giving suggestions voluntarily to us when we address the concern from reviewer Tm5Y. Your comments help *a lot* to improve our paper!\n\nSince your major concern is about the formulas, which we have corrected thanks to your awesome detailed comments, we were wondering, could you please generously consider raising your score *even a little bit* as a recognition of our efforts so far? Thank you *so much*!\n\nSincerely, \n\nAuthors\n\n", " Dear reviewer Tm5Y and n9FN,\n\nThank you *so much* for keeping giving feedback on our paper! And thank reviewer n9FN for giving us the suggestion. Following the suggestion, we train students and save checkpoints periodically over the training process, so we obtain multiple students, weak to strong. Then we use these students to estimate the *sum of covariance terms in the last line of Eq. 7*: $\\frac{1}{N^2} \\sum\\_{1\\le j <k \\le N} \\mathrm{Cov}[q(x_j), q(x_k)] $, which is our ultimate goal to estimate.\n\nPer the suggestion of reviewer n9FN, we estimate two versions of $\\frac{1}{N^2} \\sum\\_{1\\le j <k \\le N} \\mathrm{Cov}[q(x_j), q(x_k)] $:\n 1. $\\mathrm{Cov1} = \\frac{1}{N^2} \\sum\\_{1\\le j <k \\le N} \\mathrm{Cov}[q(x_j), q(x_k)] $, where $q(x) = \\mathbf{p}^{(t)}(x_i)^\\top \\log (\\mathbf{f}(x_i))$\n 2. $\\mathrm{Cov2} = \\frac{1}{N^2} \\sum\\_{1\\le j <k \\le N} \\mathrm{Cov}[q(x_j), q(x_k)] $, where $q(x) = \\mathbf{p}^{(t)}(x_i)^\\top \\log ( \\mathbf{p}^{(t)}(x_i))$ -- i.e., using the approximation in Eq. 8\n\nResults are presented below. Pair: VGG13/VGG8, Dataset: CIFAR100, DA: cutmix. We tried three students at different epochs. Format: $\\mathrm{Cov1} / \\mathrm {Cov2}$\n\n| | Epoch 10 | Epoch 150 | Epoch 240 |\n|---|---|---|---|\n| Accuracy | 49.15% | 58.66% | 73.55% |\n| Run #1 | 0.0000031704 / 0.0000036407 | 0.0000033388 / 0.0000024198 | 0.0000019557 / 0.0000027502 |\n| Run #2 | 0.0000016844 / 0.0000024425 | 0.0000017658 / 0.0000029721 | 0.0000016558 / 0.0000032665 |\n| Run #3 | 0.0000028793 / 0.0000022399 | 0.0000014990 / 0.0000029898 | 0.0000024180 / 0.0000020152|\n\nHonestly, we do see obvious patterns here. **The foremost problem, as you may notice, is that the multiple-run results vary quite a lot** (note Run #1/#2/#3 of each column are using *exactly the same* script). This literally means $\\mathrm{Cov1}$ and $\\mathrm {Cov2}$ are very challenging to estimate (and our presented results are unreliable since the variation is too large). We can actually analyze to see how challenging it is. Take $\\mathrm{Cov1}$ as example:\n- Essentially, it is a sum of $\\frac{N*(N-1)}{2}$ covariance of paired RVs. Unfornaturely, $N$ is very large here -- $N$ is the sample size of the sampled training set. In the case of CIFAR100, $N=50,000$. That makes $\\frac{N*(N-1)}{2}$ in the order-of-magnitude of $10^9$. Namely, **we mean to estimate the sum of covariance of $\\sim 10^9$ pairs of RVs**. This is very challenging if we estimate it by sampling.\n\nSo to reviewer n9FN first, sorry we cannot have the plots you suggested before the rebuttal ends because we do not have a reliable estimation of the covariance terms at present. (This said, we cannot eliminate the possibility that we did not do the estimation the best way due to the limited time. We shall keep trying your idea later. Thank you!)\n\n---\n**Then, how should we properly look at the \"well-trained student\" assumption?**\n\nAs we analyzed above, ideally, given a set of DA schemes, their \"goodness\" order is decided **with the student in the loop** (note Eq. 7 has the student $\\mathbf{f}(x)$ as a part) -- this is also more in line with our intuition (as reviewer Tm5Y mentioned in the original comments: \"*one cannot just ignore the student in determining the effectiveness of the DA method*\"). Consequently, different students (not only different networks but also the same network at different training stages) will give different DA orders in \"their\" opinions. \n\nFor practical use, we prefer just one DA order. This means, we *must* choose a student to decide the DA order. Since anyway we will choose a student, choosing a \"well-trained\" student is naturally more reasonable and pertinent to our goal (and such a student *does* exist in practice as we analyzed previously). This is how the \"well-trained student\" assumption is brought up. Results turn out to show it works pretty well *across different students*.\n\nWe will add these discussions to the manuscript as a background for the following statement\n> This formula implies an important fact that we only need the covariance of the teacher’s probability to measure the “goodness” of a certain DA technique, no need for the student\"\n\nIt should be\n> To make a metric for practical use, we have the *freedom* to decide which student is used to estimate the covariance term in Eq. 7. Then we *intentionally choose* the student that performs the same as (or very close to) the teacher to further reduce the covariance term in Eq. 7, which only involves the teacher, no need for the student. Despite not involving the student terms, the metric works pretty well in capturing the generalization error of the students trained with different DA schemes.\n\nWe believe this is the most we can do at this moment (since it's very close to the rebuttal end). **Thank you *so much* for your awesome suggestions all along the way! We are lucky to have the reviewers like you! Tremendous thanks!**\n\n\n\n\n\n\n\n\n\n\n\n\n\n", " > Thank you. I have reviewed the details in the image you posted, but this work [1] shows otherwise: KD can improve students when using ImageNet. In fact, this work uses only soft-targets from the teacher (no ground-truth labels) for KD which is contradictory to the details you posted. I.e.: ResNet-50 ResNet-18 KD obtains 71.425% whereas ResNet-18 training from scratch obtains only 69.758%. ( See Tables 1, 2 in [1] ). See https://pytorch.org/vision/stable/models.html for official pytorch model weights / accuracy. Please check.\n\n> In the revised version, please consider discussing ImageNet results.\n\nYes, exactly! Now we know KD can also work on ImageNet thanks to the very inspiring works like [1]. We mentioned the ICCV'19 paper simply to show it *was* non-trivial to make KD work on ImageNet back then and ImageNet is indeed *harder* for KD. (We'll cite [1] and indicate its remarkable KD performance on ImageNet in our paper).\n\nIn general, we are *so grateful* that you improved the score, which is a great encouragement to us! As suggested, we will include the full ImageNet results in the revised version. **Again, thank you so much!**", " Thank you. I have reviewed the details in the image you posted, but this work [1] shows otherwise: KD can improve students when using ImageNet. In fact, this work uses only soft-targets from the teacher (no ground-truth labels) for KD which is **contradictory to the details you posted**. I.e.: ResNet-50 $\\rightarrow$ ResNet-18 KD obtains 71.425% whereas ResNet-18 training from scratch obtains only 69.758%. ( See Tables 1, 2 in [1] ). See https://pytorch.org/vision/stable/models.html for official pytorch model weights / accuracy. Please check.\n\nIn the revised version, please consider discussing ImageNet results.\n\n**Considering the efforts made by the authors, I have increased my recommendation, although I stand by my review and consider this work to be borderline.**\n\n[1] Shen, Z., Liu, Z., Xu, D., Chen, Z., Cheng, K. T., & Savvides, M. (2021). Is label smoothing truly incompatible with knowledge distillation: An empirical study. In ICLR\n", " Thank you so much for the suggestion! We are working on this. Hopefully, we can get some plots before the rebuttal ends. ", " Hi,\n\nThis is not the OP reviewer but I wanted to share some of my own thoughts (which may or may not count for much). It would make sense to think of violating the 'well trained student' assumption as something that is more along a sliding scale, rather than a yes/no answer.\n\nI think this could have been supplemented with a nice scatterplot, where one plots on the x axis equation 8 and on the y axis its approximation. Points on the plot would comprise random (or all) enumerations of student/teacher pairs. I would then expect the correlation (e.g. $R^2$) between (x,y) to go down as the generalisation gap between the student and teacher increases. I don't know if you have any experiments where you intentionally make the student much worse than the teacher to see what happens, but that negative result would help with the figure, which in turn will help the story you're trying to tell.\n\nThanks.", " > Even though Proposition 1 is general, its application with your approach requires equation 8. On lines 160-161 the paper states: \"This formula implies an important fact that we only need the covariance of the teacher’s probability to measure the “goodness” of a certain DA technique, no need for the student\" But this statement is only true if the assumption of a well-trained student is true. Which is not true in general, as your new accuracy data shows. Now, it may be that the effect of this invalid assumption is minor, but you still need to (even empirically) demonstrate that this is the case in practice.\n\nThank you! We understand your point and actually agree with it. Currently, we honestly do not have more empirical evidence to show the well-trained student holds for *all* the pairs in practice (and to what degree can it be called \"well\"-trained? I do not have a rigorous answer either). Yet, we have the following comments that may help resolve your concern. \n\n- Let's go back to the key formula, Eq. 8, before the approximation. As mentioned previously, ideally, for each DA, we can calculate Eq. 8 with different students and have different DA orders. Presumably, some students may rank, say cutmix ahead of mixup, while some may rank cutmix behind mixup. Then, *which student should we trust when we want to have just one ranking of the DAs in practical applications*? This means, even if we do not have the approximation problem, we would still need to choose a certain \"oracle\" student to decide which DA is better.\n- With this as background, let's look at Eq. 8 again. **The approximation essentially says, we use the student that can perform exactly the same as (or very close to) the teacher, i.e., $\\mathbf{p}^{(t)}(x) = \\mathbf{f}(x)$, as the \"oracle\" student.** Then, the real question is, *does such a student exist in practice?* The answer is clearly YES -- we can easily find students that can mimic the teacher with a very small error (and actually, as is well known, neural networks have the capacity to approximate any function with a desired precision).\n\nHope this can help explain why our method still works well in practice. For the statement \"*This formula implies an important fact that we only need the covariance of the teacher’s probability to measure the “goodness” of a certain DA technique, no need for the student*\", we will add an explicit condition that we choose the student that can perform very closely to the teacher as the \"oracle student\" discussed above. This should make the statement more rigorous. \n\n**Again, thank you so much for being with us so far!** Let us know if you have more thoughts! Thanks a lot!", " Thank you so much for the feedback!\n\nWe understand your point! Meanwhile, we would like to mention that\n- First, it is normal in research that we see more violations when we extend the theory to a more complex practical application (that is exactly why we call it \"more complex\").\n- Second, historically, making KD effective on ImageNet is non-trivially hard (see [this screenshot from [*1]](https://tva1.sinaimg.cn/large/e6c9d24egy1h5014ag2ecj20g00amdia.jpg)). Note, despite this, our theory still helps us identify the best DA scheme CutMix-Pick on ImageNet-100 and its superiority aligns well with the proposed metric.\n- Third, we calculate the correlation coefficients (p-values) of the above ImageNet-100 results, shown below. All the p-values are still *below 5%, which means the correlation is literally **statistically significant*** even on this challenging dataset. \n - Pearson: 0.7331 (0.02463)\n - Spearman: 0.6667 (0.04987)\n - Kendall: 0.5556 (0.04462)\n\nAs we know, it is hard to get a theory that works for all cases. If our responses have resolved your major concerns, we sincerely hope you may pay more attention to the pros of our paper and generously consider raising the score even a little bit in recognition of our efforts so far. Thank you *so much* for helping us improve our paper!\n\n[*1] On the Efficacy of Knowledge Distillation, ICCV, 2019", " Thank you authors for the great effort on the rebuttal. Authors have addressed my concerns. \n\nAs I pointed out (and very nicely shown by the authors in rebuttal), when applying the proposed theory to practical problems (i.e.: ImageNet-100), there are cases that go against the proposed theory. Therefore, I’m not certain regarding the applications of the proposed theory although I acknowledge that the proposed CutmixPick achieves the lowest Std of mean prob and lowest student test error.", " Thank you for your answers. I am still concerned about the assumption of a \"well-trained student\". Your answer\n\"We lift the student term in Eq. 8 simply for a more neat/convenient form of the proposed metric when it is used in practice (no need for training the student for real). The assumption is brought up for practical use (for the metric). Even if the assumption (in Eq. 8) does not hold, our theory (Proposition 1) still holds; just the metric (Eq. 10) may not hold (for the “bad” student).\"\n\nEven though Proposition 1 is general, its application with your approach requires equation 8. On lines 160-161 the paper states:\n\"This formula implies an important fact that we only need the covariance of the teacher’s probability\nto measure the “goodness” of a certain DA technique, no need for the student\"\nBut this statement is only true if the assumption of a well-trained student is true. Which is not true in general, as your new accuracy data shows. \nNow, it may be that the effect of this invalid assumption is minor, but you still need to (even empirically) demonstrate that this is the case in practice.\n", " Dear reviewers,\n\nThank you *so much* for helping improve our paper so far!\n\nThe author-reviewer discussion period has passed around half. We are looking forward to your further comments. If you prefer to check on them after this weekend (08/06, 08/07), it is perfectly fine! Meanwhile, **we still hope you may take a quick look at least (like 5 minutes), in case you may expect more experiments/analyses/clarifications, so that we can finish them over this weekend.**\n\nThank you so much for being with us so far! Have a wonderful weekend!\n\n--- Authors, 08/05\n", " Thank you so much for following up with us!\n\nWe have revised the derivation above to make it clearer following your suggestions. The manuscript will be updated very soon **[ Edited 08/05: the manuscript has been updated ]**. Thank you so much for helping us improve the paper and considering raising the score! *If you have any further questions, let us know any time!*", " Hi, thanks for addressing my questions. I am satisfied with the re-derivation of the expectation (over S) for $\\Delta$.\n\nFor the variance term, I missed that you are using a particular identity which is the variance for a sum of random variables. It appears however that for `A4` you are missing the summation behind $C_{x_i, x_j}$ in the last two lines. I still would like this derivation to be slightly more clear using this identity [1]. Maybe you can combine the following with the explained derivation you have given me:\n\n$$\n\\begin{align} \\text{Var}[ \\sum_{k=1}^{n} x_k ] & = \\text{Cov}[ \\sum_{j=1}^{n} x_j, \\sum_{k=1}^{n} x_k] \\\\\\\\\n& = \\sum_{j=1}^{N} \\text{Var}[x_j] + 2\\sum_{j < k} \\text{Cov}[x_j, x_k]\n\\end{align},$$\n\nwhere $x_j$ is basically the $p^{(t)}(x_j) \\log f(x_j)$ random variable term (abusing notation a little here since I'm re-using x).\n\n(1) https://math.stackexchange.com/questions/2413664/different-rules-for-calculating-the-variance-of-a-sum?rq=1\n\nI am happy to increase my score after both derivations have been made clearer in the revised manuscript, but the degree to which it increases will also depend on issues and points raised with the other reviewers. Thanks.", " Thank you so much for your constructive comments! We address your concerns as follows.\n\n`Q1`: Firstly, I would recommend simply using $\\log$ instead of $\\mathcal{L}$ to denote the logarithm.\n\n`A1`: We will change all the logarithm notation to $\\log$ as you suggested. Thank you!\n\n`Q2`: In Equation (6), in line 1 you have an expectation $S \\sim D^N$, yet in line 2 it confusingly turns into an expectation $x \\sim D$ , yet you still have the inner summation. Why isn't it just this instead: \n$$\nE_{x\\sim D} [p(x)\\log f(x)] + \\text{const}\n$$ \ni.e. the expectation implies the inner summation + multiplication over $1/N$, so having both seems redundant (and incorrect). Furthermore, in the inner multiplication you're missing the transpose, so it should be $p(x_n)^{T} \\log f(x_n)$, since that is how it is defined in equation (4).\n\n`A2`: First, your comment about the transpose is correct. We'll add the missing transpose. Thanks!\n\nNext, we walk step by step from $S \\sim D^N$ to $x \\sim D$:\n\n$$ \n\\begin{aligned}\nE\\_{S \\sim D^N} [ \\Delta ] &= E\\_{S \\sim D^N} [ \\hat{R}_S(\\mathbf{f})] + \\text{Const} \\\\\\\\\n& = E\\_{ \\\\{x_1,x_2,...,x_N \\\\} \\sim D^N} [ \\frac{1}{N} \\sum\\_{n \\in [N]} p^{(t)}(x\\_n)^\\top \\log(\\mathbf{f}(x\\_n)) ] + \\text{Const} \\\\\\\\\n&= \\frac{1}{N} E\\_{ \\\\{x_1,x_2,...,x_N \\\\} \\sim D^N} [p^{(t)}(x\\_1)^\\top \\log(\\mathbf{f}(x\\_1)) + ... + p^{(t)}(x\\_N)^\\top \\log(\\mathbf{f}(x\\_N))] + \\text{Const} \\\\\\\\\n&= \\frac{1}{N} \\big( E\\_{ \\\\{x_1,x_2,...,x_N \\\\} \\sim D^N} [p^{(t)}(x\\_1)^\\top \\log(\\mathbf{f}(x\\_1))] + ... + E\\_{ \\\\{x_1,x_2,...,x_N \\\\} \\sim D^N} [p^{(t)}(x\\_N)^\\top \\log(\\mathbf{f}(x\\_N))] \\big) + \\text{Const} \\\\\\\\\n& = \\frac{1}{N} \\big( E\\_{ x_1 \\sim D} [p^{(t)}(x\\_1)^\\top \\log(\\mathbf{f}(x\\_1))] + ... + E\\_{ x_N \\sim D} [p^{(t)}(x\\_N)^\\top \\log(\\mathbf{f}(x\\_N))] \\big) + \\text{Const} \\\\\\\\\n& = \\frac{1}{N} \\cdot N \\cdot E\\_{x \\sim D} [p^{(t)}(x)^\\top \\log(\\mathbf{f}(x))] + \\text{Const} \\\\\\\\\n& = E\\_{x \\sim D} [p^{(t)}(x)^\\top \\log(\\mathbf{f}(x))] + \\text{Const}\n\\end{aligned}\n$$\n\nSo, yes! Your comment is correct! We have an extra summarization inside. Thank you *so much* for discovering this! We'll proofread the paper more carefully to eliminate such mistakes. Meanwhile, notably, **with the new equation above, it is even more clear to see that for $S_1$ and $S_2$, the $ E\\_{S \\sim D^N} [ \\Delta ] $ is the same. Namely, our conclusion in Line 146 still holds.**\n\n `Q3`: In Equation (7), I am also not sure why the last line expands out into a variance + covariance term. Covariance to me implies that you're computing the variance between two sets of random variables; don't we only have one random variable? (That random variable being $\\Delta$, the empirical risk over whatever random draw $S \\sim D$.) \n\n`A3`: We have many random variables. E.g., each sample $x$ in $S$ is taken as a random variable. And *the covariance is exactly describing the dependency among different samples* (in the form of $p^{(t)}(x) \\log(\\mathbf{f}(x))$).\n\n`Q4`: Maybe I am missing something crucial, but it seems like one could just remove the last line of Equation (7), leaving us with:\n$$\n\\mathrm{Var}\\_x [p(x)^\\top \\log(\\mathbf{f}(x))] \n$$\n\n`A4`: We explain the derivation of Eq. 7 step by step as follows:\n\n**[Edited 08/04]** Following your suggestion, we revise the following derivation to make it clearer. First, we define $q(x_i) = p^{(t)}(x_i)^\\top \\log (\\mathbf{f}(x_i))$, and use $\\mathrm{Var}[\\cdot]$ for the variance of a random variable, $\\mathrm{Cov}[\\cdot, \\cdot]$ for covariance. Then,\n$$\n\\begin{aligned}\n\\mathrm{Var}\\_S [\\hat{R}\\_S({\\mathbf{f}})] &= \\mathrm{Var}\\_S [ \\frac{1}{N} \\sum\\_{i=1}^N q(x\\_i) ] \\\\\\\\\n&= \\frac{1}{N^2} \\mathrm{Var}\\_S [ \\sum\\_{i=1}^N q(x\\_i) ] \\\\\\\\\n&= \\frac{1}{N^2} \\mathrm{Cov}\\_S [ \\sum_{j=1}^N q(x_j), \\sum_{k=1}^N q(x_k) ] \\\\\\\\\n&= \\frac{1}{N^2} \\big( \\sum\\_{i=1}^N \\mathrm{Var}\\_{x_i} [ q(x\\_i) ] + 2 \\sum\\_{1\\le j<k \\le N} \\mathrm{Cov}[ q(x_j), q(x_k) ] \\big) \\\\\\\\\n&= \\frac{1}{N^2} \\big( N \\cdot \\mathrm{Var}\\_{x} [ q(x) ] + 2 \\sum\\_{1\\le j<k \\le N} \\mathrm{Cov}[ q(x_j), q(x_k) ] \\big) \\\\\\\\\n& = \\frac{1}{N} \\mathrm{Var}\\_x[q(x)] + \\frac{2}{N^2} \\sum\\_{1\\le j<k \\le N} \\mathrm{Cov}[ q(x_j), q(x_k) ]\n\\end{aligned}\n$$", " `Q5`: then say that the variance is going to be proportional to the $p^{(t)}$ and that $\\mathbf{f}$ is held constant. Actually, it seems like from Equation (9) that the covariance is over the $p$'s for the different classes. What is confusing is that, for a given $x$, you are indexing into its predicted probability for class $i$ as as $p^{(t)}(x_i)$ , and $x_i$ is apparently the $i$'th example as you have implied in equations (3) and (4). If $p^{(t)}$ outputs a probability distribution over x, then you should be using $p^{(t)}(x)_i$ instead.\n\n`A5`: *it seems like from Equation (9) that the covariance is over the $p$'s for the different classes* -- This might be misreading. The covariance is *always* for different examples, not for different classes. \n\n`Q6`: \"Each element in S is drawn the same underlying distribution D.\" - I don't follow this, since it says earlier that $S_1$ and $S_2$ are elements from $D$ but not necessarily iid. If so, how can $E_{x \\sim S}$ turn into $E_{x \\sim D}$ ?\n\n`A6`: Thanks to your help, we update the derivation of Eq. 6. See above `A2`.\n\n`Q7`: Table 1: I appreciate that the results are averages over three runs, but please indicate the standard deviation. Since space seems a little tight in this table, maybe just indicate the stdevs below each number in parentheses. Also such information can be nicely condensed into a scatterplot with one axis denoting test accuracy and the other denoting mean stdev. When necessary, prefer plots over big tables, and leave big tables to the appendix.\n\n`A7`: We report the std in Tab. 1 as follows. Meanwhile, thanks for the suggestion! We will use plots and move the big tables (with std reported) to Appendix.\n\n| | WRN-16-2 | VGG8 | Res20 | ShuffleV2 | VGG8 | MobileV2 |\n|---|---|---|---|---|---|---|\n| KD+Identity | 0.0136 | 0.0065 | 0.0081 | 0.0137 | 0.0196 | 0.0366 |\n| KD+Flip | 0.0101 | 0.0060 | 0.0060 | 0.0072 | 0.0105 | 0.0076 |\n| KD+Flip+Crop | 0.0097 | 0.0182 | 0.0092 | 0.0062 | 0.0059 | 0.0149 |\n| KD+Cutout | 0.0090 | 0.0156 | 0.0115 | 0.0101 | 0.0055 | 0.0104 |\n| KD+AutoAugment | 0.0290 | 0.0016 | 0.0041 | 0.0099 | 0.0213 | 0.0440 |\n| KD+Mixup | 0.0143 | 0.0044 | 0.0121 | 0.0060 | 0.0176 | 0.0044 |\n| KD+CutMix | 0.0108 | 0.0145 | 0.0034 | 0.0107 | 0.0042 | 0.0178 |\n| KD+CutMixPick (S ent.) | 0.0118 | 0.0111 | 0.0095 | 0.0070 | 0.0249 | 0.0064 |\n| KD+CutMixPick (T ent.) | 0.0095 | 0.0061 | 0.0120 | 0.0148 | 0.0115 | 0.0233 |\n\n\n**Lastly, thank you so much for helping us improve the paper so far! Please let us know *asap* if you have any further questions. We are actively available during this rebuttal!**", " Thank you so much for your constructive comments! We address your concerns as follows.\n\n`Q1.1`: What is $S^*$ and how is it determined? Why is $K=640$?\n\n`A1.1`: $S^*$ is the sampled example set (i.e., a bunch of training examples) to estimate $m$ in Eq. 10. During training, we cache several batches (10 batches) of training data to make $S^*$. $K=640$ because we sample 10 batches during training. For the CIFAR100 and Tiny ImageNet datasets, batch size is 64, thus 64*10=640.\n\nThank you so much for pointing these unclear parts out! We’ll clarify them in our revised version.\n\n`Q1.2`: Would it be reasonable to calculate $m$ using the variance of the output probabilities of the teacher for the correct class over all samples?\n\n`A1.2`: $m$ is to estimate the variance of $u$, which is to estimate the $p^{(t)}(x)$ in Eq. 9 (or its prior form in Eq. 8). You can tell from Eq.9 or Eq. 8: the random variable is *only about the teacher and input, no need for the labels*. Thus, rigorously, there is no such \"*correct class*\" at all. The metric is proposed according to the theory. Since the theory does not imply using “correct class” to calculate $m$, then we believe it is more reasonable not to do so.\n\n`Q2.1`: Particularly, ImageNet results are not discussed and analyzed. Not that I have anything against CIFAR-100, Tiny-ImageNet analysis, but I tend to think that ImageNet results are critical to add merit to the findings (1000 classes, higher resolution:224 x 224). Most KD works report results on ImageNet-1K ([1, 2, 3, 4, 5]). If compute is a problem, authors can consider using a smaller dataset for experiments: ImageNet-100 (A subset of ImageNet popular in the self-supervised learning community). I believe the authors can also use publicly available pre-trained ImageNet models if required: https://pytorch.org/vision/stable/models.html\n\n`A2.1`: Thank you so much for letting us know about these relevant papers! *We will cite and discuss them in our related work*.\n\nMeanwhile, we report new results here following your suggestion: Use ImageNet-100 (a subset of 100 classes randomly drawn from the original ImageNet. The image size is 224\\*224\\*3). The teacher is ResNet34 and student is ResNet18. Then we reproduce Tab. 1 (or 2) with the **ResNet34/ResNet18 pair on ImageNet100**. Results are below. The student test error is *averaged by 3 random runs*.\n\n| | Std of mean prob. | Test err. |\n|---|---|---|\n| KD+Identity | 0.002545 | 0.6713$_{\\pm0.0029}$ |\n| KD+Flip | 0.002543 | 0.6609$_{\\pm0.0035}$ |\n| KD+Flip+Crop | 0.002456 | 0.6679$_{\\pm0.0027}$ |\n| KD+Cutout | 0.002505 | 0.6646$_{\\pm0.0030}$ |\n| KD+AutoAugment | 0.002463 | 0.6465$_{\\pm0.0078}$ |\n| KD+Mixup | 0.002365 | 0.6619$_{\\pm0.0043}$ |\n| KD+CutMix | 0.002363 | 0.6573$_{\\pm0.0055}$ |\n| KD+CutMixPick (S ent.) | 0.002215 | 0.6524$_{\\pm0.0015}$ |\n| KD+CutMixPick (T ent.) | 0.002166 | 0.6356$_{\\pm0.0054}$ | \n\nAs seen, there are a few cases that go against the proposed theory. E.g., Flip+Crop has a lower \"Std of mean prob.\" than Flip, while the student error is higher. This means that large-size dataset like ImageNet-100 is indeed more challenging and making the validation of the theory harder. This said, the general trend is still aligned with our expectation: *The proposed method CutMixPick achieves the lowest \"Std of mean prob.\", also, the lowest test student error*, implying it can generalize to the large-size dataset.\n\n**[ 08/08 Edited ]** we calculate the correlation coefficients (p-values) of the above ImageNet-100 results, shown below. All the p-values are still *below 5%, which means the correlation is literally **statistically significant*** even on this challenging dataset. \n - Pearson: 0.7331 (0.02463)\n - Spearman: 0.6667 (0.04987)\n - Kendall: 0.5556 (0.04462)\n\n`Q2.2`: What is the reason for not including Flip, Flip+Crop, Cutout, Auto-Augment, Mixup results in Tables 3, 4?\n\n`A2.2`: Since we have shown in Tab.1 and 2 that the best DA is CutMix, we only include the results of CutMix in Tab. 3 and 4 (to save computation) when we prepared the submission. During this rebuttal, we do not have enough time/resources to make up them, but we **promise to include them all in the revised version**. And note, even without these results, Tab. 1 and 2 (also the above new results on ImageNet-100) have well validated the proposed proposition and made the paper self-contained.\n", " `Q3`: For ‘Std of mean prob’ in Tables 1, 2, is it reasonable to use the training set as the training set is used for distillation (not the test set)?\n\n`A3`: We think it is reasonable because the metric is used to select the best DA when we attempt to enhance some KD algorithms. Training set is the set for training/develping algorithm. If we use the test set, it may be at the risk of peeking at test data and unfair.\n\n`Q4`: For CutMixPick experiments, what is the percentage of the training set used for distillation (after 'picking' / filtering)?\n\n`A4`: There might be a little misunderstanding here. We *append* the augmented images to the original training set (see Line 182-183), so *all* of the training set is used for distillation. We assume what you actually mean is: in each training batch, what percentage is for the original training images? The answer is 50%, see Line 206 - 207.\n\n**Lastly, thank you so much for helping us improve the paper so far! Please let us know *asap* if you have any further questions. We are actively available during this rebuttal!**", " Thank you so much for your constructive comments! We address your concerns as follows.\n\n`Q1`: Non-data manipulations, such as drop-out, can result in the same behavior as shown in figure 2a (of spreading different soft targets while keeping the same hard targets). The paper (Bouthillier, X., Konda, K., Vincent, P., and Memisevic, R. Dropout as data augmentation. arXiv preprint arXiv:1506.08700, 2015.) even considers the dropout as a type of data augmentation. So, could your approach be made even more general (than the few types of augmentation you consider)?\n\n`A1`: It might be hard to include dropout into our framework now since dropout does not explicitly change the inputs. It would be interesting to make our approach more general, yet currently, the paper in its present form may not allow us to claim so broadly. So we prefer to limit the scope of data augmentation in this paper to the conventional ones (i.e., input transformation or input mixing) to avoid overclaiming.\n\nThanks for pointing this out! We will revise the paper to make the DA concept more rigorous and cite the paper you mentioned to have a discussion regarding if we can extend the DA scope to broader.\n\n`Q2`: In lines 127-129, why is a script L used to indicate the log function, rather than the more usual log() notation? Script letters are conventionally used to indicate spaces or sets. In line 139 the script L is used to indicate a loss function, adding to the confusion.\n\n`A2`: Thank you so much for letting us know about this problem. We’ll use the $\\log$ notation following your suggestion!\n\n`Q3`: In line 154-156 the assumption is made of a \"well-trained\" student, that gives softmax outputs \"pretty equal\" to those of the teacher. However, in most practical applications of distillation, the student can be much smaller than the teacher (e.g. for network compression for edge devices). What happens to your conclusions in that case? This assumption is used to make the claim that we need only look at the teacher to judge the effectiveness of a DA method. So, is this claim still true if the assumption does not hold? In table 1, (as was done in table 3) you should give the teacher and student test accuracies to see how well the \"well-trained\" assumption holds. For CIFAR-100 and the student/teacher networks used, I would expect a significant difference in softmax outputs (e.g. 74% for ResNet56 and 69% for ResNet20).\n\n`A3`: \"*What happens to your conclusions in that case?*\" -- If the student is small or not well-trained, the KL div term will become large (think about a naive case: the student is completely a random model). Yet the covariance captures the dependency among the training examples. Given any fixed function f(*), if two inputs x1 and x2 are highly correlated, f(x1) and f(x2) will also be highly correlated, which will still make the DA a “bad” one. \n\nWe lift the student term in Eq. 8 simply for a more neat/convenient form of the proposed metric when it is used in practice (no need for training the student for real). The assumption is brought up for practical use (for the metric). Even if the assumption (in Eq. 8) does not hold, our theory (Proposition 1) still holds; just the metric (Eq. 10) may not hold (for the “bad” student).\n\nWhen it comes to practice, we do have the freedom to choose which student is used in Eq. 8. But clearly, the top-performing students are more favored. E.g., given a random student, it ranks DA1 better than DA2; meanwhile, given a well-trained student, it ranks DA2 better than DA1. Obviously, we will choose DA2 as it relates to a better student.\n\n“*In table 1, (as was done in table 3) you should give the teacher and student test accuracies to see how well the \"well-trained\" assumption holds*” -- The accuracies in Tab. 1 are reported below:\n- WRN-40-2: 75.61, WRN-16-2: ~75.3, VGG8: ~74.3\n- ResNet56: 72.34, ResNet20: ~70.7, ShuffleNetV2: ~75.9\n- VGG13: 74.64, VGG8: ~74.1, MobileNetV2: ~68.5\n\nwhere the teacher’s accuracies are exact. The student accuracies are averaged across different data augmentation schemes. As seen, there is the case where teacher and student have a gap (like VGG13/MobileNetV2). Nevertheless, they do not affect the empirical validation of our proposition.", " `Q4`: It seems surprising that an analysis of the student has no role to play in determining the effectiveness of a data augmentation technique that is being used to train that student. If no distillation was being done at all (just training using cross-entropy on the hard targets), DA still would be of some use, no? So, this suggests that one cannot just ignore the student in determining the effectiveness of the DA method. Perhaps, in light of the results in table 1, the teacher's effects dominate the student's effects in terms of judging DA performance, but the student may still have some influence. It would be nice to have some theoretical insight into why this is, rather than just throwing away the student based on the \"well-trained\" assumption.\n\n`A4`: We totally agree that the student plays a role when deciding which DA is better specific to that student. Ideally, each DA has to be evaluated by *a specific pair of teacher and student* to say whether it is better or worse than the other one -- this is exactly what Eq. 8 tells before the approximation. Yet clearly, in practice, when we try to put our theory into use, we cannot just evaluate all the pairs -- If we already run all the experiments and have the trained students, we just know which DA performs best from the student accuracy. It would be no meaning to calculate Eq. 8 (or other equations) anymore.\n\nWe will revise the statement to clarify this confusion. Thanks for letting us know about this issue!\n\n`Q5`: Does the \"pick\" aspect of the Cut-Mix-Pick help with the other DA methods? Presumably doing the data distillation on the other augmentations would also improve their results.\n\n`A5`: In table below, we report the **student test errors** of applying picking to other DA methods in addition to CutMix on CIFAR100, VGG13/VGG8 pair. $\\pm$ indicates the result is averaged by 3 random runs (mean and std reported). ***We promise to release all code/checkpoints/logs.*** **[Edited 08/03:]** The results have been updated as follows. Thanks!\n\n| DA method | W/O picking | W/ picking |\n|---|---|---|\n| Identity | 1.1856$_{\\pm0.0196}$ | 1.1922$_{\\pm0.0075}$ |\n| Flip | 1.1754$_{\\pm0.0105}$ | 1.1843$_{\\pm0.0075}$ |\n| Flip+Crop | 1.1537$_{\\pm0.0059}$ | 1.1824$_{\\pm0.0096}$ |\n| Cutout | 1.1279$_{\\pm0.0055}$ | 1.0760$_{\\pm0.0087}$ |\n| Autoaugment | 1.1273$_{\\pm0.0213}$ | 1.0231$_{\\pm0.0028}$ |\n| Mixup | 1.1194$_{\\pm0.0176}$ | 1.0323$_{\\pm0.0119}$ |\n\nThe \"W/O picking\" results are from Tab. 1 in the paper (std is added). \"W/ picking\" is new. As seen, the proposed picking scheme (Sec. 4.2) also improves other popular data augmentations like Cutout, Autoaugment, and Mixup. But it does not improve upon Identity/Flip/Flip+Crop. This is not surprising because the default DA is Flip+Crop; the augmented samples are actually pretty similar to the original ones. Then, picking the samples with higher entropy will select out those similar samples, causing the covariance in a batch to increase, which will lead to higher student error per our theory . \n\n`Q6`: In section 5.1 the authors say that they do not look at accuracy, as the derivations are based on error, and sometimes a network can give high accuracy but also high error. But accuracy is typically what people are interested in when using networks, not the value of the loss function. It may be that by focusing on loss (error) one is biasing the student to become more confident, like the teacher, and perhaps overly confident, leading to reduced accuracy. In any case, table 3 shows accuracies, so I am not sure why this was not done in section 5.1.\n\nA6: We agree that accuracy is used more often in practice. Yet when we attempt to theoretically answer the question “what makes a good DA in KD”, it might be better to make the empirical validation *exactly the same* as how the theory is developed so that we can know whether the theory is correct or wrong. \n\nLower loss typically implies higher accuracy, yet not necessarily. We observe this in our experiments and also noted by prior works (like [19]).\n\nThe inconsistency between Tab. 3/4 and 1/2 causes confusion. Thank you for letting us know this! We will\n- change all the measures to test loss in Tab 3/4 to make them consistent.\n- report the accuracy results in our supplementary material (to confirm that accuracy may not be well aligned with loss)\n- discuss how we can extend the proposition to using accuracy as the measure for generalization\n\n**Lastly, thank you so much for helping us improve the paper so far! Please let us know *asap* if you have any further questions. We are actively available during this rebuttal!**\n", " Thank you so much for your constructive comments! We address your concerns as follows.\n\n`Q1`: Weaknesses: There are three contributions in the method part: (1) data augmentation (2) longer training and (3) cutmixpick. (1) and (2) are already investigated in works [1][2] [1] Cui, Wanyun, and Sen Yan. \"Isotonic Data Augmentation for Knowledge Distillation.\" IJCAI2021 [2] Beyer, Lucas, et al. \"Knowledge distillation: A good teacher is patient and consistent.\" CVPR2022. The improvement from (3) is very minimal.\n\n`A1`: We agree that [1] and [2] are related to our works since they also study the KD problem and are relevant to DA. We will cite these two papers and discuss them in our related work section. \n\nYet it is worth noting that our work is *distinct* from [1] and [2]. Reviewer JbXW summarizes the three contributions in our method part (i.e., Sec. 4). Yet, this summarization might *miss the major point* of our paper. \n- Although the proposed CutMix-Pick algorithm in Sec. 4 is one claimed contribution, it is *not the major one* -- see our summarized contributions in Line 65 - 74.\n- Notably, our paper title, core theory part (Sec. 3), summarized contribution (Line 65 - 74), and conclusion (Line 336 - 342), *all* highlight the major point/contribution of this paper: what defines a “good” DA in KD and we attempt to have a theoretical and precise answer to this scientific question. **The derived answer (Proposition 1 and metric in Eq. 10) is what we claimed as the major contribution (see our summarized contributions in Line 65 - 74)**. In this regard, *none of the prior works have answered this question in a theoretical manner*, including [1] and [2]. Thus, we believe our paper is novel.\n- Reviewer JbXW summarizes “*longer training*” as a contribution to our method, which might be a misreading. Note the longer training is introduced in Line 298 - Line 303, which is in our “Experimental Results” section, not the methodology part (Sec. 3 and 4). Clearly, we never consider it as a \"contribution\" from this paper. We have the longer training experiments simply to show how the proposed theory can be used for higher performance in practice, as an extra bonus. Even without the “longer training”, note the paper is self-contained: theory proved (Proposition 1) and empirically validated (Tab. 1 and 2).\n\n**Lastly, thank you so much for helping us improve the paper so far! Please let us know *asap* if you have any further questions. We are actively available during this rebuttal!**\n", " Knowledge distillation (KD) is to improve a low-capacity student network's performance with a high-capacity teacher network. Current works focus on how to define KD loss. This work proposes to improve KD from data augmentation (DA). This work proposes an entropy-based data-mixing DA to improve two KD methods: KD and CRD. Strengths:\n1. The method is simple and clearly presented.\n2. The experiments are done on different data augmentation techniques.\n3. Results on CIFAR-100 and TinyImageNet show increased performance.\n\nWeaknesses:\nThere are three contributions in the method part: (1) data augmentation (2) longer training and (3) cutmixpick. (1) and (2) are already investigated in works [1][2]\n[1] Cui, Wanyun, and Sen Yan. \"Isotonic Data Augmentation for Knowledge Distillation.\" IJCAI2021\n[2] Beyer, Lucas, et al. \"Knowledge distillation: A good teacher is patient and consistent.\" CVPR2022.\nThe improvement from (3) is very minimal.\n\n\nAfter rebuttal:\nThe authors have addressed my concerns. I increased my score to boardline accept after considering other reviewrs' comments. The main concern is the novelty of the proposed methods (see weakness). The authors have addressed the the limitations and potential negative societal impact of their work.", " The paper establishes a connection between data augmentation (DA) and generalisation of student-teacher training, namely showing theoretically that given two subsequences of the original dataset D (where the subsequences differ by some data augmentation scheme), the subsequence that performs better is the one that induces less variation in the predicted probabilities of the teacher network.\n\n**Edited review**\n\nIn light of the authors _active discussion and contributions_ during this phase, as well as their addressal of my own concerns, I will tentatively raise my score from 4 to 7. Obviously this is conditional on some changes to the manuscript, namely:\n- Making the math more digestible (we already discussed this in great detail)\n- Preferring plots to large tables where applicable, or having plots supplement them. I leave this to the authors' discretion since space constraints will mean decisions will have to be made as to what should be a table vs what should be a plot, and what should be relegated to the appendix.\n- Further work on plotting Equation 8 vs its approximation vs both 'bad' and 'good' students. The authors have acknowledged this and even provided preliminary results.\n\nThanks, and good work. # Strengths\n\n- The efficacy of any DA scheme for student training could in principle be evaluated before the training of any student model, since computing the variance term $V[\\Delta]$ only requires the pretrained teacher model.\n\n- Experiments support the proposed theory, and are numerous, run over many different architectural variants as well as data augmentation schemes.\n\n- Proposal of an entropy-based scheme to improve results.\n\n# Weaknesses\n\nSome of the notation in Section 3.1 and 3.2 is incredibly confusing, and looks to be rushed. Firstly, I would recommend simply using $\\log$ instead of $\\mathcal{L}$ to denote the logarithm. Alternatively, if you want to be more abstract, you can simply define the cross-entropy loss as $\\mathcal{L}_{CE}(x, y; f) = y^T f(x)$ and it would make equation (6) more readable. In fact, you have already defined it as such in Equation (1).\n\nIn Section 3.2, I have several concerns. In Equation (6), in line 1 you have an expectation $S \\sim D^N$, yet in line 2 it confusingly turns into an expectation $x \\sim D$, yet you still have the inner summation. Why isn't it just this instead:\n\n$E_{x \\sim D} [ p(x) \\log f(x) ] + \\text{const}$\n\ni.e. the expectation implies the inner summation + multiplication over $1/N$, so having both seems redundant (and incorrect). Furthermore, in the inner multiplication you're missing the transpose, so it should be $p(x_n)^{T} \\log f(x_n)$, since that is how it is defined in equation (4).\n\nIn Equation (7), I am also not sure why the last line expands out into a variance + covariance term. Covariance to me implies that you're computing the variance between two sets of random variables; don't we only have one random variable? (That random variable being $\\Delta$, the empirical risk over whatever random draw $S \\sim D$.) Maybe I am missing something crucial, but it seems like one could just remove the last line of Equation (7), leaving us with:\n\n$V_x[ p(x)^T \\log f(x) ]$,\n\nthen say that the variance is going to be proportional to the $p^{(t)}$ and that $f$ is held constant. Actually, it seems like from Equation (9) that the covariance is over the $p$'s for the different classes. What is confusing is that, for a given $x$, you are indexing into its predicted probability for class $i$ as as $p^{(t)}(x_i)$, and $x_i$ is apparently the $i$'th example as you have implied in equations (3) and (4). If $p^{(t)}$ outputs a probability distribution over x, then you should be using $p^{(t)}(x)_i$ instead. \n\n\"Each element in S is drawn the same underlying distribution D.\" - I don't follow this, since it says earlier that $S_1$ and $S_2$ are elements from $D$ but not necessarily iid. If so, how can $E_{x \\sim S}$ turn into $E_{x \\sim D}$?\n\nTable 1: I appreciate that the results are averages over three runs, but please indicate the standard deviation. Since space seems a little tight in this table, maybe just indicate the stdevs below each number in parentheses. Also such information can be nicely condensed into a scatterplot with one axis denoting test accuracy and the other denoting mean stdev. When necessary, prefer plots over big tables, and leave big tables to the appendix. My questions mainly lie in the aforementioned weaknesses. n/a", " The paper presents a theoretical development of a straightforward to use measure of effectiveness of data augmentation techniques for distillation. It proposes that this measure need only be based on an analysis of the teacher, without consideration of the student. The paper also presents an enhanced version of the cut-mix data augmentation technique, which performs a distillation of the augmented dataset to maximize the information content of the data. The method yields an informative measure that, empirically, can be reliably used to judge the efficacy of different data augmentation schemes, at least for the methods considered.\n\nThe justification and derivation of the proposed measure is reasonable, but it (possibly) depends on an overly strong assumption on the student to be \"well-trained\". This may not be the case in some applications where the student has a much lower capacity than the teacher. However, the proposed measure may still be effective, but would need more detailed theoretical justification to show this.\n\nThe cut-mix-pick data augmentation technique demonstrates improved performance over the standard cut-mix method.\n Non-data manipulations, such as drop-out, can result in the same behavior as shown in figure 2a (of spreading different soft targets while keeping the same hard targets).\nThe paper (Bouthillier, X., Konda, K., Vincent, P., and Memisevic, R. Dropout as data augmentation. arXiv preprint arXiv:1506.08700, 2015.) even considers the dropout as a type of data augmentation. So, could your approach be made even more general (than the few types of augmentation you consider)?\n\nIn lines 127-129, why is a script L used to indicate the log function, rather than the more usual log() notation? Script letters are conventionally used to indicate spaces or sets. In line 139 the script L is used to indicate a loss function, adding to the confusion.\n\nIn line 154-156 the assumption is made of a \"well-trained\" student, that gives softmax outputs \"pretty equal\" to those of the teacher. However, in most practical applications of distillation, the student can be much smaller than the teacher (e.g. for network compression for edge devices). What happens to your conclusions in that case? This assumption is used to make the claim that we need only look at the teacher to judge the effectiveness of a DA method. So, is this claim still true if the assumption does not hold?\nIn table 1, (as was done in table 3) you should give the teacher and student test accuracies to see how well the \"well-trained\" assumption holds. For CIFAR-100 and the student/teacher networks used, I would expect a significant difference in softmax outputs (e.g. 74% for ResNet56 and 69% for ResNet20).\n\nIt seems surprising that an analysis of the student has no role to play in determining the effectiveness of a data augmentation technique that is being used to train that student. If no distillation was being done at all (just training using cross-entropy on the hard targets), DA still would be of some use, no? So, this suggests that one cannot just ignore the student in determining the effectiveness of the DA method. Perhaps, in light of the results in table 1, the teacher's effects dominate the student's effects in terms of judging DA performance, but the student may still have some influence. It would be nice to have some theoretical insight into why this is, rather than just throwing away the student based on the \"well-trained\" assumption.\n\nDoes the \"pick\" aspect of the Cut-Mix-Pick help with the other DA methods? Presumably doing the data distillation on the other augmentations would also improve their results.\n\nIn section 5.1 the authors say that they do not look at accuracy, as the derivations are based on error, and sometimes a network can give high accuracy but also high error. But accuracy is typically what people are interested in when using networks, not the value of the loss function. It may be that by focusing on loss (error) one is biasing the student to become more confident, like the teacher, and perhaps overly confident, leading to reduced accuracy. In any case, table 3 shows accuracies, so I am not sure why this was not done in section 5.1. There is no discussion of limitations and potential negative societal impacts. However, distillation techniques, to the extent they can be used to train smaller networks, may positively affect societal impacts related to high power usage during training and inference time.", " The major contributions of this paper are 2-fold:\n1) The authors suggest that given a fixed teacher model, a good data augmentation (DA) scheme is characterized by a lower variance of the teacher’s mean output probability. This claim is supported by statistical analysis and empirical results (image classification).\n\n2) An entropy-based sample picking scheme is introduced to synthetically reduce the variance of the teacher’s mean probability. This scheme (CutMixPick) further improves the results. **Strengths:**\n1) Setups with lower variance (although it is not clear how $u$ is calculated, see weaknesses below) obtains acceptable improvements in CIFAR-100 and Tiny-ImageNet experiments.\n\n\n**Weaknesses:**\n\nThough this work is executed well and the image classification results show improvements, the novelty and significance of this work are limited. See below:\n1) The clarity of Section 3.2 can be improved. Though proposition 1 seems interesting, I have questions regarding the Std of the teacher’s mean output probability. It is unclear as to how $u$ in equation 9 is calculated. Particularly:\n- What is $S^*$ and how is it determined? Why is $K=640$?\n- Would it be reasonable to calculate $m$ using the variance of the output probabilities of the teacher **for the correct class** over all samples?\n2) Experiment coverage / results are limited: \n- Particularly, ImageNet results are not discussed and analyzed. Not that I have anything against CIFAR-100, Tiny-ImageNet analysis, but I tend to think that ImageNet results are critical to add merit to the findings (1000 classes, higher resolution:224 x 224). Most KD works report results on ImageNet-1K ([1, 2, 3, 4, 5]). If compute is a problem, authors can consider using a smaller dataset for experiments: ImageNet-100 (A subset of ImageNet popular in the self-supervised learning community). I believe the authors can also use publicly available pre-trained ImageNet models if required: https://pytorch.org/vision/stable/models.html\n- What is the reason for not including Flip, Flip+Crop, Cutout, Auto-Augment, Mixup results in Tables 3, 4?\n3) For ‘Std of mean prob’ in Tables 1, 2, is it reasonable to use the training set as the training set is used for distillation (not the test set)?\n4) For CutMixPick experiments, what is the percentage of the training set used for distillation (after 'picking' / filtering)?\n\nOverall I enjoyed reading this paper. In my opinion, the weaknesses of this paper outweigh the strengths. But I’m willing to change my opinion based on the rebuttal. \n\n\n=====================\n\n[1] Müller, Rafael, Simon Kornblith, and Geoffrey E. Hinton. \"When does label smoothing help?.\" Advances in neural information processing systems 32 (2019).\n\n[2] Shen, Z., Liu, Z., Xu, D., Chen, Z., Cheng, K. T., & Savvides, M. (2021). Is label smoothing truly incompatible with knowledge distillation: An empirical study. In ICLR\n\n[3] Chandrasegaran, K., Tran, N. T., Zhao, Y., & Cheung, N. M. (2022). Revisiting Label Smoothing and Knowledge Distillation Compatibility: What was Missing?. ICML\n\n[4] Heo, Byeongho and Kim, Jeesoo and Yun, Sangdoo and Park, Hyojin and Kwak, Nojun and Choi, Jin Young (2019). A Comprehensive Overhaul of Feature Distillation. ICCV\n\n[5] Tang, Jiaxi, et al. \"Understanding and improving knowledge distillation.\" arXiv preprint arXiv:2002.03532 (2020).\n Please see Weaknesses section above for a list of all questions.\n\nRemark : I managed to only study the main text. Unfortunately, I only skimmed through the supplementary, but didn't study in detail due to its length / my time-constraints. The authors have discussed limitations / potential societal impacts in Supplementary Section 6." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 7, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 4, 3 ]

[ "h193_rVJfgV", "8qF-zRm7kmt", "a-R3Y-7Pp0a", "Bclvdf7t0in", "Bih03GkXgJ", "iHArleH0vaB", "Bclvdf7t0in", "PbGsE8syp3n", "3FirgJ3JgqI", "UvkEOgN_wL_", "Mh6MOKvbiqs", "WECmLYG0VOr", "nips_2022_6avZnPpk7m9", "a-R3Y-7Pp0a", "YrO73iAT3Gq", "eaVXVhySeUk", "eaVXVhySeUk", "jZtCYAS3H9", "jZtCYAS3H9", "ClNwppdtx6z", "ClNwppdtx6z", "0tPoRCfEnw", "nips_2022_6avZnPpk7m9", "nips_2022_6avZnPpk7m9", "nips_2022_6avZnPpk7m9", "nips_2022_6avZnPpk7m9" ]

[ "1VBrr5PyyBV", "qP0PGiSj7d6", "dNasDBSCDnx", "1UiOp6730mA", "860DlDAf1is", "IH6wdhqhzu", "wRUP6i1qfbl", "OdTr2pXE2DB", "9__5KmWX8qU", "5-cN-AUSf9-", "cVAgZsLmfAv", "lh5DKv8sMQM", "YJ2jXwme3C2", "H2qy1GPqgkN", "PuCDI2ydm2X", "-ve5-Yx-37j" ]

[ "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " First of all, we thank you for your follow-up comments – we are happy to provide more context to the best of our abilities. Our responses are as follows:\n1. **IBC + MinGPT:** \na. **Success rate:** The IBC + MinGPT model completes 0 tasks after 72 hours of training on both Kitchen and Block Pushing tasks. \n b. **Reason behind slow convergence:** We hypothesize two reasons for the slow convergence: \n * Firstly, the InfoNCE objective in IBC results in training the transformer with a contrastive loss that is much slower to converge compared to the supervised Cross-Entropy or MSE loss.\n * Secondly, with a historical context h(s), the IBC model trains the energy E(a, h(s)) or E(a, s, h(s)). The historical context h(s) starts untrained, which creates a chicken and egg problem where improving h(s) might make the old energy estimate E(a, h(s)) less useful. \n This problem is not as severe when using conv. nets to encode images in the IBC paper because of the deep image prior [1] which shows even an untrained convnet can be useful to extract and restore image information. We see a similar effect where we use a ImageNet-pretrained ResNet representation on our quite off-domain CARLA task and still get positive results. No such useful prior is known about untrained attention-based models.\n2. **Capturing expert demonstrations:** We believe, and reviewer oVB2 seems to agree, that our response satisfactorily answers this question; but to recap (with added emphasis): \n > As you can see from table 2 and figure 4 in our paper, BeT rollouts capture multiple modes in the demonstration distributions, and approximate the demonstration distribution better with a higher entropy (table 2) than any of the baselines. However, **BeT does not perfectly imitate the state distribution in the demonstrations**, which is why you may see phenomena like table 2 or figures 4 and 5 where the demonstration distribution is slightly different from the BeT rollout distribution. We believe perfectly capturing demonstration distribution with a BeT could be an interesting research question, of which our paper is only laying the foundation. \n\n We hope this explains the relationship between expert demonstrations’ distribution and BeT rollout distribution better. \n3. **Limitations and Societal Impacts:** Thank you for pointing out the limited discussion about societal impacts. Given the early stage research this work addresses, we do not foresee significant societal impacts. In our commitment to open science, we are open-sourcing all of our code and data, which can help in understanding potential societal impacts in the future. Regarding limitations, we believe that the two significant limitations of our current work, and potential directions for future research, are the lack of real robot results and the lack of conditional behavior generation with deep RL. Both of these limitations have already been mentioned in Sec. 5. \nAre there other limitations you would like us to add in this section?\n\nWe hope that our clarifications above have resolved your remaining concerns. In light of our discussion, we would like to politely ask if you are willing to increase your score. \n\n\n[1] Ulyanov, Dmitry, Andrea Vedaldi, and Victor Lempitsky. \"Deep image prior.\" Proceedings of the IEEE conference on computer vision and pattern recognition. 2018.\n", " Thanks for performing additional experiments. I would still like to see IBC results at least in this discussion, either intermediate results after 72 hours or on tasks other than Kitchen or both. Also, what is your assumption for why IBC + minGPT converges slower?\n\nI would like to echo reviewer oVB2's question \"In Figure 5, BeT with history seems to prefer the red mode over the other two modes. While in the dataset all three modes are equally likely. It is unclear, if the BeT model can capture the true underlying distribution of expert demonstrations?\", which did not seem to be answered in your response.\n\nI think the **limitations** are not really discussed in Sec. 5. I recommend expanding that. Also, the authors chose to not discuss **societal impacts**. Is there a reason?", " The rebuttal has addressed most of my concerns. I have raised my score accordingly. The only remaining concern of significance is that the experimental setting is, in general, quite simple, e.g. on CARLA, and quite far removed from the complex scenarios, e.g. with respect to the routes and traffic density in CARLA, compared to the SOTA methods. Nevertheless, the paper does make a solid contribution.", " Thank you for the detailed response. My concern about similarities to Trajectory Transformer has been addressed, and I'll raise my score to a 7.", " Dear reviewers, \nWe would like to invite you once again to share any follow up questions that you may have following our rebuttal, so that we can respond to them before the quickly approaching author response period. Otherwise, assuming we have responded to your concerns satisfactorily through our updates to the paper and our comments, we would like to ask you if you are willing to increase your review scores. \nRegards, \nAuthors of \"Behavior Transformers: Cloning $k$ modes with one stone\"", " The overall discussion makes me more confident about my assessment (4->5)", " First of all, we thank you for your insightful review of the paper. We agree with you that the most exciting applications for algorithms such as BeT is in the real world, and would like to follow up this work with such applications in the future.\n\nNow, to answer your questions:\n\n1. **K-means vs Uniform Quantization**: Firstly, we ran an ablation experiment with uniform quantization, added to table 3 now, which shows that while uniform quantization performs competitively on lower action dimension environments, its performance is below k-means on higher dimensions. We primarily chose k-means over uniform or quantile discretization for the same reason.\n\n Uniform or quantile discretization per-dimension requires one of three things to happen: it needs an exponential blowup in the number of action bins, or an autoregressive action prediction causing quadratic blowup in transformer computation, or an assumption of independence between the action dimensions. Faced with such trade-offs, we instead chose k-means which only requires one extra matrix operation every step for discretizing or recovering actions. Complexity-wise, we believe that the extra overhead is worthwhile to keep our model small and fast. We believe the task of action discretization is worthy of additional research, as shown by concurrent research such as AQuaDem [1] presented in ICML 2022.\n\n\n2. **Run-time computational consideration for BeT**: We currently present the run-time requirements of BeT compared with IBC in the computation considerations section, namely 1.65 second average runtime for each complete episode of Block-Push, as opposed to 17.70 seconds for IBC. In terms of raw computation time to determine one action from the observations, in the Kitchen environment, BeT took 2.8 ms, while IBC took 52 ms, Trajectory transformer took 867.86 ms, and a simple MLP, as the fastest point of comparison, took 0.5 ms..\n\n At the same time, with our design choices, our run-time is asymptotically faster than possible transformer based baselines. Run-time computational expenses of a transformer depends on a few major points beyond the size of the transformer and the length of the historical context: in our case, linearly on the number of discrete bins, and quadratically on the number of tokens per actions or states. In BeT, using k-means discretization implies the number of bins can be much lower than uniform quantization. At the same time, treating one (state, action) pair as one input/output token pair yields an $O( (|S| + |A|)^2 )$ speedup over approaches like Trajectory Transformer, where each state action pair is encoded as $|S| + |A|$ input/output token pairs.\n\nWe hope the above responses answer your questions sufficiently, and we thank again for your kind and positive feedback. \n\n[1] Dadashi, Robert, et al. \"Continuous Control with Action Quantization from Demonstrations.\" arXiv preprint arXiv:2110.10149 (2021).", " We thank you deeply for your thoughtful review. We have added a further baseline for Trajectory Transformer according to your suggestion, and added further discussion in the paper highlighting their difference in the Related Works section. We summarize the difference here as well:\n\n1. **Differences between BeT and trajectory transformer**: Firstly, we ran Trajectory Transformer on the Kitchen environment, where it failed to complete any tasks for unconditioned, greedy, or beam search rollouts. We would like to note that this environment is more complicated than the MuJoCo environments (HalfCheetah, Hopper, Walker2d, and Ant) that the paper experimented on and has an order of magnitude fewer samples on the training set.\n\n While we agree that BeT and Trajectory Transformer based behavior cloning both use some type of discretization to fit demonstration datasets with a minGPT, we believe that is where the similarities end. The primary differences between the algorithms is in our design choices: namely what distributions they model, and consequently how they treat the observations.\n\n a. **Modeled distribution**: From a provided set of demonstrations, trajectory transformers model the joint distribution P(action, observations). On the other hand, BeT models the conditional distribution P(action | observations). Modeling the joint distribution requires MinGPT to model the forward dynamics of the environment, which can be arbitrarily difficult based on the environment.\n\n b. **Observation discretization**: Because trajectory transformers have to model the observations as well, it needs to discretize the observation space. As a result, TT cannot extend to high dimensional observational spaces, such as visual observations. This limitation is also acknowledged by the authors of Trajectory Transformers. BeT, on the other hand, does not model the observations and thus does not need to discretize them. Thus BeT can scale to arbitrarily high dimensional observations, as we show in the CARLA environment experiments, where BeT learns behaviors from high dimensional visual observations.\n\n c. **Efficient historical encoding**: Trajectory transformer encodes each (state, action) pair into a total of $|S| + |A|$ input/output tokens, while BeT encodes them into one input/output token. On a base MinGPT implementation that means a $O( (|S| + |A|)^2 )$ efficiency gain for BeT, or for example 4761x less compute for the same historic context in the Kitchen environment. \n\n We have added a summary of the above discussions in the appendix to better elucidate the differences for our readers.\n\n2. **Limitations of k-means**: As you have already gathered, the k-means discretization can be insufficient for binning the actions for very small values of $k$, and we have observed this for $k=1$ or $3$. Our algorithm implicitly assumes a lower variance of actions per bin, which we ensure by using a Bayesian GMM to pick our hyperparameter k. Additionally, there has recently been advances on task-aware action discretizations, such as AQuaDem [1] presented in ICML 2022, which could be worthwhile for more complicated action distributions.\n\nI hope the discussion above answers your questions. We thank you once again for the extremely valuable feedback.\n\n[1] Dadashi, Robert, et al. \"Continuous Control with Action Quantization from Demonstrations.\" arXiv preprint arXiv:2110.10149 (2021).", " We thank you for your insightful comments on our paper. To address your concerns, we have run several additional baselines and ablations, and provide clarifications below.\n\n1. **Proper discussion of prior work in learning from multi-modal experiences**: According to your suggestion, we have added an exposition to learning from multi-modal experiences in the introduction and elaborated the relevant section in Related Work further. Currently, the SOTA here revolves around learning goal-conditioned models. However, multi-modal behavior policies are orthogonal to goal-conditioned learning, as we can easily imagine multiple ways of achieving the same goal. We believe that the scope of multi-modal imitation is wider than learning multi-modal behavior policy learning, and BeT mostly focuses on the latter. Nonetheless, this discussion will aid the reader to understand the landscape of the field.\n\n2. **Further empirical comparison with transformer-based MDN and IBC**: As per your review, we ran our MDN and IBC baselines with the transformer backbone and historical context.\n\n * We found the MDN with transformer architecture to be a strong baseline, with stronger performance than MDN with MLP as presented in [1]. However, it still underperforms the transformer with k-means binning, for example by about 15-17% on the Kitchen and Block Push environments, and by 70% on the CARLA environment.\n * Adding historic context via a minGPT-style encoder significantly slowed down the optimization of the IBC model – to the point of no convergence after 72 hours of training on the Kitchen environment. Note that the IBC results we presented in the paper still takes historical context into account through frame-stacking, and takes about 30 hours to converge on the same environment and the same hardware. BeT on the same dataset and same hardware takes less than an hour to train.\n\n3. **Clarification of metric**: On table 3, we report our results normalized by the average number of task successes of standard BeT. Task success is defined per-task, such as reaching the end goal in CARLA, pushing some blocks to target in Block Push, and completing different tasks in the kitchen environment.\n\n4. **Implementation Complexity**: While we find that any attempts at comparison between two implementations are subjective at best, we would like to point out that beyond boilerplate code added to create ablations and comparison between baselines, our core method is implemented in less than 350 lines in the supplementary submission, split into the implementation of k-means discretizer and the minGPT backbone. On the other hand, the complexity in IBC implementation comes not in the model definition, but in action sampling, namely DFO and Langevin sampling methods, which are implemented in around 400 lines in the official IBC repo.\n\n At the end of the day, we expect such complexity to be abstracted away from the end user in the format of libraries, and we tried our best to organize and polish our released code, as well as to make our methods fast and memory-lean to enable easier downstream improvements. Additionally, our model is computationally light, with between $10^4$-$10^6$ parameters for the tasks presented here and can be trained to completion in around an hour on a single desktop GPU, which should also positively contribute to downstream research velocity.\n\n5. **Suggested related work**: We thank the reviewer for the suggestion, and have added it to the related work section. However, we would like to note that [3] relies on continued interaction with the environment in training time following the imitation learning framework introduced by GAIL [4].\n\n\n6. **Formatting issues**: We have updated the paper to be selectable and searchable. We apologize for any inconveniences caused by this. \n\nIn summary, we hope that our clarifications help address some of your concerns around our work. We have made every effort to modify the text in the paper to make these points clear. In light of our clarifications above, we would like to politely ask if you are willing to increase your score assuming we have addressed your concerns. Otherwise, please let us know if you have additional questions.\n\n[1] Florence, Pete, et al. \"Implicit behavioral cloning.\" Conference on Robot Learning. PMLR, 2022. \n[2] Official IBC implementation, https://github.com/google-research/ibc#run-train-eval \n[3] Hausman, K., Chebotar, Y., Schaal, S., Sukhatme, G. and Lim, J.J., 2017. Multi-modal imitation learning from unstructured demonstrations using generative adversarial nets. Advances in neural information processing systems, 30. \n[4] Ho, Jonathan, and Stefano Ermon. \"Generative adversarial imitation learning.\" Advances in neural information processing systems 29 (2016).", " Thank you for your insightful comments and constructive feedback on our paper. We are glad that you find our work simple, and easy to understand. To address your concerns, we have run several additional baselines and ablations, and provide clarifications below.\n\n1. **Variance captured by BeT**:\n\n > It is unclear if the method can truly deal the variance in expert demonstrations, expect for the simplistic point mass environments… It is unclear, if the BeT model can capture the true underlying distribution of expert demonstrations?\n\n We would like to point to the diversity of modes covered by BeT in complex environments beyond point-mass. As you can see from table 2 and figure 4 in our paper, BeT rollouts capture multiple modes in the demonstration distributions, and approximate the demonstration distribution better with a higher entropy (table 2) than any of the baselines. However, BeT does not perfectly imitate the state distribution in the demonstrations, which is why you may see phenomena like table 2 or figures 4 and 5 where the demonstration distribution is slightly different from the BeT rollout distribution. We believe perfectly capturing demonstration distribution with a BeT could be an interesting research question, of which our paper is only laying the foundation.\n\n As you suggested in your first point:\n\n > Even after k-means discretization in L106, there could be considerable variance within each cluster.\n\n k is a hyperparameter of our algorithm, and the Bayesian GMM algorithm that we used to choose k specifically tries to reduce the variance within each cluster. Further, once we have chosen a k, you are correct in identifying that we make an assumption in using L2 loss for offsets. Namely, we assume that **once the conditioning state is fixed**, the action distribution assigned to a bin is unimodal. Note that this still allows the action distribution in a bin to be multimodal while conditioned by different states. With our assumption, we reduce the problem of multimodal action prediction into multimodal bin prediction and unimodal action prediction over such bins.\n\n\n2. **Importance of Transformer**: Per your feedback, we added new baselines to our paper (Table 3) with different historical context models, namely LSTMs and Temporal convolution based models. In our experiments, we see that they generally get vastly outperformed by Transformers. Additionally, in our experience they are much harder to train stably. In particular, LSTM-based model performance is less than 5% of minGPT-based model performance in all cases, while Temporal Convolution has approx. 75% of minGPT performance in the best case. Please see table 3 for detailed results.\n\n\n3. **Motivation behind baselines**:\n\n > Prior state of the art works such as GAIL [a] are not considered as baselines… The motivation behind the choices of the baselines should be made clear\n\n While GAIL is an important work in imitation learning, it is not compatible with our setting since it learns by interacting with the environment while training. On the other hand, we only consider and compare behavioral cloning algorithms that learn from offline demonstration data without any further interactions with the environment. We chose our baselines (VAE, Flow, and IBC) inspired by state-of-the-art behavior learning algorithms respectively [1, 2, 3] that use state-of-the-art generative model based architectures capable of learning multi-modal behaviors from offline demonstration data. Additionally, we create further baselines by ablating and studying different parts of our algorithm. We hope that you find the motivation behind our baselines clear with this explanation, and find that they reflect the state-of-the-art in learning from multi-modal demonstrations.\n\n\n4. **CARLA environment**: Per your request, we have added further details about the CARLA environment in the appendix. To summarize, we generate demonstrations by a standard trajectory-following agent with some injected noise in the actions of the demonstrators. The variance in the demonstrations come mostly from the bi-modal distributions of path taken, and the injected noise in the actions.\n\n We intentionally keep the CARLA environment simple with no traffic participants because we wanted this environment to be the simplest image-based step beyond the point-mass environments, showing BeT behaviors with two very clear modes of demonstrations.", " \n5. **Failure of VAE in CARLA**: \n > Why does the VAE baseline fail completely on the CARLA experiments?\n\n The CARLA experiments are our longest time-horizon experiments in the paper (with more than 550 timesteps, as opposed to around 100 timesteps on Block push or 280 timesteps on Kitchen). Thus any method with significant high-frequency action noise (in this case, VAE/flow/IBC) struggles to perform well, since the success/failure metric is binary and going out of distribution in just one out of 550+ timesteps is enough to make them fail.\n\n\nIn light of the above clarifications, assuming we have addressed your concerns, we would like to politely ask if you are willing to increase your score. Otherwise, please let us know if you have additional questions and we would be more than happy to discuss further. \n\n[1] Pertsch, Karl, Youngwoon Lee, and Joseph Lim. \"Accelerating Reinforcement Learning with Learned Skill Priors.\" Conference on Robot Learning. PMLR, 2021. \n[2] Singh, Avi, et al. \"Parrot: Data-Driven Behavioral Priors for Reinforcement Learning.\" International Conference on Learning Representations. 2020. \n[3] Florence, Pete, et al. \"Implicit behavioral cloning.\" Conference on Robot Learning. PMLR, 2022.", " We thank the reviewers for your insightful and constructive feedback. We are glad that this work was received positively, although some important concerns were raised. To address these concerns, we have run **all** the additional baselines that were requested. While a detailed response to your feedback is available in individual replies to your review, a summary of our revision is presented below:\n1. **Comparison with more baselines and ablations:** We have performed the following baselines and ablations experiments: \n 1. Comparisons with transformer-based MDN (reviewer 4yjG). This baseline performs better than the MLP-based MDN presented in IBC [1], but still falls short of BeT performance, for example by 14% in the Kitchen environment or 70% in CARLA.\n 2. Transformer-based IBC (reviewer 4yjG), which unfortunately slows down convergence to the point where we trained for 72 hours and yet could not converge to a local minima. \n 3. Uniform quantization head instead of k-means (reviewer uHYM), which performs competitively with other baselines but falls behind BeT by 4-10% across environments. \n 4. Trajectory transformers sans-rewards (reviewer xCyV), which required a $O((|A| + |S|)^2)$ blowup in computational cost on the straightforward implementation (for example, 4761x more compute on Kitchen) and failed to complete any tasks on the Kitchen environment.\n 5. Alternative historical context models, such as LSTM and Temporal Convolutions (reviewer oVB2), which were much more unstable to train and perform significantly worse than transformer-based models in all environments. In particular, LSTM-based models’ performance is below 5% of minGPT-BeT models in all cases, while Temporal Convolution has approx. 75% of minGPT performance in the best case. \n\n With our new experiments, we see a general trend that transformer based models outperform other architectures, such as MLPs, LSTMs, or temporal convolutions. Importantly, at the same time, the presented k-means discretizer based BeT outperforms all other discretization or multi-modal prediction methods such as uniform quantizations or MDN. We have added the results from these experiments in the ablation section and the appendix.\n\n2. **Additional discussion on prior works:** Addressing comments by reviewer 4yjG and reviewer xCyV, we added further discussion about prior approaches in learning from multi-modal demonstrations, and how our approach in learning a single multi-modal policy differs from them. Specifically, we differentiate between the standard goal-conditioned policy learning approach from our approach, and discuss how the distribution modeled in BeT is different and conceptually simpler than preceding works.\n\n3. **Added environment details:** Per reviewer oVB2’s comments, we added further details about the CARLA self-driving environment in the appendix section, specifically about the variance in the demonstrations and existence of distractors.\n\n4. **Updated details on computational considerations:** As suggested by reviewer uHYM, we updated our computational considerations section to highlight both training and evaluation running times and efficiency gains compared to baselines. In general, we have found that during rollouts, our model can be 10-25x faster than IBC, and 300x faster than Trajectory Transformers.\n\n5. **Formatting updates:** As suggested by reviewer oVB2, we added equation numbers, and made the PDF selectable and searchable per the suggestion of 4yjG. \n\nWe hope that these updates to our paper inspire further confidence in our work. At the same time, we invite any further questions or feedback that you may have on this paper. \n\n[1] Florence, Pete, et al. \"Implicit behavioral cloning.\" Conference on Robot Learning. PMLR, 2022.\n", " This paper proposes an imitation learning method to take into account the variance in expert demonstrations. In detail, a novel Behaviour Transformer model is proposed, which uses a k-means clustering based pre-processing approach to extract k modes from the noisy expert demonstrations. The proposed approach exploits the ability of transformer based approaches to predict complex multi-modal distributions. The proposed model is evaluated on diverse tasks such as, CARLA, Block Pushing and Franka Kitchen. Strengths,\n* The proposed method is simple and is able to capture the variance of expert demonstrations as demonstrated in case of the point mass environments.\n* The paper is well written and easy to understand.\n* The paper includes ablations on the effect of discrete binning, action offsets and historical contexts, which shows the importance of these components.\n\n\nWeaknesses,\n\n* Effect of L2 loss in L130: Even after k-means discretization in L106, there could be considerable variance within each cluster. Using the L2 loss as in L130 would kill this variance? In case of the point mass environment in Figure 2 and 5, this loss would not have a large effect as the within cluster variance is low. The paper should include examples where the true variance of the expert demonstrations is captured.\n\n* In Figure 5, BeT with history seems to prefer the red mode over the other two modes. While in the dataset all three modes are equally likely. It is unclear, if the BeT model can capture the true underlying distribution of expert demonstrations?\n\n* Importance of the transformer model: While there is not denying the effectiveness of transform models, for the simple tasks considered here, e.g. point mass environments, it is not clear if the MinGPT model is actually necessary. It would be interesting to consider a LSTM based baseline as it would enable the modelling of historical contexts unlike MLPs considered in Table 3. \n\n* The CARLA experimental setting seems very simple. It is also unclear how the expert demonstrations are captured? The amount of variance (if any) in the expert demonstrations is unclear. This is further illustrated by the fact that RBC baseline which cannot deal with variance in the expert demonstrations works so well. Moreover, the paper should include further details like number of traffic participants in the scene, so that the reader can correctly judge the complexity of the task. \n\n* Baselines: The paper compares to only simple baselines like VAE, Flow and IBC. Prior state of the art works such as GAIL [a] are not considered as baselines.\n\n* Equation numbers are missing, e.g. L130.\n\n[a] Generative Adversarial Imitation Learning, Ho et. al. In addition to the points above,\n\n* The motivation behind the choices of the baselines should be made clear? Currently the baselines chosen are quite simple.\n\n* It is unclear if the method can truly deal the variance in expert demonstrations, expect for the simplistic point mass environments?\n\n* Why does the VAE baseline fail completely on the CARLA experiments? Currently the paper does not discuss the limitations of the the proposed BeT model in detail, e.g. wrt the computational resources required for training, whether the proposed method scales to large scale datasets and tasks, the suitable application areas.", " This paper tackles the problem of behavioral cloning from distributionally multi-modal experience. The proposed solution is \"Behavior Transformers\" (BeT). Specifically, the authors propose clustering continuous actions into discrete bins using k-means, and model multi-modal policy as categorical distributions with a transformer-based sequence model.\n\nEmpirical evaluations are performed on five environments ranging from simple diagnostic point mass to high-dimensional robotics and self-driving environments. Comprehensive analysis is provided to prove that BeT is indeed capable of learning multi-modal behavior in these environment and better than the baseline methods chosen by the authors. Detailed ablations studies are presented to analyzed the importance of each components of the proposed methods. Strengths\n* Very clear problem statement about imitating multi-modal experience (Sec. 2) and issues with canonical BC that assumes an unimodal expert.\n* Clear empirical evidence that BeT is able to imitate multi-modal behavior (Sec. 3.3)\n* Use diverse testing environments ranging from simple point mass to high-dimensional robotics and self-driving environments.\n* Sufficient ablations that analyze the importance of describe binning, action offsets, interaction history, and transformer architecture.\n\nWeaknesses:\n* Imitating multi-modal experience is well-acknowledged problem. However, how the proposed method different from previous contributions in this line is barely discussed. Furthermore, I think there should be citation and discussion about prior efforts in introduction. Intended or not, it somewhat gives me an impression as if this is the first work tackling multimodal imitation learning. \n* Insufficient empirical comparison: The only previous contribution about multimodal imitation learning that this work compare with is \"Implicit Behavioral Cloning\" (IBC) [22]. Because of the IBC paper shows outperforming Mixture Density Network (MDN) [7], a well-established baseline for multi-modal imitation learning, the authors skipped comparing with MDN. These naturally trigger the following questions: (1) Have you compared to MDN or other approaches using mixture distributions apple-to-apple, using the same transformer and also historical context? (2) The exact same question for the comparison between BeT and IBC. Both MDN and IBC can be more easily implemented than the proposed clustering and binning and trained end-to-end. Without fair comparisons, I don't feel convinced about using the proposed method.\n\n\n * Table 3 shows average BeT performance at the task. Can you be more specific about what they are averaged across?\n* The text in the pdf cannot be searched and selected. This makes review difficult.\n* Is this a related work? Hausman, K., Chebotar, Y., Schaal, S., Sukhatme, G. and Lim, J.J., 2017. Multi-modal imitation learning from unstructured demonstrations using generative adversarial nets. Advances in neural information processing systems, 30. Very little to no discussion on limitations and potential negative societal impact. Please add relevant pieces to the conclusion section. ", " The paper presents an approach to imitation learning using transformers. The core challenge this work aims to tackle is enabling imitation learning methods to better handle multiple behavior modes in demonstration data. The key idea amounts to learning a hybrid discrete+residual action representation using k means, then using a minGPT transformer architecture to produce actions conditioned on the history of observations and actions. The experiments show strong performance on tasks with multi-modality in the demonstrations compared to baselines, importance of each of the components, and some qualitative examples highlighting the methods ability to capture multimodality. *Strengths*\n- The paper tackles an important problem in handling multi-modal behavior in demonstration data. Handling such data will be important for enabling imitation learning algorithms to scale to broader datasets. \n- The proposed approach is clean, simple, and well motivated. Indeed sequence models seem to be able to capture very multi-modal distributions in text, and by discretizing actions it makes sense that the sequence model can also capture multi-modality in behavior.\n- Experiments are also thorough, and compare the method to most of the relevant baselines (Implicit BC, Nearest Neighbors, BC) across multiple environments. The qualitative examples also nicely highlight how the method captures many modes in behavior, and how historical context is important for doing so.\n- The ablations show that changing the architecture or removing the action binning/offset both hurt performance, suggesting that all of the components are important.\n- Overall, the paper is well written.\n\n*Weaknesses*\n- The most significant weakness/question I have with this work is the novelty compared to the Trajectory Transformer (Janner et al). In the related work this paper simply states Trajectory Transformer as different because it focused on Offline RL. However, the Trajectory Transformer paper also proposes a version of the method that can be used for pure imitation learning (not just offline RL), and has corresponding experiments. Moreover, TT also tokenizes actions, and uses minGPT to generate sequences. The Trajectory Transformer paper proposes using beam search to guide actions toward certain goals, but without the beam search, the unconditional generation seems very similar to what is being proposed in BeT. I can see some implementation differences like the masked MT loss and the k-means for discretization, but at a high level the methods appear very similar. At the very least, the current related work significantly underplays the similarities to TT, and I think a more comprehensive discussion of how the two are related is important. It should probably also be added as a comparison.\n - Can the authors explain the differences of their approach with the imitation learning version of trajectory transformer? A comparison would also be good to see.\n- A more minor point: are there places where k-means fails is insufficient for binning the actions? I can imagine cases where small differences in the action can have huge impacts in task success, and perhaps k means may incorrectly group two functionally different actions to the same group. Perhaps there are ways of doing task-aware discretization of the actions. Yes.", " This paper describes a method for Behavior Cloning that leverages 1) a transformer-based architecture to model the state-action relationships, thereby lifting some of the Markovian assumptions many BC architectures make, and 2) a discrete+continuous residual action representation, which enables the model to learn a multimodal action representation more easily through binning of the discrete action clusters, while not incurring a large loss of precision by explicitly learning a continuous offset from the cluster centers. Strengths:\n- the proposed architecture is well-motivated: much of recent works in BC have pointed at the weaknesses the model proposes to address, and the model architecture derives very naturally from the goals of addressing those weaknesses.\n- the experimental results compare against strong baselines, and ablation experiments clearly tease out why the model performs well against them.\n- the paper is limpid, well-organized and immediately useful to the community.\n\nWeaknesses:\n- No real-world experiment. This may not be essential in this context, but would inform how practical it is to deploy this kind of architecture in a real-time, real-world system. 1- I am very curious about the choice of k-means as a discretization scheme vs. e.g. uniform quantization. Given the added correction term, it is not immediately obvious that performing k-means on the action is worth the added complexity. A uniform binning would also be more general and potentially would generalize better across tasks and embodiments. I would have loved to see that particular ablation.\n2- The paper doesn't mention computational considerations at run-time, only at training time. I would have liked to see some discussion of the tradeoffs here, particularly if the model is to be used for real-time continuous control. Nothing comes to mind." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 7, 8 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 5 ]

[ "qP0PGiSj7d6", "9__5KmWX8qU", "cVAgZsLmfAv", "OdTr2pXE2DB", "nips_2022_agTr-vRQsa", "wRUP6i1qfbl", "-ve5-Yx-37j", "PuCDI2ydm2X", "H2qy1GPqgkN", "YJ2jXwme3C2", "YJ2jXwme3C2", "nips_2022_agTr-vRQsa", "nips_2022_agTr-vRQsa", "nips_2022_agTr-vRQsa", "nips_2022_agTr-vRQsa", "nips_2022_agTr-vRQsa" ]

[ "wMhfYyMsKFm", "dKUSOnT9H-w", "dyiKmA2CW1Y", "k3syKxm9RuX", "jC8CimEKtpe", "P8M17nZVp6K", "4E5vIhlxN9a", "8klHHtS5tua", "zj1YQ48d4bC", "9AmzA4k08eH", "ihyqYlXfmY", "09gg1dybTjl", "QgrZS8-pHRk", "L5iGHCnkY6N", "zJHLKFA27ix", "XGBHrBKHI0W", "1nA60WQ20v", "Z4kn0K_8PW0" ]

[ "author", "author", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank you again for your valuable comments and the kind support of this work. ", " Thanks very much for your appreciation and recognition，but may I respectively ask you to rise your rating for our paper to promise an acceptance, thanks.", " Dear authors, your response has cleared my concerns.\nThanks,\ni4CE", " Dear authors of Paper 726,\n\nI appreciate the detailed feedback and the additional experimental results. I think most of my questions have been adequately addressed, which makes me more confident in suggesting to accept the paper.", " Dear Reviewer u4Xd\n\nWe sincerely thank you for the constructive feedback and support. And we promise to add the comparison table of the training cost to the supplementary material in the revision.", " Thank the authors for the response. \n\nThe authors conduct the Synscapes->Cityscapes adaptation experiments and provide the experiments. Despite only one round of training, i.e., one stage, which is less than the default setting, the improvement over the vanilla source-only result is clear and significant, showing the effectiveness of the proposed method. \n\nThe authors also carefully discuss the reason why the improvement of Synscapes->Cityscapes is less than GTA5->Cityscapes, and give a table to compare the recent advanced methods w.r.t the training cost, where the results demonstrate that the proposed method can reach better performance with less training steps. It is highly encouraged to add this comparison to the paper. \n\nBesides, the authors also respond to the questions including the difference between the proposed method and DACS/DSP, the explanation in the table, more domain bridging strategies as pointed out by PF8F, the intermediate model selection as pointed out by i4CE, the ablation w.r.t. hyper-parameters by xZqY, etc. \n\nOverall, the major concerns have been addressed. Considering the novelty and technical contribution, I would like to keep my rating.", " Dear reviewer PF8F:\n\nWe sincerely thank you for the time and comments. We have provided corresponding responses and experimental results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest,\nAuthors of Paper 726", " Dear reviewer i4CE:\n\nWe sincerely thank you for the review and comments. We have provided corresponding responses and clarifications, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest,\nAuthors of Paper 726", " We sincerely appreciate all reviewers for your time and efforts in the review. We are delighted and encouraged to see our paper get all positive ratings, and we have carefully rephrased our paper (see red marks) to correct typos and update missing citations in the revision. Other detailed questions are answered accordingly in each column below.", " Thanks for your time to carefully read our paper and give valuable suggestions. We have fully addressed your concerns below.\n\n**Q1: Clarification about the positioning with respect to prior work.**\n\n**A1:** Thanks for your reminder. We will add an extra explanation to illustrate the position of our work w.r.t prior works in the next revision: a comprehensive and broader formulation of conducting domain bridging (DB) could be divided into three branches – in the input space, in the output space, and the joint space. FDA[A] and the generative-based methods belong to the first branch that performs DB in the input space, self-training-based methods belong to the second one, and data mixing-based methods belong to the last one. The proposed framework mainly focuses on taking full advantage of complementary data-mixing-based methods and belongs to the last branch as well.\n\n**Q2: What does \"unexpected artifacts in the global input space\" mean? What \"optimization constraints\" are referred to?**\n\n**A2:** As shown in [15, 21, 66] and our re-implementation results, these DB methods based on generative style transfer techniques are prone to produce **unexpected artifacts** when transforming source domain images to target domain styles (**especially** in the case of **high-resolution** inputs), such as producing additional tree-covered areas in the sky and overly \"imagining\" palm trees as leafy trees (e.g., Figure 6(b) in [21], and Figure 3 in [66]). The **optimization constraints** arise from the fact that, regardless of the semantics of the artifact regions, their corresponding pixel-level Ground-Truth would remain unchanged.\n\n**Q3: Why the paper only evaluates two domain bridging strategies in the ensemble?**\n\n**A3:** As shown in Table 1(c) of the main paper, we have experimented with style transfer-based, global blending-based, coarse region-based, and fine region-based domain bridging (DB) methods individually or in combination and found that the combination of coarse region-based DB methods and fine region-based ones outperforms all others. Moreover, here we further conducted model ensemble experiments among the ClassMix, FMix, and CowMix methods, and that’s why we chose such two representative strategies of coarse-based and fine-based DBs for implementation.\n\n*Table A: The comparison of model ensemble experiments between FMix and ClassMix. The number (e.g., 1) denotes different runs of the same DB method.*\n| | FMix1 | FMix2 | ClassMix1 | ClassMix2 |\n|-----------|-------|-------|-----------|-----------|\n| FMix1 | 49.9 | - | - | - |\n| FMix2 | 50.8 | 50.2 | - | - |\n| ClassMix1 | 54.3 | 55.0 | 55.5 | - |\n| ClassMix2 | 54.5 | 55.2 | **55.9** | 55.8 |\n\n*Table B: The comparison of model ensemble experiments between CowMix and ClassMix. The number (e.g., 1) denotes different runs of the same DB method.*\n| | CowMix1 | CowMix2 | ClassMix1 | ClassMix2 |\n|-----------|---------|---------|-----------|-----------|\n| CowMix1 | 50.6 | - | - | - |\n| CowMix2 | 51.5 | 50.3 | - | - |\n| ClassMix1 | 55.2 | 54.8 | 55.5 | - |\n| ClassMix2 | 55.6 | 55.4 | **55.9** | 55.8 |\n\n**Q4: Supplemental experiments about FDA[A].**\n\n**A4:** This frequency domain-based style transfer technique belongs to the style transfer-based DB methods, in which $\\beta$ controls the extent to which the amplitude spectrum is exchanged. Table C shows the results of source-only and pseudo-labeling adaptation experiments using the FDA technique, which we found to be more effective than those in Table 1(a). Additionally, as shown in Table D, we combined ClassMix and FDA(S→T) in the same way as Table 1(c) to conduct the model ensemble experiments and observed hardly any improvement.\n\n*Table C: The comparison of FDA under source-only (S→T) and pseudo-labeling (T→S) settings and various $\\beta$.*\n| | $\\beta$ | mIoU |\n|-----|---------|------|\n| S→T | 0.01 | 40.9 |\n| S→T | 0.05 | **42.0** |\n| S→T | 0.09 | 41.2 |\n| T→S | 0.01 | 26.6 |\n| T→S | 0.05 | 39.3 |\n| T→S | 0.09 | **43.1** |\n\n*Table D: The comparison of the model ensemble combining ClassMix and FDA.*\n| | ClassMix+FDA($\\beta=0.01$) | ClassMix+FDA($\\beta=0.05$) | ClassMix+FDA($\\beta=0.09$) |\n|----------------------------|----------------------------|----------------------------|----------------------------|\n| ClassMix+FDA($\\beta=0.01$) | 52.7 | - | - |\n| ClassMix+FDA($\\beta=0.05$) | **52.9** | 52.4 | - |\n| ClassMix+FDA($\\beta=0.09$) | 52.4 | 51.9 | 50.2 |", " **Q5: There is a related work on domain bridges for semantic segmentation that was not included: [B].**\n\n**A5:** As we have replied in Q1, this work of [B] falls under the category of generative style transfer DB methods and is not our focus. We have already cited it in the revision.\n\n**Q6: In line 185, shouldn't the reference go to Eq. 3?**\n\n**A6:** Thanks. We have already corrected it in the revision.\n\n**Q7: Why do the mixing weights in Eq. 11/12 help? Aren't the softmax values (i.e., scores) already an indication of how far away a sample is from the decision boundary?**\n\n**A7:** The parameterized softmax layer is more prone to be biased toward the supervised source domain than the pseudo-labeled target domain, which hinders the prediction in the target domain. Thus we compute the feature centroid for each class over the entire target domain and modulate the predicted probabilities on the fly according to the distance between the feature response and the feature centroids for the teacher network.\n\n**Q8: It would be good to point the reader to the supplemental material for a detailed description of the training strategy. And it's hard to understand and see the details in Figure 1.**\n\n**A8:** Thank you for the valuable suggestions. Figure 1 is just for explaining the motivation. Due to the limited space, we put the algorithm in supplementary material rather than a framework figure in the main paper. And we have pointed out the location of the algorithm at the start of Sec. 3.3 of the revision for a clearer understanding of the proposed framework.\n\n**Q9: Potential societal impacts are not discussed.**\n\n**A9:** We are sorry for the missing discussions about the potential societal impacts. It might be used in undesirable applications like surveillance or military UAVs for the purpose of domain adaptive semantic segmentation. Legal limitations on the applications of semantic segmentation algorithms could be a potential defense. And we have already updated this in the limitation section of the revision.", " Thank you so much for the detailed and thoughtful review! We have fully addressed the concerns as follows:\n\n**Q1: The performance in Synscapes to Cityscapes.**\n\n**A1:** We further conducted experiments on the benchmark of Synscapes to Cityscapes and reported them below. An interesting finding is that even though the source-only models trained on the Synscapes dataset perform significantly better than those trained on GTA, the final adaptation performance of Synscapes is lower than that of GTA. We analyze this is because of the lack of fine-tuning of hyperparameters and the lack of diversity in the style of Synscapes. Moreover, our proposed framework not only achieves satisfactory adaptive performance on both GTA and Synscapes datasets but also their combination (GTA and Synscapes) can further improve the performance to an impressive 69.0% mIoU. This is thanks to our naturally constructing intermediate domains between target and multiple source domains to facilitate knowledge transfer.\n| Method | mIoU |\n|-------------|----------|\n| Source only | 47.8±0.2 |\n| Stage1 CRP | 55.3±0.4 |\n| Stage1 FCP | 55.9±0.7 |\n| Stage1 CKD | **57.1**±0.9 |\n\n**Q2: What do the numbers righter after the approach name in Tables 2, 3, and 4 mean?**\n\n**A2:** This is an indication of the year in which the method was proposed, in order to make it easier for the reader to understand the currency of the method being compared. We have already updated the complete name for venues in the revision for clarity.\n\n**Q3: The ‘soft distillation’ choice and the explanation are missing in that table, which is a bit confusing.**\n\n**A3:** Thanks for your valuable suggestion to improve our paper. The column 'hard distillation' in the CKD step indicates that the hard distillation was used (if it is ticked), otherwise, it means soft distillation. For easy understanding, we have already updated the caption of this table in the revision.\n\n**Q4: Clarification about the training efficiency.**\n\n**A4:** We provided a detailed comparison of the training efficiency. As shown in the following table, our method achieved better performance after one round of training with smaller input size, fewer GPUs, fewer iterations, and fewer post-processing steps than other SOTA methods. Furthermore, our method could still achieve gains of 1.5% mIoU with one more training round, while still being more efficient than other SOTA methods.\n| Method | Input size | Total GPUs | Total iterations | Pseudo-label generation | Prototype generation | mIoU |\n|--------------------|------------|------------|------------------|-------------------------|----------------------|------|\n| ProDA+*distill*[62] | (896,512) | 4 | 238K | √ | √ | 57.5 |\n| UndoDA+*distill*[31] | (896,512) | 4 | 238K | √ | √ | 59.3 |\n| CPSL+*distill*[27] | (896,512) | 4 | 238K | √ | √ | 60.8 |\n| DDB-round1 | (512,512) | 1 | 80K | × | √ | 61.2 |\n| DDB-round2 | (512,512) | 1 | 160K | × | √ | **62.7** |\n\n**Q5: The difference between DACS and DSP which also utilizes the data mixing technique in UDA is not well stated in the paper.**\n\n**A5:** We thank the reviewer for the valuable comment, and we have incorporated the missing references and discussed them as follows: Based on the cross-domain ClassMix technique, DACS only mixes the source and target domains to obtain an intermediate domain, but DSP mixes not only the source and target domains but also the source and source domains, so as to effectively reduce the domain gap. Different from them, we explored a variety of ways to construct DBs and found that the coarse-wise DB (e.g., CutMix) and fine-wise DB (e.g., ClassMix) methods were complementary. Based on this, we propose a dual-path DB method to effectively exploit such complementary properties to achieve better results.", " We are encouraged to see that you found our work interesting, extensive experiments contained, and well-written. We have endeavored to address your concerns as follows:\n\n**Q1: Clarification about the student model training.**\n\n**A1:** There seems to be a misunderstanding about the generation of pseudo labels in the CKD step. Notably, we use pseudo labels generated from two original teacher models rather than from the EMA models to teach the student model.\n\n**Q2: Clarification about the main contribution of this paper.**\n\n**A2:** First and foremost, we would like to thank you for acknowledging that our first contribution of analyzing different data mixing techniques is of interest. Then, we must emphasize that this work mainly aims to tackle the DASS task through a new perspective of domain bridging. Specifically, this work goes beyond a naïve/simple combination of existing mixings, like CutMix, ClassMix, etc., and innovatively explores a framework dubbed Deliberated Domain Bridging (DDB) to well-coordinate coarse region mixing (e.g., CutMix) and fine class mixing (e.g., ClassMix). Two independent bridging paths in Dual-path Domain Bridging (DPDB) are developed and focus on extracting complementary knowledge. In addition, a Cross-path Knowledge Distillation (CKD) step based on the teacher-student mechanism as well as a win-win alternating optimization strategy are carefully designed, which is the icing on the cake.\n\n**Q3: How the intermediate model is selected at each stage?**\n\n**A3:** We just use the latest checkpoint in each stage, which does not involve any supervision leak risk.\n\n**Q4: Details about the multi-source and multi-target experiments.**\n\n**A4:** In fact, we treat the multi-source datasets and multi-target datasets as one domain and **combine them directly**, which results in a single-source and single-target domain setting. Notably, there is **no tailored design** under these settings and the proposed DDB outperforms the previous SOTA methods by a large margin (10.0% and 11.1% mIoU gains under the multi-source and multi-target domain settings, respectively).\n\n**Q5: Typos about the reference of Eqn.3 instead of Eqn.2.**\n\n**A5:** We have already corrected these typos in the revision.\n\nYour constructive comments and criticisms will greatly assist us in improving this work. Please do not hesitate to contact us if you have any further questions.\n", " We thank you for the positive comments on the novelty of our approach and paper writing. We also appreciate your valuable suggestions on the supplement of ablation experiments. We have accordingly refined our paper as follows:\n\n**Q1: About the training efficiency and complexity.**\n\n**A1:** Our method is more efficient than other SOTA methods, compared to recent methods such as ProDA [62], UndoDA [31], and CPSL [27] where they typically use **four** GPUs and a total of **four** training rounds (about 60K iterations in each round, and one round of warm-up, one round of self-training, and two rounds of self-supervised self-distillation), our method only uses **one** GPU after performing **one** round of DPDB and CKD steps (40K iterations in each step) but achieves a superior performance of 61.2% mIoU. Moreover, these compared methods have almost reached the performance bottleneck after four rounds of training, while our method could still achieves gains of 1.5% mIoU in the second round of optimization.\n\n**Q2: Show a brief study about how the authors can extend the proposed approach to end-to-end simple learning architecture.**\n\n**A2:** Thanks. We have accordingly tried a heuristic end-to-end learning architecture as follows:\n* ***Architecture:*** Instead of leveraging two independent teacher models to learn complementary knowledge in coarse region-path and fine class-path, we propose a single model equipped with a shared backbone and two segmentation heads for distinct DB paths and one attention head for fusing the segmentation predictions. Specifically, the attention head has the same architecture as segmentation heads, while the last convolution layer only has one output channel and is followed by a Sigmoid activation function. Moreover, we build an EMA model for generating the denoised pseudo label on the fly.\n* ***Pipeline:*** We first feed the source image into the end-to-end model to calculate the cross-entropy loss items in the source domain like Eqn. 4. Next, we utilize the fused prediction of the EMA model to generate the pseudo label and confidence-based weight map for the clean target image, which enables the calculation of bridging loss items like Eqn. 7 for different bridging images and their corresponding segmentation heads. Moreover, we feed the augmented target image into the model and calculate the cross-entropy loss on the fused prediction and pseudo label for optimizing the attention head.\n* ***Results:*** We conducted experiments on the GTA5→Cityscapes benchmark and listed the performance of the end-to-end scheme and the original scheme. As shown in the table below, the results of the end-to-end manner in the single-stage are better than the DPDB even with the average ensemble. Moreover, as a result of the end-to-end architecture integrating complementary knowledge from the two domain bridging paths in the training process, both CRP and FCP variants perform better than the original ones.\n| Method | mIoU |\n|---------------------|------|\n| Stage1 CRP | 56.5 |\n| Stage1 FCP | 58.2 |\n| Stage1 Avg Ensemble | 59.3 |\n| End-to-End CRP | 58.7 |\n| End-to-End FCP | 59.3 |\n| End-to-End Fused | **60.1** |\n\n**Q3: Ablation study on the momentum of EMA in the DPDB step.**\n\n**A3:** Thanks. We setted the momentum $\\alpha$ following the most of the mainstream self-training DASS methods such as DACS [49], DAFormer [23], etc. Here, we further conducted ablation experiments on $\\alpha$, and found that $\\alpha=0.99$ will lead to better and more stable results.\n| Momentum | 0.9 | 0.99 | 0.999 | 0.9999 |\n|----------|----------|----------|----------|----------|\n| mIoU | 58.3±0.4 | **58.5**±0.3 | 58.4±0.3 | 54.2±0.1 |\n\n**Q4: Ablation study on the augmentation strategy for the input of the student model in the CKD step.**\n\n**A4:** Thanks. We further conducted corresponding ablation experiments and reported the results. As shown below, combining the Gaussian blur and color jitter augmentation techniques leads to the best performance.\n| Gaussian blur | Color jitter | mIoU |\n|---------------|--------------|----------|\n| | | 61.0±0.2 |\n| √ | | 61.2±0.2 |\n| √ | √ | **61.5**±0.3 |", " This paper proposes an effective Deliberated Domain Bridging (DDB) for domain adaptive semantic segmentation (DASS). To this end, it takes advantage of two data mixing techniques, region-level mix and class-level mix, to train two corresponding teacher models, which eventually guide one student model on the target domain. It has been tested on several benchmarks (GTA5 to Cityscapes, GTA5 + Synscapes to Cityscapes, GTA5 to Cityscapes + Mapillary).\n - Strengths:\n1. It is a well-written paper that addresses the limitations of previous methods (e.g., global interpolation -> pixel-wise ambiguity), toy game to show the justification of using both coarse-grained and fine-grained DB, and proposes novel learning architecture with multi-teacher and single-source distillation method.\n2. The proposed method is well proven to be effective with several benchmarks (e.g., single-source, multi-source, and multi-target settings) by widening the gap with the previous state of the arts in each benchmark.\n\n- Weaknesses:\n1. As the author illustrated in limitations, I am also a bit concerned with the training efficiency and complexity since the proposed method requires alternating optimization processes. One of the simple end-to-end optimizations is conducting EMA training on one model by combining region-level and class-level mixing techniques. It would be better to show a brief study about how the authors can extend this to end-to-end simple learning architecture.\n2. Lack of ablation study on some hyperparameters: 1) alpha in equation 5: the authors suggested updating the teacher models with EMA to avoid a denoised pixel-wise pseudo label. To prove it, an ablation study on alpha needs to be explored. 2) x_aug in equation 9: need to empirically show justification using augmentation input for a student model. Please answer the questions from the above weaknesses. Yes, the authors addressed the limitation.", " To address UDA in semantic segmentation, this work uses two types of data mixing strategies to artificially create intermediate bridging domains between source and target. The paper starts with a detailed analysis comparing different data mixing strategies, either done globally (mixup[61]) or locally ( CowMix [13], FMix [17], CutMix [60] and ClassMix [42]). The analysis demonstrates favorable results when using local data mixing strategies for UDA in segmentation, in particular CutMix (coarse region-wise mixing) and ClassMix (fine class-wise mixing). \n\nBased on results of the analysis, this work proposes a simple way to combine the two mixing strategies CutMix and ClassMix. \nIn the course of training, there are five models: two teacher models trained with CutMix and ClassMix, two EMA models of the two teachers, one student model trained using teachers' pseudo-labels.\n\nTraining is done in multiple rounds (fixed as 4 in the experiments). In each round:\n- The two teachers are first trained separately with CutMix and ClassMix\n- The student is then trained with pseudo-labels of two EMA models of the two teachers. Pseudo-label of a given target sample is determined as a weighted combination of softmax scores of the two EMA models (Eqn. 12). The weights have size $H \\times W \\ K$ with $K$ classes; at each spatial position, the weight vector over $K$ classes is the softmax over the feature distance to class centroids (Eqn. 11). Color jittering and gaussian blurs are used on target sample when training the student.\n- The two teachers are initialized by the student.\n\n ** Strengths **\nOverall this is an interesting technical paper that combines multiple existing strategies, namely CutMix [60], ClassMix [42], mean teacher [42], prototypical weighting [62] and pseudo-labelling [30]. Empirical results demonstrate better performance than previous SOTAs on comparable backbone (resnet101) and segmentation framework (deeplab-v2). Experiments are extensive. The paper is well-written and easy to follow.\n\n** Weaknesses **\n- My main concern is with the technical novelties of this work. The analysis comparing different mixing techniques, claimed as the first contribution, is somewhat interesting. However the main proposed approach is merely a mix of previous works. Actually there are no new insights that I could get from this work. \n\n- It's not clear to me how is the intermediate model selected at each stage. Is the target's validation set used to select the best model? If true, is there a risk of supervision leak from target validation set?\n\n- Missing details for the multi-source and multi-target experiments.\n\nI'm currently on the borderline, slightly leaning toward the positive side, thanks to the good results. My final decision will be adjusted based on the feedback from the authors and the discussion with other reviewers.\n\n** Typos **\n- L185: Eqn. 3 instead of Eqn. 2\n- SuppMat: Algo.1 - L7 & L12: Eqn. 3 instead of Eqn. 2\n\n========== Post-rebuttal\nI thank the authors for being active during the rebuttal and addressing all of my concerns. I'm happy to increase my score. - DAFormer (CVPR'22) is a recent work demonstrating great DA performance thanks to the robustness of transformer-based Segformer model. As the proposed strategy is agnostic to the model choice, I'm wondering to which extent one can push the performance by combining the proposed and DAFormer Limitation on training complexity is discussed in the supplementary material.\nNo discussion on potential negative societal impacts was given.", " This paper proposes a deliberated domain bridging (DDB) method for domain adaptative semantic segmentation, where the target labels are not available during the training. In DDB, there are two parts: 1) a dual-path domain bridging step to train two teacher models with two intermediated domains using the coarse-wise and fine-wise, i.e., region-level and semantic-level, data mixing techniques. 2) a cross-path knowledge distillation step to adaptively transfer the knowledge from the two teacher models to a student model. The two steps are repeated for several rounds for a good performance. Extensive experiments on both single-source domain and multi-source multi-target domain settings are conducted to validate DDB’s superiority. Pros:\n1. This paper proposes an effective method to significantly boost the UDA segmentation performance in various settings.\n2. The comprehensive ablations are done to clearly show 1) the complementarity between the two teacher models and 2) the effectiveness of the distillation step.\n\nCons:\n1. Since GTA5 to Cityscapes and GTA5 + Synscapes to Cityscapes are done, what is the performance in Synscapes to Cityscapes? This experiment shows which dataset contributes more to adapt to the real dataset.\n2. There are too many symbols, which makes the paper hard to follow. What do the numbers righter after the approach name in Tables 2, 3, and 4 mean? For example, ADVENT(19), BDL (19), FADA(20), etc.\n3. The authors claim that soft distillation and hard distillation are compared in Table 5. However, the ‘soft distillation’ choice and the explanation are missing in that table, which is a bit confusing.\n4. DDB requires two rounds for a good convergence. In each round, it needs to train three individual models and calculate two groups of category centroids by scanning the target training set for two teacher models respectively. This makes the approach cumbersome and may require more training time than others. The authors are encouraged to discuss the above issue with detailed analysis. Besides, this cumbersome training process seems in conflict with the stated ‘elegant’ method.\n5. The following paper can be included for comparison since it also studies the data mixing technique in UDA semantic segmentation. Besides, the difference between DACS which also utilizes the data mixing technique in UDA is not well stated in the paper.\n\nDsp: Dual soft-paste for unsupervised domain adaptive semantic segmentation. Proceedings of the 29th ACM International Conference on Multimedia. 2021: 2825-2833.\n See the weakness. The authors discuss the limitations of this paper in the supplementary material. No negative social impact has been discussed. ", " This paper is about unsupervised domain adaptation for the task of semantic segmentation. The paper argues for the importance of gradually bridging the domain gap, instead of a direct attempt to transfer a model from the source to the target domain. Motivated by an empirical analysis about different data mixing technologies, the paper explores two region-based mixing strategies (coarse regions and finer class-wise/mask regions) as domain bridges. Specifically, two models are trained on the two different domain bridges (Dual-Path-Domain-Bridge), which act as ensembled supervision for a single student model (Cross-path knowledge distillation). This student model can then initialize the teacher models for another round of these two steps. Experimental results in three different settings confirm the effectiveness of the proposed approach with state-of-the-art results on standard benchmarks. ### Strengths\n- The ablation studies in Tables 5-7 are great and showcase the impact of individual components\n- The results are impressive, with a clear improvement on the standard benchmark (GTA5->CityScapes), as well as other settings (multi-source and multi-target)\n- The experiments in Table 1 are a good motivation for the choice of data mixing strategies (CutMix and ClassMix)\n\n\n\n### Weaknesses\n\n- The writing, specifically the motivation and positioning with respect to prior work, needs improvement.\n - There may be alternative domain bridges than data mixing, like methods that rely on self-training and choose confident target pseudo labels as intermediate source domain.\n - The justification for exploring new domain bridges in lines 37-41 is vague and unclear: What are \"unexpected artifacts in the global input space\"? What \"optimization constraints\" are referred to?\n- I do not see why the paper only evaluates two domain bridging strategies in the ensemble. One could also include more. Relating to ensemble methods, one could expect improvements if an additional data mixing strategy is \"orthogonal\". One recent successful example for a global mixing strategy is [A] and could be easily integrated.\n- There is a related work on domain bridges for semantic segmentation that was not included: [B]\n- In line 185, shouldn't the reference go to Eq. 3?\n- I do not quite understand why the mixing weights in Eq. 11/12 help. Aren't the softmax values (i.e., scores) already an indication how far away a sample is from the decision boundary?\n- It would be good to point the reader to the supplemental material for a detailed description of the training strategy.\n- It's hard to understand and see details in Figure 1.\n\n\n**References:**\n- [A] FDA: Fourier Domain Adaptation for Semantic Segmentation. Yang and Soatto. CVPR'20\n- [B] Domain Bridge for Unpaired Image-to-Image Translation and Unsupervised Domain Adaptation. Pizzati et al. WACV'20 Please see few questions under \"weaknesses\" above Potential societal impacts are not discussed. I think a paper on domain adaptation should include a discussion about potential biases that are carried over from source domains (specifically because these are often synthetic data which often contains some hand-crafted components, like object sampling distributions, etc.)." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 5, 5, 4 ]

[ "k3syKxm9RuX", "dyiKmA2CW1Y", "8klHHtS5tua", "4E5vIhlxN9a", "P8M17nZVp6K", "09gg1dybTjl", "Z4kn0K_8PW0", "XGBHrBKHI0W", "nips_2022_ievxJqXwPCm", "Z4kn0K_8PW0", "Z4kn0K_8PW0", "1nA60WQ20v", "XGBHrBKHI0W", "zJHLKFA27ix", "nips_2022_ievxJqXwPCm", "nips_2022_ievxJqXwPCm", "nips_2022_ievxJqXwPCm", "nips_2022_ievxJqXwPCm" ]

[ "OB7l08-I05z", "LNx-kMEu9YC", "i0kQAfB5v8B", "_iVhwM0dPrF", "zm8tQTuah66", "DAl5FALoshn", "RdCbUWsRIbB", "SN1g22Q9_fM", "m69Da5QZDRK", "wDgSHSERWD" ]

[ "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I appreciate the authors' rebuttal. Since EG3D was indeed a concurrent work, I think it is fair to not consider it in this review. Hence I am leaning towards acceptance.", " Thank you, that answers my questions.", " Thank you for the quick reply to our rebuttal.\n\n1. Yes, exactly. We ran all methods using our implementation of the depth and pose metric, so results are mutually comparable. The evaluation of methods using our own implementation is also why our reported numbers for EG3D vary slightly from the numbers reported in their paper (Depth: 0.29(ours) vs 0.31 and Pose: 0.0018(ours) vs 0.005).\n\n2. Thanks for the comment, we will adjust the tone accordingly. Please note, however, that at date of submission, only arxiv preprints of the respective projects were available and no code was released, hence a direct comparison was not possible.\n\n3. Yes, after the submission deadline we found that at R_G=128^3 Minkowski’s sparse convolution provides no speed up over PyTorch’s dense convolution for our generator architecture. We did not train a model with R_G=256^3, though. Whether the sparse or dense implementation is faster does not only depend on the sparsity but also on the number of channels and on the resolution.\nWe hence believe that both, a variant using Minkowski’s sparse implementation and a variant with PyTorch’s dense implementation can be valuable to the community. We will discuss both implementations in the camera ready version and include both implementations in our code release.\nNote that this is only a change in implementation and using the dense implementation will not change that the generated grids are sparse, as we still have to prune them for efficient volume rendering.\n\n4. The purpose of the pose conditioning is to model biases in the training data. For example, in FFHQ people tend to smile with an open mouth more often when seen from the front than from the side. Hence, whether a person smiles with an open mouth is correlated to the camera pose in the training data. As this will also change the geometry, the density prediction is also conditioned on the pose. Another example is that children are photographed mostly from the front. Hence, we observe that conditioning our trained generator on a centered pose will often generate a child while conditioning on a camera pose on the side does not. This can also be seen in the pose conditioning ablation we added in the response to Reviewer eE7o (https://imgur.com/a/y7d4njy), where the middle row corresponds to the centered camera pose. For EG3D the reasoning for conditioning the generator is the same.\nWe will follow your suggestion and include a comparison for training without pose conditioning to the final version.", " I thank the authors for the rebuttal. It has largely answered all my concerns. I just want to ask some clarifying questions and also get some more insight into the issues raised by the other reviewers.\n\n1) The newly provided depth/pose numbers for the other methods were obtained by extracting their results and applying your own implementation of the metrics to all of them? I am just checking that they are mutually comparable.\n\n2) In the paper you strongly emphasize that EG3D and GRAM are concurrent works which I took for granted but after seeing the other reviews, I realized that CVPR papers were already accepted long before the NeurIPS submission. Perhaps it would be fitting to tone this down a bit. Also please update the references to include the venue instead of arxiv (that applies more broadly).\n\n3) Regarding the Minkowski convolution (Reviewer eE7o) - Do I understand it correctly that in the revised version you will only use dense convolutions for the 256^3 grid size? Does that mean that you tested Minkowski at R_G=256 and it does provide a performance benefit over dense convolution there? However, it provides no benefit at R_G=128 resolution? Can you please point me to the experiment with R_G > 128?\n\n4) Regarding the pose conditioning of the generator (Reviewer eE7o): I still do not see why is the generator conditioned by the pose. Why should the pose change the density distribution? I see a similar conditioning of the triplane in EG3D. Does this follow the same reasoning? Thank you for the test-time example figure. Is it possible to also provide a comparison of *training* with and without this feature in the final version (can be in the supplement)?\n", " Thank you for your constructive comments and valuable concerns.\n\n> For instance, L264 seem to suggest that EG3D is less view consistent than the proposed method but no such effect is shown.\n\nWe agree and will replace the statement with: \n“This is expected as the neural renderer adds flexibility while sacrificing 3D-consistency, see Fig. 4.” -> “This is expected as a neural renderer can add flexibility. But, as shown in Fig. 4, for StyleNeRF it reduces 3D-consistency.”\n\n> The authors also argue, that the advantage of their method is the possibility of faster rendering after the first frame (Table 3). However, the same could be said about EG3D as it also could precompute the StyleGAN representation and then just sample the features the same way the new paper does. \n\nWe agree that this is possible but remark that EG3D still needs to densely query the 3D representation. For caching the tri-plane features, EG3D reports a speed up from 27FPS to 36FPS at resolution 256^2 (Table 3 in their paper). Instead, our approach only queries 3D space sparsely which allows rendering at 167FPS.\n\n> There are no quantitative experiments done to validate the claim of better geometry and 3D consistency (L74). The authors could also attempt to measure depth and pose accuracy as done in previous work [4]. Since there is still a small CNN used for the image refinement it does not seem obvious that the method is perfectly view consistent.\n\nThe code for computing the metrics in [4] is not publicly available. For this rebuttal, we implemented our own version of the depth and pose metric following the description in [4]. Below, we report the results for our approach, GRAM, StyleNeRF and EG3d for reference. We also report the standard deviation across the 1024 samples used for evaluation. While the results agree with our qualitative analysis of view consistency in Figure 4 and the supplementary video, we find that both metrics are very sensitive to the latent code and the sampled poses, as indicated by the large standard deviations. As no established evaluation pipeline exists, our results should not be directly compared to the numbers in [4] as the implementation and pose sampling might differ. We will add this experiment to the supplementary.\n| | Depth ↓ | Pose ↓ |\n|-----------|-----------------|---------------------------|\n| StyleNeRF | -- | 0.051 ± 0.047 |\n| GRAM | 0.48 ± 0.24 | 0.013 ± 0.013 |\n| EG3D | 0.29 ± 0.30 | 0.0018 ± 0.0031 |\n| VoxGRAF | 0.33 ± 0.23 | 0.00045 ± 0.00079 |\nNote that for StyleNeRF depth can only be rendered at resolution 32^2 and we thus omit evaluating the Depth metric for it.\n\n> The authors only ablate the loss L_DV and only in terms of sparsity. Neither of the losses that are used for regularization (there are 4 in total) is evaluated in terms of end-to-end performance impact.\n\nWe ablate the performance of all four regularizers below on models trained on FFHQ with R_I=128 and R_G=64. The regularizers do not significantly impact end-to-end performance measured in FID but help to stabilize training (L.208). We will add this ablation to the supplementary. \n| | FID |\n|---------------------------------------|------|\n| full | 14.2 |\n| w/o L_DV | 14.8 |\n| w/o L _TV | 15.1 |\n| w/o L_cvg^fg | 14.6 |\n| w/o L_cvg^bg | 14.8 |\n\n> The training is extremely costly even compared to MLP-based NeRF GANs (L224).\n\nOur method’s training time (3-8d) is comparable to EG3D (8.5d), StyleNeRF(3d) and GRAM (3-7d), all reported on 8 Tesla V100 GPUs.\n> If voxels are pruned based on visibility in \"a\" rendered view (L167), cannot they be later missing after occlusion changes due to a new viewpoint at test time?\n\nWe only prune voxels based on the rendered view for training. At inference, we prune voxels solely based on their density to amortize the rendering costs per scene. We find that this does not visibly affect the rendered images. We will clarify this in the paper.\n", " Thank you for reading and reviewing our work. We appreciate your feedback and address your concerns below.\n\n> Why is this approach better than EG3D [4]? (...) Quantitative comparisons that author report seem to be aligned with this, and qualitative experiments are not showed (I would encourage authors to report those). \n\nWe remark that [4] was developed concurrently to our work and at the time of submission no code of [4] was publicly available. We contacted the authors beforehand, but unfortunately we could not get access to preliminary code. Hence, it was not possible to add [4] to the qualitative comparisons in the paper but we added quantitative results from [4] to compare with them to the best of our abilities.\n\n> I'd like authors to convince me that this paper introduces some different capability compared to [4] or that they solve the problem better. In the current form, I do not think the paper is doing a good job at convincing the reader that this method is pushing the state of art.\n\n- In contrast to [4] our model learns to disentangle background and foreground. This can be useful for many downstream applications, e.g. to integrate generated assets into new environments.\t\n- One major limitation of [4] is the slow volume rendering because querying 3D space densely is prohibitively costly (L.48). E.g. in [4] it is stated that increasing the rendering resolution from 64^2 to 128^2 (while keeping the remaining architecture fixed) almost doubles the time to train on 1000 images from 24s to 46s. In contrast, our approach queries 3D space sparsely which makes volume rendering more efficient. \n- Due to EG3D’s slow volume rendering, [4] relies on a neural render (2D CNN) to synthesize images which may entangle viewpoint and 3D content (L.35) and requires additional regularization to reduce this effect. Instead, our approach generates a sparse representation that can be rendered efficiently without a neural renderer.\nWe argue that generating 3D content at high resolution directly is desirable for many downstream applications, e.g. for integrating assets into physics engines (L.53). Our approach improves image fidelity over state-of-the-art methods without neural rendering and reduces the gap to models that build heavily on neural rendering (Table2, L.285). \n- Sparse voxel grids further allow to amortize the rendering costs per scene, s.t. our approach can render novel views of a generated instance at 167FPS at image resolution 256^2. We remark that [4] can cache the tri-plane features, i.e. the first part of the forward pass. As shown in [4], this increases rendering speed from 27FPS to 36FPS while being run on faster hardware than our model. \n\nWe would like to reiterate that at date of submission no code of [4] was publicly available and hence an in-depth comparison was not possible. We compared to the best of our abilities by including quantitative results from their paper in our work. We hope that our arguments are able to resolve your concerns.", " Thank you for the valuable comments and feedback. \n> My main critique is around the description of viewpoint dependence. Plenoxels stores spherical harmonic coefficients in the voxels, while the proposed method seems to store RGB values without directional dependence (Eq. 3.). This is a quite significant departure from other NeRF-inspired representations, and should be made more explicit in the discussion of the method (Section 3.1).\n\nOur 3D generator is conditioned on the pose and thereby contains directional dependence. We will clarify this in L.156 by adding:\n“Note that in contrast to most existing coordinate-based 3D-aware GANs, see Eq. 1, we do not condition the 3D generator on the view direction (per-ray). Instead, we follow [4] and condition it on the pose ξ (per-image) to model directional dependencies.“\n\n> It is somewhat surprising that the foreground generator is conditioned on the camera pose ξ since the volumetric grid can be rendered from arbitrary viewpoints ξ′ ,even those that it was not conditioned on. Could the authors clarify for which results in the paper ξ=ξ′ ? Would it be a viable ablation to compare two animated sequences, one with ξ=ξ′ at each frame, and one where the generator was invoked only once?\n\nWe sample the camera pose for conditioning ξ randomly for all results in the paper, i.e. ξ is in general different from ξ′ for all shown results. The suggested ablation is indeed interesting. The results provided via the link below illustrate that the pose conditioning is not only used to model slight changes, e.g. of the eyes or the smile, but can alter the general appearance of the generated instance. However, by fixing the pose conditioning during inference, view-consistent images can be generated. We will add this ablation to the supplementary. \n\nhttps://imgur.com/a/y7d4njy \n\nFigure 1: Effect of pose conditioning. From left to right we vary the pose used for rendering ξ′ and from top to bottom we vary the pose used for conditioning ξ. All samples are generated using the same latent z.\n\n> What is the speedup gained from using sparse convolutions at grid sizes > 32^3?\n\nAfter the submission deadline we realized that for our generator with voxel grids up to resolution 128^3, the sparse convolution implementation of the Minkowski library does not provide significant gains over PyTorch’s dense convolution (memory is slightly reduced but runtime increases). We will therefore add another variant of our generator to the camera ready version that replaces Minkowki’s sparse convolution with PyTorch’s dense convolution. Note that changing the implementation of the convolution operation will not change the sparsity of the generated voxel grids. A sparse representation remains key for fast volume rendering and can still only be obtained by pruning the grid based on the output of the previous resolution. Hence, the pruning operator ρ and the progressive growing of the model remain unchanged. We will add this ablation to Table 1 as changing the convolution implementation will mainly reduce the runtime for the generator forward pass t_G^fg+bg while it might slightly increase memory. We will further include a comparison on FID but expect that the results will be similar for both models as the computation itself does not change.\nLastly, we remark that in initial experiments we indeed found Minkowski’s sparse convolution advantageous for runtime and memory. While changes to the generator architecture (e.g. lower channel dimension at higher resolution) neutralized these benefits, future work might still profit from sparse convolutions when going to larger grid resolutions and larger scenes. Hence, we consider both variants interesting to the reader and we will release our source code including both variants.", " The paper introduces a 3D-aware image generation network that usess a Plenoxels-style voxel grid [1] as its scene representation. The complete network architecture consists of a sparse 3D CNN generator with novel upsampling layers that ensure sparsity of the upsampled densities. The full resolution voxel grid has size $128^3$ and stores RGB+density values for the occupied voxels. \n\nIn a parallel branch, there is a 2D GAN (following StyleGAN v2) that generates the scene background.\n\nThe sparse voxel grid is rendered at the required output resolutoin using conventional volume rendering techniques. The foreground is post-processed by a shallow (two hidden layers) refinement CNN, whose output is then composited on the the background image. \n\nAt training time, the resulting image is passed to a discriminator based on StyleGAN2. The authors describe several regularizing losses, including a novel sparsity term on the voxel densities.\n\nThe authors report both quantitative and qualitative comparisons to state-of-the-art 3d-aware GANs and demonstrate results that demonstrate a high degree of geometric consistency across viewpoints. \n\n[1] Yu et al. Plenoxels: Radiance Fields without Neural Networks. 2022 This is a strong paper with an original technical contribution in the sparse CNN generator and the use of a sparse RGB-density voxel grid as the representation for a 3D-aware GAN. The voxel visualizations in the paper, as well as the animated sequences in the supplemental video, demonstrate the geometric plausibility of the generated representations.\n\nThe paper is very well written and the discussion of related works is thorough. The comparisons to related work are quite comprehensive, and a key ablation study is included.\n\nA particularly exciting aspect of the method is the very fast rendering times (after a slower initial generation of the voxel grid), which could allow this technique to run at interactive framerates on low-powered platforms.\n\n\n--\n\nEven though the results exhibit high geometric consistency, the visual quality of the generated still frames does not quite match that of some other methods. This limitation is acknowledged in the paper.\n\nMy main critique is around the description of viewpoint dependence. Plenoxels stores spherical harmonic coefficients in the voxels, while the proposed method seems to store RGB values without directional dependence (Eq. 3.). This is a quite significant departure from other NeRF-inspired representations, and should be made more explicit in the discussion of the method (Section 3.1).\n\nIt is somewhat surprising that the foreground generator is conditioned on the camera pose $\\xi$, since the volumetric grid can be rendered from arbitrary viewpoints $\\xi'$, even those that it was not conditioned on. Could the authors clarify for which results in the paper $\\xi = \\xi'$ ? Would it be a viable ablation to compare two animated sequences, one with $\\xi = \\xi'$ at each frame, and one where the generator was invoked only once?\n - See previous section for questions about voxel & generator view dependence.\n - What is the speedup gained from using sparse convolutions at grid sizes > $32^3$? The authors are clear about the limitations of their work. Societal impacts are adequately discussed.", " Authors propose an approach to generate high quality images from a latent code that are multi-view consistent. The intuition is to replace the MLP that is used to parameterized radiance fields, with a hybrid approach that relies on sparse 3D convolutions to speed up the rendering time. Additionally, they propose a way to disentangle the foreground and background. ++ Relevant problem for the community. Generating high quality renderings with an adversarial approach is an unsolved problem despite the recent progress\n\n++ Clarity: the paper is overall clear, authors put lots of effort to describe every details of the approach. They sufficiently discuss limitations and ethical concerns.\n\n\n-- Novelty, Contributions and Experiments. Whereas the general idea is interesting, the first thing that comes to mind once reading this paper is: why is this approach better than EG3D [4]? Indeed, they tackle the same problem and I would argue that the results of EG3D are actually better. Quantitative comparisons that author report seem to be aligned with this, and qualitative experiments are not showed (I would encourage authors to report those). According to authors, the main difference between their approach is explained at l142-l143, which is \"In contrast to recent works, we do not use a coordinate-based MLP..\". While this is true, it is not demonstrated that the proposed method is actually better. The main question is around novelty and experiments/comparisons. I'd like authors to convince me that this paper introduces some different capability compared to [4] or that they solve the problem better. In the current form, I do not think the paper is doing a good job at convincing the reader that this method is pushing the state of art.\n\n---\nPost rebuttal: Authors made the fair point that [4] was concurrent work and there was no code release at the time of the submission. Hence I am leaning towards acceptance. Yes, discussed.", " The paper proposes a novel 3D GAN architecture for rendering of 3D consistent objects supervised by collection of single-view images. The key innovation is the introduction of sparse voxel grid as a more computationally efficient representation when compared to the most commonly used MLPs. The authors describe how sparsity is enforced and used to reduce memory constraints of their approach. As a result, they can render medium-sized images from their voxel grid directly without need to explicit upsampling. The validation shows the method produces better images at lower computation cost than previous work and it is in some respects competitive with more recent methods published in parallel. \n[Originality] \n\n1) The method combines an established concept of NeRF-based 3D-GAN with previously described sparse voxel convolutions. The authors further describe several key tricks that are required for successful and efficient training. Many of them are inspired by similar work, but at least the loss L_D seems unique to this publication. Overall, the technical contribution is incremental but, nevertheless, it leads to a significant improvement upon SOTA in the target application (here I ignore the parallel work).\n\n\n[Clarity]\n\n2) The exposition is very clear, easy to read and I have not discovered many typos or grammar issues.\n\n3) I find problematic the way how parallel work is discussed. GRAM, StyleNERF, and EG3D are all parallel work so they do not count against contributions of this paper. I appreciate that the authors tacked the task of discussing their properties and that they included them in their result tables. However, I am not entirely sure all conclusions that they have made are fully substantiated. For instance, L264 seem to suggest that EG3D is less view consistent than the proposed method but no such effect is shown. Both methods use internal 128px representation for the radiance field and therefore, any further processing increasing the output image resolution is in principle similar for both. The authors also argue, that the advantage of their method is the possibility of faster rendering after the first frame (Table 3). However, the same could be said about EG3D as it also could precompute the StyleGAN representation and then just sample the features the same way the new paper does. In general, I find these over-extended assumptions about parallel work both not properly validated and also unnecessary. As these work are not counted as a previous work, there is no need to prove that the new method is in all or any respects better. The authors should rather focus on properties of their own work and show why it is excellent. Since the general architecture and performance appears quite similar, focusing on the possibilities of the explicit voxel representation seem like a clear goal.\n\n[Validation]\n\n4) The method is evaluated on common datasets and the results are clearly better than previous work and comparable to parallel work. The results are limited to 256px resolution with is also comparable to recent methods.\n\n5) There are no quantitative experiments done to validate the claim of better geometry and 3D consistency (L74). The authors could also attempt to measure depth and pose accuracy as done in previous work [4]. Since there is still a small CNN used for the image refinement it does not seem obvious that the method is perfectly view consistent.\n\n6) The extracted shapes appear quite noisy (Fig. 5). \n\n7) The authors only ablate the loss L_DV and only in terms of sparsity. Neither of the losses that are used for regularization (there are 4 in total) is evaluated in terms of end-to-end performance impact.\n\n8) The training is extremely costly even compared to MLP-based NeRF GANs (L224).\n\n\n[Significance]\n\n9) The paper tackles a relevant problem of 3D representation generation and it does take a path distinct from other work. While it is not clear whether the method actually is clearly better than some of the parallel work, it does clearly beat the previous baselines. The voxel representation may have practical benefits that have not been mentioned in the paper. E.g. I can imagine that they would be easier to edit in a 3D modeler. However, no such application has been shown.\n\n\n[Conclusion]\n\n10) While I see some issues with the exposition, the paper is of a high quality overall. The discussion of the performance and relation to other work can be addressed. The bigger concern is the small scope of the validation. While the most critical image synthesis quality is directly evaluated on common datasets, this leads to a total of three numbers reported in Table 2. The 3D consistency, design ablation (with exception of Table 1) and the shape quality are not directly validated in a quantifiable way. That being said, I do not suspect such experiments to significantly change the narrative of the paper so I am still inclined towards acceptance, especially if the authors can improve upon these aspects in the final version. 11) If voxels are pruned based on visibility in \"a\" rendered view (L167), cannot they be later missing after occlusion changes due to a new viewpoint at test time?\n 12) The authors have mentioned the performance may drop is scene is more complex and pruning is not very effective. Other limitations I suspect is the lack of geometric smoothness in extracted shapes and the high training cost.\n" ]

[ -1, -1, -1, -1, -1, -1, -1, 7, 5, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, 3, 3, 4 ]

[ "DAl5FALoshn", "i0kQAfB5v8B", "_iVhwM0dPrF", "zm8tQTuah66", "wDgSHSERWD", "m69Da5QZDRK", "SN1g22Q9_fM", "nips_2022_b90lKL1IqcF", "nips_2022_b90lKL1IqcF", "nips_2022_b90lKL1IqcF" ]

[ "gOOsAF-QGqW", "F4KkKZoj_c8", "KmjoCIUlrRB", "YofjfiVCGC", "UUgQMTrE09", "uWuHy7Yyt4b", "xGXPrMNETeV", "kcIJRR1PDjc", "6DfniVRuul", "HepkOcAvaKm", "TprsIrA-39z", "_IHQtBWS3ea", "_641aCNHdXyv", "r_HRB09L0IO", "3YHve2Bhba", "6hPPTS2l8_r", "ntFxVSpE46", "CsKmDmOKQB", "K5SSEQ2npkb", "PNsOETJ6aGv", "1FKNgKnON92", "VmA3nJ7c9M-", "hbowoeqlnbq", "j852NMggfwv", "6XRVVcN3_ZB", "Z27T25YoQdA", "VzjEgWVanXS", "nvOE5jXoIR6", "Lg5AqAG0VoI" ]

[ "author", "author", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank all reviewers and area chairs for their valuable time and comments. After discussing with reviewers and providing more clarifications/results/analyses, we would like to give a brief response.\n\nReviewer mWKh (denoted as R1), Reviewer LKyp (denoted as R3), and Reviewer J9TR (denoted as R4) all hold a **positive** side for our work. Our responses have covered their questions.\n\nAlthough Reviewer RMwD (denoted as R2) gives a negative score in the first round, R2 upgrades his rating and approves our new experiments after the rebuttal. For further concerns of R2, we find that all those concerns have been well addressed in our rebuttal and the main paper. R2 can easily find the corresponding responses.\n\nThe source code and related pretrained models have been provided in supplementary file and anonymous site. We will also make all of them public soon!\n\nWe thank all reviewers and area chairs again!\n\nBest,\n\nAuthors", " `Diss-Q2-1:` *Sorry for the late. But I have to say that the openreivew system is very unfriendly for reviewers. I spent lots of time to find a way to access my comments and make a response.* \n\n`Diss-A2-1:` Thanks for spending time familiarizing the use of the openreview system and responding to our discussions.\n\n\n\n`Diss-Q2-2:` *Thanks for author's response. I see that authors provided multiple additional experiments to support their contribution.*\n\n`Diss-A2-2:` Thanks for reading the experiments we did in our rebuttal. And thanks for recognizing these work for supporting our contributions.\n\n\n\n`Diss-Q2-3:` *However, I still concern about the novelty and the significance of this work. Compared to Swin Transformer, the major contribution of this work should be a newly proposed window shifting mechanism for image restoration.*\n\n`Diss-A2-3:` **For \"the major contribution\"**. In addition to a newly proposed window shifting mechanism, there are other innovations and contributions. We have responded to some **similar** questions, like `Q1-2`, `Q2-1`, and `Q3-4`. You can refer to `A1-2`, `A2-1`, and `A3-4`. However, we still list more specifics here.\n\nA novelty self-attention mechanism: rectangle window self-attention (**Rwin-SA**) and locality complementary module (**LCM**). \n\nCompared to Swin Transformer, the above three designs are equally important for image restoration. We demonstrate the effect of three components in our **ablation study**.\n\nWe also show them here (**Table 1(a) and Table 1(b) in the main paper**). Output size is 3$\\times$256$\\times$256 to calculate FLOPs.\n\n| Network | PSNR | SSIM | FLOPs |\n| ------------------------- | :-------: | :--------: | :----: |\n| Square w/o shift | 32.50 | 0.9325 | 281.8G |\n| Square w/ shift | 32.75 | 0.9347 | 281.8G |\n| Rectangle w/o axial-shift | **32.66** | **0.9334** | 281.8G |\n| Rectangle w/ axial-shift | **32.91** | **0.9360** | 281.8G |\n\n**(1)** Under **the same complexity**, Rwin-SA outperforms the square window attention (local window in Swin Transformer). Moreover, with axial-shift, our method obtains **0.16 dB** gain over the square window with shift operation in Swin Transformer.\n\n| Network | PSNR | SSIM | FLOPs |\n| ------------- | :-------: | :--------: | :----: |\n| CAT-R w/o LCM | 32.91 | 0.9360 | 281.8G |\n| CAT-R w/ LCM | **32.98** | **0.9361** | 282.7G |\n| CAT-A w/o LCM | 33.01 | 0.9354 | 349.7G |\n| CAT-A w/o LCM | **33.11** | **0.9363** | 350.6G |\n\n**(2)** The LCM module achieves a performance improvement while slightly increasing the model complexity.\n\n\n\n`Diss-Q2-4:` *Basing on the comparison to SwinIR, it's hard to say the performance gains are brought by the proposed mechanism or the increases of parameters and Flops. However I think this version deserves a borderline score.*\n\n`Diss-A2-4:` **For \"the comparison to SwinIR\"**. We have responded to this question in `Q1-1`, `Q3-1`, and `Q4-2`. You can refer to `A1-1`, `A3-1`, and `A4-2`. However, we still list the specifics here.\n\nWe provide a comparison of similar model sizes and FLOPs in **supplementary material** Table 2. And we have merged the results (**CAT-R-2**) into **Table 4** in the main paper. We also show them here. Output size is 3$\\times$512$\\times$512 to calculate FLOPs.\n\n| Method | Params (M) | FLOPs (G) | Set5 | Set14 | B100 | Urban100 | Manga109 |\n| ------- | :--------: | :-------: | :-------: | :-------: | :-------: | :-------: | :-------: |\n| SwinIR | 11.90 | 215.3 | **32.92** | 29.09 | 27.92 | 27.45 | 32.03 |\n| CAT-R-2 | 11.93 | 216.3 | 32.91 | **29.13** | **27.93** | **27.59** | **32.16** |\n\n| Method | EDSR | RCAN | HAN | CSNLN | SwinIR | CAT-R (ours) | CAT-A (ours) | CAT-R-2 (ours) |\n| -------------- | :---: | :---: | :---: | :------: | :----: | :----------: | :----------: | :------------: |\n| PSNR (dB) | 26.64 | 26.82 | 26.85 | 27.22 | 27.45 | 27.62 | 27.89 | **27.59** |\n| FLOPs (G) | 823.3 | 261.0 | 269.1 | 84,155.2 | 215,3 | 292.7 | 360.7 | 216.3 |\n| Parameters (M) | 43.09 | 15.59 | 16.07 | 6.57 | 11.90 | 16.60 | 16.60 | 11.93 |\n\nOur CAT-R-2 obtains a similar model size, FLOPs with SwinIR but obtains better performance. Therefore, the performance gains come from our proposed methods.\n\n\n\n**Please let us know if you have any unsolved or other concerns. Thanks.**", " Sorry for the late. But I have to say that the openreivew system is very unfriendly for reviewers. I spent lots of time to find a way to access my comments and make a response.\nThanks for author's response. I see that authors provided multiple additional experiments to support their contribution. \nHowever, I still concern about the novelty and the significance of this work.\nCompared to Swin Transformer, the major contribution of this work should be a newly proposed window shifting mechanism for image restoration. \nBasing on the comparison to SwinIR, it's hard to say the performance gains are brought by the proposed mechanism or the increases of parameters and Flops.\nHowever I think this version deserves a borderline score. ", " Dear Reviewer **RMwD**,\n\nIn the discussion period, **all other three reviewers** have discussed with us and admitted that we have **addressed their concerns** well. \n\nWe have sent you **several calls for discussions**. But, you still have not responded to us.\n\nWe believe it is **professional** to participate in the discussion before the ending date **August 9**. \n\n**Could you please provide your feedback?** Thanks.\n\nBest,\n\nAuthors", " Dear Reviewer RMwD ,\n\n\nThanks again for your precious time and valuable comments.\n\n\nAfter rebuttal, Reviewer mWKh (denoted as R1), Reviewer LKyp (denoted as R3), and Reviewer J9TR (denoted as R4) now agree that our response solves their concerns. The concerns include several points as follows.\n\n**(1)** The differences between **axial-shift and shift operation** in Swin Transformer.\n\n**(2)** The differences between CAT (or axial-Rwin) and **CSwin**.\n\n**(3)** Apply our CAT to other image restoration tasks, and compare with more methods (e.g., **Uformer and Restormer**). \n\n\n\nAre there any deficiencies in our rebuttal? Whether the corresponding responses and results we provide cover your concerns? The discussion period ending date is **August 9**. Please let us know if you have any unsolved or other concerns. Thanks.\n\n\n\nBest,\n\nAuthors", " Thanks for the rebuttal. The authors provide the results of CAT applied for real image denoising, where the proposed CAT still performs comparable to or better than recent methods, like CVPR2022 papers: Uformer and Restormer. Other responses (e.g., fair comparisons with similar model size, discussions with CSWin). I have also checked the updated paper and found that the corresponding parts have been revised well. I am satisfied with the rebuttal, which has addressed all my concerns. I keep my original rating as strong accept.", " Thanks for providing very detailed feedback with extensive experiments and explanations. All my concerns have been well addressed. The authors provided the real image denoising comparisons with CVPR’22 papers and still achieved good performance. I notice that the authors started to adopt their method for real image denoising and updated their results/logs/models during the discussion period, which convinced me a lot!\n\nI also read the comments from other reviewers. The new experiments in the rebuttal make the paper more solid. So, I would like to keep my original rating and recommend acceptance. ", " Thanks for providing so-detailed responses including extensive experiments. My concerns have been well addressed as follows.\n\n(1) For fair comparisons with similar model size and FLOPs, I am satisfied with the provided results.\n\n(2) For other image restoration tasks, I appreciate that the authors provide real denoising results and compare with recent works, like Uformer and Restormer. The proposed CAT achieves good results.\n\n(3) The authors also compared with CSWin and discuss the differences with shift operation in Swin Transformer.\n\nI also read other reviewers comments and the corresponding responses carefully. The authors provide training log and models in supplementary file, which makes the work more solid. So, I would like to upgrade my rating and vote for acceptance.", " Dear Reviewer J9TR ,\n\nThanks for your valuable time and comments. We have responded to the related questions.\n\n\n\n**(1)** We modify the caption of **Fig. 3** in the main paper.\n\n**(2)** We provide **a variant CAT** of similar model size and FLOPs in supplementary material and merge the result into **Table 4** in the main paper.\n\n**(3)** We show **the model size and FLOPs** of CAT for JPEG compression artifact reduction.\n\n**(4)** We provide analysis and experiments to show the differences between the key ideas of our work (e.g., axial-Rwin) and **CSwin**.\n\n**(5)** Finally, we apply our method to **real Image Denoising**. The performance of our CAT is **comparable to or better** than other methods (**MIRNet, Uformer, and Restormer**).\n\n\n\nPlease let us know if you have any unsolved or other concerns. Then, we have enough time to provide further feedback. Thanks.\n\nBest,\n\nAuthors", " Dear Reviewer LKyp ,\n\nThanks for your valuable time and comments. We have responded to the related questions.\n\n\n\n**(1)** We merge the result (CAT-R-2) into **Table 4** in the main paper.\n\n**(2)** We explain the **small improvement** in quantitative results for JPEG artifact reduction.\n\n**(3)** We clarify the **pipeline** for JPEG artifact reduction and provide the **pseudo-code** of the reconstruction module.\n\n**(4)** We clarify the differences between **axial-shift and shift operation** in Swin Transformer.\n\n**(5)** Finally, we apply our method to **real Image Denoising**. The performance of our CAT is **comparable to or better** than other methods (**MIRNet, Uformer, and Restormer**).\n\n\n\nPlease let us know if you have any unsolved or other concerns. Then, we have enough time to provide further feedback. Thanks.\n\nBest,\n\nAuthors\n\n", " Dear Reviewer RMwD ,\n\nThanks for your valuable time and comments. We have responded to the related questions.\n\n**(1)** We explain our **contribution and novelty**, including analysis and experiments to demonstrate the differences between axial-Rwin and **CSwin**. Furthermore, we analyze the difference between axial-shift and shift operations in Swin Transformer.\n\n**(2)** We discuss more existing Transformer methods and modify the **related work** in the main paper.\n\n**(3)** We compare our method with **Uformer and Restormer** on real image denoising. The **comparable or better performance** of our CAT demonstrates the superiority of our method.\n\n**(4)** Finally, we experiment on **color JPEG compression artifact reduction**, and our method **outperforms SwinIR**.\n\nPlease let us know if you have any unsolved or other concerns. Then, we have enough time to provide further feedback. Thanks.\n\nBest,\n\nAuthors", " Dear Reviewer mWKh ,\n\nThanks for your valuable time and comments. We have responded to the related questions.\n\n\n\n**(1)** We provide **a variant CAT** of similar model size and FLOPs in supplementary material and merge the result into **Table 4** in the main paper.\n\n**(2)** We clarify the differences between **axial-shift and shift operation** in Swin Transformer.\n\n**(3)** We explain the **small improvement** for JPEG artifact reduction.\n\n**(4)** We apply our method to **real Image Denoising**. The performance of our CAT is **comparable to or better** than other methods (**MIRNet, Uformer, and Restormer**).\n\n**(5)** Finally, we provide analysis and experiments to show the differences between our CAT and **CSwin**.\n\n\n\nPlease let us know if you have any unsolved or other concerns. Then, we have enough time to provide further feedback. Thanks.\n\nBest,\n\nAuthors", " `Q1-6:` Please tell the differences between CAT and CSwin [10].\n\n`A1-6:` The main differences can be summarized into two points.\n\n**(1)** Axial-Rwin is inspired by CSwin and is close to CSwin in form, but it is only a special case of our proposed rectangle window self-attention. Regular-Rwin we proposed is a more general form and more flexible. In other words, the attention mechanism in CSwin is a special case proposed in our paper.\n\n**(2)** We also propose two operations: axial-shift and LCM module, to enhance Rwin-SA. \n\nWe compare the differences between CAT (CAT-A, CAT-R) and CSwin in the following table. And replace our Cross Aggregation Transformer Block with CSWin Transformer Block proposed by CSwin in the CAT model to form a Transformer model. The implementation of CSwin is consistent with CAT-A. We train and test on image SR (×2). FLOPs are measured when the output size is set to 3×256×256, and PSNR values are tested on Urban100 (×2).\n\n| Method | attention mechanism | shift operation | LCM | Parameters | FLOPs | PSNR |\n| ------ | :---------------------------------------: | :-------------: | :--: | :--------: | :-------: | :-------: |\n| CSwin | cross-shaped window self-sttention | x | x | 16.45M | 350.7 | 33.73 |\n| CAT-A | (axial) rectangle-window self-attention | √ | √ | 16.46M | **350.7** | **34.26** |\n| CAT-R | (regular) rectangle-window self-attention | √ | √ | 16.46M | **282.7** | **34.08** |\n\nWe can see that the method we proposed is more suitable for image restoration tasks than CSwin.", " We thank all reviewers for their valuable time and comments. Based on the comments of four reviewers, we have modified the main paper and added additional experiments and analyses in the supplementary material.\n\n**For the main paper.** \n\n1. We add the inspiration of CSwin for axial-Rwin in introduciton and method. \n2. We discuss more Transformers in related work, including CSwin and Uformer. \n3. We add a more reasonable comparison in model size analyses.\n\n**Note:** In the latest submitted paper, the modifications are marked in blue font.\n\n\n\n**For the supplementary material.**\n\n1. Experiment on real image denoising.\n2. Experiment on color JPEG compression artifact reduction.\n3. Other numerical results, including the comparison between CSwin and CAT.\n4. Analysis of difference between axial-shift and shift operation in Swin Transformer.\n\n", " `Q2-7:` In related work, the discussion of the existing tranformer methods is insufficient, and the author should analyze CSWin and Uformer.\n\n`A2-7:` Thanks for pointing it out. We further analyze CSWin and Uformer and add this part to related work.\n\n**CSWin** computes self-attention in the horizontal and vertical stripes in parallel. The parallel strategy can enlarge the receptive area without introducing additional computational costs. However, the width of the stripes is crucial for the receptive field. Small width limits the receptive field, thus affecting the performance of the model. However, increasing the stripe width increases the computational complexity, which is not conducive to model application. This problem comes from the lack of interaction between the stripes, which limits the growth of the receptive field.\n\nIn addition, The **Uformer** [ref4] model is also proposed in image restoration, using U-Net structure and local window attention. It also adds depthwise convolution in feed-forward network (FFN). But it is limited by the lack of direct interaction between windows.\n\nWe also discuss other Transformer methods further. **CeiT** uses convolution operations in token embedding and FFN to enhance Transformer locality. **Focal** incorporates both fine-grained local and coarse-grained global interactions. For a discussion of other Transformer methods, **please refer to `A2-2`**.\n\n\n\n`Q2-8:` More experiments on color JPEG image restoration should be conducted.\n\n`A2-8:` Thanks for suggesting applying our method to color JPEG image restoration. We apply our CAT and SwinIR to **color JPEG compression artifact reduction** with JPEG compression qualities of 40. We train on DIV2K, Flickr2K, BSD500, and WED. And we have four testing datasets: Set5, Set14, LIVE1, and Urban100, with JPEG compression qualities of 40. We compare our CAT with SwinIR.\n\nDue to time issues, we only completed part of the training (fininshed iterations = 200K, target total iterations = 1600K) for both CAT and SwinIR. But under the same training conditions, our CAT outperforms SwinIR on all datasets. Quantitative comparisons are shown in the following table.\n\n| Method | Set5 | | Set14 | | LIVE1 | | Urban100 | |\n| ------ | :-------: | :--------: | :-------: | :--------: | :-------: | :--------: | :-------: | :--------: |\n| | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM | PSNR | SSIM |\n| SwinIR | 37.44 | 0.9487 | 35.74 | 0.9319 | 35.01 | 0.9370 | 35.42 | 0.9520 |\n| CAT | **37.51** | **0.9491** | **35.87** | **0.9326** | **35.11** | **0.9380** | **35.76** | **0.9536** |\n\nWe have added this part to the supplementary material and provided more comparative results. Please refer to **Sec. 4.2** in the **supplementary material** for details.\n\n", " `Q2-4:` In Swin Transformer [19], Hu et al. proposed a shifted window operation, whose shifting directions include horizontal and vertical, and the shifting range of each direction is [0, k], where k is the size of the window. In this paper, author proposes a axial-shift (the horizontal one is called H-shift and the vertical one is called V-shift) operation for Rwin-SA, whose shifting range is set as sh/2 and sw/2, where sh and sw are the size of the rectangle window. The difference between shifted window operation [19] and axial-shift operation is caused by the shape of the window, so I personally think axial-shift and shifted window operation [19] are the same. Please explain in more detail the difference between V-shift and H-shift, and the difference between axial-shift and shifted window operation [19].\n\n`A2-4:` Thanks for your question. We clarify them as follows.\n\n**For \"the difference between V-shift and H-shift\".** For V-shift and H-shift, the implementation is the same, but the shift distance is different. In a special case: the height and width of V-Rwin is [$h'$, $w'$] and H-Rwin is [$w'$, $h'$]. Here $h'$ and $w'$ are constants. Then the displacement distance of V-Shift is ($\\frac{h'}{2}$, $\\frac{w'}{2}$), and H-shift is ($\\frac{w'}{2}$, $\\frac{h'}{2}$), where the first parameter represents the downward distance, the second represents the left distance. \n\n**For \"the difference between axial-shift and shifted window operation\".** \n\n**(1)** Our axial-shift references the design of the shift option in Swin Transformer. However, our proposed axial-shift operation adopts a grouped parallel design. Different shift distances are used to match the corresponding Rwin-SA (V-Rwin and H-Rwin). Specifically, **we use different shift operations in different attention heads**, and the shift operation corresponds to the attention mechanism in the head.\n\n**(2)** However, the shift operation in Swin Transformer performs the same shift operation on all heads. This issue makes it hard to achieve sufficient interaction between windows, limiting the growth of the receptive field.\n\n**(3)** Furthermore, the shift operation in Swin Transformer can be viewed as a special case of our axial-shift. When the axial-shift displacement distances are the same in all heads, the shift operation in each attention head is the same. Then it degenerates into the shift operation in Swin Transformer.\n\n**We have responded to another similar question, `Q2-1`. Please refer to `A2-1` for more details.**\n\n\n\n`Q2-5:` this paper proposes a Rectangle-Window Self-Attention (Rwin-SA), which utilizes horizontal and vertical rectangle window (H-Rwin and V-Rwin) attention in different heads parallelly. Furthermore, authors also proposes an axial rectangle window (axis-Rwin), in which the length of one side is fixed as the image resolution H or W. However, the axial rectangle window division method has been proposed in CSWin [10], so this part should be marked in reference [10].\n\n`A2-5:` Thanks for pointing it out. We have marked \"the axial rectangle window division method has been proposed in CSWin\" in our main paper. However, the method proposed in this paper is still different from CSwin.\n\n**(1)** Axial-Rwin is inspired by CSwin and is close to CSwin in form, but it is only a special case of our proposed rectangle window self-attention. Regular-Rwin we proposed is a more general form and more flexible. In other words, the attention mechanism in CSwin is a special case proposed in our paper. \n\n**(2)** At the same time, some methods in high-level tasks, like image classification, use operations similar to axial-Rwin. However, in low-level tasks, such as image restoration, there is still a lack of corresponding attempts. We successfully apply axial-Rwin to image restoration. \n\n**We have responded to another similar question, `Q2-1`. Please refer to `A2-1` for more details.**\n\n\n\n`Q2-6:` More recent methods should be compared to demonstrate the superiority of the proposed method, such as Uformer and Restormer.\n\n`A2-6:` Thanks for the valuable suggestions. Following the suggestions of R2, we compare with more methods like Uformer and Restormer on image denoising (real image denoising). We build our CAT model with our proposed **cross aggregation Transformer block** and the encoder-decoder-based **UNet architecture** (refer to Restormer). \n\nThe experiment and comparison show that our CAT outperforms or is comparable to other methods, such as Uformer and Restormer. **We have responded to another similar question, `Q2-3`. Please refer to `A2-3` for more details.**\n\n", " `Q2-3:` More recent methods should be compared to demonstrate the superiority of the proposed method.\n\n`A2-3:` Thanks for the valuable suggestions for comparing our method with other methods. Following the suggestions of R2, we compare our method with more methods like Uformer and Restormer.\n\nWe apply our proposed **cross aggregation Transformer block** to the encoder-decoder-based **UNet architecture** to construct CAT (refer to Restormer). We apply our CAT to real image denoising.\n\nWe use SIDD training dataset to train our CAT. The training settings (**totaling 300K iterations**) and training process are the same as Restormer. We test our model on SIDD and DND datasets. The comparison of our CAT with the state-of-the-art methods: MIRNet, Uformer, and Restormer, is shown in the following table.\n\n| Method | Provenance | Params | SIDD | | DND | |\n| ------------------------------------------------------------ | ---------- | :----: | :-------: | :-------: | :-------: | :-------: |\n| | | | PSNR | SSIM | PSNR | SSIM |\n| MIRNet | ECCV 2020 | 31.79M | 39.72 | 0.959 | 39.88 | 0.956 |\n| Uformer-S [used for comparison in Table 6 of Restormer] | CVPR 2022 | 20.63M | 39.77 | 0.959 | 39.96 | 0.956 |\n| Uformer-B [results shown in CVPR 2022 camera ready] | CVPR 2022 | 50.88M | 39.89 | 0.960 | 40.04 | 0.956 |\n| Restormer [training iterations: 300K] | CVPR 2022 | 26.11M | **40.02** | **0.960** | 40.03 | 0.956 |\n| CAT [ours, **completed trained**; training iterations: 300K] | our method | 25.77M | 40.01 | **0.960** | **40.05** | **0.956** |\n| CAT+ [ours, **self ensemble**] | our method | 25.77M | **40.05** | **0.960** | **40.08** | **0.956** |\n\n\n\n**(1)** We can observe that our CAT outperforms MIRNet, Uformer-S, and Uformer-B on all datasets. And our CAT performs better than Restormer on DND and is comparable to Restormer on SIDD. Moreover, the parameter of our CAT is smaller than all models compared, except Uformer-S. \n\n**(2)** Meanwhile, if we further enlarge the model size of our CAT, the model performance will improve further. This conclusion can be drawn from the comparison of Uformer-S and Uformer-B.\n\n**All these results demonstrate the superiority of our proposed method.** \n\n**(3)** We have added this part to the supplementary material. Please refer to **Sec. 4.1** in the **supplementary material** for details (the online test result of DND is shown in **Fig. 3**). Moreover, we have updated the test code and pretrained model to our source code (in **Anonymous Github**) for reviewers to test and check.\n\n", " `Q2-2:` In this paper, the discussion of the existing transformer methods is insufficient.\n\n`A2-2:` Thanks for pointing it out. We have modified our paper (related work). And we discuss more Transformer methods below.\n\n**(1)** Although Transformer has made breakthroughs in the computer vision field, its quadratic complexity of input size limits the scope of use. Many works have been proposed to reduce the computational complexity. **Swin** uses local window attention and realizes the interaction between windows through shift operations. But the 8$\\times$8 square window limits the receptive field of the Transformer. **PVT** reduces the size of keys ($K$) and values ($V$) through projection, but this operation may cause information loss. **HaloNet** **[ref1]** uses local window attention and realizes the interaction between windows through halo operations, but its receptive field grows slowly. **CSWin** proposes cross-shaped window attention, but simple horizontal and vertical stripes require a large window to obtain a sufficient receptive field. Therefore, it is difficult to guarantee a sufficient receptive field within the limited complexity. **Twins** uses a combination of global and local attention operations, and **XCiT** **[ref2]** uses channel-attention instead of spatial-attention. \n\n**(2)** Meanwhile, many methods propose using convolution to enhance Transformer. For example, **CPVT** uses convolution to calculate position encoding. **CMT** **[ref3]** uses convolution to replace linear projection in multi-head self-attention (MHSA). However, these methods cannot effectively add local information to Transformer. \n\n**(3)** The **Uformer** model is also proposed in image restoration, using U-Net structure and local window attention. It also adds depthwise convolution in feed-forward network (FFN). But it is limited by the lack of direct interaction between windows.\n\n**(4)** However, our proposed CAT model, through Rwin-SA, can effectively realize the interaction between windows while ensuring linear complexity. And further increase the window interaction by axial-shift. Moreover, the LCM module realizes the global and local coupling.\n\n**[ref1]** Ashish Vaswani, Prajit Ramachandran, Aravind Srinivas, Niki Parmar, Blake Hechtman, and Jonathon Shlens. Scaling local self-attention for parameter efficient visual backbones. In CVPR, 2021\n\n**[ref2]** AlaaeldinAli, HugoTouvron, MathildeCaron, PiotrBojanowski, MatthijsDouze, ArmandJoulin, Ivan Laptev, Natalia Neverova, Gabriel Synnaeve, Jakob Verbeek, et al. Xcit: Cross-covariance image transformers. In NeurIPS, 2021\n\n**[ref3]** Jianyuan Guo, Kai Han, Han Wu, Yehui Tang, Xinghao Chen, Yunhe Wang, and Chang Xu. Cmt: Convolutional neural networks meet vision transformers. In CVPR, 2022\n\n", " `Q2-1:` the contribution and novelty of this paper are not convincing enough. The proposed axial rectangle window has been designed in other work. Besides, the proposed axial-shift operation is the same as shifted window operation in Swin transformer.\n\n`A2-1:` Our work has enough contribution and novelty. We clarify them as follows.\n\n**For \"axial rectangle window has been designed in other work\".** Although our axial-Rwin is inspired by CSwin, the method proposed in this paper is still different from CSwin.\n\n**(1)** Axial-Rwin is inspired by CSwin and is close to CSwin in form, but it is only a special case of our proposed rectangle window self-attention. Regular-Rwin we proposed is a more general form and more flexible. In other words, the attention mechanism in CSwin is a special case proposed in our paper. \n\n**(2)** Some methods in high-level tasks, like image classification, use operations similar to axial-Rwin. However, in low-level tasks, such as image restoration, there is still a lack of corresponding attempts. We successfully apply axial-Rwin to image restoration. \n\nTo demonstrate **the effectiveness of our CAT**, we compare the performance of CAT-A and CSwin on image SR ($\\times$2). The CSwin model uses our CAT architecture and replaces our Cross Aggregation Transformer Block with the CSWin Transformer Block. The implementation details and training settings are the same for CAT and CSwin. The FLOPs are measured when the output size is set to 3$\\times$256$\\times$256. The comparison results are shown in the following table.\n\n| Method | Parameters | FLOPs | Set5 | Set14 | B100 | Urban100 | Manga109 |\n| ------ | :--------: | :---: | :-------: | :-------: | --------- | :-------: | :-------: |\n| CSwin | 16.45M | 350.7 | 38.40 | 34.42 | 32.46 | 33.73 | 39.83 |\n| CAT-A | 16.46M | 350.7 | **38.51** | **34.78** | **32.59** | **34.26** | **40.10** |\n\nWe can see from the above table that CAT-A performs much better than CSwin with a similar model size and computational complexity.\n\n**For \"axial-shift operation is the same as shifted window operation in Swin transformer\".** Our axial-shift references the design of the shift operation in Swin Transformer. However, the axial-shift we proposed is different from the shifted window operation in Swin Transformer. \n\n**(1)** The most significant difference between axial-shift and the shift operation in Swin Transformer is that axial-shift adopts **a grouped parallel design**. Axial-shift is divided into V-Shift and H-Shift operations, which act on different attention heads and correspond to V-Rwin and H-Rwin. However, the shift operation in Swin Transformer performs the same shift operation in all heads. \n\n**(2)** Based on axis-shift, Rwin can realize more window interaction, thereby expanding the receptive field and improving model performance. We can find that the performance of Rwin with axial-shift is much better than the square window with shift operation in Swin Transformer from **ablation study** Table 1 (a). We show them here. Output size is 3$\\times$256$\\times$256 to calculate FLOPs, and PSNR values are tested on Urban100 ($\\times$2).\n\n| Network | PSNR | SSIM | FLOPs |\n| ------------------------- | :-------: | :--------: | :----: |\n| Square w/o shift | 32.50 | 0.9325 | 281.8G |\n| Square w/ shift | 32.75 | 0.9347 | 281.8G |\n| Rectangle w/o axial-shift | 32.66 | 0.9334 | 281.8G |\n| Rectangle w/ axial-shift | **32.91** | **0.9360** | 281.8G |\n\n**(3)** Furthermore, the shift operation in Swin Transformer can be viewed as a special case of our axial-shift. When the axial-shift displacement distances are the same in all heads, the shift operation in each attention head is the same. Then axial-shift degenerates into the shift operation in Swin Transformer. In general, our axial-shift is more general and efficient.\n\n**Overall.** Our work has enough contribution and novelty. We propose rectangle window attention (axial-Rwin is a special case) and successfully apply it to image restoration. We also propose axial-shift that matches Rwin and locality complementary module (LCM) to enhance Rwin. Moreover, our proposed CAT performs well and drives the development of Transformer in image restoration.\n\n", " `Q4-5:` The authors said in the ‘Conclusion’ part that the proposed CAT could also be used for other image restoration tasks. Did the authors try those tasks and/or get some preliminary results?\n\n`A4-5:` We try to apply our CAT on real image denoising and achieve some preliminary results.\n\nWe apply our proposed **cross aggregation Transformer block** to the encoder-decoder-based **UNet architecture** to construct CAT (refer to Restormer). We apply our CAT to real image denoising.\n\nWe use SIDD training dataset to train our CAT. The training settings and training process are the same as Restormer. We test our model on SIDD and DND datasets. The comparison of our CAT with the state-of-the-art methods: MIRNet, Uformer, and Restormer is shown in the following table.\n\n| Method | Provenance | Params | SIDD | | DND | |\n| ------------------------------------------------------------ | ---------- | :----: | :-------: | :-------: | :-------: | :-------: |\n| | | | PSNR | SSIM | PSNR | SSIM |\n| MIRNet | ECCV 2020 | 31.79M | 39.72 | 0.959 | 39.88 | 0.956 |\n| Uformer-S [used for comparison in Table 6 of Restormer] | CVPR 2022 | 20.63M | 39.77 | 0.959 | 39.96 | 0.956 |\n| Uformer-B [results shown in CVPR 2022 camera ready] | CVPR 2022 | 50.88M | 39.89 | 0.960 | 40.04 | 0.956 |\n| Restormer [training iterations: 300K] | CVPR 2022 | 26.11M | **40.02** | **0.960** | 40.03 | 0.956 |\n| CAT [ours, **completed trained**; training iterations: 300K] | our method | 25.77M | 40.01 | **0.960** | **40.05** | **0.956** |\n| CAT+ [ours, **self ensemble**] | our method | 25.77M | **40.05** | **0.960** | **40.08** | **0.956** |\n\n\n\nWe can observe that our CAT outperforms MIRNet, Uformer-S, and Uformer-B on all datasets. And our CAT performs better than Restormer on DND and is comparable to Restormer on SIDD. Moreover, the parameter of our CAT is smaller than all models compared, except Uformer-S. Overall, our CAT outperforms or is comparable to other methods.\n\nWe have added this part to the supplementary material. Please refer to **Sec. 4.1** in the **supplementary material** for details. Moreover, we have added test code and pretrained model to our source code (Anonymous Github) for reviewers to test and track.\n\nWe also plan to apply our CAT to more image restoration tasks in the future. ", " `Q4-1:` In Figure 3, the meanings of H, W, sl should be given in the caption.\n\n`A4-1:` Thanks for the suggestion. We have modified the caption of Figure 3 in the paper as follows.\n\nIllustration of attention expansion, directional features aggregation, and axial-Rwin. $H$, $W$, and $sl$ mean height, width, and the other side length.\n\n\n\n`Q4-2:` In Table 4, the authors provide model size, FLOPs, and PSNR comparisons. The proposed CAT obtains the highest performance. However, the proposed CAT has a larger model size and FLOPs than the related work SwinIR. It would be much better if the authors provide comparisons with SwinIR using similar parameter number and FLOPs.\n\n`A4-2:` Thanks for the suggestion. We **already provided** a comparison of similar model sizes and FLOPs in **supplementary material** Table 2. We also show them here. Output size is 3$\\times$512$\\times$512 to calculate FLOPs.\n\n| Method | Params (M) | FLOPs (G) | Set5 | Set14 | B100 | Urban100 | Manga109 |\n| ------- | :--------: | :-------: | :-------: | :-------: | :-------: | :-------: | :-------: |\n| SwinIR | 11.90 | 215.3 | **32.92** | 29.09 | 27.92 | 27.45 | 32.03 |\n| CAT-R-2 | 11.93 | 216.3 | 32.91 | **29.13** | **27.93** | **27.59** | **32.16** |\n\nOur CAT-R-2 obtains a similar model size, FLOPs with SwinIR but obtains better performance. \n\n\n\n`Q4-3:` Some details should be made more clear. For example, for image SR, the authors provide two versions of CAT: CAT-R and CAT-A. For JPEG compression artifact reduction, the authors only show CAT. It is not very clear about its model size and FLOPs.\n\n`A4-3:` Thanks for pointing it out. For JPEG compression artifact reduction, we employ **CAT-A**, and since only one model is proposed, we abbreviate it as CAT. We provide its model size and FLOPs as follows. Output size is 1$\\times$128$\\times$128 to calculate FLOPs, and PSNR values are tested $q$=40.\n\n| Method | Params (M) | FLOPs (G) | LIVE1 | Classic5 | Urban100 |\n| ---------- | :--------: | :-------: | :-------: | :-------: | :-------: |\n| SwinIR | 11.49M | 213.6 | 34.67 | 34.52 | 35.50 |\n| CAT (ours) | 16.20M | 346.4 | **34.72** | **34.58** | **35.73** |\n\nOur proposed CAT outperforms SwinIR and has a larger model size and FLOPs than SwinIR. Due to time issues, we previously did not train a CAT of similar size to the SwinIR model. But we provide a model with similar parameter sizes and FLOPs to SwinIR on image SR, and our model outperforms SwinIR. Please refer to `A4-2` for more details. Moreover, we will propose a variant of CAT with a similar model size and FLOPs for JPEG compression artifact reduction in the future.\n\n\n\n`Q4-4:` Please discuss the differences between the key ideas of the work (e.g., axial-Rwin) and CSWin.\n\n`A4-4:` The main differences can be summarized into three points: \n\n**(1)** Axial-Rwin is inspired by CSwin and is close to CSwin in form, but it is only a special case of our proposed rectangle window self-attention. Regular-Rwin we proposed is a more general form and more flexible. In other words, the attention mechanism in CSwin is a special case proposed in our paper.\n\n**(2)** Some methods in high-level tasks, like image classification, use operations similar to axial-Rwin. However, in low-level tasks, such as image restoration, there is still a lack of corresponding attempts. We successfully apply axial-Rwin to image restoration. \n\n**(3)** We also propose two operations: axial-shift and LCM module, to enhance Rwin-SA. \n\nTo demonstrate **the effectiveness of our CAT**, we compare the performance of CAT-A and CSwin on image SR ($\\times$2). The CSwin model uses our CAT architecture and replaces our Cross Aggregation Transformer Block with the CSWin Transformer Block. The implementation details and training settings are the same for CAT and CSwin. The FLOPs are measured when the output size is set to 3$\\times$256$\\times$256. The comparison results are shown in the following table.\n\n| Method | Parameters | FLOPs | Set5 | Set14 | B100 | Urban100 | Manga109 |\n| ------ | :--------: | :---: | :-------: | :-------: | --------- | :-------: | :-------: |\n| CSwin | 16.45M | 350.7 | 38.40 | 34.42 | 32.46 | 33.73 | 39.83 |\n| CAT-A | 16.46M | 350.7 | **38.51** | **34.78** | **32.59** | **34.26** | **40.10** |\n\nWe can see from the above table that CAT-A performs much better than CSwin with a similar model size and computational complexity.\n\n", " `Q1-4:` The authors claim that the method is for image restoration. Then, how would the CAT perform for other image restoration tasks? Will it still achieve SOTA performance?\n\n`A1-4:` There are two ways to use CAT for other image restoration tasks:\n\n**(1)** Use the model architecture shown in Fig. 1. For different tasks with different reconstruction modules, keep the other modules unchanged. For example, for image denoising and deblurring, the reconstruction module is consistent with the one for JPEG artifact reduction.\n\n**(2)** Apply our proposed cross aggregation Transformer block to the encoder-decoder-based UNet architecture (like Restormer). \n\nWe use the **second** way to build the CAT model and apply it to real image denoising. Our CAT outperforms or is comparable to other methods.\n\nWe use SIDD training dataset to train our CAT. The training settings and training process are the same as Restormer. We test our model on SIDD and DND datasets. The comparison of our CAT with the state-of-the-art methods: MIRNet, Uformer, and Restormer is shown in the following table.\n\n| Method | Provenance | Params | SIDD | | DND | |\n| ------------------------------------------------------------ | ---------- | :----: | :-------: | :-------: | :-------: | :-------: |\n| | | | PSNR | SSIM | PSNR | SSIM |\n| MIRNet | ECCV 2020 | 31.79M | 39.72 | 0.959 | 39.88 | 0.956 |\n| Uformer-S [used for comparison in Table 6 of Restormer] | CVPR 2022 | 20.63M | 39.77 | 0.959 | 39.96 | 0.956 |\n| Uformer-B [results shown in CVPR 2022 camera ready] | CVPR 2022 | 50.88M | 39.89 | 0.960 | 40.04 | 0.956 |\n| Restormer [training iterations: 300K] | CVPR 2022 | 26.11M | **40.02** | **0.960** | 40.03 | 0.956 |\n| CAT [ours, **completed trained**; training iterations: 300K] | our method | 25.77M | 40.01 | **0.960** | **40.05** | **0.956** |\n| CAT+ [ours, **self ensemble**] | our method | 25.77M | **40.05** | **0.960** | **40.08** | **0.956** |\n\n\n\nWe can observe that our CAT outperforms MIRNet, Uformer-S, and Uformer-B on all datasets. And our CAT performs better than Restormer on DND and is comparable to Restormer on SIDD. Moreover, the parameter of our CAT is smaller than all models compared. Overall, our CAT outperforms or is comparable to other methods, except Uformer-S.\n\nWe have added this part to the supplementary material. Please refer to **Sec. 4.1** in the **supplementary material** for details. Moreover, we have updated the test code and pretrained model to our source code (in **Anonymous Github**) for reviewers to test and check.\n\nWe also plan to apply our CAT to more image restoration tasks in the future. \n\n\n\n`Q1-5:` Do all the training and testing details between SwinIR and CAT for image SR and JPEG artifact reduction keep the same? If there has some differences, please clarify them.\n\n`A1-5:` Thanks for asking for those details. There is no difference in the training and testing details between CAT and SwinIR.\n\n\n\n", " \n\n`Q3-4:` Is the axial-shift in CAT exactly the same as the shift operation in SwinIR? If not, please tell the differences.\n\n`A3-4:` The axial-shift is different from the shift operation in SwinIR. We clarify them as follows.\n\n**(1)** Our axial-shift references the design of the shift option in Swin Transformer. However, our axial-shift adopts a grouped parallel design. Axial-shift is divided into V-Shift and H-Shift operations, which act on different attention heads and correspond to V-Rwin and H-Rwin. However, the shift operation in Swin Transformer performs the same shift operation in all heads. \n\n**(2)** Based on axial-shift, Rwin can achieve more window interactions, thereby expanding the receptive field and improving model performance. We can find that the performance of Rwin with axial-shift is much better than the square window with shift operation in Swin Transformer from **ablation study** Table 1 (a). We show them here. Output size is 3$\\times$256$\\times$256 to calculate FLOPs, and PSNR values are tested on Urban100 ($\\times$2).\n\n| Network | PSNR | SSIM | FLOPs |\n| ------------------------- | :-------: | :--------: | :----: |\n| Square. w/ shift | 32.75 | 0.9347 | 281.8G |\n| Rectangle. w/ axial-shift | **32.91** | **0.9360** | 281.8G |\n\n**(3)** Furthermore, the shift operation in Swin Transformer can be viewed as a special case of our axial-shift. When the axial-shift displacement distances are the same in all heads, the shift operation in each attention head is the same. Then axial-shift degenerates into the shift operation in Swin Transformer. Overall, our axial-shift is more general and efficient.\n\n\n\n`Q3-5:` Can the method be applied to other image restoration tasks well? Like image denoising and deblurring. If so, how is the performance of CAT? Will CAT still achieves SOTA performance?\n\n`A3-5:` Our method can be applied to other image restoration tasks (like real image denoising) and outperforms or is comparable to other methods.\n\nWe apply our proposed **cross aggregation Transformer block** to the encoder-decoder-based **UNet architecture** to construct CAT (refer to Restormer). We apply our CAT to real image denoising.\n\nWe use SIDD training dataset to train our CAT. The training settings and training process are the same as Restormer. We test our model on SIDD and DND datasets. The comparison of our CAT with the state-of-the-art methods: MIRNet, Uformer, and Restormer is shown in the following table.\n\n| Method | Provenance | Params | SIDD | | DND | |\n| ------------------------------------------------------------ | ---------- | :----: | :-------: | :-------: | :-------: | :-------: |\n| | | | PSNR | SSIM | PSNR | SSIM |\n| MIRNet | ECCV 2020 | 31.79M | 39.72 | 0.959 | 39.88 | 0.956 |\n| Uformer-S [used for comparison in Table 6 of Restormer] | CVPR 2022 | 20.63M | 39.77 | 0.959 | 39.96 | 0.956 |\n| Uformer-B [results shown in CVPR 2022 camera ready] | CVPR 2022 | 50.88M | 39.89 | 0.960 | 40.04 | 0.956 |\n| Restormer [training iterations: 300K] | CVPR 2022 | 26.11M | **40.02** | **0.960** | 40.03 | 0.956 |\n| CAT [ours, **completed trained**; training iterations: 300K] | our method | 25.77M | 40.01 | **0.960** | **40.05** | **0.956** |\n| CAT+ [ours, **self ensemble**] | our method | 25.77M | **40.05** | **0.960** | **40.08** | **0.956** |\n\n\n\nWe can observe that our CAT outperforms MIRNet, Uformer-S, and Uformer-B on all datasets. And our CAT performs better than Restormer on DND and is comparable to Restormer on SIDD. Moreover, the parameter of our CAT is smaller than all models compared, except Uformer-S. Overall, our CAT outperforms or is comparable to other methods.\n\nWe have added this part to the supplementary material. Please refer to **Sec. 4.1** in the **supplementary material** for details. Moreover, we have updated the test code and pretrained model to our source code (in **Anonymous Github**) for reviewers to test and check.\n\nWe also plan to apply our CAT to more image restoration tasks in the future. \n\n", " `Q3-1:` For the model size analyses in Table 4, CAT-R and CAT-A perform better than other compared ones, but their parameter numbers are not the smallest or still higher than SwinIR. In supplementary file, the authors gave a more reasonable comparison (see Table 2), which should be included in the main paper.\n\n`A3-1:` Thanks for the valuable suggestion. We have merged the results (CAT-R-2) into Table 4. We also show them here. Output size is 3$\\times$512$\\times$512 to calculate FLOPs, and PSNR values are tested on Urban100 ($\\times$4).\n\n| Method | EDSR | RCAN | HAN | CSNLN | SwinIR | CAT-R (ours) | CAT-A (ours) | CAT-R-2 (ours) |\n| -------------- | :---: | :---: | :---: | :------: | :----: | :----------: | :----------: | :------------: |\n| PSNR (dB) | 26.64 | 26.82 | 26.85 | 27.22 | 27.45 | 27.62 | 27.89 | 27.59 |\n| FLOPs (G) | 823.3 | 261.0 | 269.1 | 84,155.2 | 215,3 | 292.7 | 360.7 | 216.3 |\n| Parameters (M) | 43.09 | 15.59 | 16.07 | 6.57 | 11.90 | 16.60 | 16.60 | 11.93 |\n\n\n\n`Q3-2:` For JPEG artifact reduction, the quantitative results do not show too much improvement of CAT over SwinIR. It would be better if the authors can give more analyses.\n\n`A3-2:` Thanks for the suggestion. We do more analysis on this part as follows.\n\n**(1)** Our CAT has a more robust representational ability to recover structural contents and texture details due to rectangle window self-attention. However, for the JPEG artifact reduction testing datasets: LIVE1 and Classic5, the number of images they contain is small (5 and 29), and the texture features are not rich. So the overall improvement effect is not obvious. Nevertheless, the difference is evident from the visual comparison (like Fig. 6 carnivaldolls).\n\n**(2)** In the **supplementary material** Table 3, we test CAT and SwinIR on the Urban100 dataset, which with more directional and repetitive texture features. The performance of CAT is much better than that of SwinIR, with a **0.25 dB** improvement. We also show them here (only PSNR).\n\n| Method | q=10 | q=20 | q=30 | q=40 |\n| ------ | :-------: | :-------: | :-------: | :-------: |\n| SwinIR | 30.55 | 33.12 | 34.58 | 35.50 |\n| CAT | **30.80** | **33.38** | **34.81** | **35.73** |\n\n\n\n`Q3-3:` There are image restoration (i.e., image SR and JPEG artifact reduction) applications are conducted. The pipeline in Figure 1 mainly takes image SR as an example. Can the authors give more details about the pipeline for JPEG artifact reduction? Or the only difference is that the upscaling module is removed? Please clarify this.\n\n`A3-3:` The only difference between the pipeline for JPEG artifact reduction and image SR is the reconstruction module. Other modules: shallow feature extraction and deep feature extraction, remain unchanged. \n\n**For JPEG artifact reduction**, the reconstruction is just a convolution layer. And the low-quality input $I_{LQ}$ is then added to the convolution output to produce a high-quality output $I_{HQ}$. **For image SR**, the reconstruction module is an upsampling and two convolution layers. \n\nThe pseudo-code for **the reconstruction module** is as follows.\n\n```python\n# input is the low-quality input\n# _x is the ouput of the deep feature extraction module\n\n# for image SR\nx = convolution(_x)\noutput = convolution((upsample(x))\n# for JPEG compression artifact reduction\noutput = input + convolution(_x)\n```\n\n\n\n", " `Q1-1:` In Table 4, the parameter number and FLOPs of CAT are larger than those in SwinIR. A better and more reasonable way is to keep similar model size and FLOPs and then show comparisons.\n\n`A1-1:` Thanks for your suggestion. We **already provided** a comparison of similar model sizes and FLOPs in **supplementary material** Table 2. We also show them here. Output size is 3$\\times$512$\\times$512 to calculate FLOPs.\n\n| Method | Params (M) | FLOPs (G) | Set5 | Set14 | B100 | Urban100 | Manga109 |\n| ------- | :--------: | :-------: | :-------: | :-------: | :-------: | :-------: | :-------: |\n| SwinIR | 11.90 | 215.3 | **32.92** | 29.09 | 27.92 | 27.45 | 32.03 |\n| CAT-R-2 | 11.93 | 216.3 | 32.91 | **29.13** | **27.93** | **27.59** | **32.16** |\n\nOur CAT-R-2 obtains a similar model size, FLOPs with SwinIR but obtains better performance.\n\nWe have merged the results (CAT-R-2) into Table 4. We also show them here. \n\n| Method | EDSR | RCAN | HAN | CSNLN | SwinIR | CAT-R (ours) | CAT-A (ours) | CAT-R-2 (ours) |\n| -------------- | :---: | :---: | :---: | :------: | :----: | :----------: | :----------: | :------------: |\n| PSNR (dB) | 26.64 | 26.82 | 26.85 | 27.22 | 27.45 | 27.62 | 27.89 | 27.59 |\n| FLOPs (G) | 823.3 | 261.0 | 269.1 | 84,155.2 | 215,3 | 292.7 | 360.7 | 216.3 |\n| Parameters (M) | 43.09 | 15.59 | 16.07 | 6.57 | 11.90 | 16.60 | 16.60 | 11.93 |\n\n\n\n`Q1-2:` The detailed differences between axial-shift and the shift option in Swin Transformer are not very clear to me.\n\n`A1-2:` Thanks for asking for those details. We clarify them as follows.\n\n**(1)** Our axial-shift references the design of the shift option in Swin Transformer. However, our axial-shift adopts a grouped parallel design. Axial-shift is divided into V-Shift and H-Shift operations, which act on different attention heads and correspond to V-Rwin and H-Rwin. However, the shift operation in Swin Transformer performs the same shift operation in all heads. \n\n**(2)** Based on axial-shift, Rwin can achieve more window interactions, thereby expanding the receptive field and improving model performance. We can find that the performance of Rwin with axial-shift is much better than the square window with shift operation in Swin Transformer from **ablation study** Table 1 (a). We show them here. Output size is 3$\\times$256$\\times$256 to calculate FLOPs, and PSNR values are tested on Urban100 ($\\times$2).\n\n| Network | PSNR | SSIM | FLOPs |\n| ------------------------- | :-------: | :--------: | :----: |\n| Square. w/ shift | 32.75 | 0.9347 | 281.8G |\n| Rectangle. w/ axial-shift | **32.91** | **0.9360** | 281.8G |\n\n**(3)** Furthermore, the shift operation in Swin Transformer can be viewed as a special case of our axial-shift. When the axial-shift displacement distances are the same in all heads, the shift operation in each attention head is the same. Then axial-shift degenerates into the shift operation in Swin Transformer. Overall, our axial-shift is more general and efficient.\n\n\n\n`Q1-3:` For JPEG artifact reduction, the performance improvements of CAT over SwinIR are not very obvious, although the visual differences are obvious. Please give some explanations.\n\n`A1-3:` Thanks for your question. We explain it below.\n\n**For \"the visual differences are obvious\".** The proposed CAT uses rectangle window self-attention, which can capture different features in horizontal and vertical directions for each pixel. This property enables CAT to recover more directional and repetitive texture features. So in the visual comparison of Fig. 6, CAT can recover more texture information, and the visual effect is better than SwinIR. \n\n**For \"performance improvements of CAT over SwinIR are not very obvious\".** **(1)** For the JPEG artifact reduction testing datasets: LIVE1 and Classic5, the number of images they contain is small (5 and 29), and the texture features are not rich. So the overall improvement effect is not obvious. Nevertheless, the difference is evident from the visual comparison (like Fig. 6 carnivaldolls).\n\n**(2)** In the **supplementary material** Table 3, we test CAT and SwinIR on the Urban100 dataset, which with more directional and repetitive texture features. The performance of CAT is much better than that of SwinIR, with a **0.25 dB** improvement. We also show them here (only PSNR).\n\n| Method | q=10 | q=20 | q=30 | q=40 |\n| ------ | :-------: | :-------: | :-------: | :-------: |\n| SwinIR | 30.55 | 33.12 | 34.58 | 35.50 |\n| CAT | **30.80** | **33.38** | **34.81** | **35.73** |\n\n", " A new Transformer based method, named as cross aggregation Transformer (CAT), was proposed for high-quality image restoration. The authors proposed three main components: rectangle-window self-attention, axial-shift operation, and locality complementary module (LCM). Their effects are demonstrated by extensive ablation study results. The main comparisons show the superior of the proposed CAT. Strength\n\n- The authors proposed to aggregate deep features across different windows with expanded sensing area, which is reasonable and effective for image restoration. \n\n- A new shift operation named axial-shift operation was proposed to further increase the interaction of different windows.\n\n- A Conv operation named locality complementary module (LCM) was proposed to make good use of its translation invariance and locality, enabling the model to capture both global and local information.\n\n- Experiments are extensive. The ablation study shows the effect of each proposed new component. The main quantitative and visual comparisons with recent methods, like SwinIR, demonstrate that the proposed CAT is a promising Transformer based method. \n\n- The authors provided source code and pretrained models for results reproduction. These materials could help other researchers for further investigations and improvements. For example, it would be easy to apply for this method for image denoising, derain, dehazing et al. with the provided code. \n \n- The authors also show some visualization results using LAM and compare with SwinIR. According to the visualization results (Fig. 2 in supp.), the proposed CAT captures a larger receptive field. This observation is consistent with the claim in ‘Abstract’ about the long-range dependencies estimation. \n\n- The main paper and supplementary file are well prepared. The writing is pretty good and easy to read. The motivation is clear and reasonable. The paper is carefully organized. \n\nWeakness\n\n- In Table 4, the parameter number and FLOPs of CAT are larger than those in SwinIR. A better and more reasonable way is to keep similar model size and FLOPs and then show comparisons.\n\n- The detailed differences between axial-shift and the shift option in Swin Transformer are not very clear to me. - For JPEG artifact reduction, the performance improvements of CAT over SwinIR are not very obvious, although the visual differences are obvious. Please give some explanations.\n\n- The authors claim that the method is for image restoration. Then, how would the CAT perform for other image restoration tasks? Will it still achieve SOTA performance?\n\n- Do all the training and testing details between SwinIR and CAT for image SR and JPEG artifact reduction keep the same? If there has some differences, please clarify them.\n\n- Please tell the differences between CAT and CSwin [10]. In supplementary file, the limitations and potential negative societal impact of the work have been briefly discussed.", " This paper proposes an image restoration model, named Cross Aggregation Transformer (CAT). Specifically, this paper designs the Rectangle-Window Self-Attention (Rwin-SA), which utilizes horizontal and vertical rectangle window multi-head attention parallelly. The proposed Locality Complementary Module incorporates the inductive bias of CNN into Transformer to complement the self-attention mechanism. Ablation experiments prove that the LCM improves model performance with negligible computational cost. A series experiments on different datasets demonstrate that the CAT outperforms recent state-of-art methods on two image restoration tasks: image SR and JPEG compression artifacts reduction.\n Strengths:\n1. This paper proposes an image restoration model, named Cross Aggregation Transformer (CAT). Specifically, this paper designs the Rectangle-Window Self-Attention (Rwin-SA), which utilizes horizontal and vertical rectangle window multi-head attention parallelly.\n2. The proposed Locality Complementary Module incorporates the inductive bias of CNN into Transformer to complement the self-attention mechanism. Ablation experiments prove that the LCM improves model performance with negligible computational cost.\n\nWeakness:\n1. the contribution and novelty of this paper are not convincing enough. The proposed axial rectangle window has been designed in other work. Besides, the proposed axial-shift operation is the same as shifted window operation in Swin transformer.\n2. In this paper, the discussion of the existing transformer methods is insufficient.\n3. More recent methods should be compared to demonstrate the superiority of the proposed method.\n 1. In Swin Transformer [19], Hu et al. proposed a shifted window operation, whose shifting directions include horizontal and vertical, and the shifting range of each direction is [0, k], where k is the size of the window. In this paper, author proposes a axial-shift (the horizontal one is called H-shift and the vertical one is called V-shift) operation for Rwin-SA, whose shifting range is set as sh/2 and sw/2, where sh and sw are the size of the rectangle window. The difference between shifted window operation [19] and axial-shift operation is caused by the shape of the window, so I personally think axial-shift and shifted window operation [19] are the same. Please explain in more detail the difference between V-shift and H-shift, and the difference between axial-shift and shifted window operation [19].\n\n2.this paper proposes a Rectangle-Window Self-Attention (Rwin-SA), which utilizes horizontal and vertical rectangle window (H-Rwin and V-Rwin) attention in different heads parallelly. Furthermore, authors also proposes an axial rectangle window (axis-Rwin), in which the length of one side is fixed as the image resolution H or W. However, the axial rectangle window division method has been proposed in CSWin [10], so this part should be marked in reference [10]. \n\n3. More recent methods should be compared to demonstrate the superiority of the proposed method, such as Uformer and Restormer.\n4. In related work, the discussion of the existing tranformer methods is insufficient, and the author should analyze CSWin and Uformer.\n5. More experiments on color JPEG image restoration should be conducted. The contribution and novelty of this paper are not convincing enough. More recent methods should be compared to demonstrate the superiority of the proposed method.", " The authors proposed cross aggregation Transformer (CAT) for image restoration, where the long-range dependencies are well considered. The proposed CAT uses the rectangle window self-attention (Rwin-SA) with axial-shift and aggregates the features cross different windows. Plus, they proposed a locality complementary module (LCM) to capture both local and global information. The main results on classic image restoration applications, like image SR and JPEG artifact reduction, show the superior performance of CAT quantitatively and visually. Strengths:\n\n(1) Firstly, the paper writing, organization, method, illustration figures (e.g., the pipeline in Figure 1), results are pretty good, which impress me a lot! I believe this paper is carefully prepared. \n\n(2) The idea of CAT is novel and a promising step to investigate more powerful Transformer based methods for high-quality image restoration.\n\n(3) The authors proposed cross aggregation Transformer block as the basic unit to form the image restoration networks. In the block, there three key parts: rectangle-window self-attention, axial-shift operation, and locality complementary module. The effect of each part has been demonstrated with ablation study experiments. \n\n(4) The main results with other leading methods are also extensive. The authors conducted experiments on image SR and JPEG artifact reduction. According to the quantitative (i.e., Tables 2 and 3) and visual (i.e., Figures 5 and 6) comparisons, we can further see the superior performance of the CAT.\n\n(5) The authors provided more variant models of the proposed one and achieved further improvements, also indicating the promising representation ability of CAT.\n\n(6) In supplementary file, the authors provided convergence analyses on CAT-A-CAT-R, CAR-R-2, and SwinIR using multiple testing sets. These results show that various CAT models performs better than the basic SwinIR. \n\nWeaknesses:\n\n(1) For the model size analyses in Table 4, CAT-R and CAT-A perform better than other compared ones, but their parameter numbers are not the smallest or still higher than SwinIR. In supplementary file, the authors gave a more reasonable comparison (see Table 2), which should be included in the main paper. \n\n(2) For JPEG artifact reduction, the quantitative results do not show too much improvement of CAT over SwinIR. It would be better if the authors can give more analyses. (1) There are image restoration (i.e., image SR and JPEG artifact reduction) applications are conducted. The pipeline in Figure 1 mainly takes image SR as an example. Can the authors give more details about the pipeline for JPEG artifact reduction? Or the only difference is that the upscaling module is removed? Please clarify this.\n\n(2) Is the axial-shift in CAT exactly the same as the shift operation in SwinIR? If not, please tell the differences.\n\n(3) Can the method be applied to other image restoration tasks well? Like image denoising and deblurring. If so, how is the performance of CAT? Will CAT still achieves SOTA performance? In supplementary file, the authors have discussed the limitations and potential negative societal impact. Overall, I agree with the views of the authors.", " The authors propose a new image restoration model, cross aggregation Transformer (CAT). The key idea is the rectangle-window self-attention, which uses horizontal and vertical rectangle window attention in different heads parallelly. The axial-shift operation is further introduced to different window interactions. They further propose a locality complementary module to incorporate some useful properties of CNN into Transformer. The ablation study and main results support the contributions well. Strengths\n1. The proposed method cross aggregation Transformer (CAT) is simple yet efficient. It has been a good Transformer based method for high-quality image restoration applications. \n2. All proposed components are stated clearly and logically, like rectangle-window self-attention, axial-shift operation, and locality complementary module. \n3. The ablation study results are extensive and demonstrate the effects of each proposed component.\n4. The main comparisons with recent leading methods (e.g., SwinIR) further show the superior of the proposed one. According to Table 2, we can see the best and second-best results are almost achieved by the proposed method CAT. The visual differences between the proposed CAT and other methods are very obvious, and further show the effectiveness of the proposed CAT. Similar observations happen for image JPEG compression artifact reduction.\n5. The overall writing and organization are pretty good. \n6. The authors also provide code and pre-trained models for reproduction, which further shows the solidness of the work.\n\nWeaknesses\n1. In Figure 3, the meanings of H, W, sl should be given in the caption.\n2. In Table 4, the authors provide model size, FLOPs, and PSNR comparisons. The proposed CAT obtains the highest performance. However, the proposed CAT has a larger model size and FLOPs than the related work SwinIR. It would be much better if the authors provide comparisons with SwinIR using similar parameter number and FLOPs. \n3. Some details should be made more clear. For example, for image SR, the authors provide two versions of CAT: CAT-R and CAT-A. For JPEG compression artifact reduction, the authors only show CAT. It is not very clear about its model size and FLOPs. \n 1. Please discuss the differences between the key ideas of the work (e.g., axial-Rwin) and CSWin.\n2. The authors said in the ‘Conclusion’ part that the proposed CAT could also be used for other image restoration tasks. Did the authors try those tasks and/or get some preliminary results?\n No, the authors did not discuss too much about the limitations or potential negative societal impact. It would be better if the authors can discuss some limitations.\n" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 4, 8, 8 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 4, 5, 5 ]

[ "nips_2022_wQ2QNNP8GtM", "KmjoCIUlrRB", "YofjfiVCGC", "VzjEgWVanXS", "VzjEgWVanXS", "Lg5AqAG0VoI", "HepkOcAvaKm", "_IHQtBWS3ea", "Lg5AqAG0VoI", "nvOE5jXoIR6", "VzjEgWVanXS", "Z27T25YoQdA", "Z27T25YoQdA", "nips_2022_wQ2QNNP8GtM", "VzjEgWVanXS", "VzjEgWVanXS", "VzjEgWVanXS", "VzjEgWVanXS", "VzjEgWVanXS", "Lg5AqAG0VoI", "Lg5AqAG0VoI", "Z27T25YoQdA", "nvOE5jXoIR6", "nvOE5jXoIR6", "Z27T25YoQdA", "nips_2022_wQ2QNNP8GtM", "nips_2022_wQ2QNNP8GtM", "nips_2022_wQ2QNNP8GtM", "nips_2022_wQ2QNNP8GtM" ]

[ "nE8tFBz0B4p", "75wwWSeYZ-v", "pSsSGvJ8d7E", "bN1t_pEfNvS", "h7JD-FfQigz", "TYUMI7jNuDG", "LrmL6IalSG", "Eed9ZTFAgsJ", "yShCaviCHCi", "7zifPaybfhd", "5GDCA1gDD6E", "4RAp62Ly3Xm", "Dze7gDSV_tL", "Ai7bCg-yGJF", "1vJ1yCvzRQj", "Zx0dt72fi5L", "BRv6no2Wnse", "P8N4RWJ07X", "XAzD-gDqJ92", "N1wk8skA2CU" ]

[ "official_reviewer", "author", "author", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " I thank the authors for the response, which helps me understand a bit more about the paper. The work is interesting, but it needs to be refined. I would like to maintain a borderline reject.", " We would like to thank all reviewers for their time, generous comments, and suggestions for improving the paper. \n\nBesides the responses provided on a point-by-point basis, we have also updated the manuscript/supplementary to improve the paper. We wish to summarize the earlier updates to the experimental evaluations and manuscript/supplementary uploaded. \n\n--- \n> ### New experiments\n\n\n 1. **More Challenging Environments to Demonstrate the Effectiveness of Reward Shifting:** We additionally experiment on four continuous control tasks including locomotion and robotics (HalfCheetah-SparseReward, Humanoid, FetchReach, FetchPush) to highlight the general applicability of reward shifting. See Figure 12, Figure 13 in Appendix D.2, Appendix D.3 : (https://openreview.net/attachmentid=iCxRsZcVVAH&name=supplementary_material)\n\n 2. **Less Challenging Environments to Show Reward Shifting is not Over-optimistic:** We adjusted the difficulty in the maze navigation task we used in Figure 1 by varying the distance between the starting point and the goal point, and used exactly the same reward shifting to show even in simple environments, explorative behaviors introduced by reward shifting will not step too far in exploration and the learning efficiency can still be guaranteed. See Figure 11 in Appendix D.1 (https://openreview.net/attachment?id=iCxRsZcVVAH&name=supplementary_material)\n\n\n--- \n> ### Summary of updates to manuscript & supplementary\n\n\nWe've highlighted the changes made to our manuscript and supplementary material in different colors (blue for the phase-I rebuttal and orange for the phase-II rebuttal).\n\n**Clarifications**\n- We updated Table 1, to highlight the flexibility of reward shifting.\n- We updated the presentation in the related work section, to better differentiate reward shifting from previous works.\n- We updated the captions for Figure2 and Figure3, clarified the notions, and colorized the curves. \n- We rephrased the method and experiment sections on reward shifting for value-based curiosity-driven exploration.\n- We did multiple passes on writing for a clearer presentation.\n\n**Extended Related Work**\n- Extended discussions on count-based exploration methods are added to Appendix E.1\n- Discussions on ensembles and distributional RL are added to Appendix E.2\n- Discussions on model-based exploration and uncertainty estimation are added to Appendix E.3\n\n\n---\n\nWith our responses and paper updates, we hope that we have addressed the reviewers' concerns. Please let us know if there were any further questions or comments. We are eager to do our utmost to address them!\n\nThank you for your kind consideration :)\n\nPaper 716 Authors\n\n", " Dear reviewer wKjq,\n\nThank you again for your review and we believe we have addressed all your concerns. Considering the author-reviewer discussion period is coming to a close, please let us know if there are any other questions you may have.\n\nWe believe reward shifting for value-based DRL is an important topic for research, with our work providing a significant contribution. If our response to your question was satisfactory, we would appreciate it enormously if you would consider raising your score.\n\nBest wishes,\n\nAuthors #716", " Thanks again for reviewing our paper.\n\nWe were curious if there should remain any other concerns on your part. We are happy to clarify further should you remain unsatisfied.\n\nBest wishes,\n\nPaper #716 Authors", " Given the limited time for the discussion period. We were curious if there should remain any other concerns on your part. **We believe that we have addressed the concerns mentioned in your review, and are happy to clarify further should you remain unsatisfied.**\n\nBest wishes,\n\nPaper #716 Authors", " I appreciate your enthusiasm to engage and receive feedback, but it takes time to review changes, and daily nag messages are annoying and do not help your case.\n\nPlease see my comments on your changes attached to my rebuttal acknowledgement at the top.", " Thanks again for reviewing our paper.\n\nWe were curious if there should remain any other concerns on your part. We believe that we have addressed the concerns mentioned in your review, and are happy to clarify further should you remain unsatisfied.\n\nBest wishes,\nPaper #716 Authors", " Thanks again for reviewing our paper.\n\nWe were curious if there should remain any other concerns on your part. We believe that we have addressed the concerns mentioned in your review, and are happy to clarify further should you remain unsatisfied.\n\nBest wishes,\nPaper #716 Authors", " We are sincerely grateful for your time and energy in the review process.\n\nIn light of our responses and updated draft uploaded on Aug.2, we would appreciate it if the reviewer could kindly let us know of any leftover concerns. We would be happy to do our utmost to address them.\n\nThank you!\nPaper 716 Authors", " We would like to thank all reviewers for their time and useful feedback for improving the paper. We have responded to each reviewer separately, but would like to summarize our changes here to streamline potential discussion.\n\n---\nDuring the phase1 rebuttal, we've:\n\n- 1. [**Presentation**] updated our paper and appendix and re-wrote some sections to improve the presentation, and marked the re-phrased parts with blue text, including but not limited to:\n - In the related work section, we include discussions on the works mentioned by the reviewer, and updated the phrasing in Table 1. We added extended discussions on related work at Appendix E.\n - In the method sections, we updated the presentation and formally introduce the notions before figures. We also updated the captions to make it clearer.\n - We’ve entirely rephrased the presentation in section 4.3.2 and section 5.3.\n\n- 2. [**Experiments**] added three sets of new experiments in Appendix D. \n - In Appendix D.1, we experiment on the maze tasks with different size to show that reward shifting improves exploration in hard-exploration tasks, and does not decrease learning efficiency in easier tasks.\n - In Appendix D.2, we experiment on SparseHalfCheetah and Humanoid to show reward shifting can be applied to hard continuous control tasks.\n\n---\n\nHere please find the link to the updated appendix (for additional experiments in Appendix D; and extended discussions on related work in Appendix E.)\nhttps://openreview.net/attachment?id=iCxRsZcVVAH&name=supplementary_material", " \n\nThank you for your elaborate feedback. We will address each question and weakness in turn.\n\n---\n\n### Q1: Language/ Writing.\n- We’ve updated the draft and mainly re-write the following sections to address this problem, including but not limited to:\n - In the related work section, we include discussions on the works mentioned by the reviewer, and updated the phrasing in Table 1. We added extended discussions on related work at Appendix E.\n - In the method sections, we updated the presentation and formally introduce the notions before figures. We also updated the captions to make it clearer.\n - We’ve entirely rephrased the presentation in section 4.3.2 and section 5.3.\n\n\n### Q2: Extended Related Work \n- (a) We’ve updated our related work section and extended the discussions in Appendix. B to address this question. \n- (b) Specifically, DORA constructed an additional MDP to estimate the Exploration-value as a generalized counter for count-based exploration, yet those count-based methods are orthogonal to reward shifting: in intrinsic reward methods, an agent must **first experience** a new $(s,a)$ pair before receiving a high intrinsic reward --- this is extremely hard with an arg-max style policy. On the other hand, with optimistic initialization, the rarely-visited $(s,a)$ pairs will naturally have higher $Q$-values **before experiencing** it --- as the frequently-visited pairs have updated their values with a negatively shifted reward. From such a perspective, reward shifting not only works by itself motivates exploratory behaviors but can also be seamlessly plugged into intrinsic reward methods to **encourage the first visitation** of new states. We’ve updated this difference to section 4.3.2.\n- (c) Moreover, we do not intend to use our experiments to show that reward shifting is beating other methods of online exploration or offline exploitation, but use those experiments to demonstrate the key insight of reward shifting is equivalent to different initializations that can generally be applied to value-based methods. Combining DORA with reward shifting is also a promising direction to gain further improvement. \n- (d) In Distributional RL literature [1-5], the distribution of the $Q$-value, rather than the mean scaler, is estimated. Distributional-RL focuses on stochastic reward mechanisms and smooths the temporal difference learning at a distributional level, and can be applied to risk-sensitive scenarios [6] where the worst-case performance can be controlled [7]. In those scenarios, systematic uncertainty is the crucial issue to address, whereas, in our work, we focus on deterministic transition dynamics and use OFU to tackle the epistemic uncertainty in the section of RRS. \n- (e) Besides [8, 9], several previous works discussed ensemble methods for exploration, both for discrete control [10] and for continuous control [11, 12]. However, in our work, we show that more exploratory behavior can emerge with the help of reward shifting under only a single $Q$-value network — as proof of the concept that negative reward shift is equivalent to optimistic initialization.\n\n\n\n\n\n### Q3: More Challenging Environments/ additional Experiments\n- (a) We **added new experiments** on the **SparseHalfCheetah** introduced in VIME (a reward of +1 is provided only when the forward velocity is larger than 5 units per timestep) and **Humanoid** — a high dimensional continuous control task in the MuJoCo locomotion suite to verify the effectiveness of reward shifting in exploration. \n- (b) In SparseHalfCheetah, we find a negative reward shift leads to more explorative behavior and improves the learning efficiency while a positive reward shift hinders the learning efficiency. \n- (c) In Humanoid, we find using a reward shift can drastically improve the asymptotic performance by ~$+60\\%$.\n- (d) Experiments are repeated with $8$ runs.\n\n\n\n\n### Q4: Figures 2 and 3 I found kind of confusing.\n- We’ve updated and colorized the captions to make the presentation clearer. We also updated the presentation and formally introduce the notions before the figures.\n", " \n\n### Q5: Motivating Example in Figure 1.\n- In figure 1, we provided a simple example in a tabular case to show the (negative) reward shifting is a simple yet effective way of boosting exploration. We tried to make the motivating example clear enough for readers to grasp the key insight of our work and develop the insight into different settings later in our work. An alternative choice is to use the continuous control task examples like SparseHalfCheetah or Humanoid, but in this way, there is no clear analogy as Count-Based exploration in the tabular cases and will be relatively more complicated as a motivating example.\n\n\n### Q6: Table 1\n- We use Table 1 to manifest that reward shifting is a generally applicable method that covers both exploration and exploitation (offline RL). We don’t intend to compare against other methods but aim to contrastively present the flexibility and generality of reward shifting. At the same time, Table 1 contextualizes the novelty of reward shifting with previous works. We’ve updated the caption and part of the layout of Table 1 to make it clearer.\n\n\n### Q7: Experiment design in RND v.s. DQN\n- (a) To demonstrate the effectiveness of reward shifting in discrete action space exploration, comparing the results of DQN and DQN + reward shifting is enough to draw the conclusion.\n\n- (b) On the other hand, in previous works, RND is always combined with policy-based discrete control algorithms like PPO. In our work, we want to use our key insight to answer the question that why naive attempts of combining value-based methods like DQN with RND will fail — adding a positive intrinsic reward like RND is harmful for exploration as it is equivalent to a pessimistic initialization. \n\n- (c) According to Figure 6, we can find:\n - (1). DQN > RND: vanilla RND with positive intrinsic reward is always worse than DQN: adding a positive intrinsic reward like RND is harmful for exploration as it is equivalent to a pessimistic initialization. \n - (2). DQN-0.5 > DQN: adding a negative reward shifting is equivalent to optimistic initialization and helps exploration.\n - (3). RND-1.0 > DQN; RND-1.5 > DQN-0.5: RND is effective for exploration (i.e., improve over DQN) as long as the intrinsic reward bonus is always negative.\n - (4). RND-1.5 > RND-1.0: increasing the magnitude of the negatively shifted reward can further improve the exploration performance — reward shifting can either work in isolation or get combined with other exploration algorithms as they are working orthogonally.\n\n- (d) We’ve entirely rephrased the presentation in Section 4.3.2 and Section 5.3 to make it clearer.\n\n### Q8: when does it perform poorly?\n- Our experiments have shown that for conservative exploration tasks, reward shifting may perform poorer than the baselines when the shifting constant is too large (e.g., shifting constant = 50, which is approximately 10 - 20 times larger than the maximal step-wise reward of the environment. cf. Figure 7.), as it can be over-pessimistic on extrapolations.\nFor optimistic exploration tasks, reward shifting also may perform pooer than the baselines when the shifting constant is too large (e.g., shifting constant = -10, which is more than 10 times larger than the potential episodic return for navigation tasks. cf. Figure 10.).\n\n\n### Q9: Stochastic Reward\n- In this work, we focused on deterministic reward and transition dynamics. In the deterministic settings, the source of uncertainty can be solely attributed to the epistemic uncertainty and hence help informative exploration. When it comes to stochastic environments, the entanglement of aleatoric uncertainty and epistemic uncertainty will make the problem much more difficult [13] as intrinsic motivation methods may get trapped by pursuing the actions that result in high aleatoric uncertainty in certain circumstances (e.g., the Noisy-TV) [14]. Using reward shifting to disentangle those two sources of uncertainty is a promising future direction.\n", " \n\n---\n### References\n\n[1] Bellemare, Marc G., Will Dabney, and Rémi Munos. \"A distributional perspective on reinforcement learning.\" International Conference on Machine Learning. PMLR, 2017.\n\n[2] Dabney, Will, et al. \"Distributional reinforcement learning with quantile regression.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 32. No. 1. 2018.\n\n[3] Lyle, Clare, Marc G. Bellemare, and Pablo Samuel Castro. \"A comparative analysis of expected and distributional reinforcement learning.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 33. No. 01. 2019.\n\n[4] Barth-Maron, Gabriel, et al. \"Distributed distributional deterministic policy gradients.\" arXiv preprint arXiv:1804.08617 (2018).\n\n[5]Dabney, Will, et al. \"A distributional code for value in dopamine-based reinforcement learning.\" Nature 577.7792 (2020): 671-675.\n\n[6] Urpí, Núria Armengol, Sebastian Curi, and Andreas Krause. \"Risk-averse offline reinforcement learning.\" arXiv preprint arXiv:2102.05371 (2021).\n\n[7] Delétang, Grégoire, et al. \"Model-Free Risk-Sensitive Reinforcement Learning.\" arXiv preprint arXiv:2111.02907 (2021).\n\n[8] Chen, Richard Y., et al. \"Ucb exploration via q-ensembles.\" arXiv preprint arXiv:1706.01502 (2017).\n\n[9]Chen, Richard Y., et al. \"UCB and infogain exploration via q-ensembles.\" arXiv preprint arXiv:1706.01502 9 (2017).\n\n[10] Lee, Kimin, et al. \"Sunrise: A simple unified framework for ensemble learning in deep reinforcement learning.\" International Conference on Machine Learning. PMLR, 2021.\n\n[11] An, Gaon, et al. \"Uncertainty-based offline reinforcement learning with diversified q-ensemble.\" Advances in neural information processing systems 34 (2021): 7436-7447.\n\n[12] Chen, Xinyue, et al. \"Randomized ensembled double q-learning: Learning fast without a model.\" arXiv preprint arXiv:2101.05982 (2021).\n\n[13] Clements, William R., et al. \"Estimating risk and uncertainty in deep reinforcement learning.\" arXiv preprint arXiv:1905.09638 (2019).\n\n[14] Burda, Yuri, et al. \"Large-scale study of curiosity-driven learning.\" arXiv preprint arXiv:1808.04355 (2018).\n", " \nThank you for your time and feedback. We would like to respond to each weakness and question in turn.\n\n---\n\n### Q1: Performance, Experiment results in Figure 4, Figure 5, Figure 6.\n\n- (a) Our experiment results in Figure 4 show that positive reward shifting consistently improves learning performance in terms of both computational efficiency and asymptotic performance. Importantly, in Walker, reward shifting (~ +3000) **drastically outperforms **CQL(~+1500) by **more than $100\\%$**.\n\n- (b) For Figure 5, 1e6 timestep is a conventional choice of the deep RL literature. We follow the set-ups provided in our baseline [1]. The sample efficiency of RRS is 2.5x, 1.9x, 2.0x, 1.5x, and 1.6x higher than the TD3 baseline on the five tasks — **this is a 1.8x improvement on average.**\n\n- (c) In Figure 6, our experiment results demonstrate reward shifting improves performance on discrete action space exploration tasks. **It is clear in the results** that using negative reward shifting in DQN drastically outperforms the baseline, and applying negative reward shifting also clearly improves RND.\n\n### Q2: Different settings.\n- \"how to find the balance of the conservative and optimistic exploration’’ is the well-known dilemma for online RL, but is **not true** for the offline setting [2]. Also in deep-exploration tasks, the exploration is far more important than exploitation, as otherwise there is nothing that can be exploited at all (e.g., reward sparse tasks[3]). In our paper, we propose the reward shifting that is generally applicable to both online and offline settings — **this is not** ``attempting different reward shifting settings for each environment’’, but **demonstrating the efficacy of the underlying insight with a variety of tasks**. \n\n\n### Q3: ``This paper treats each class of methods differently’’\n- Throughout our paper, we demonstrate the idea that \n`` *L40-41* A positive reward shifting leads to conservative exploitation, while a negative reward shifting leads to curiosity-driven exploration.’’. \nAll settings, analyses, and experiments work together to prove the generality of the proposed insight *L40-41*.\n\n### Q4: ``there is only one baseline algorithm for each class of methods’’\n- **This is not true**. For offline-RL, we made a comparison based on both BCQ and CQL. For online exploration, we compared with DQN (with DQN + reward shifting) and RND (with RND + reward shifting). For continuous control, we compare against TD3, TD3 + ensemble, BootstrappedTD3.\n\n### Q5: Why the baselines in 5.2 and 5.3 are different?\n- Because **benchmark algorithms for continuous control and discrete control are different**. DQN[4] can not be used for continuous control and the idea of learning a policy that selects the action with a maximum $Q$-value function is extended to continuous control by DPG[5], followed by an extended deep version DDPG[6], and then comes TD3[1] that further improves over DDPG.\n", " \n### Q6: How about the total amount of computing between the baselines and the algorithms in this paper?\n- The hardware and computational time are provided in Appendix C. **As we have noted in Checklist 3(d).** In general, shifting the reward does not introduce further computation burden except in the continuous control tasks, our method of Random Reward Shift (RRS) requires two additional $Q$-value networks. In our PyTorch-based implementation, those additional networks can be easily implemented and optimized in a parallel manner, and the extra computational burden is equivalent to using a $\\sqrt{3}$ times wider neural network during optimization. It is worth noting that RRS is computationally much cheaper than the Bootstrapped TD3, where additional policy networks are also needed.\n\n\n\n### Q7: What are the advantages and disadvantages of the proposed method compared to similar exploration enhancement algorithms? Lack of description or theoretical comparisons.\n- We presented the difference between reward shifting and related works in Table 1, and discussed it in detail in Section 4.3.2. We've included an extended discussion on related works in Appendix E.\n\n### Q8: Why does EnsemleTD3 perform worse than TD3 in Figure 5?\n- (a) First of all, the claim of ``EnsemleTD3 performs worse than TD3 in Figure 5’’ **is not true** — Ensemble TD3 only underperforms TD3 in one of the five environments. \n- (b) Ensembling policies in RL are not as trivial as in supervised learning: there is no fixed dataset for training a diverse set of models. Instead, policies need to interact with the environment and collect the replay buffer for its learning. For the pursuance of sample efficiency, we definitely can not let $K$ TD3 agents interact with the environments and update their policies in isolation. In our work, we implement this Ensemble TD3 by using multiple value networks with reward shift constant $0$, and randomly update the policy with one of those value networks, where instability can be introduced and hinder the performance. This set of experiments works as an ablation study to clarify the source of performance gain from RRS.\n\n### Q9: How can fairness be guaranteed by using only 3 Q networks in Figure 5?\n- (a) In our experiments, 10 random seeds are used to demonstrate the statistical differences between performances. We provided experiments with other choices (i.e., 7 networks rather than 3) on the number of Q networks in Appendix C.2.\n- (b) Could the reviewer please explain more on this question for clarity?\n\n\n### Q10: Is the Reward Shift approach better than Count-Based or other approaches? \n- Reward shift can be regarded as an extended version of the count-based exploration while the latter can not be applied to continuous state space. In our experiments, RND is a proxy of such count-based exploration. For a fair comparison, in all experiments, we use exactly the same hyper-parameters for DQN/RND and their combination with reward shifting.\n\n---\n### References\n\n[1] Fujimoto, Scott, Herke Hoof, and David Meger. \"Addressing function approximation error in actor-critic methods.\" International conference on machine learning. PMLR, 2018.\n\n[2] Fujimoto, Scott, David Meger, and Doina Precup. \"Off-policy deep reinforcement learning without exploration.\" International conference on machine learning. PMLR, 2019.\n\n[3] Plappert, Matthias, et al. \"Multi-goal reinforcement learning: Challenging robotics environments and request for research.\" arXiv preprint arXiv:1802.09464 (2018).\n\n[4] Mnih, Volodymyr, et al. \"Human-level control through deep reinforcement learning.\" nature 518.7540 (2015): 529-533.\n\n[5] Silver, David, et al. \"Deterministic policy gradient algorithms.\" International conference on machine learning. PMLR, 2014.\n\n[6] Lillicrap, Timothy P., et al. \"Continuous control with deep reinforcement learning.\" arXiv preprint arXiv:1509.02971 (2015).\n", " Thank you for your comments and questions. We would like to respond to your questions and weaknesses. \n\n-----\n\n### Q1: Update Figure 2 and 3:\n\n - We’ve updated the captions in figure 2, 3 and colorized different notions for clarity.\n\n### Q2. Local Uncertainty Estimators\n\n- (a) Yes, combining multiple neural networks for uncertainty estimation is a well-established method [1], and has been explored in the context of RL for discrete control [2]. \n\n- (b) In this work, applying multiple reward shifting constant leads to multiple value functions, those different value functions can be used to estimate the local uncertainty by $v(s,a) = \\mathbb{E}[(Q_i(s,a) - \\mathbb{E}[Q(s,a)])^2]$.\n\n### Q3: Under what range will the method fail?\n\n- (a) Our experiments have shown that for conservative exploration tasks, reward shifting may perform poorer than the baselines when the shifting constant is too large (e.g., shifting constant = 50, which is approximately 10 - 20 times larger than the maximal step-wise reward of the environment. cf. Figure 7.), as it can be over-pessimistic on extrapolations and thus limits the generalization ability of policies. For optimistic exploration tasks, reward shifting also may perform pooer than the baselines when the shifting constant is too large (e.g., shifting constant = -10, which is more than 10 times larger than the potential episodic return for navigation tasks. cf. Figure 10.). \n\n- (b) We further demonstrate the benefits of reward shifting for deep-exploration tasks and the on-par performance of reward shifting on easier tasks that do not require deep exploration. **The results are updated in Figure 11 in Appendix D.1**. \nWe experiment on the maze environment and change the size of the maze to vary from 2 to 20, denoted as S2, S5, S10, S15, and S20, separately. We find in easy tasks (S2, S5, S10), both count-based exploration and reward shifting perform similarly to the $\\epsilon$-greedy exploration, while on challenging tasks (S15, S20), more explorative behavior encouraged by reward shifting and count-based exploration is important for efficient learning.", " \n\n\n### Q4: Finding the best bias parameter.\n- (a) In general, it’s hard to find a constant that works for all environments as the reward scales in those environments are different. However, as discussed in A2, we can draw some heuristic guidance on the selection of such a hyper-parameter: for exploration tasks, using a constant with a large absolute value (compared to the scale of the reward of a specific task) will lead to exploratory behavior, thus more suitable for hard-exploration tasks. For exploitation tasks, using a relatively small constant can be safer and will not limit the extrapolation of policies.\n- (b) In practice, we find reward shifting outperforms baselines under a wide range of settings in conservative exploitation (cf., Figure 7) and consistently outperforms baselines for curiosity-driven exploration (in Maze tasks where deep exploration is necessary, cf., Figure 10 in appendix).\n\n### Q5: scaling parameter $k$\n- As discussed in the paper, adjusting the scaling parameter $k$ does not change the optimal policy for discrete control (cf., Remark 1) and is equivalent to using a different learning rate for continuous control (cf., Remark 2). Therefore, we put our focus on reward shifting rather than scaling in this paper.\n\n### Q6: Other OFU methods, Rmax\n- While Rmax focuses on model-based methods, we study reward shifting for the value-based model-free algorithms. Nonetheless, extending the basic idea of reward shifting to model-based RL — especially for uncertainty estimation based on different shifted reward mechanisms — is an interesting future direction. \n\n### Q7: Universal bonus v.s. per state-action bonus?\n- (a) Initializing the function approximation with a universal constant to motivate exploration does not conflict with the fact that such a ‘bonus’ can be different during learning, \n- (b) We take the count-based exploration as an example and compare it with reward shifting: in count-based exploration, the intrinsic reward $r_{\\mathrm{intrinsic}}(s,a) = \\frac{1}{K(s,a)}$, where $K(s,a)$ is the number of times the state-action pair $(s,a)$ has been visited, is added to the original reward function, the values of those intrinsic reward for different $(s,a)$ are the same at beginning, but varies during learning as different $(s,a)$-pairs are equally visited. In reward shifting, the value estimation for frequently-visited $(s,a)$-pairs is more precise (e.g., with MC estimation), and much lower than the rarely-visited pairs whose values are still close to the optimistic initialization. \n- (c) Different from count-based exploration where different (and importantly, **non-static**) bonus values are explicitly added to the reward function (hence, the aleatoric uncertainty of the value estimation is increased during learning as the bonus value varies), in reward shifting, such an intrinsic motivation is implicitly implemented by (**static**) optimistic initialization — the underlying optimal $Q$-value function is static during learning. \nMoreover, it is worth noting that count-based exploration can not be applied to continuous scenarios while reward shifting is generally applicable.\n\n\n----\n### References\n\n[1] Lakshminarayanan, Balaji, Alexander Pritzel, and Charles Blundell. \"Simple and scalable predictive uncertainty estimation using deep ensembles.\" Advances in neural information processing systems 30 (2017).\n\n[2] Osband, Ian, et al. \"Deep exploration via bootstrapped DQN.\" Advances in neural information processing systems 29 (2016).\n", " This paper proposes a reward shaping mechanism that trades of exploitation/exploration, by considering adding a negative vs. positive intrinsic constant leads to curiosity driven and conservative exploitation respectively, also they study the effect of positive constant reward multiplication acts as a different learning rate. Based on this simple remark they study how offline and online RL can benefit from this shifting approach.\n\n\n Strengths:\nThis paper is very well written and clear it studies a simple yet widely applicable problem in RL and curiosity driven approaches for exploration. It provides a derivation to how reward shifts affect the optimal value function, and their equivalence to different initialisations.\nIt tackles an important problem in exploration and provides interesting insights.\n\nWeaknesses:\nThe paper does not show case the ranges under which this constant shifts work well, for too large gaps the the agent will never exploit or explore depending on sign? \nThere is also a trade-off between the multiplicative weight k and the bias? Can the authors clarify how these interact with each other?\nHow to best estimate a good b that provides a LB or UB? Can these parameters be learned? \n\n Questions:\n(See above)\n. can the Q_UB-Q_LB provide a good uncertainty estimate locally? \nMinor:\n. missing meaning of each line if both fig.3 and fig. 2 \n. yellow in line166 (no yellow lines exist)\n - The paper studies how constant bias shift affect the value based learning agents as the constant is the same for all action/state space. In intrinsically motivated exploration this is not the case and it is a different one per state/action. Can the authors elaborate on insights of what this means and whether the current approach can make certain cases blind to exploration since the gap now is too big or small.\n- how other OFU methods apply in this setting, such as Rmax.", " The paper first shows that reward shifting is equivalent to diversified Q-value network initialization in deep-RL. This kind of phenomenon can influence learning efficiency. Then, using the key insight, the paper presents three scenarios to show the benefit of reward shifting. Finally, the paper conducts experiments to prove the key insight in three scenarios. Strengths:\n1. The paper shows that reward shifting is equivalent to diversified Q-value network initialization in deep-RL. This is the key point throughout the paper.\n2. In 4.3.1, the paper proposes that Q-value can be written in the form of a linear combination.\n3. The experiments compare many conditions in one environment. \n\nWeakness:\n1. The experiment results are not reliable enough. In Figure 4, the paper shows four kinds of Hopper environment and one kind of Walker environment. And the result in the Walker environment is not so obvious. More environments and more experiments in each environment are needed to compare. The experiment shown in Figure 6 has the same problem. In Figure 5, only 1e6 steps of environmental interactions are used, resulting in policies that have not yet converged in most tasks.\n2. The theoretical proof is not good insufficient. We should be more concerned about how to find the balance of the conservative and optimistic exploration, rather than attempting different reward shifting settings for each environment.\n3. The innovation of this paper requires further discussion. This paper is based on an intuitive idea to optimize multiple classes of methods such as offline and online. This paper treats each class of methods differently, and there is only one baseline algorithm for each class of methods, which makes me worry about the universality of this optimization. 1. In lines 40-41, is there any theoretical proof of this conclusion? Can you make sure in most of the conditions, the key insight is true?\n2. Why the baselines in 5.2 and 5.3 are different?\n3. How about the total amount of compute between the baselines and the algorithms in this paper?\n4. What are the advantages and disadvantages of the proposed method compared to similar exploration enhancement algorithms? Lack of description or theoretical comparisons.\n5. Why does EnsemleTD3 perform worse than TD3 in Figure 5?\n6. How can fairness be guaranteed by using only 3 Q networks in Figure 5?\n7. There is no doubt that negative reward shifting will lead to more exploratory behavior, but is the Reward Shift approach better than Count-Based or other approaches? In Figure 1, Count-Based and epsilon-greedy can also be adjusted for exploration ability by hyperparameters, are these adjusted to be optimal in the experiment? Yes.", " This paper studies how reward shifting can be used to encourage or discourage exploration without modifying optimal behavior in deep Q-learning algorithms. The authors demonstrate how reward shifting can be used in different contexts where exploration is desirable or undesirable and show that it can improve performance on a range of tasks. The core idea proposed by this paper, reward shifting, is shown to be both simple and effective. A simple method (both conceptually and to implement) is more likely to see wider adoption and further work, so that is a significant strength of this paper.\n\nI do feel there are a number of significant issues to be addressed to make this paper great, however. To be clear, I like this work, but I find it hard to recommend it be accepted without substantial modifications (particularly the points below). If these issues can be addressed I think this will be a good paper and a valuable contribution to the field.\n\n-The clarify of the writing is poor. I found the paper generally understandable, so this isn't a fatal flaw, but it made understanding more difficult than it needed to be. Apologies if I'm mistaken, but this paper comes across as written by scientists not fluent in English, and regardless of acceptance status I strongly encourage the authors to take a careful editorial pass (preferably with an English-fluent colleague's help) to improve the language. This will greatly improve the presentation and lead to more people reading and citing this paper in the future.\n\n-The paper feels somewhat padded. Given the simplicity of the core idea it doesn't take much space to explain how reward shifting works, and the paper as is (IMO) spends more space than needed on it. This space could be better spent addressing some of the points below, or increasing the size of the results figures (which are a little too small to read without zooming in).\n\n-The idea of reward shifting is not novel, though I do not know of any work that explores it in the way this paper does. I think the novel contribution is significant and worthy of publication here, but a longer discussion of related work seems important for a paper like this one that applies an old idea in a new way to good effect.\n --There is related work using value function initialization, which is equivalent to reward shifting, to perform exploration. For example DORA, which is cited in this paper but not discussed, uses biased initialization for exploration, which should perform similarly to reward shifting, and seems like a natural point of comparison.\n--Similarly, biased value ensembles have been proposed before, but such methods don't seem to be discussed (Some related works: \"A distributional code for value in dopamine-based reinforcement learning\" by Dabney et al, \"UCB Exploration via Q-Ensembles\" by Chen et al)\n\n-The experiments cover several cases and domains, which is good, but the comparison to RND seems odd as it focuses on simple minigrid environments and doesn't include any hard exploration continuous MDP tasks where baseline naive exploration methods perform poorly, which were the intended use case for RND. For example, the Sparse HalfCheetah environment proposed by VIME or other continuous control exploration tasks similar to the MuJoCo gym tasks already tested would be easy to compare on without additional modification to the algorithm.\n\n-I'd like to see some exploration of the limitations of reward shifting (see limitations section). Some other suggestions (less critical stuff):\n\n-Consider using a non-gridworld example for figure 1. This paper is mostly concerned with deep RL and continuous MDPs, so leading with gridworld results seems odd.\n\n-Figures 2 and 3 I found kind of confusing. I see and like the intent, but it's hard to piece together what's happening based on the caption and equations in the panels. Consider cleaning up the captions and labeling the lines with descriptive labels rather than equations/symbols that haven't been fully introduced/explained at that point in the paper.\n\n-I don't like table 1. It's a matter of preference, but I don't find it informative. Consider focusing on the domains/use-cases for reward shifting instead of the comparison to previous methods.\n\n-I didn't understand the point about RND-1.0 being compared to vanilla DQN. RND has a variable reward bonus, so I'm not sure why it should neatly cancel out when reward shifted.\n\n This paper doesn't discuss the limitations of reward shifting, which I think is a significant issue. The experiments presented show reward shifting to work well on a variety of tasks, but when does it perform poorly? \n\nI think it might have issues with stochastic rewards, for example (offhand it seems like it might work but with worse bounds?)\n\nHow does reward shifting perform on harder exploration tasks, or larger/more complex off-policy datasets? Even if it under-performs compared to dedicated methods there is value in a simpler and more general but less specialized algorithm, so I'd love to see the results regardless of outcome.\n\nRegarding societal impact, I don't think this work has any direct negative impact risks." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 4, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 5, 4 ]

[ "pSsSGvJ8d7E", "nips_2022_iCxRsZcVVAH", "XAzD-gDqJ92", "P8N4RWJ07X", "XAzD-gDqJ92", "LrmL6IalSG", "N1wk8skA2CU", "XAzD-gDqJ92", "nips_2022_iCxRsZcVVAH", "nips_2022_iCxRsZcVVAH", "N1wk8skA2CU", "N1wk8skA2CU", "N1wk8skA2CU", "XAzD-gDqJ92", "XAzD-gDqJ92", "P8N4RWJ07X", "P8N4RWJ07X", "nips_2022_iCxRsZcVVAH", "nips_2022_iCxRsZcVVAH", "nips_2022_iCxRsZcVVAH" ]

[ "yWgWd3SR3GC", "bh2mltBvc6b", "A0MMqtfaqLN", "wy3DMy5ENTa", "0YBgaNynY6C", "c-BE_bgyAA", "CgbdeGOX9G" ]

[ "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for the authors’ effort in the feedback. All my concerns have been answered. I would recommend accepting this work.", " We thank the reviewer for the valuable comments and will add the discussions below to our revised paper.\n\n\n> More qualitative comparisons and analysis on the non-rigid ray transformation \n\nWe add more qualitative comparisons of the non-rigid ray transformation in Figure 2 in the link https://sites.google.com/view/totalselfscan. The results show that the ray transformation significantly improves the image quality. Without the ray transformation, there will be severe artifacts on the head, hands, and edge of the body. The reason is that the self-rotating video includes very limited human poses, and each point on the body is seen from a very limited range of view directions. Therefore, the color field network has difficulty producing high-quality rendering under novel human poses. Replacing the input view directions with global ones is a reasonable way to improve the generalization.\n\n\n\n> The prior of pose-dependent deformations\n \nTo model pose-dependent deformations, we may leverage the existing multi-view human motion datasets to learn a generalizable pose-dependent deformation regressor, which can be conditioned on the human pose and canonical human geometry feature. Once learned, the generalizable regressor can be applied to new input data or can be further finetuned on the input data to improve the results.", " We thank the reviewer for the valuable comments and will add the discussions below to our revised paper.\n\n\n\n> The use of parametric models\n\nThe use of parametric models indeed makes the problem easier but will not harm the applicability of the proposed method as we focus on human body reconstruction. \n\nThe SMPL+H model gives reasonable hand geometry but it is quite coarse and lacks details. In Figure 1 in the link https://sites.google.com/view/totalselfscan, we show the comparison of hand geometry from the SMPL+H model and our reconstructed model. The results show that our method produces more detailed hand geometry such as bones and palm print.", " We thank the reviewer for the valuable comments and will add the discussions below to our revised paper.\n\n> Potential of the FLAME model\n\n\nWe thank the reviewer for the suggestion. As shown in RigNeRF [1] and IMavatar [2], the FLAME model can provide fine-grained face animation, given data with sufficient facial expressions. However, the data we currently collect does not contain rich expressions. In future work, we will collect the corresponding data and try to animate the face using the FLAME model.\n\n\n\n\n> More additional details of the method\n\nWe will add more details about the method and update the overall diagram in the revised paper. The $L^{body}$ loss equals the $L^p$ loss in Equation (10) when the part $p$ denotes the body.\n\n\n> Non-rigid ray transformation\n\nTo avoid unexpected artifacts under novel human poses, the non-rigid ray transformation makes the color unchanged with view direction, which sacrifices the view-dependent effect and makes the rendering less natural. Thus, there is a trade-off between better generalization to novel poses and more photo-realistic rendering. \n\n\n> Comparison with traditional graphics pipeline\n\nThe traditional multi-view reconstruction methods cannot deal with the monocular self-portrait video in which the human is moving. A recent work VideoAvatar[3] proposed to deform a template body mesh to fit the image observations (e.g. silhouettes), but the reconstruction is less realistic due to the limited geometry accuracy and blurred texture map. \n\n\n### References\n\n[1] Athar, ShahRukh, et al. \"RigNeRF: Fully Controllable Neural 3D Portraits.\" CVPR 2022.\n\n[2] Zheng, Yufeng, et al. \"Im avatar: Implicit morphable head avatars from videos.\" CVPR 2022.\n\n[3] Alldieck, Thiemo, et al. \"Video based reconstruction of 3d people models.\" CVPR 2018.", " The paper presents a new method that creates full-body avatars from self-portrait monocular videos. The proposed method specifically models the body, the head, and the hands, the neural volumetric renderings of which are later fused together. Qualitative and quantitative evaluations demonstrate the superiority of the proposed method. Paper strengths:\n- The proposed new method demonstrates clear progress of neural human avatars, achieving sharp and clear renderings under novel views and novel poses.\n- The proposed method is compared against strong existing baselines and ablated carefully.\n\nPaper weaknesses:\n- Despite the FLAME model being used for the head, its potential does not seem to be fully utilized. The facial expression remains static in the final results which significantly increases the uncanniness.\n- The method description could benefit from more additional details. For instance, the latent code is mentioned several times but there lacks a description of it in the overall diagram. The $L^{body}$ loss was not defined in the main text.\n- The non-rigid ray transformation seems to make the texture static across view directions. Was this the reason why the results seem quite rigid? Also, how does the proposed method perform when compared with a traditional graphics pipeline such as deformation transfer? It would be great if the authors could address the above mentioned points in the weaknesses section. There are no potential negative societal impact of this paper.", " This paper proposes to reconstruct the human body with detailed hands and face, leveraging separately recorded hand and face videos. Strengths\n1. The proposed pipeline is sound. Leveraging separate videos for body, face and hands at different scales makes sense; the fusion of geometry and appearance is well designed; the use of non-rigid ray transformation technique for free-view novel pose synthesis is reasonable. \n2. The experiment results show more visually appealing results.\n3. An additional SynTotalHuman dataset is proposed.\n\nWeaknesses\nMy major concern is related to the use of parametric models as the foundation for reconstruction that undermines the technical significance of the paper. The reconstructed hands are claimed to be more refined than prior works, given that SMPL+H is used. Even without any replacement estimation, the SMPL+H already gives good geometry. This is particularly questionable as the examples shown all have bare hands. Please see the Weaknesses section. No additional limitations or potential negative societal impact.", " This work aims at reconstructing the full-body human from several monocular self-rotation videos including the face, hands, and body videos. Compared to the priors, this work improves the local details significantly with the acceptable cost of several extra part videos and more training time. The experiment results prove the effectiveness of the proposed framework and each introduced component. Strengths\n\n- The proposed multi-part networks can utilize information from different part videos to learn better local details. The ablation study in Figure5(a) and Table3 show the effectiveness of multi-part networks. I believe part-based data and modeling is the right way to enhance the details for complex objects like humans. \n\n- To connect the observation space and the canonical space, this work first uses part-based deformation fields to transform the sample points from each observation space, and then performs the geometry and appearance composition to generate a unified model.\n
Sufficient experiments and comparisons have been done to show the superiority of TotalSelfScan.\n\n- Two new datasets are introduced for part-based model evaluation. I believe they can also benefit the computer vision/graphics community.\n\n- Limitations and reasonable potential future solutions have been well discussed. I believe these can also benefit the following works. \n\nWeaknesses\n\n- The non-rigid ray transformation seems a nice strategy to alleviate the unnatural color artifacts. I would expect more qualitative comparisons and analysis on this part.\n Overall, this work is easy to follow and useful for real human reconstruction applications. I am interested in the prior of pose-dependent deformations discussed in the limitation. I think it is the key limitation of TotalSelfScan when applied to animation. I would expect more discussion on this part. The limitations and potential negative societal impact have been well described." ]

[ -1, -1, -1, -1, 7, 6, 7 ]

[ -1, -1, -1, -1, 4, 4, 4 ]

[ "bh2mltBvc6b", "CgbdeGOX9G", "c-BE_bgyAA", "0YBgaNynY6C", "nips_2022_lgj33-O1Ely", "nips_2022_lgj33-O1Ely", "nips_2022_lgj33-O1Ely" ]

[ "LzT7kbsWNaC", "xPBzVldABte", "xEAl7fcvlD", "dMsOQMxJlce", "1r8GsFTJZy", "jc6AXln9a_", "99-uxjgNCbi", "qntPRKmWSJl", "p4wbN2TBjw", "Wl9neW5kbD5", "ccOrWYObTM", "fzwsYq0Eugi", "ituZsgRBBlIl", "1f_212SYaDAF", "1wMiuOqOJh", "2mFGERe0rPQ", "0QouSVlRys7", "pxzfHSfBdh", "zXjO2yvGOEi", "1q2oN6W1SD8", "n_w2z7l38F", "jFk3dYVtln-", "2GYnhDYK8a" ]

[ "author", "author", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear reviewers and ACs: \n\nWe sincerely thank all reviewers for their insightful feedback and constructive suggestions. \n\n\nWe would like to emphasize that our work not only introduces a simple yet effective module InvResMLP for scaling up PointNet++. Our work also proposes a systematical analysis of the modern training strategies in the point cloud domain. Although it is known by some people that improving training strategies can lead to good performance, it is not known by many until our work: (i) *what* are the better training strategies, and (ii) *how much improvement exactly can each strategy lead to*. We show that, without any architecture change, vanilla PointNet++ optimized with the improved training strategies can achieve comparable performance to SOTA. By further scaling up PointNet++, its performance can be raised to outperform SOTA point-based methods in various benchmarks (S3DIS, ScanObjectNN, and ShapeNetPart). We believe these new observations and findings are rather meaningful and helpful for the community. \n\n\nWith regards to the revision, we will incorporate the insightful suggestions of the reviewers as follows:\n\nAccording to Reviewer 1's suggestions, we will revise Tab. 3 to add results of representative models optimized with the improved training strategies. \n\nAccording to Reviewer 2’s suggestions, we will add SGD baselines in the ablation study. \n\nAccording to the suggestions from Reviewer 3 and Reviewer 4, we will add the experiment in the larger-scene dataset ScanNet in revision. We find PointNet++ with improved training and scaling strategies can reach a comparable performance to MinkowskiNet and Point Transformer. \n\nAccording to Reviewer 3's comments, we will also mention the limitation of the current point-based methods in outdoor scene understanding, and provide our findings in SemanticKITTI in the supplementary.\n\nAccording to Reviewer 4’s suggestions, we will further explore the bottleneck structure and add this study in revision.\n\nWe will improve other minor points mentioned by all reviewers in revision. \n\nThank you all for the valuable suggestions.\n\nThanks,\n\nPaper 703 Authors", " \nThank you for the comments and the request for additional experiments. We appreciate the time spent by the reviewer. We would like to highlight the following: \n\n\n1. Our paper does not try to push the rope towards neither point-based methods nor voxel-based methods. Our work focuses on point-based methods and aims at improving the classical PointNet++ without sophisticated architecture engineering. \n\n\n2. New observations and findings are also meaningful and helpful for the community. The intention of this work is not to propose new architecture, yet trying to draw the attention of the point cloud community to the training and scaling strategies, which are truly important. Although it is known by *some* people that improving training strategies can lead to *good* performance for PointNet++, it is **NOT known** by *many*: (i) **what** are the better training strategies, and (ii) a particular **finding** that the performance of PointNet++ can be raised to reach or even outperform **SOTA** point-based methods. ", " Thanks very much for the additional experiments and comments!\n\nThe reviewer does acknowledge the experiments on a new dataset SemanticKITTI within a very short time: \n* I agree with you that the improved training strategies + larger radius can achieve better performance, which is also well-known for lots of researchers in the 3D community. \n* The inferior performance does verify the concern of the reviewer that the structure of PointNet++ is not suitable for large-scale scenes, actually we also do not notice that there are any other recent approaches using this PointNet++-like structure as a backbone network.\n\nNevertheless, I have to say that the most concerns are still the technical contributions of this paper: \n* The exhaustive ablation experiments about some well-known data augmentation. \n* A residual block \n\nActually, these two contributions can be applied to lots of structures, not just PointNet++. Although the reviewer acknowledges the efforts and experiments of the authors to show a clear engineering exploration of these factors, both of them are not significant to be published at NeurIPS. \n\nAs for the surprising finding that PointNet++ can also achieve very good performance on multiple datasets, actually, it is not that surprising since both the reviewer and some other researchers have known this fact for a long time, maybe just because the baseline of PointNet++ is not that strong. \n\nAccording to the above reasons, I can not recommend an accept rating. \n \n\n", " Thank you for the constructive comments.\n\n> Q: *I would kind remind the authors that \"first to introduce something from B to A\" does not mean it is good or novel.*\n\n**A:** We thank the reviewer for pointing this out. We highlight that our main contributions are the systematical analysis of the training strategies in various benchmarks and the finding that the performance of the classical network PointNet++ can be improved to the state-of-the-art level. Apart from the main contributions, our introduced InvResMLP module is also proven to be effective. We thank that our contributions are recognized by you and other reviewers. \n\n\n> Q: *I believe fine-tunning the hyper-parameters for bootleneck structure carefully could achieve bettter performance.*\n\n**A:** We thank the reviewer for this constructive suggestion. We will further explore the bottleneck structure and add this study in our revision. ", " We thank the reviewer for the additional comments. \n\n> Q: *why PointNeXt is still applicable and suitable for large-scale outdoor scenes?*\n\n**A:** We successfully show that the performance of PointNet++ can be surprisingly **improved by over 20 mIoU** by **only** adopting improved training and model scaling strategies. We highlight that this achievement is made **within only 4 days**. Given more parameter tuning (e.g. radius, learning rate, data augmentations), we believe the mIoU can be further improved to achieve at least a close performance to other point-based methods. \n\nHowever, we do acknowledge that compared to voxel-based methods, the point-based methods (not only PointNeXt) fail to prove their strength for outdoor scenes in the current landscape. We think this inferiority is because of the non-uniform nature of outdoor scenes, which causes difficulties for neighbor querying and local aggregation in point-based methods. We will mention this in the limitation part and leave it as future work.\n\n\n> Q: *How many points does PointNeXt utilize in each level?*\n\n**A:** We use an *initial* radius of 0.4m. The radius is doubled by default when the point cloud is downsampled (mentioned in manuscript L136-137). Since we have four stages in the PointNeXt architecture, the radius for the last stage is 6.4m, which can cover core parts of most objects of interest, such as cars, pedestrians, e.t.c. We note that there might be a radius other than 0.4m that can lead to better performance. With regards to the number of points, we always query k=32 neighbors, which is the same as PointNet++. \n\n> Q: *What's the advantage of PointNeXt compared with the voxel-based method? Especially for the large-scale outdoor scenes.*\n\n**A:** View-based, voxel-based, and point-based are the three mainstream point cloud processing schemes. All of them are widely used. Point-based methods are comparable to the voxel-based methods in indoor scene perception, and especially dominate the application where the input point cloud is small-scale. The focus of our work is the point-based method, where we show the classical point-based method PointNet++ can be improved to reach SOTA point-based performance. Nevertheless, we agree with the reviewer that the point-based methods fail to prove their strength for outdoor scenes in the current landscape (please refer to question 1 for details). \n\n\n> Q: *Why PointNeXt can be faster than voxel-based methods since there are lots of customized CUDA operations (FPS, set abstraction)?*\n\n**A:** We mentioned in the discussion part I that we replaced FPS with random sampling to speed up PointNet++ by 4 times from 10 ins./sec. to 42 ins./sec. \n", " Thanks for the detailed feedback!\n\nThere are some further questions for discussion: \n* Can you comment a bit about why PointNeXt is still applicable and suitable to large-scale outdoor scenes? Since its performance (48+%) is much lower than SOTA (60-70% mIoU), and is also lower than other Point-based method like KPConv (58.8%) and RandLA-Net (53.9%). \n* How many points does PointNeXt utilize in each level? Do you apply 0.4 radius in each level? Is it enough to capture a large scene with a small number of points (e.g., 256) and 0.4 radius? \n* What's the advantage of PointNeXt compared with voxel-based method? Especially for the large-scale outdoor scenes. Speed or performance? This is the most important concern. A good illustration and analysis can convince the reviewer that the improvement on PointNet++ is meaningful to the whole 3D community. And the reviewer does not understand why PointNeXt can be faster than voxel-based methods since there are lots of customized CUDA operations (FPS, set abstraction). ", " Thank you for the responses, which address my concern regarding the effectiveness of the relative coordinate normalization. \n\nI recognize the contribution of the paper but its novelty is not that significant. Therefore, I lean towards keeping my rating 6. ", " Thanks for the further responses.\n\n1. Author claimed \"PointNeXt is the first to show that ...\" \nI would kind remind the authors that \"first to introduce something from B to A\" does not mean it is good or novel. \n\n2. Thanks for the further experiments, that makes more sense. And I believe fine-tunning the hyper-parameters for bootleneck structure carefully could achieve bettter performance.\n\n", " \nThank you for the recognition of our work. We appreciate your encouraging comments: \"it provides systematical analysis and comparisons\" and \"may inspire the community and help a lot,\" which are exactly the original intention of our study. We address your additional concerns as follows.\n\n\n> **Q**: *the contributions in architecture (say, Inv-Res-Block, weight decay) still cannot convince me.*\n\n\n**A**: (i) With regards to Inv-Res-Block, PointNeXt is the first to show that InvResMLP inspired by 2D architectures can work effectively for 3D point cloud understanding. By combining InveResMLP and PointNet++, we propose a new architecture that achieves SOTA performance. (ii) With regards to relative position normalization, we find that without it, the network is learned to ignore the relative positions since their values are of small magnitude. \n\n\n> **Q**: *PointNeXt-XL with Bottleneck Structure*\n\n\n We thank the reviewer for this suggestion. Here, we provide four additional experiments. (1) PointNeXt-XL with Bottleneck (C=64 -> C=65) to make the throughput the same as PointNeXt-XL by width scaling (increasing channels); (2) PointNeXt-XL with Bottleneck (C=64 -> C=70) to make the FLOPs the same as PointNeXt-XL by width scaling; (3) PointNeXt (C=140) to make the number of parameters the same as PointNeXt-XL by width scaling; (4) PointNeXt-XL with Bottleneck (B=[3,6,3,3] -> B=[4,7,4,4]) to make the number of parameters the same as PointNeXt-XL by depth scaling (appending more blocks). PointNeXt-XL outperforms all the variants with bottleneck structures. \n\n**Table R4-B: Ablation study on bottleneck structures on S3DIS.**\n| Method | mIoU (%) | Params (M) | FLOPs (G) | Throughput |\n|--------------------------------------------|--------------|------------|-----------|------------|\n| PointNeXt-XL | $70.5\\pm0.3$ | 41.5 | 84.8 | 45 \n| PointNeXt-XL with Bottleneck (Baseline) | $69.1\\pm0.2$ | 8.7 | 71.0 | 50 |\n| PointNeXt-XL with Bottleneck (C=65) | $67.9$ | 9.0 | 73.2 | 45 |\n| PointNeXt-XL with Bottleneck (C=70) | \t$68.9$ | 10.4 | 84.8 | 39 |\n| PointNeXt-XL with Bottleneck (C=140) | $68.3$ | 41.6 | 336.3 | 18 |\n| PointNeXt-XL with Bottleneck (B=[4,7,4,4]) | $69.8$ | 10.8 | 87.2 | 43 |\n\n", " \n> **Q**: *Differences with PointTransformer in terms of training strategies?*\n\nWe have provided the training differences between our PointNeXt and Point Transformer in S3DIS in the submitted **supplementary material** (Table IV). For easy review, we additionally show the comparison of training strategies in Table R3-E. PointNeXt differs from Point Transformer in the optimizer, the LR scheduler, label smoothing, random rotation, random jittering, height appending, color dropping, and color jittering. Pls refer to Table R3-E for details. \n\nNote that Point Transformer did not officially conduct experiments in ScanNet. The reported values of Point Transformer in Table R3-D are from Stratified Transformer [3]. We compare the training strategies between our PointNeXt and Stratified Transformer in ScanNet in Table R3-F. PointNeXt differs from Stratified Transformer in the lr, LR decay, weight decay, random jittering, and color auto-contrast. Pls see Table R3-F for details. \n\n[3] Lai, Xin, Jianhui Liu, Li Jiang, Liwei Wang, Hengshuang Zhao, Shu Liu, Xiaojuan Qi, and Jiaya Jia. \"Stratified Transformer for 3D Point Cloud Segmentation.\" In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8500-8509. 2022.\n\n**Table R3-E: Training strategies used in PointTransformer and our PointNeXt in S3DIS**\n| $\\textbf{Method}$ | $\\textbf{PointTransformer}$ | $\\textbf{PointNeXt (Ours)}$ |\n|-------------------------------|:-------------------------:|:-------------------------:|\n| Epochs | 100 | 100 |\n| Batch size | 16 | 32 |\n| Optimizer | SGD | AdamW |\n| LR | 0.5 | $0.01$ |\n| LR decay | multi step | cosine |\n| Weight decay | $10^{-4}$ | $10^{-4}$ |\n| Label smoothing $\\varepsilon$ | 0.0 | 0.2 |\n| Random rotation | no | yes |\n| Random scaling | [0.9, 1.1] | [0.9, 1.1] | |\n| Random jittering | no | sigma=0.005 |\n| Height appending | no | yes |\n| Color dropping | no | 0.2 |\n| Color auto-contrast | yes | yes |\n| Color jittering | yes | no |\n| mIoU (\\%) | 73.5 | 74.9 |\n\n**Table R3-F: Training strategies used in StratifiedTransformer and our PointNeXt in ScanNet**\n| $\\textbf{Method}$ | $\\textbf{StratifiedTransformer}$ | $\\textbf{PointNeXt (Ours)}$ |\n|-------------------------------|----------------------------------|-----------------------------|\n| Epochs | 100 | 100 |\n| Batch size | 8 | 8 |\n| Optimizer | AdamW | AdamW |\n| LR | 0.006 | $0.001$ |\n| LR decay | multi step with warm up | multi step |\n| Weight decay | 0.05 | $10^{-4}$ |\n| Label smoothing $\\varepsilon$ | 0.0 | 0.0 |\n| Random rotation | yes | yes |\n| Random scaling | [0.8, 1.2] | [0.8, 1.2] |\n| Random jittering | no | sigma=0.005 |\n| Height appending | no | yes |\n| Color dropping | 0.2 | 0.2 |\n| Color auto-contrast | no | yes |\n| Color jittering | no | no |\n| Test mIoU (\\%) | 73.7 | 71.2 |\n\n\n", " Thank you for the constructive suggestions. We address the concerns below: \n\n\n> **Q**: *Concerns about technical contribution.*\n\n**A**: We respect the reviewer's opinion. With regards to technical contributions, we would like to highlight two points. 1) Our work is a comprehensively empirical study, presenting a surprising finding (especially in the current landscape of increasingly sophisticated and complicated deep networks): with improved training and model scaling strategies, the performance of the simple baseline PointNet++ can be significantly improved and outperform SOTA. We think that this finding would bring some meaningful impact to the community and facilitate future innovations along this path. 2) PointNeXt is the first to show that InvResMLP inspired by 2D architectures can work effectively for 3D point cloud understanding. By combining InveResMLP and PointNet++, we propose a new architecture that gets SOTA performance. This successful introduction of existing modules from one domain to another domain is also commonly deemed novel in the literature. \n\n\n> **Q**: *Performance of PointNet++ in outdoor scenes with large reception region.*.\n\n**A**: Thank you for pointing out this new scenario. PointNeXt is applicable in outdoor scenes and can achieve reasonable performance with real-time efficiency. In Table R3-C, we show that the reported performance of PointNet++ (20.1 mIoU) can be increased by **+28.4** mIoU to reach 48.4 mIoU in the SemanticKITTI test set while being 4 times faster, by adopting our proposed training strategies, a dataset-specific radius (0.4m), relative position normalization, and the random sampling in replacement of the original furthest point sampling. Below we share the technical details in SemanticKITTI. \n\n\nThere are two significant differences between segmenting outdoor scenes in SemanticKIITI and segmenting indoor scenes in ScanNet / S3DIS: (i) the perception region is much larger (~100 meters v.s. ~10 meters), and (2) high efficiency requirement. Due to (i), we ablate the *initial radius and find that simply increasing it from 0.1m to 0.4m gives around 10 mIoU higher in validation*. Because of (ii) we replace furthest point sampling in PointNet++ with *random sampling* as suggested by RandLA-Net [1]. Random rotation, random scaling, random jittering, and height appending are used as data augmentations. Models are trained with CrossEntropy loss, AdamW optimizer, an initial learning rate of 0.001, a multistep learning rate scheduler (decay rate 0.1 at epochs 30 and 40), and a batch size of 16 for 50 epochs. \n\n\n**Table R3-C: Ourdoor semantic segmentation on SemanticKITTI.**\n\n| Method | val mIoU | test mIoU | Throughput |\n| ----------------------------- | -------- | --------- | ---------- |\n| PointNet | - | 14.6 | - |\n| RandLA-Net | - | 53.9 | - |\n| PointNet++ | - | 20.1 | 10 |\n| **PointNet++ (Ours, r=0.1m)** | 37.3 | 35.4 (+15.3) | 42 |\n| **PointNet++ (Ours, r=0.4m)** | 47.2 | - | 42 |\n| **PointNeXt-S** | 48.9 | 48.4 (+28.3) | 42 |\n\n\n\n\n[1] Hu, Qingyong, Bo Yang, Linhai Xie, Stefano Rosa, Yulan Guo, Zhihua Wang, Niki Trigoni, and Andrew Markham. \"Randla-net: Efficient semantic segmentation of large-scale point clouds.\" In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 11108-11117. 2020.\n\n\n> **Q**: *Results on ScanNet Test Set*.\n\nWe provide the results on ScanNet Test Set in Table R3-D. Per submission policy of ScanNet, one paper can only submit one result per track per two weeks [2]. We are only able to get the testing result of PointNeXt-XL at this time. PointNeXt achieves 72.5 mIoU in validation and 71.5 mIoU in testing. Note that we do not perform voting in validation and testing unlike previous methods (e.g. Stratified Transformer). Experiments show that PointNeXt can be extended to ScanNet and is able to increase the originally reported performance of PointNet++ by **+15.5 mIoU** by the improved training and model scaling strategies.\n\n**Table R3-D: Scene segmentation on ScanNet.**\n| Method | val mIoU (%) | test mIoU (%) |\n| ----------------------- | ------------ | ------------- |\n| Point Transformer | 70.6 | - |\n| MinkowskiNet | 72.0 | 73.4 |\n| Stratified Transformer | 74.3 | 73.7 |\n| PointNet++ | 53.5 | 55.7 |\n| **PointNet++ (Ours)** | 57.2 (+3.7) | - |\n| **PointNeXt-B (Ours)** | 68.0 (+14.5) | - |\n| **PointNeXt-XL (Ours)** | 72.5 (+19) | 71.2 (+15.5) |\n\n\n[2] https://kaldir.vc.in.tum.de/scannet_benchmark/documentation#submission-policy\n", " After reading other reviewers' comments and authors' rebuttals, I would keep my score and suggest acceptance. \n\nAs I stated previously, one reason I like this work is that it provides systematical analysis and comparisons between recent works instead of proposing something new but trivial. I do think this paper may inspire the community and help a lot. \n\nHowever, the contributions in architecture (say, Inv-Res-Block, weight decay) still cannot convince me. \n\nAlso, for the PointNeXt-XL with Bottleneck Structure, authors should keep the parameters number and FLOPs same as PointNeXt-XL for a fair comparison (by adding blocks), not simply replacing to bottleneck structure. ", " Thanks for providing the rebuttal.\n\nI agree that this paper has a positive impact to the community by systematically investigating the data augmentation and PointNet++ to achieve better performance. \n\nHowever, the technical contribution and the generalizability of PointNet++ are still the main concern, and this paper is more like a meaningful technical report but not a good academic publication. From the reviewer's perspective, the only new thing is the normalization of relative coordinates, but the experiments show that it has slight performance gains (also mentioned by other reviewers). \n\n\nFor the rebuttal, I have the following questions: \n\n* Large-scale dataset: the scale of the dataset not only contains the number of points but also the perception region. \n * Although S3DIS contains a huge number of points, the region is very small (indoor scene), and very dense points within a small region don't make sense since you can easily voxelize the points and only segment the sampled points and extend to neighboring points. \n * In contrast, the point cloud in outdoor scenes makes more sense due to a real point cloud and much larger perception region. Are PointNet++ still applicable to achieve good performance on such a large perception region? Compared with the voxel-based method, can it still achieve a good trade-off between performance and efficiency? Considering the limited time, the reviewer does not really need very good performance but need the authors to convince the reviewer that it is feasible. \n\n* For the experiments on ScanNet, can you also report the performance on test set leaderboard? Since this paper tailors to a high-performance framework with sorts of engineering techniques, the comparison with state-of-the-art works on test set is important. \n\n* Since the paper argues that this is the first comprehensive study about data augmentation and optimization strategies, can you compare the differences with PointTransformer in terms of these techniques? It would convince the reviewer more that this work is meaningful instead of writing something other paper adopted but not mentioned in their paper. ", " \n> **Q**: *In Line 142, \"without normalization, ... larger weight...\", distributions of position encoding layer weights*.\n\n**A**: We investigate the distributions of weights of the last position encoding layer in the pretrained PointNeXt-XL with and without relative coordinate normalization. Interestingly, we find PointNeXt-XL with normalization learns position weights (mean -0.06, std 1.1) close to the weights of features (mean 0.05, std 1.8) in terms of magnitude. However, PointNeXt-XL without normalization only learns position weights (mean -0.007, std 0.5) 10 times smaller than features weights (mean -0.05, std 0.2) in terms of magnitude. This shows that without normalization, the network tends to be optimized to ignore relative positions because of their small values.\n\n> **Q**: *In Line 143, \"This makes ..., ... weight decay...\" What results would weight decay cause?*\n\n**A**: Weight Decay is a regularization technique that tends to reduce the magnitude of the weights towards zero. The relative position is small without normalization, so the Neural Network needs larger weights to apply $\\Delta p$, otherwise, the effect of the relative position will be neglectable. This increases optimization difficulties. ", " Thank you for the positive recognition of our work and the valuable comments. We address the issues as follows:\n\n> **Q**: *\"The radius is dataset-specific\" is not a finding.*.\n\n**A**: Thank you for pointing this out. We will revise the paper to address this concern.\n\n> **Q**: *Inv-Res-Block presents nothing new*. \n\n**A**: To the best of our knowledge, we are the first to study such an inverted residual block in the point cloud field. This simple module is also practical for point cloud understanding and can help achieve state-of-the-art performance. We believe that this unified design between images and point clouds also benefits the computer vision community.\n\n> **Q**: *Conduct experiments on large datasets*. \n\n**A**: We conducted experiments on S3DIS, which is well-known for its large scale in the point cloud domain. One room in S3DIS dataset contains an average of 795K points, which is even over five times larger than ScanNet (around 146K points per room) in terms of the number of points.\n\nHere we provide additional experiments on ScanNet. We use similar training strategies on S3DIS for ScanNet experiments. Random rotation, random scaling, color auto-contrast, random color dropping, and height appending are used as data augmentations. Models are trained with CrossEntropy loss, AdamW optimizer, an initial learning rate of 0.001, a multistep learning rate scheduler (decay rate 0.1 at epochs 70 and 90), and a batch size of 16 for 100 epochs. The initial radius is set to 0.05. Results of PointNet++ and PointNeXt optimized with the above training strategies on the ScanNet *Val set* are provided in Table R4-A. PointNet++ trained with our strategies achieves 57.2 mIoU, outperforming the originally reported values by 3.7 mIoU. Our PointNeXt-B outperforms the PointNet++ by 14.5 mIoU. Our largest variant PointNeXt-XL achieves **72.5** mIoU, outperforming the voxel-based method MinkowskiNet. Note we do NOT perform any voting. Due to the limited time, we can only train and evaluate PointNet++, PointNeXt-B, and PointNeXt-XL. \n\nTable R4-A: Scene segmentation on Scannet Val Set.\n| Method | OA (%) | mAcc (%) |mIoU (%) | \n| -------- | -------- | -------- |-------- |\n| Point Transformer | -|-\t|70.6|\n| MinkowskiNet | - | -\t|72.0| 1.0 |\n| Stratified Transformer | -|-\t|74.3| \n| PointNet++ | -|-\t|53.5| \n| **PointNet++ (Ours)** | 83.0\t|67.5|\t57.2| \n| **PointNeXt-B (Ours)** | 88.5\t|76.0|\t68.0| \n| **PointNeXt-XL (Ours)** | 89.8\t| 79.6|\t72.5| \n\n> **Q**: *In Line 45, \"For the S3DIS segmentation benchmark, can increase by 13.6% \". Is it achieved by training strategies*. \n \n**A**: Yes, this is the result of PointNet++ with our training strategies alone without any change to the architecture. \n\n> **Q**: *Why consider InvBlock*. \n\n**A**: This design is inspired by Transformer i.e., where the hidden dimension of the MLP block is four times wider than the input dimension. InvBlock is also a successful module for image understanding proposed in MobileNetV2. \n\n> **Q**: *What if change to bottleneck structure*. \n\n**A**: We thank the reviewer for this question. We replace the inverted structure with a bottleneck structure (bottleneck ratio = 4) in PointNeXt-XL. As shown in Table R4-B, the inverted block outperforms the bottleneck counterpart.\n\n\nTable R4-B: Scene segmentation on S3DIS.\n| Method | OA (%) | mAcc (%) | mIoU (%) |\n| -------- | -------- | -------- |-------- |\n| PointNeXt-XL with Bottleneck Structure | $89.6\\pm0.4$|\t$75.3\\pm0.2$\t| $69.1\\pm0.2$|\n| PointNeXt-XL | **$90.6\\pm0.2$**\t|**$76.8\\pm0.7$**|\t**$70.5\\pm0.3$**|\n\n\n> **Q**: *Compared to other modifications, normalizing the relative positions by Eq. (2) could not be considered a \"significant influence (Line 138)\".* \n\n**A**: We thank the reviewer for pointing this out. We will revise the paper to tone down this claim.", " We respect the reviewer's opinion, however, we believe that our work strongly alines with NeurIPS standards and has a positive impact on the community. We address the reviewer's comments below:\n\n> **Q**: *data augmentation and optimization strategies are well-known tricks*.\n\n**A**: We agree it is known that applying more advanced training strategies mostly leads to better performance. However, our work is the first to formally and comprehensively study the incremental effect of those strategies. Specifically, our work answers the following two *previously unsolved* fundamental questions, (i) *which* training strategies to apply, and (ii) *how much improvement* can the training strategies lead to. The merits of our work include that, first, we *quantify the effect of each strategy* and provide a state-of-the-art combination of training strategies for each benchmark. Second, we showcase that simply by adopting our training strategies, without any change to the architecture, the performance of PointNet++ can be improved significantly (see Tab. 4 and Tab. 5 for specific numbers of improvements), and even surpass SOTA in some cases (Tab. 4). \n\n\n> **Q**: *InvResMLP is straightforward*. \n \n**A**: Our work does not aim to propose any new architectural innovations. Instead, we choose to look in an orthogonal equally important direction which is network training strategies. With regards to the architecture modification, we borrow and combine successful architectural designs from the 2D domain (as cited in our paper) and introduce them to the field of point clouds (the proposed InvResMLP module). Surprisingly, we are the first to show that this simple InvResMLP module can work effectively in 3D point cloud understanding and allow us to outperform the SOTA. We believe that this finding is of great benefit to the community.\n\n\n> **Q**: *hard to scale to large point cloud scenes*. Can PointNeXt be extended to larger scenes like ScanNet and SemanticKITTI?\n\n**A**: We appreciate the reviewer's comment. We argue that PointNeXt can be easily deployed to any large-scale dataset. In the manuscript, we have shown the superiority of PointNeXt in a large-scale dataset, Stanford *Large-Scale* 3D Indoor Spaces dataset (S3DIS). Note that S3DIS is well-known for its large scale in the point cloud domain, where one room contains an average of 795K points, which is even over five times larger than ScanNet (around 146K points per room) in terms of the number of points.\n\n\nNevertheless, we do understand the encouragement for the additional experiments on ScanNet and SemanticKIITI. Due to the limited rebuttal time, we choose to focus on ScanNet. We use similar training strategies on S3DIS. Random rotation, random scaling, color auto-contrast, random color dropping, and height appending are used as data augmentations. Models are trained with CrossEntropy loss, AdamW optimizer, an initial learning rate of 0.001, a multistep learning rate scheduler (decay rate 0.1 at epochs 70 and 90), and a batch size of 16 for 100 epochs. The initial radius is set to 0.05. Results of PointNet++ and PointNeXt optimized with the above training strategies on the ScanNet *Val set* are provided in Table R3-A. PointNet++ trained with our strategies achieves 57.2 mIoU, outperforming the originally reported values by 3.7 mIoU. Our PointNeXt-B outperforms the PointNet++ by 14.5 mIoU. The largest variant PointNeXt-XL achieves 72.5 mIoU, outperforming the voxel-based method MinkowskiNet. Note we do NOT perform any voting. Due to the limited time, we can only train and evaluate PointNet++, PointNeXt-B, and PointNeXt-XL. Our experiments show that PointNeXt can be extended to ScanNet and achieves better performance than the point-based methods Point Transformer and the voxel-based method MinkowskiNet. \n\n\nTable R3-A: Scene segmentation on ScanNet Val Set.\n| Method | OA (%) | mAcc (%) |mIoU (%) | \n| -------- | -------- | -------- |-------- |\n| Point Transformer | -|-\t|70.6|\n| MinkowskiNet | - | -\t|72.0| 1.0 |\n| Stratified Transformer | -|-\t|74.3| \n| PointNet++ | -|-\t|53.5| \n| **PointNet++ (Ours)** | 83.0\t|67.5|\t57.2| \n| **PointNeXt-B (Ours)** | 88.5\t|76.0|\t68.0| \n| **PointNeXt-XL (Ours)** | 89.8\t| 79.6|\t72.5| \n\nResults of previous methods in Table R3-A are from Stratified Transformer [1]. \n\n[1] Lai, Xin, Jianhui Liu, Li Jiang, Liwei Wang, Hengshuang Zhao, Shu Liu, Xiaojuan Qi, and Jiaya Jia. \"Stratified Transformer for 3D Point Cloud Segmentation.\" In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8500-8509. 2022.", " > **Q**: *Information about scaling is confusing*. \n\n**A**: (i) As mentioned in Line 167-169, PointNet++ used different model configurations in classification, part segmentation, and semantic segmentation tasks. Compared to PointNet++ for classification and part segmentation in terms of the number of convolutional layers, PointNeXt-S is a scaled-up variant. Compared to PointNet++ for semantic segmentation on S3DIS, PointNeXt-S is a scaled-down variant. We will revise the paper to make this point more clear. \n\n(ii) We thank the reviewer for pointing out that the scaling rule for ShapeNetPart differs from others. We found that the performance was saturated with depth scaling on ScanObjectNN and ShapeNetPart. This is mainly due to the small scales of these two datasets (refer to Line 255-264). We will clarify this in the revision.", " We thank the reviewer for the constructive suggestions and valuable feedback. We answer all the comments below and will revise the manuscript accordingly.\n\n> **Q**: *Relative coordinates normalization is not significant*. \n \n**A**: Thank you for the interest in our relative coordinates normalization. Note that we did not claim normalization can significantly improve performance. The benefit of the proposed normalization is that it *improves performance consistently without an overhead*. It is a single-line code that averagely produces +0.4 mIoU on S3DIS (Tab. 5) and +0.3 OA on ScanObjectNN (Tab. 4). We also found that normalization has a larger impact on bigger models (e.g., +2.3 mIoU for PointNeXt-XL, Tab. 7) compared to smaller models (e.g., +0.4 mIoU for PointNet++). This might be because the bigger model is harder to optimize compared to the smaller models, and our normalization allows for achieving an easier optimization.\n\n> **Q**: *Include SGD as a reference*. \n\n**A**: We thank the reviewer for this helpful suggestion. We provide the results of SGD here and will add them to the revised manuscript. Note that SGD might require a different learning rate (lr) compared to Adam and AdamW, thus we test SGD with different learning rates (lr * 0.1, lr, lr * 10, lr * 50, lr * 100). In the tables below, we include the results of PointNet++ optimized using SGD with the best learning rate on ScanObjectNN and S3DIS, respectively. AdamW produces better results than SGD and Adam on both benchmarks.\n\n\n| ScanObjectNN | OA (\\%) | $\\Delta$ |\n| --------------------------------------- | :----------: | :------: |\n| PointNet++ | 77.9 | -- |\n| ... | ... | ... |\n| $+$ Label Smoothing | $85.0\\pm0.5$ | +1.3 |\n| $+$ Adam $\\rightarrow$ AdamW (lr=0.002) | $85.6\\pm0.1$ | +0.6 |\n| $+$ AdamW $\\rightarrow$ SGD (lr=0.002) | $84.8\\pm0.1$ | -0.8 |\n\n\n\n| S3DIS | mIoU (%) | $\\Delta$ |\n| -------------------------------------- | :----------: | :------: |\n| PointNet++ | 51.5 | -- |\n| ... | ... | ... |\n| $+$ Label Smoothing | $61.9\\pm0.1$ | +0.4 |\n| $+$ Adam $\\rightarrow$ AdamW (lr=0.01) | $62.5\\pm0.6$ | +0.6 |\n| $+$ AdamW $\\rightarrow$ SGD (lr=0.5) | $59.4\\pm0.5$ | -3.1 |\n", " Thank you for the constructive suggestions and valuable feedback. All comments are addressed below. We will revise the paper in light of the provided comments. \n\n> **Q**: *Generalization of the training strategies*. \n\n**A**: Along with PointNet++, we provided three other networks optimized with our training strategies, including *PointMLP*, PointNet, and DGCNN in Tab. 6. The proposed training and scaling strategies can improve the overall accuracy (OA) of PointMLP by 1.7 from 85.4±0.3 to 87.1±0.7 on ScanObjectNN. The results and analysis of PointMLP have been discussed in the manuscript (Line 323-330).\n\nAs suggested, we further evaluate our training strategies on SimpleView [1]. Note that SimpleView is a view-based method, whereas our training strategies focused on point-based methods. Therefore, some of the proposed strategies might not be applicable for view-based methods, e.g., height appending. Despite that, we can still observe that our training strategies improve the performance of SimpleView by 1.5 from 80.5 to 82.0±0.4 OA. We will report this result with relevant discussion in the revision. \n\n[1] Goyal, Ankit, et al. \"Revisiting point cloud shape classification with a simple and effective baseline.\" International Conference on Machine Learning. PMLR, 2021.\n\n> **Q**: *Missing parameters or FLOPs*. \n \n**A**: Model parameters and FLOPs were omitted in Tab. 2 and Tab. 3 because of the limited space in the manuscript. Here we provide the number of parameters, FLOPs, and throughputs of representative methods on ScanObjectNN in Tab. R1-A and on ShapeNetPart in Tab. R1-B. The results in the tables show that PointNeXt surpasses state-of-the-art point-based methods with fewer parameters and lower computational costs. We will provide the number of parameters, FLOPs, and throughput in the revision.\n\n\nTable R1-A: Object classification on ScanObjectNN. \n| Method | OA | mAcc | Params. (M) | FLOPs (G)| Throughput (ins./sec.) |\n|---------------------------------------|----------------------------------------|-----------------------------------------|:-------:|:-----:|:-------------:|\n| DGCNN | 78.1 | 73.6 | 1.8 | 4.8 | 402 |\n| DGCNN (**Ours**) | $\\textbf{86.0}\\pm0.5$ | $\\textbf{84.0}\\pm0.7$ | 1.8 | 4.8 | 402 |\n| PointMLP | $85.4\\pm1.3$ | $83.9\\pm1.5$ | 13.2 | 31.4 | 191 |\n| PointMLP (**Ours**) | $\\textbf{87.1}\\pm0.7$ | $\\textbf{85.6}\\pm1.1$ | 13.2 | 31.4 | 191 |\n| SimpleView | 80.5 | - | 0.8 | 6.7 | 102 |\n| SimpleView (**Ours**) | $\\textbf{82.0}\\pm0.4$ | $\\textbf{78.4}\\pm0.5$ | 0.8 | 6.7 | 102 |\n| PointNet++ | 77.9 | 75.4 | 1.5 | 1.7 | 1872 |\n| PointNet++ (**Ours**) | $86.1\\pm0.7$\t| $84.2\\pm0.9$ | 1.5 | 1.7 | 1872 |\n| PointNeXt-S (**Ours**) | $\\textbf{87.7}\\pm0.4$ | $\\textbf{85.8}\\pm0.6$| 1.4 | 1.6 | 2040 |\n\n\n\nTable R1-B: Part segmentation on ShapeNetPart. \n| Method | Ins. mIoU | Params. (M)| FLOPs (G)| Throughput (ins./sec.) |\n|---------------------|----------------|:-------:|:-----:|:-------------:|\n| PointNet | 83.7 | 3.6 | 4.9 | 1184 |\n| DGCNN | 85.2 | 1.3 | 12.4 | 147 |\n| CurveNet | 86.8 | 5.5 | 5.1 | 97 |\n| PointNet++ | 85.1 | 1.0 | 4.9 | 705 |\n| PointNeXt-S | $86.5 \\pm 0.0$ | 1.0 | 4.5 | 782 |\n| PointNeXt-S (C=64) | $86.9 \\pm 0.1$ | 3.7 | 17.6 | 431 |\n| PointNeXt-S (C=160) | $87.2 \\pm 0.0$ | 22.3 | 109.3 | 77 |\n\n> **Q**: *Add results with improved training strategies in Tab. 2*. \n \n**A**: We thank the reviewer for this helpful suggestion. We will add them into Tab. 2 in the revision. \n\n> **Q**: *Potential misrepresentation of prior work*. \n\n**A**: Thank you for pointing this out. We will revise the paper to reflect that SimpleView compares models across different training strategies. Moreover, we will highlight that the performance of SimpleView can be further improved using our training strategies. \n\n", " As the title suggests, the paper revisits and studies PointNet++, a popular neural network for point cloud representation learning. Based on the study, the paper discovers two results: first, it proposes a set of training strategies to boost the performance on PointNet++ so that it achieves SOTA results on various benchmarks; and second, it shows how PointNet++ can be modified and scaled to further boost performance. Strengths:\n- The paper achieves impressive performance on various benchmarks (87.7% on ScanObjectNN, 74.9% mean IOU on S3IS, 87.2 IOU on ShapeNetPart)\n- The paper conducts a systematic study showing the improvement in performance because of various factors (Table 4 and Table 5). In my opinion, such findings are useful.\n- The paper adopts ways to improve the PoinNet++ architecture. This could be useful for future research as they can use a more improved and modern version of PointNet++.\n- The paper shows how the findings about training strategies are generalizable to network architectures in Table 6, however, this result should be made more rigorous as discussed in the weaknesses section.\n\nWeaknesses:\n- The study showing that the findings about training strategies are generalizable to other networks is very useful (as discussed in the strengths) but limited. Specifically, only two other networks have been evaluated. I would suggest evaluating at least one simple model like SimpleView and a recent model like PointMLP.\n- It is unclear why information about FLOPs has been omitted in Table 2 and Table 3. It would be important for readers to know the strengths and limitations of various methods. Similarly, information about Parameter Count is only omitted in Table 3 for the ShapeNetPart dataset. It is unclear why specific parameters are omitted for different datasets in the main paper.\n- In Table 2, PointNet, DGCNN, and additional models (SimpleView, PointMLP) with improved training strategy should be added, so that readers can quantify the difference in performance purely as a result of network architecture and also compare models across parameter count, throughput and FLOPs.\n- Potential misrepresentation of prior work: The paper says “However, SimpleView simply adopts the same training strategies as DGCNN. In contrast, we conduct a systematic study to quantify the effect of each data augmentation and optimization technique”. It seems like a misrepresentation of prior work as SimpleView does compare models across different augmentation and optimization schemes, and finds that the ones used in DGCNN are better. The paper should provide more information about what is meant in this comparison.\n- Information about scaling is confusing. From my understanding, PointNeXt-S is the smaller valiant (L182-L185), however, in Table 4 PointNeXt-S is mentioned alongside Scale-up. Similarly, scaling rules for ShapeNetPart are not consistent (Table 3). Does the usual scaled-up model not perform well on this dataset? If so, this should be discussed.\n Several questions have been asked in the Weakness sections. Overall the paper has merits but there are parts where the paper is weak. I will update my review based on the rebuttal. NA", " The paper aims to improve PointNet++ by slightly modifying PointNet++, increasing model scale and employing a few training strategies. Comprehensive experiments on S3DIS for semantic segmentation, ScanObjectNN for real-world object classification, and ShapeNetPart for object part segmentation. 1. Although the novelty seems limited, the paper may have a positive effect on the community. Some existing works (even actually also based on PointNet++) just follow the trend and apply popular techniques to point clouds without very convincing reasons. The paper may cool down such behaviours. \n\n2. The paper looks solid. The proposed method achieves several SOTAs on multiple tasks and datasets. 1. The novelty seems a bit limited. The receptive field scaling (normalization) looks interesting and technically sound. However, according to the ablation study, the improvement is not that significant. \n\n2. In Table 4 and Table 5, it cloud be better to include SGD as a reference. \n No significant limitations. ", " This paper explores a variety of tricks to improve the performance of PointNet++ for point cloud classification and segmentation. They first show that by incorporating modern training strategies and data augmentations, the vanilla version of PointNet++ can be improved significantly. Then, to scale the PointNet++ for better performance, they propose the InvResMLP that adopts residual connection and separate MLPs in Set Abstraction layer to support scalable PointNet++, where the relative coordinates are also normalized to ease the model optimization. The experiments demonstrate that the proposed improved version of PointNet++ (PointNeXt) achieves promising performance on 3D semantic segmentation (S3DIS), 3D object classification (ScanObjectNN) and 3D part segmentation (ShapeNetPart). Strengths:\n* The paper conducts extensive experiments to explore various data augmentation and training strategies, which greatly improve the performance of vanilla PointNet++.\n* Although simple, the proposed normalization of relative coordinate is reasonable for easing the optimization. \n* The experiments show that the proposed InvResMLP can enable a larger model to improve the model performance. \n\nWeaknesses:\n* Although the reviewer agrees that the authors have systematically explored the potential of vanilla PointNet++, the technical contribution of this paper is still not enough to be published at NeurIPS: see below comments. \n* The explored data augmentation and training strategies are well-known tricks for training a point cloud model, and it is also well-known that vanilla PointNet++ can achieve much better performance than the original officially reported performance. \n* The proposed InvResMLPis is also straightforward by adding a residual connection (to solve vanishing gradient) and moving more MLPs after max-pooling (to reduce calculations). \n* The PointNet++ is hard to scalable to larger point cloud scenes, such as some outdoor scenes, and also the performance of PointNet++ series is inferior to sparse-voxel-based networks (like in larger dataset ScanNet). This paper does not show that an improved version of PointNet++ can still be the next-generation framework for point cloud processing in such a larger dataset. \n How about the performance of PointNeXt in larger datasets like ScanNet? Can it be extended to larger outdoor scenes like SemanticKITTI? The limitations have been well discussed in the paper. ", " In this paper, authors work on the point cloud understanding task and point out that we may need to revisit the training startegies and scaling methods in thi field. By detailed analysis and experiments, authors claimed that a large improvement in this field is introduced by these two aspects, rather than the network architecture designs in recent years. Furthermore, authors also introduce micro designs to improvement the PointNet++, and achieve state-of-the-art performance in three benchmarks. \n\nI like this paper, revisting the training strategies and micro designs instead of proposing something \"novel\" and new. I will give an accpet. Strengths:\n1. I like the motivation in this paper. A revisiting in point cloud understanding is necessary and can help others greatly.\n2. The detailed experiments and analysis make the experimental results solid. \n3. The presentation and organization are good. \n\nIn general, I like this paper and recommend accept.\n\nWeaknesses:\n1. In L138, the authors claimed that \"the radius is dataset-specific ...\" This phenomenon is not a finding. We can always expect detailed hyper-parameters can cause varying performances on different datasets. A general fixed setting is appreciated.\n2. InvResMLP present nothing new. the Inv-Res-Block has been proposed by MobileNetV2 and ConvNeXt already. \n3. For the experiments, I acknowledge authors repeated all experiments three times. However, a critical issue is that all three datasets are small. To prove the main idea's effectiveness, I suggest authors conduct experiments on large datasets, like ScanNet for segmentation and SUN RGB-D for object detection. \n 1. In L45， authors claimed that \"For the S3DIS segmentation benchmark, can increase by 13.6% \". Is this simply achieved by training strategies (i.e., data augmentation and optimization techniques) and without any modifications to network structure?\n\n2. I wonder why the authors consider the InvBlock design? What if we change it to a bottleneck structure in ResNet? \n\n3. From Tab.4 and Tab. 5, we can see that normalizing the relative positions by Eq. (2) could only improve the performance by 0.3\\% for both ScanObjectNN and S3DIS. Compared to other modifications, it could not be considered a \"significant influence (L138)\".\n\n4. In L142, the authors claimed: \"without normalization, ... larger weight...\" I am interested in the distributions of position encoding layer weights. Also, if the authors cloud explain L143, \"This makes ..., ... weight decay...\" What results would weight decay cause? Authors addressed the limitations and potential negative societal impact of their work." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 6, 4, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 4, 5, 5 ]

[ "nips_2022_EAcWgk7JM58", "xEAl7fcvlD", "1r8GsFTJZy", "qntPRKmWSJl", "jc6AXln9a_", "Wl9neW5kbD5", "pxzfHSfBdh", "p4wbN2TBjw", "fzwsYq0Eugi", "ccOrWYObTM", "ituZsgRBBlIl", "1f_212SYaDAF", "2mFGERe0rPQ", "1wMiuOqOJh", "2GYnhDYK8a", "jFk3dYVtln-", "zXjO2yvGOEi", "n_w2z7l38F", "1q2oN6W1SD8", "nips_2022_EAcWgk7JM58", "nips_2022_EAcWgk7JM58", "nips_2022_EAcWgk7JM58", "nips_2022_EAcWgk7JM58" ]

[ "EeFmr-V0FNj", "V9wSPPhhp2Q", "RDlJK5DiF_", "8hwgk53FqJ8", "IstzT1eqW2r", "WZIuZ2Zf9g", "_Q2bpNZQ6xsS", "etvQiqBbaNS", "kwTMLCvo9hC", "WZsfJ7YeHpI", "z6JwFlxiy8B", "LSr0VSxfLff", "arD_qaGqu5Q", "WxEnunbhMei" ]

[ "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " - Thank you for adding variances. \n- An honest discussion of limitations is often a good starting point for future work. Thank you for pointing out possible limitations in the rebuttal.\n- I have raised my rating from six to seven.\n\n- My only concern at this point is the source code. I don't think the results are reproducible without it. In the past, I have seen source code promises, that ultimately failed to materialize. I have adjusted my rating in good faith. ", " ____\n__(Question 1) Could you double check that the accuracies and confidence intervals are in the same scale? .... the confidence intervals do seem a bit small.__\n\nYes, the scale of the resultant tables is all percentage (%) levels. We agree that 95% ci seems a bit small at first glance, but this is because of the large number of samples (N). Since 95% CI is calculated from $z\\frac{\\sigma}{\\sqrt N}$, the scale of 95% CI is affected by the number of samples. If the number of samples is extremely large, then the 95% CI would be decreased at seemed.\nFor instance, in Table 4, ASH activation function with MR-CNN achieved 71.1% (=0.711) accuracy and 0.06% (=0.0006) 95% CI. Here, those values were calculated from 900 samples in which average is 0.711, 0.00990183 standard deviation ($1.96 \\times \\frac{0.00990183}{\\sqrt 900} = 0.0006$). Although the minimum value of the samples is 69.41% (=0.6941) and the maximum value of the sample is 72.79% (= 0.7279), 95% ci seems a bit small due to a large number of samples.\nTo clarify the experimental environment, we will modify the manuscript as below (Question 2).\n\n____\n\n__(Question 2) Experimental details are lacking, for example: number of runs for confidence intervals__\n\nWe understand and agree that the experimental details are important including the number of trials and exhibiting the experimental environment. As we mentioned, the experiments are based on the previous paper [1], but we now agree that a detailed illustration of our own experimental environment would be better for the understanding of readers rather than referring to the previous studies. We will update the experimental environment in Appendix A (Supplementary File), as follows:\n\n*In the experiments, we basically employ the same environment as the previous study [1], including hyperparameters, trials, and repeated runs. In our experiments, all deep learning models have trained three different learning rates three times, and thus each deep learning model is trained nine times for each learning rate. Furthermore, nine times training were repeated by varying random initialization and random sampling ten times. Therefore, totally 900 samples are produced for each model. Tables in the main results are generated from the statistical analysis of those 900 samples, by indicating mean values and 95% confidence interval.*\n\n____\n\n\n__(Question 3) Figure 3 is still missing axis values on the plot, the caption to Figure 3 doesn't mention which dataset, architecture, or hyperparameters lead to those loss curves__\n\nWe previously updated information about Figure 3 in the caption. We hope you find information at the end of Caption 3 (Page 9). The X-axis indicates the percentage of the training process (0-100%), the Y-axis indicates the validation loss, and the range is (0, 0.8).\n\n____\n\n__(Question 4) Figure 3 doesn't mention which dataset, architecture, or hyperparameters lead to those loss curves__\n\nAs we illustrated in the main paper (in Caption 3), the graph was averaged from every trial, every hyperparameter, and every task, including classification, detection, and segmentation. We understand that simple averaging degrades the statistical analysis detail, but we illustrated Fig. 3 by averaging all trials since the previous works [1-3] related to activation functions have exhibited similar results. In addition, since the tendency of [training epoch]-[validation loss] has exhibited similar trends, we would illustrate the averaged graph to simplify the tendency from every task. The result demonstrates that the usage of ASH activation could provide early convergence compared to other activation functions, and this tendency has been observed in every task of classification, detection, segmentation, and even image generation.\n\n____\n\n__(Question 5) In Table 1 an ASH result is bolded even though it is outperformed by PLeLU, in Table 1 it is not clear which column corresponds to which architecture, and in general the writing is difficult to follow.__\n\nSorry for the missing detail, we will modify the incorrect table by re-bolding the PReLU result (78.7 ± 0.03).\n\nIn addition, as the same with the previous question, (as mentioned Caption) the results of Table 1 are averaged from all trials, all hyperparameters, and all repeated runs of ResNest, WRN, and DenseNet. We illustrated Table 1 by averaging all trials like the previous works [1-3], but we understand that illustrating our experimental details are important, we will update the manuscript to the above questions.\n\nFurthermore, we will look over the overall manuscript carefully and correct all the grammatical errors, and we will further take the English Editing Service. Although our writing style and some errors in our manuscript would not be satisfactory for the reviewer,we believe that our manuscript could exhibit the technical novelty of ASH activation function through well-organized mathematical explanations and proofs.\n\n____", " Thank you for clarifying, and I apologize for misunderstanding that the repeated runs were already conducted for the initial submission.\n\nCould you double check that the accuracies and confidence intervals are in the same scale? For example, the accuracy is multiplied by 100 (0.748 becomes 74.8) and it is unclear whether the same was done to the confidence interval. Often individual runs can vary by a percentage point, and at first glance the confidence intervals do seem a bit small. \n\nMy main concern about the statistical significance of the results has been addressed. In its current form, I would consider the paper a weak reject and increase my score from 3 to 4.\n\nI'm now satisfied with the technical results of the paper, but the writing itself would benefit from another round of improvement. Experimental details are lacking, for example: number of runs for confidence intervals, Figure 3 is still missing axis values on the plot, the caption to Figure 3 doesn't mention which dataset, architecture, or hyperparameters lead to those loss curves, in Table 1 an ASH result is bolded even though it is outperformed by PLeLU, in Table 1 it is not clear which column corresponds to which architecture, and in general the writing is difficult to follow.\n\nIf the writing issues were not present I would consider the paper a weak accept / score of 5. There is obviously time to address them before publication but in my opinion they should not still be unresolved at this stage of reviewing.", " Dear Reviewer ecwn.\n\nThank you for your comments and for taking the time to review my paper. \n\nWe agree that the statistical analysis and statistical values are crucial in the paper. However, the related information has been already shown in the manuscript (Lines 252, 254, 268, and 284).\n\nAs mentioned in the manuscript, we conducted the experiments in environments that are as similar as possible to the previous paper [1]. In the previous paper, they tested the model with three different parameters three times. Hence, one model was tested nine times, and we showed the statistical values that are averaged from nine trials. Furthermore, we have already applied the repeated runs, but we only missed to exhibit standard deviation values in the tables of the previous manuscript. Hence we only updated the tables by adding standard deviation values without any changes in mean values.\n\nTo clarify the manuscript, we will revise the manuscript or supplementary file by adding detailed environmental descriptions.\n\n\n\nAgain, Thank you for your comments, and we agree that your comments have improved the quality of the manuscript.\n\n\nThanks.\n\n\n[1] Ramachandran, Prajit, Barret Zoph, and Quoc V. Le. \"Swish: a self-gated activation function.\" arXiv preprint arXiv:1710.05941 7.1 (2017): 5.", " I appreciate the authors taking the time to address my comments. Although the tables now include confidence intervals, the number of samples is not mentioned. Also, the mean accuracy is identical in every entry to that in the original manuscript. It seems like the updated accuracies (which should have changed with repeated runs) were left out. \n\nThese shortcomings are serious: it is impossible to gauge the significance of the paper because of them, and I significantly disagree with the reviewers awarding this paper high scores.", " We thank the reviewers' comments and we agree that they could have improved the quality of the manuscript.\n\nIn the initial submission, we skipped several experimental results that are necessary to exhibit the outstanding properties of ASH activation function. However, as the reviewers commented, we modified the missing experimental results, including statistical analysis and comparison analysis using various versions of ASH activation functions. We utilized a 95% confidence interval (95% C.I.) to exhibit statistical analysis. Finally, we modified the manuscript and the appendix files. \n\nAgain, the contributions of ASH activation function are the following:\n\n(1) We conducted mathematical modeling for ASH in an effective form to be trainable and parametric, and thus ASH exhibits parametric and adaptive properties. The baseline threshold of ASH is trainable during the training phase, and the threshold value is adaptively changing according to the contexts of inputs without heavy calculation.\n\n(2) We theoretically verified ASH adaptively changes its threshold alongside the stochastic distribution of inputs. This implies ASH provides outputs regarding the entire contexts of inputs, as well as leads to better feature extraction.\n\n(3) We theoretically verified that ASH exhibited general formula for Swish activation function and provided the mathematical explanations for the superior performance of Swish, which was empirically searched in the previous works.\n\n(4) We experimentally showed that ASH improves the performance of deep learning models for various tasks as well as shortens training time, in terms of early convergence.", " ____\n__(Weakness) The major weakness I see, is that the authors compare their activation mostly with other non-trainable activations. However, it is known that trainable activation functions such as [1], etc., usually perform better and such comparisons are missing in the empirical evaluation.__\n\nIn the experiments, we compared ASH activation function to Leaky ReLU and Parametric ReLU which are trainable activation functions and commonly utilized in deep learning networks.\n\nHowever, thank you for introducing an interesting paper. We reviewed the paper, and we found that both activation functions exhibit the trainable property. However, ASH activation function exhibits a difference in recognizing the contextual information of inputs as well as adaptive thresholding properties. We added the reference to this paper, and we would like to examine quantitative analysis alongside ASH activation function in future work.\n\n____\n\n__(Question 1) I'm thinking of the similarities of this activation with dropout. In particular, I'm wondering if the cancelation of the elements, should lead to a scale adjustment? It would seem like that could be beneficial as in dropout.__\n\nYes, this study initially has started from the adaptive dropout methods, and thus ASH activation function exhibits a cancelation property. Therefore, ASH activation function could provide the benefit in terms of sparsity as a dropout [1]. Additionally, we commonly utilized normalization methodologies with ASH activation function in the deep learning applications, and the detailed architecture could be found in the GitHub codes after the publishment.\n\n____\n__(Question 2) Now, considering the cancelation induced by the activation function, there are big parts of the network that won't receive gradient updates if they are not in the top k%. Would it make sense to introduce something like a negative tail or a scaling factor for the elements below the top k%? Think of Leaky ReLU.__\n\nAs the reviewer commented, the variable could not be updated by the backpropagation when the corresponding output is not in the top-k\\% percentile. This could happen in some samples. However, deep learning networks commonly employ a large number of images to train the networks, and thus it rarely happens that one variable could not be included in the top-k\\% percentile in terms of data augmentation. We were impressed by the reviewers’ comments and they could have improved the quality of the manuscript.\n\nWe agree that the scaling factor for the elements below the top-k\\% percentile could be effective and we conducted the related experiments before the initial submission. The experiment showed that the Leaky ASH (L-ASH) exhibited slower convergence for the optimization due to the increased number of trainable parameters and decreased sparsity. During the experiments, we noticed that the sparsity of ASH activation function could provide superior benefits for the optimization of deep learning networks. As the reviewers commented, we added the comparisons analysis of ASH activation function in Appendix H (Supplementary File).\n\n____\n\n__(Question 3) Furthermore, as one would normally use these activation functions through the network. I'm wondering if there is some effect of vanishing gradients happening, or signal reduction, due to the cancellation imposed after each layer. I could imagine that if the learned parameter would cancel 90% of the signal at each layer, this could introduce a strong loss of information.__\n\nYes, we agree that if $k$ percentile is fixed, some effect of vanishing gradients happens. However, since rectification is performed depending on the values (contexts) of the input, and as mentioned above question, when there are many images for training, it is significantly unlikely that convolutional variables would continue to be rectified (canceled), and thus the gradient vanishing problem is not likely to be critically issued.\n\nIt is commonly observed that the important features are localized when passing through the layers of a deep learning network. By observation through the experiments, a large percentile is employed in the deep depth, and thus many informative features are passed rather than rectified. Therefore, the important information and features are not filtered out due to the adaptive thresholding.\n\n____\n__(Question 4) I'm also wondering whether this is a new approach for signal compression?.....__\n\nYes, this study initially has started from the adaptive dropout methods. We were impressed by the reviewer’s comment and we agree with this comment. We modified the Discussion section (Supplementary File) by adding this comment as part of the future work. Thank you for the innovative comment.\n\n____", " ____\n__(Weakness 1) Research in the paper should be presented as a novel extension of the SwisH activation function since it is the more generalized form Abstract.__\n\nThank you for the comments, and we modified the abstract and introduction to follow your suggestions. \n\n____\n__(Weakness 2) Research should have placed the full name for the ASH activation function (Adaptive SwisH) in the \"abstract\" section.__\n\nThank you for the comments, and we modified the abstract and introduction to follow your suggestions. \n\n____\n__(Weakness 3) Equation 10 needs more steps.__\n\nThank you for the comments, and we added more steps in Appendix G (Supplementary File).\n\n____\n__(Weakness 4) Mention mathematical proofs for accuracy, sparsity, training time, and localization property as part of potential future work__\n\nWe modified the related paragraph (3. Early Convergence and Optimization) and Discussion section (Supplementary File) to enhance the potential of ASH activation function.\n\n____\n__(Question) Why were only 3 models considered for each experiment (classification, object detection, segmentation)?__\n\nWe mainly applied ASH activation functions to the task in which the role of the activation function is significantly issued, even in the image generation task (previously posted on the Supplementary Files). Since vision-based analysis could exhibit the properties of activation functions in a visual manner alongside the mathematical proofs, we mainly utilized the vision-based tasks. Text- and transformer-based analysis could be further discussed for future work.\n\n____\n__(Limitation) The authors addressed the fact that they did not search for the best performing parameters. Instead, they justified this by stating that allowing the network to learn these parameters on its own is more similar to how human neurons work. For future work, it would be nice to see the comparison between setting the threshold for z_k and letting the network learn these parameters naturally.__\n\nIn the initial submission, we already explored the influence of the trainable property of ASH activation function. However, we skipped the related experiments due to the clear intuition that the fixed threshold is significantly similar to ReLU and the experiments significantly demonstrate the limitations of the fixed threshold.\n\nHowever, as the reviewers commented, we added the comparisons analysis of ASH activation function in Appendix H (Supplementary File). The result shows that the 50\\% sampling could be fully optimized even slow. In contrast, 10\\% and 90\\% sampling could not be fully optimized due to the negative effects of extreme rectification by fixed threshold values.\n____", " ____\n__(Question 1) How is k determined? Is it fixed, or learnable? Is it the same across a network, or different for each layer? What values for k are used in the experiments?__\n\nAccording to the Z-Table, $k$ and $z_k$ are associated in terms of Z-score as illustrated in Equations (4) and (5). In addition, $z_k$ is determined to be trainable (line 190-191). Therefore, $k$ is also trainable in ASH. Furthermore, $k$ ($z_k$) exhibits different values across a network (different values for each layer), as illustrated in Property 1 (Supplementary File Line 16-17) and Discussion (Supplementary File Page 5). In the training phase, all $k$s are initialized as 50% (0.5) and $z_k$s are as 0.0 based on Z-Table. \n\n____\n__(Question 2) The approximation of Heaviside step function relies on a large value of alpha. How does this affect the analysis in Equation 10?__\n\nIn Equation (10), the second line and the third line are mathematically the same. To approximate the Heaviside step function into a hyperbolic tangent or sigmoid function, those functions require a large coefficient in front of $x$. More detailed explanations are illustrated in Appendix G section (Supplementary File).\n\n____\n__(Limitation 1) Some claims are excessive and unsubstantiated. For example: \"our activation function exhibits outstanding performance in any deep learning applications,\" or \"the experiments empirically discovered that the Swish activation function is the best performance activation function.\"__\n\nThe novel properties of ASH activation function are well explained in Supplementary File (Appendix A-F) and experimental results. The main highlights of ASH activation function are (1) achieving high accuracy in various tasks of classification, detection, and segmentation [Experimental results], (2) adaptive attention mechanism [Appendix D and E], and (3) early convergence from the early epochs with lower loss values and high accuracy [Appendix C and F]. Additionally, we modified Abstract and related paragraph in Main text to exhibit detailed properties of ASH activation function (high accuracy and early convergence), as well as the experimental results by adding statistical analysis.\n\nFurthermore, “the experiments empirically discovered that the Swish activation function is the best performance activation function.” is addressed in the original paper on the Swish activation function (Ramachandran et al., 2017), and we excerpted this to highlight the relations between Swish and ASH. To clarify, we added the reference in this sentence.\n\n____\n__(Limitation 2) The experiments do not show any case in which ASH is outperformed by any other function. The implication is that it is universally the best activation function. This implied claim is problematic because there are no repeated runs (with the exception of 3 runs in Table 1) nor any statistical significance tests to back up these results. See checklist item 3c.__\n\nWe modified the related Tables according to your and other reviewers’ thoughtful comments. We modified the manuscript by adding 95% Confidence Interval (C.I.) with mean values.\n\n____\n__(Limitation 3) Figure 3 has no numbers on the x or y axes.__\n\nWe modified Figure 3. \n\n____\n", " ____\n__(Weaknesses) For a statistically motivated paper, it would have been neat to see variance values alongside the reported mean accuracy in the experimental section.__\n\nWe modified the tables related to experiments by adding variances to clarify the statistical analysis.\n\n____\n__(Questions 1) Line 17: The source code repository seems to be offline?__\n\nYes, but it will be online on GitHub after the publication.\n\n____\n__(Questions 2) Line 8: Does ASH mean something? - I found the meaning in Line 218. ASH stands for Adaptive SwisH. Perhaps this definition happens a little late in the paper?__\n\nSorry for the missing abbreviation from the abstract. We modified the manuscript.\n\n____\n__(Questions 3) Line 72: What does Swish mean? Are SiLU and Swish synonymous? Could the exact definition be briefly given here?__\n\nTechnically, SiLU and Swish are the same activation function using the sigmoid function. SiLU is firstly introduced in [1], and Swish is advanced in [2]. Mathematically, the SiLU (Sigmoid Linear Unit) and Swish exhibit similar formulas; $\\text{SiLU(x)} = x\\sigma(x)$ and $\\text{Swish}(x) = x\\sigma(\\beta x)$, where $\\sigma(x)$ is sigmoid function. \n\n____\n__(Questions 4) Equation 1: Is the ASH-function a real-valued variant of the modRelu introduced in [arjovski16]? The authors may be interested in adding a citation and discussing the differences. [arjovski16] Unitary Evolution Recurrent Neural Networks https://arxiv.org/pdf/1511.06464.pdf__\n\nThank you for introducing an interesting paper. We reviewed the paper, and we found that the modRelu is the modification of ReLU activation function but it is an odd function (symmetric). ModReLU and ASH have a similar property that they rectify inputs at specitic point, not zero like ReLU. However, the coefficient and bias of ASH activation function are trainable and depend on the context of inputs, and thus ASH exhibit more statistical significance. We added the reference to this paper, and we would like to examine quantitative analysis alongside ASH activation function in future work. \n\n____\n__(Questions 5) Line 172: Do we have a citation for a Z-table, for convenience?__\n\nYes, basic Statistic books say it. The reference was added to the manuscript.\n\n____\n__(Questions 6) Table 1: What is the variance here? Tables 2 and 3: Is the mean accuracy shown here? What about the variance?__\n\nWe modified the manuscript by adding 95\\% Confidence Interval (C.I.) with mean values.\n\n____\n__(Limitation 1) Potential problems that were observed during training or hyperparameter tuning. Perhaps some negative properties have been observed at some point while working with the ASH activation?__\n\nAs discussed in Appendix C (Supplementary File Line 37-39), in the detection task, it is noticed that ASH activation function exhibited over-weighted localization, and thus the confidence scores were somewhat decreased. However, after the end of the training networks, the localization property increased the confidence score again, and it resulted in increasing accuracy and decreasing loss values, at the end of the training process.\n\n____\n__(Limitation 2) Reasons for not reporting the variance on the mean experiment values for the Image-Net experiments?__\n\nWe initially refer [2], so we missed the statistical reports. We modify the related tables.\n\n____\n__(Limitation 3) Perhaps some theoretical drawbacks exist that readers should be aware of?__\n\nPerhaps the value of $z_k$. We examined many experiments using various values of $z_k$, but we could not provide a mathematical generalization. Rather, we only concluded the relation between ASH’s depth and $z_k$. $z_k$ of ASH in a deeper depth exhibited smaller values (even negative values) compared to $z_k’$ of another ASH in a shallower depth. We noticed this phenomenon by observing GRAD-CAM as shown in Supplementary Fig. 2. Additionally, we noticed that by statistically analyzing the distribution of $z_k$.\n\nIntuitively, a wide range of activations is required to recognize entire contexts of an image in a deeper depth, whereas a narrow range of activations is required to rectify features in a shallower depth in image recognition, especially a classification task. In contrast, consistent activation of the target object is required, in the segmentation or detection tasks.\n\nWe appended this intuition rather than mathematical analysis in the Discussion section to highlight the characteristics of ASH activation function.\n\n____\n\n[1] Hendrycks, Dan, and Kevin Gimpel. \"Gaussian error linear units (gelus).\" *arXiv preprint arXiv:1606.08415* (2016).\n\n[2] Ramachandran, Prajit, Barret Zoph, and Quoc V. Le. \"Searching for activation functions.\" *arXiv preprint arXiv:1710.05941* (2017).", " The paper \"Stochastic Adaptive Activation Function\" successfully establishes a link between the statistics of feature selection and the recently proposed Swish-activation function.\nBuilding upon the theoretical connection, an ASH (Adaptive Swish) non-linearity appears in the theory part.\nThe experimental part tests the new activation function Image net 2012, CIFAR-10, CIFAR-100, MS-COCO, and PASCAL VOC. The paper reports improved performance on every dataset and every network.\n Strengths:\n- The paper couples the Swish activation function to probability theory.\n- The authors find improved performance for their ASH activation function across the board.\nThe numerical results are in line with those reported in https://arxiv.org/pdf/1710.05941;%20http://arxiv.org/abs/1710.05941.pdf for CIFAR-10.\n- To the best of my knowledge, the contribution is novel. But I haven't been working looking into activation functions for some time (see confidence score below).\n\nWeaknesses:\n- The paper is hard to read at times.\n- For a statistically motivated paper, it would have been neat to see variance values alongside the reported mean accuracy in the experimental section.\n\n - Line 17: The source code repositrory seems to be offline?\n- Line 8: Does ASH mean something?\n - I found the meaning in Line 218. ASH stands for Adaptive SwisH. Perhaps this definition happens a little late in the paper?\n- Line 72: What does Swish mean? Are SiLU and Swish synonymous? Could the exact definition be briefly given here? \n- Equation 1: Is the ASH-function a real-valued variant of the modRelu introduced in\n [arjovski16]? The authors may be interested in adding a citation and discussing the differences.\n [arjovski16] Unitary Evolution Recurrent Neural Networks https://arxiv.org/pdf/1511.06464.pdf\n\n- Line 172: Do we have a citation for a Z-table, for convenience?\n- Table 1: What is the variance here?\n- Tables 2 and 3: Is the mean accuracy shown here? What about the variance?\n \n\n Limitations are not discussed at all. All numbers are perfect. Is the experimental section too good to be true?\n\nA discussion of limitations could include:\n- Potential problems that were observed during training or hyperparameter tuning. Perhaps some negative properties have been observed at some point while working with the ASH activation?\n- Reasons for not reporting the variance on the mean experiment values for the Image-Net experiments?\n- Perhaps some theoretical drawbacks exist that readers should be aware of?", " In this paper, the authors present the Adaptive SwisH (ASH) activation function, which is a more generalized form of the SwisH activation function. They present the parametric and adaptive properties of the ASH function and prove the baseline threshold of the ASH function is trainable during the training phase and that the threshold value adaptively changes according to the contexts of inputs. Additionally, they prove that the ASH function does not require heavy computations compared to some other activation functions. In terms of experiments, they show that the ASH activation function outperforms other activation functions on classification, object detection, and segmentation tasks. Strengths\n- proved parametric and adaptive properties of ASH function\n- proved baseline threshold of the ASH function is trainable during the training phase and that the threshold value adaptively changes according to the contexts of inputs without heavy calculation\n- proved ASH function is a generalized version of the SwisH activation function\n\nWeaknesses\n Overall\n - research in the paper should be presented as a novel extension of the SwisH activation function since it is the more generalized form\n Abstract\n - should have placed the full name for the ASH activation function (Adaptive SwisH) in the \"abstract\" section\n Method\n - equation 10 needs more steps\n Main Result\n - Mention mathematical proofs for accuracy, sparsity, training time, and localization property as part of potential future work\n Why were only 3 models considered for each experiment (classification, object detection, segmentation)? The authors addressed the fact that they did not search for the best performing parameters. Instead, they justified this by stating that allowing the network to learn these parameters on its own is more similar to how human neurons work. For future work, it would be nice to see the comparison between setting the threshold for zk and letting the network learn these parameters naturally.\n", " The authors propose a new trainable activation function that unlike most activation functions that work element-wise, this one activates over complete layers. \n\nMore precisely, the activation function behaves like a ReLU, either activating with the input value, or cancelling to zero when deactivating. However, the activation criteria is whether the element is in the top k% of the elements in the layer.\n\nThe threshold is then controlled by a learnable parameter, making it a trainable activation function. The paper is very interesting and I believe it could have applications and connections to other areas in deep learning.\n\nThe paper is well written and the empirical evaluation shows that the proposed activation works well.\n\nThe major weakness I see, is that the authors compare their activation mostly with other non-trainable activations. However, it is known that trainable activation functions such as [1], etc., usually perform better and such comparisons are missing in the empirical evaluation.\n\n[1] Molina, Alejandro, Patrick Schramowski, and Kristian Kersting. \"Padé Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks.\" International Conference on Learning Representations. 2019. The empirical evaluation shows that this activation function is valuable and it works. \nI have however a series of questions that could be interesting to analyze to better understand the proposed method.\n\nI'm thinking of the similarities of this activation with dropout. In particular, I'm wondering if the cancelation of the elements, should lead to a scale adjustment? It would seem like that could be beneficial as in dropout.\n\nNow, considering the cancelation induced by the activation function, there are big parts of the network that won't receive gradient updates if they are not in the top k%. Would it make sense to introduce something like a negative tail or a scaling factor for the elements below the top k%? Think of Leaky ReLU.\n\nFurthermore, as one would normally use these activation functions through the network. I'm wondering if there is some effect of vanishing gradients happening, or signal reduction, due to the cancellation imposed after each layer. I could imagine that if the learned parameter would cancel 90% of the signal at each layer, this could introduce a strong loss of information.\n\nI'm also wondering whether this is a new approach for signal compression?. Consider a fixed top k% parameter. This directly implies that the number of outputs after the activation is a fraction of the size of the output. This is potentially equivalent to a reduction layer.\nHere you do not get a dimensionality reduction, as for every input still different outputs could activate. But there is a compression in the amount of data reaching the next layer. If you were to control the percentage of information dropped, you could construct something like an auto-encoder and get the benefit of signal compression, without the effort needed in compressing the dimensionality. no negative societal impact", " This paper proposes an rectifier based activation function where the threshold is set to the upper k% of the input tensor values. - Originality: The main originality in this paper comes from determining a threshold based on a percentile from the input entries. To my knowledge, this has not been considered before. \n\n- Quality: The main issue with the paper is that there are no statistical significance tests for the final results. This prevents drawing any substantial conclusions from the results, which hurts the paper's quality.\n\n- Clarity: The writing is at times difficult to follow and understand, but the mathematics appear sound.\n\n- Significance: The paper would be much more significant with repeated runs and statistical significance tests, but as-is, it is unsignificant. - How is k determined? Is it fixed, or learnable? Is it the same across a network, or different for each layer? What values for k are used in the experiments?\n\n- The approximation of heaviside step function relies on a large value of alpha. How does this affect the analysis in Equation 10? - Some claims are excessive and unsubstantiated. For example: \"our activation function exhibits outstanding performance in any deep learning applications,\" or \"the experiments empirically discovered that the Swish activation function is the best performance activation function.\"\n\n- The experiments do not show any case in which ASH is outperformed by any other function. The implication is that it is universally the best activation function. This implied claim is problematic because there are no repeated runs (with the exception of 3 runs in Table 1) nor any statistical significance tests to back up these results. See checklist item 3c.\n\n- Figure 3 has no numbers on the x or y axes." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 7, 9, 3 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 4, 4, 5 ]

[ "WZsfJ7YeHpI", "RDlJK5DiF_", "8hwgk53FqJ8", "IstzT1eqW2r", "kwTMLCvo9hC", "nips_2022_wtuYr8_KhyM", "arD_qaGqu5Q", "LSr0VSxfLff", "WxEnunbhMei", "z6JwFlxiy8B", "nips_2022_wtuYr8_KhyM", "nips_2022_wtuYr8_KhyM", "nips_2022_wtuYr8_KhyM", "nips_2022_wtuYr8_KhyM" ]

[ "nLJQPIKBbd", "KYhMYWv3axQ", "fG-k2FoVcfU", "QxhhzQqsh50", "dbtiwN1AiEx", "03VdJoPiGWd", "jZ1WxLuWrEx", "btzhyOYiV7y", "jaOKce1QBXd", "NF2oRxFryGB", "4gYIeq9tj3KL", "flvFodYDVAm", "fyZd4vGBPBp", "saD2IJIP2W2", "_8_fQbMBul", "8krOTLgLNkF", "WYeSUMbe6n8", "mfvjiw2Vpn", "9TcvwldS5io", "wf7AfZTAaZT", "hCeMBT1lrN5", "eG17XHYLBjt", "qlnIz_SJbGE" ]

[ "author", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your insightful comment. Here is our response.\n\nIn the data reusing framework, the random data selection plays the role of constraining the model to be close to the initialization (pre-trained model), in that it uniformly samples images from the pre-training data and aims to maintain the generic solution. In contrast, the similarity-based data selection such as UOT reuses task-related data to enrich the downstream training data and guides the pre-trained model to learn _task-specific_ representations, instead of maintaining the generic feature representation of the pre-trained model. Our experiment in Table 1 has shown that learning task-specific features (UOT) is better than keeping the general features (Random) in downstream task on a variety of datasets, unveiling the fundamental difference between our work and catastrophic forgetting. \n\nWe kindly note that we do not deny the potential connection between Lemma 1 and catastrophic forgetting, but delete the sentence in case it raises the misconception that our work is motivated by catastrophic forgetting. The reviewer’s insightful question helps us better clarify the difference between ours and catastrophic forgetting and we will add the above discussion to an updated version. \n\nIt would be deeply appreciated if our response could address the concerns and the reviewer could raise the score. We are willing to answer follow-up questions if the discussion does not fully address your concern.\n", " Authors discuss that a fine-tuning phase usually does not have enough data for the lengthy training (line 149); hence, the use of pretraining helps to have better generalization because it's not overly fitting to the given task. From my understanding on this, the additional pre-training data plays a role of regularization and thus helping the model to perform better in the end. This feels a very similar argument of \"Catastrophic failure\" cases because the work also suggest to prevent model to move too far from the pretrained solution (generic) and will not be overly optimized to the downstream task.\n\nSince authors deny this connection, I wonder what the main reason of this improvements using pre-training data is that authors suggest? Can you discuss on this point?", " Thanks the authors for the response.", " Thanks again for your time and effort in handling our paper. We would like to note that we have an experiment with 5 trials during the discussion phase.\n\nHere is the table for UOT fine-tuning and standard fine-tuning with mean and std of 5 trials using supervised ResNet18. We report the p value of unpaired t test for the 8 datasets: on all datasets the benefit of UOT fine-tuning is statistical significant.\n| Dataset | Dogs | Cars | CUB | Pets | SUN | Aircraft | DTD | Caltech |\n|----------|------|------|-----|------|-----|----------|-----|---------|\n| Standard | 82.59±0.21 | 85.80±0.12 | 75.22±0.21 | 90.85±0.41 | 58.22±0.24 | 77.11±0.43 | 69.95±0.58 | 89.07±0.69 |\n| UOT | 84.59±0.22 | 86.96±0.11 | 76.99±0.31 | 91.71±0.20 | 58.78±0.22 | 78.15±0.46 | 70.85±0.29 | 91.08±0.24 |\n| p value | <0.0001 | <0.0001 | <0.0001 | 0.0015 | 0.0025 | 0.0031 | 0.0073 | 0.0001 |\n\nWe hope our responses and clarifications address your concerns.", " We thank the reviewer for providing valuable feedbacks during the discussion phase so that we have the opportunity to address concerns and clarify some key issues. It is greatly appreciated that the reviewer agrees to raise the score if we provide the statistical test for the effectiveness of UOT. Here are our response and new experimental results.\n\n* Though we admit that there exist certain pre-trained datasets that are not publicly available as mentioned in the Conclusion section, most widely used pre-trained datasets such as ImageNet (for vision models like ResNet, ViT, etc), Wikipedia and C4 (for NLP models like BERT, T5, etc) are readily accessible. Moreover, using such pre-training data with a pre-trained model to improve fine-tuning has been investigated by published papers, such as Co-Tuning [R5] (NeurIPS) for vision applications and [R3,R4] (ICML and ICLR) for NLP applications.\n\n[R3] Guu, K., Lee, K., Tung, Z., Pasupat, P., & Chang, M. (2020, November). Retrieval augmented language model pre-training. In International Conference on Machine Learning (pp. 3929-3938). PMLR.\n\n[R4] Khandelwal, U., Levy, O., Jurafsky, D., Zettlemoyer, L., & Lewis, M. (2019, September). Generalization through Memorization: Nearest Neighbor Language Models. In International Conference on Learning Representations.\n\n[R5] You, Kaichao, et al. \"Co-tuning for transfer learning.\" Advances in Neural Information Processing Systems 33 (2020): 17236-17246.\n\n\n* We implement the 2-phase training using a supervised ResNet18 on CUB and Caltech. The accuracy is 74.21% and 84.44% respectively, which is higher than the training from scratch result 71.75% and 61.96% but still worse than the standard fine-tuning (75.49% and 90.11%) and our improved UOT result (77.21% and 91.11%). We think the reason is that the pre-training on closely related source data has the risk of overfitting and cannot learn a general feature representation that provides a good initialization for various downstream tasks and alleviates the risk of overfitting. \n\n* Here is the table for UOT fine-tuning and standard fine-tuning with mean and std of 5 trials using supervised ResNet18. We report the p value of unpaired t test for the 8 datasets: on all datasets the benefit of UOT fine-tuning is statistical significant.\n| Dataset | Dogs | Cars | CUB | Pets | SUN | Aircraft | DTD | Caltech |\n|----------|------|------|-----|------|-----|----------|-----|---------|\n| Standard | 82.59±0.21 | 85.80±0.12 | 75.22±0.21 | 90.85±0.41 | 58.22±0.24 | 77.11±0.43 | 69.95±0.58 | 89.07±0.69 |\n| UOT | 84.59±0.22 | 86.96±0.11 | 76.99±0.31 | 91.71±0.20 | 58.78±0.22 | 78.15±0.46 | 70.85±0.29 | 91.08±0.24 |\n| p value | <0.0001 | <0.0001 | <0.0001 | 0.0015 | 0.0025 | 0.0031 | 0.0073 | 0.0001 |\n\nThanks again for your patience and valuable feedbacks.\n", " \nThanks the author for the responses.\n\nAgain, for the \"The practical use of your proposed problem\" , I don' think you answered my very first question. I was questioning that \"giving both pretraining data and pretrained models\" is a strong assumption and maybe unrealistic in practice whether people likely to use. I was trying to see if you found any scenarios to motivate the use. I do not mean 'vision' or 'nlp'. Sorry if my question confuses you.\n\nI appreciate the responses and the soundness of work and i find it interesting. However, relatively compared to other papers in Neurips, i cannot see much significant contributions and impacts of this work to the ML community, in research methodology and practical use.\nNevertheless, I am willing to increase my score to 5 as if the updated stds from the authors show that the improvements in table 1 is statistically significant.\nBest,", " **For Q13, the reason I asked for std because (1) randomness may have huge effect in the result, and (2) the results your method achieves are not beyond the SOTA reported by others. Here, I do not mean to achieve SOTA, but because of (2), (1) can take place and can become a factor to the gap of best models.**\n\n\nA: As we have shown in A13, the standard deviation is not huge in our understanding. We would provide the standard deviation of other datasets when the experiment is finished. \n\nHope our clarification will address your concerns.", " Thanks for your clarification. Here is a quick response. \n\n**The practical use of your proposed problem. I think the problem setting is interesting but just wonder when we will benefit from collecting more pretraining data (and in which case they are also available) and trade-off this cost of collecting+training with small increases of accuracy? that's what I mean \"under which scenarios\" (Q14) . This leads to my second question (Q16) -- if we can show that this setting is widely applicable then it's great.**\n\nA: Again, we have shown that the method is effective in a wide range of image classification datasets. And the correlation between similarity and performance has been shown in Figure 4b in the updated paper, which shows a higher similarity leads to a better performance in general. \n\n**Sufficiency of evidence for the effectiveness of the proposed method. Please correct me if I did not understand correctly, but as I understood, the theorem is to inspire your method, not the guarantee of the effectiveness of your method (my question Q17).**\n\nA: The theorem guarantees that the generalization upper bound is reduced if the gap between selected source and target data is small, which directly leads to the pre-training data selection and the algorithm. Note that the delta in Theorem 1 is the maximum distance between input gradients of source and target data, with the UOT data selection, the distance should be smaller than without the selection, meaning that the in theory the UOT method would be not worse that the reuse method of pre-training data WITHOUT selection. Since the $\\delta$ in Theorem 1 could be arbitrary large, the excess risk bound could be very large, which leads to worse performance of the naive reuse method without selection. However, by contrast, the UOT method could perform better by carefully controlling $\\delta$. Empirically, Figure 2 in the updated version shows that UOT learns a quite good similarity measure because most bird classes (58 out of 59) from ImageNet are selected in the top-100 similarity vector to CUB. Could the reviewer explain what is the meaning of “the guarantee of the effectiveness of your method” by giving an example? Does the reviewer mean the proof for the effectiveness of UOT? Since the current paper focuses on the improvement of fine-tuning, a theoretical contribution on optimal transport theory is out of the scope of our current paper.\n\n\n**Thus, the empirical evidence needs to be sufficient and representative for the general finetuning setting. The datasets are all object-classification vision datasets. For Q16, I don't mean to have huge-dataset experiment but more representative as your proposed method doesn't limit the scope to only vision. I believe that similar simple experiments but in other modalities (rather than vision) will make your message more convincing.**\n\n\nA: As we have responded to Reviewer phCA, we agree that NLP experiments are also interesting to explore, but due to limited space, the current paper focuses on the theoretical analysis and the fine-tuning of supervised and self-supervised computer vision models with “solid ablation study” (by Reviewer phCA). We notice that there are already some NLP papers proposing to retrieve data for better pre-training and fine-tuning, e.g. [R3,R4], and our analysis has the potential to provide a theoretical justification for using pre-training in NLP. We will try our best to run an NLP experiment, but given the limited time it is not guaranteed to be finished within the discussion period.\n\n[R3] Guu, K., Lee, K., Tung, Z., Pasupat, P., & Chang, M. (2020, November). Retrieval augmented language model pre-training. In International Conference on Machine Learning (pp. 3929-3938). PMLR.\n\n[R4] Khandelwal, U., Levy, O., Jurafsky, D., Zettlemoyer, L., & Lewis, M. (2019, September). Generalization through Memorization: Nearest Neighbor Language Models. In International Conference on Learning Representations.\n\n**Otherwise, if I understood correctly, the authors meant to frame the contribution of the paper as both theory and methodology. While they are coherent and the message is solid, the contribution of each end seems to be less significant.**\n\n\nA: In the theory part, the theoretical contribution explains why and when re-using pre-training data in the fine-tuning can be effective, which has not been studied in existing literature and has a substantial contribution. In the methodology part, the UOT data selection has been shown to be effective on 8 vision datasets, with not only the supervised model, but also the self-supervised model, which again has not been investigated before. Thus, we believe the contributions in both ends are significant. \n\n\n", " Thanks authors for prompt responses. I appreciate the clarification.\n\nI think you might have not fully understood some of my points. So please let me clarify more clearly. \nMy concerns are at two main points.\n1. The practical use of your proposed problem. I think the problem setting is interesting but just wonder when we will benefit from collecting more pretraining data (and in which case they are also available) and trade-off this cost of collecting+training with small increases of accuracy? that's what I mean \"under which scenarios\" (Q14) . This leads to my second question (Q16) -- if we can show that this setting is widely applicable then it's great. \n\n2. Sufficiency of evidence for the effectiveness of the proposed method. Please correct me if I did not understand correctly, but as I understood, the theorem is to inspire your method, not the guarantee of the effectiveness of your method (my question Q17). \n- Thus, the empirical evidence needs to be sufficient and representative for the general finetuning setting. The datasets are all object-classification vision datasets. For Q16, I don't mean to have huge-dataset experiment but more representative as your proposed method doesn't limit the scope to only vision. I believe that similar simple experiments but in other modalities (rather than vision) will make your message more convincing. \n- Otherwise, if I understood correctly, the authors meant to frame the contribution of the paper as both theory and methodology. While they are coherent and the message is solid, the contribution of each end seems to be less significant. \n\nFor Q13, the reason I asked for std because (1) randomness may have huge effect in the result, and (2) the results your method achieves are not beyond the SOTA reported by others. Here, I do not mean to achieve SOTA, but because of (2), (1) can take place and can become a factor to the gap of best models. ", " **Q18: For Q8, what I suggested is to use selected subset of pretraining data and the finetuning dat which should be computationally similar to your approach. The setting in Table 1 sufficiently seem doable with small models (ResNet) and small finetuning datasets. Though I trusted the results, I am not quite sure why with 100K samples +finetuning data, the ResNet18 gets much lower performance. Have you trained in 2 phases: first pretraining data, then finetuning data?**\n\nA18: We did not use the 2-phase training, since the 2-phase setting has already been investigated in [R1,R2] and is not the problem setting we are studying in this paper. We did not compare ours with [R1,R2], since they need to re-pre-train the model for every new dataset, which requires more time and efforts than our fine-tuning approach, see Line 95-100. We are running the 2-phase experiment now on several datasets and will report them when finished. \n\n[R1] Cui, Yin, et al. \"Large scale fine-grained categorization and domain-specific transfer learning.\" Proceedings of the IEEE conference on computer vision and pattern recognition. 2018.\n\n[R2] Chakraborty, Shuvam, et al. \"Efficient conditional pre-training for transfer learning.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022.", " **Q13: (Statistically significant difference between scores) Have you computed the standard deviations of reported scores in the Table 1 and the scored reported in the your answer to Q8? If so, can you please report them. To me, the differences between methods for most of the datasets are not enormous with respect to baseline accuracies and maybe not statistically significant.**\n\nA13: Since we choose the best performance for both baselines and our method, we believe the comparison is fair. In the response to Reviewer phCA, we run 5 trials for UOT fine-tuning on CUB and Caltech with the supervised pre-trained ResNet18, the result is 76.99%±0.31% and 91.08%±0.24%, which are also clearly higher than the maximum performance of the baselines. We are running the 5-trial experiment on other datasets.\n\n\n**Q14: (Motivation) When and why is the problem setting useful? as we need to have both pretrained models, pretraining data, and finetuning data. I think the authors suggest a use-case when the target task has very limited labeled data (If so, I believe both types of data needs to be relevant.) Other than that, I do not get under which scenario the setting is useful in the general finetuning setting?**\n\nA14: The problem setting is shown in Fig. 1, and the reason why this setting is useful is demonstrated by our theoretical analysis, where re-using pre-training data that is close to the downstream task will improve the generalization bound. The effectiveness of the proposed UOT fine-tuning is shown on 8 general fine-tuning data sets with both supervised and self-supervised pre-trained model. Please elaborate on which specific point is not fully understood. Are you asking how different the pre-trained data can be before it no longer is useful for fine-tuning? Note that in the updated version, we show the experiment of using different subsets of ImageNet according to the UOT similarity in Fig 4b and Line 374-379. The experiment indicates that the dissimilar data hurt the performance when added to fine-tuning and highlights the importance of similarity-based data selection.\n\n**Q15: (Significance) As mentioned the main contribution of the analyses is to show the usefulness of proper pretraining data selection, rather than study the defined problem (showing the upper bound of the risks).**\n\nA15: We do not quite understand the reviewer’s point. What is the meaning of “the usefulness of proper pretraining data selection” and “study the defined problem (showing the upper bound of the risks)”? Both Lemma 1 and Theorem 1 assume the pre-training and fine-tuning pipeline and explain the reason why pre-training data selection is effective with the upper bound of risks, see our proof in Line 667-694 of the full paper. Empirically, we show the usefulness of using the selected pretraining data through improved performance on 8 general fine-tuning datasets with both supervised and self-superised pre-trained models. \n\n**Q16: The experiments only focus on very simple vision datasets with small models and small downstream tasks (and achieve lower performances than performance), so I am not convinced whether this method really works for general cases , e.g., pretrained language models or large pretrained vision models.**\n\nA16: As we note in the response to all reviewers, the major contribution lies in both the theoretical understanding of using pre-training data in the fine-tuning stage (Theorem 1) and the proposed UOT data selection method. Though we agree that any paper can be made better with more experiments, the current experiment has shown the effectiveness of UOT fine-tuning in both supervised and self-supervised pre-trained models on a wide range of datasets, which is acknowledged by Reviewer **718u**, **HBDj** and **phCA**. \n\n**Q17: Justification of the usefulness of pretraining data. As previously mentioned, the analyses do not directly lead to the design of the method. I would like to understand the justification and intuition why the pretraining data helps as we assume the pretrained models already captured good representation of pretraining data (overlapping between data and models).**\n\nA17: As we have claimed, the data selection approach is informed by Theorem 1. Note that though the pre-trained model learns general representations for the whole pre-trained data, not good representations for a specific downstream task. To better learn specialized features in downstream task, a similar subset of pre-training can be re-used in the downstream task. Theorem 1 states that better generalization bounds can be achieved by selecting the pre-training data that is closer to the downstream data. Thus we design our UOT selection algorithm based on feature similarity to select the pre-training subset. Our design is corroborated by experiment in Table 1.\n\n\n", " Thanks the authors for the responses. \nI've read all the comments, but I have some concerns. \n\n1. (Statistically significant difference between scores) Have you computed the standard deviations of reported scores in the Table 1 and the scored reported in the your answer to Q8? If so, can you please report them. To me, the differences between methods for most of the datasets are not enormous with respect to baseline accuracies and maybe not statistically significant. \n\n2. (Motivation) When and why is the problem setting useful? as we need to have both pretrained models, pretraining data, and finetuning data. \nI think the authors suggest a use-case when the target task has very limited labeled data (If so, I believe both types of data needs to be relevant.)\nOther than that, I do not get under which scenario the setting is useful in the general finetuning setting?\n\n3. (Significance) As mentioned the main contribution of the analyses is to show the usefulness of proper pretraining data selection, rather than study the defined problem (showing the upper bound of the risks). \nThe experiments only focus on very simple vision datasets with small models and small downstream tasks (and achieve lower performances than performance), so I am not convinced whether this method really works for general cases , e.g., pretrained language models or large pretrained vision models.\n\n4. Justification of the usefulness of pretraining data. As previously mentioned, the analyses do not directly lead to the design of the method. I would like to understand the justification and intuition why the pretraining data helps as we assume the pretrained models already captured good representation of pretraining data (overlapping between data and models).\n\n5. For Q8, what I suggested is to use selected subset of pretraining data and the finetuning dat which should be computationally similar to your approach. The setting in Table 1 sufficiently seem doable with small models (ResNet) and small finetuning datasets. Though I trusted the results, I am not quite sure why with 100K samples +finetuning data, the ResNet18 gets much lower performance. Have you trained in 2 phases: first pretraining data, then finetuning data?\n\nThanks,", " **Q8: I suggest the authors to try simple but related baselines: training both pretraining data and target data without pretrained models.**\n\nA8: This is a good question. Training from scratch often takes much more time than starting from a pre-trained model. The target data size is often much smaller compared with the pre-training data. Such imbalance is an obstacle to learning the target task. Starting from a pre-trained model, the time and imbalance issue are not serious, since the pre-trained model already learns a good initialization for optimization and the model has a lower loss on the pre-training data, which will not affect learning in the target task. We run this baseline on CUB and Caltech with supervised ResNet18 and find the accuracy is 71.75% and 61.96%, which is far below the fine-tuning accuracy and indicates the importance of using the pre-trained model. We will run more experiment on other datasets and add the result later.\n\n**Q9: What happen if we use stronger pretrained models?**\n\nA9: Since a ResNet18 is used in our experiment, the performance in Table 1 does not match the state-of-the-art performance achieved by larger models. A small model is used to show the effectiveness of UOT fine-tuning in such resource-limited cases. We run the experiment using a supervised pre-trained ResNet50 and find that the UOT fine-tuning increases the accuracy of standard fine-tuning from 80.64% to 81.24% on CUB and from 88.90% to 90.82% on Dogs, indicating that the proposed method is effective for a larger supervised pre-trained model. More experiments on other datasets are still running. We kindly note that we use a larger model (ResNet50) in self-supervised pre-training experiment, and the performance of UOT fine-tuning is quite competitive in Table 1b.\n\n**Q10: In figure 3a-2, why don’t we have the label-based line?**\n\nA10: This is a good question. Unlike CUB and Dogs, the object classes in Caltech are diverse. So the correspondence between labels of Caltech and of ImageNet cannot be trivially obtained. For datasets like Caltech, our feature-based data selection method is more appropriate than the label-based data selection.\n\n**Q11: In figure 3b, what is the accuracy gap?**\n\nA11: The accuracy gap means the accuracy of UOT fine-tuning minus standard fine-tuning.\n\n**Q12: The authors may consider the impact of the work on utilizing more pretraining data than standard fine-tuning.**\n\nA12: ImageNet is open sourced and widely used in the research community. With our UOT fine-tuning, we improve the performance of pre-trained models in target tasks, which we believe has no negative societal impact. However, our method has a limitation when the pre-training data is private (e.g., JFT-3B). As mentioned by the reviewer, our method also incurs larger computational cost than not using selected pre-training data during fine-tuning, but this cost is still much less than when training from scratch. \n", " We thank the reviewer for the careful reading and constructive feedbacks, with with we believe our updated paper is more clear and the experiment is much more convincing for readers. Here are our responses to the comments.\n\n**Q1: If the selected pretrained data is more valuable than the pretrained model, why don’t we train the model from pretraining data and the fine-tuning data?**\n\nA1: Our paper does not claim that the pre-trained data is more valuable than the pre-trained model. The analysis in Sec. 2 shows that the pre-trained model can be potentially improved by using pre-training data in the fine-tuning process. Kindly note that both the pre-trained model and a selection of the pre-training data are used in fine-tuning, thus both are important. If the pre-trained model is not used as the basis for fine-tuning, then we lose the benefit of the general representation learned from large-scale data, see the experiment in Q8.\n\n**Q2: Does the use of large pretraining data contradict to the purpose of fine-tuning?**\n\nA2: The main purpose of fine-tuning from pre-trained models is to leverage the general representation learned from large-scale data, which is useful when the downstream data is limited. The purpose of our study is to show that it is possible to improve the performance of a downstream task where the labels are limited by better leveraging the existing pre-training data. While this incurs additional cost in fine-tuning due to larger data, we also see improved downstream performance without needing to collect new downstream data. We also note that we use the SGD with mini-batch in the training and keep the ratio between source and target batch size to be 1, so the required GPU memory is increased but the computational time keeps roughly the same (only the data sampling overhead).\n\n**Q3: How K-mean on high-dimensional data is useful to provide distinguishable clusters (especially with Euclidean distance)?**\n\nA3: On some fine-grained classification tasks (Dogs and CUB), we find that the performance of UOT is much higher than random selection, indicating that the K-means learns meaningful feature clustering.\n\n**Q4: The justification of the real effect of pretraining data.**\n\nA4: Our theoretical analysis in Sec 3.1 indicates that with such a regularization term, the performance is potentially higher than the standard fine-tuning. Specifically, Table 1a shows that the UOT fine-tuning improves upon the standard one on 7/8 datasets with an average increase 2.93% when using the ResNet50.\n\n**Q5: Writing can be improved.**\n\nA5: Thanks for your careful reading. We have revised those typos in the updated version.\n\n**Q6: Fig.3a shows that 100-class setting provides the best overall performance of method while other settings result in lower performance than the label-based selection.**\n\nA6: Fig. 3a shows the performance of using different number of classes from ImageNet on CUB. The figue shows that the performance is always higher than other two baselines across different class numbers. Notice that the label-based selection is considered as an oracle for CUB data since we are able to select all related source data based on the label text. But as mentioned in Line 51-54, label-based selection is not as general as UOT data selection since the former depends on correspondence between labels.\n\n**Q7: It’s better to show with more settings when the pretraining data is much smaller.**\n\nA7: We simulate the small pre-training data by subsampling half of images from each class of ImageNet. On CUB and Caltech, the UOT fine-tuning achieves 77.03% and 91.00% accuracy respectively, which only drop 0.18% and 0.11% compared with using the full ImageNet. The experiment shows that even with half of ImageNet, fine-tuning with UOT data selection is still quite effective. We have added this experiment to the updated paper in Line 380-385.\n\n", " We thank the reviewer for the insightful comments. We are glad that the reviewer considers our experiment and ablation study to be solid and extensive, and appriciate the novelty of the excess risk bound and the effectiveness of the proposed approach. Here are the responses to your comments.\n\n**Q1: Novelty is limited.**\n\nA1: See the comment for the novelty issue.\n\n**Q2: Running this for more trials and reporting error bars would make the trends more convincing.**\n\nA2: Since we choose the best performance for both baselines and our method, we believe the comparison is fair. We run 5 trials for UOT fine-tuning on CUB and Caltech with the supervised pre-trained ResNet18, the result is 76.99%±0.31% and 91.08%±0.24%, which are also clearly higher than the maximum performance of standard fine-tuning.\n\n\n**Q3: Would it be possible to add at least 1-2 NLP experiments as well?**\n\nA3: Thanks for mentioning NLP experiments. We agree that NLP experiments are also interesting to explore, but due to limited space, the current paper focuses on the theoretical analysis and the fine-tuning and analysis of supervised and self-supervised computer vision models. However, we believe that the theoretical analysis is quite general and may also hold for NLP data. We notice that there are already some NLP papers proposing to retrieve data for better pre-training and fine-tuning, e.g. [R1,R2], and our analysis has the potential to provide a theoretical justification for using pre-training in NLP. We will work towards this direction in the future.\n\n[R1] Guu, K., Lee, K., Tung, Z., Pasupat, P., & Chang, M. (2020, November). Retrieval augmented language model pre-training. In International Conference on Machine Learning (pp. 3929-3938). PMLR.\n\n[R2] Khandelwal, U., Levy, O., Jurafsky, D., Zettlemoyer, L., & Lewis, M. (2019, September). Generalization through Memorization: Nearest Neighbor Language Models. In International Conference on Learning Representations.\n\n**Q4: How strong are the assumptions? Do they hold in practice?**\n\nA4: We have four assumptions for the main assumption as stated in the Appendix B. The Assumptions 1,2 and 3 generally hold for neural network functions, which are non-convex. The PL condition has been theoretically and empirically observed in training deep neural networks [R3,R4]. It is widely used to establish convergence in the literature of non-convex optimization, please see [R5,R6,R7,R8] and references therein.\n\n\n[R3] Allen-Zhu, Zeyuan, Yuanzhi Li, and Zhao Song. \"A convergence theory for deep learning via over-parameterization.\" International Conference on Machine Learning. PMLR, 2019.\n\n[R4] Yuan, Zhuoning, et al. \"Stagewise training accelerates convergence of testing error over SGD.\" Advances in Neural Information Processing Systems 32 (2019).\n\n[R5] Wang, Zhe, et al. \"Spiderboost and momentum: Faster variance reduction algorithms.\" Advances in Neural Information Processing Systems 32 (2019).\n\n[R6] Karimi, Hamed, Julie Nutini, and Mark Schmidt. \"Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition.\" Joint European conference on machine learning and knowledge discovery in databases. Springer, Cham, 2016.\n\n[R7] Li, Zhize, and Jian Li. \"A simple proximal stochastic gradient method for nonsmooth nonconvex optimization.\" Advances in neural information processing systems 31 (2018).\n\n[R8] Charles, Zachary, and Dimitris Papailiopoulos. \"Stability and generalization of learning algorithms that converge to global optima.\" International Conference on Machine Learning. PMLR, 2018.\n", " Thanks for your constructive comments on our paper, and noting the novelty of our UOT data selection and its effectiveness. Here are our responses to your comments.\n\n**Q1: Selecting the subset of the pretraining data for the downstream task is not novel.**\n\nA1: See the response for novelty. \n\n**Q2: Authors do not have many baseline methods in their empirical evaluation other than very simple ones.**\n\nA2: We compare with a recent improved fine-tuning baseline Co-Tuning in the supervised pre-training setting. In self-supervised pre-training, we only compare with random and greedy-OT selection since there are no fine-tuning baselines targeting self-supervised training as far as we know. As we note in Line 95-100 and Line 278-280, [R1] is a conditional pre-training method instead of a fine-tuning method, so we believe the comparison is not fair.\n\n**Q3: Sometimes we do not have the access to the pretraining data.**\n\nA3: It is a good question. The assumption that the pre-training data are readily available during the fine-tuning is generally satisfied for a wide range of computer vision tasks, since the most commonly used pre-training data ImageNet is free for non-commercial use. The disk usage of the ImageNet is ~150 GB, which is affordable for common servers. In the case where the pre-training data is larger than the available storage capacity, a subset of the pre-training data could be used. We subsample 50% images from each class of ImageNet and use the 50% ImageNet data in the supervised ResNet18 fine-tuning. On CUB and Caltech, the UOT fine-tuning achieves 77.03% and 91.00% accuracy respectively, which only drop 0.18% and 0.11% compared with using the full ImageNet. The experiment indicates that even with half of ImageNet, fine-tuning with UOT data selection is still quite effective. We agree that availability of the pre-training is a limitation, especially for private datasets such as JFT-3B, so we have added this to the limitation.\n\n**Q4: ResNet18 is a bit too small. Did they consider larger pretrained models?**\n\nA4: ResNet18 is often used in cases where memory and/or computation are limited. We use a small model to show the effectiveness of UOT fine-tuning in such resource-limited cases. We run the experiment using a supervised pre-trained ResNet50 and find that the UOT fine-tuning increases the accuracy of standard fine-tuning from 80.64% to 81.24% on CUB and from 88.90% to 90.82% on Dogs, indicating that the proposed method is effective for a larger supervised pre-trained model. More experiments on other datasets are still running. We kindly note that we use a larger model (ResNet50) in self-supervised pre-training experiment, and the performance of UOT fine-tuning is quite competitive in Table 1b. \n\n**Q5: One of the motivations of using the pretraining data is to prevent “catastrophic forgetting”?**\n\nA5: We kindly note that preventing catastrophic forgetting is not one of the motivations. We mention catastrophic forgetting in the comment of Lemma 1 to indicate the possibility that our analysis shows the possible connection between Lemma 1 and catastrophic forgetting. Our experiment aims to improve the performance of the target task, instead of combatting the forgetting of pre-training data. We deleted this sentence to prevent misunderstanding.\n\n\n[R1] Chakraborty, Shuvam, et al. \"Efficient conditional pre-training for transfer learning.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022. \n", " **Q8: There are also methods that directly select the data that can benefit the target task, such as [R2].**\n\nA8: [R2] proposes to optimize a weight for the target data samples instead of selecting pre-training data for improving fine-tuning. Such target-weighting methods are compatible with ours, which selects source data, and future work will consider their combination. We added the discussion to the updated version of our paper (Line 105-107) and cited the mentioned work.\n\n[R2] Dukler et al, DIVA: Dataset Derivative of a Learning Task, ICLR 2022\n\n**Q9: The limitation is not discussed.**\n\nA9: The limitation of our method when the pre-training data are not accessible is added in Line 393-396.\n", " Thanks for your valuable comments and appriciating our strength in both theory and experiment. Here are our responses for your comments.\n\n**Q1: The reason why source data can help for target tasks is not well understood.**\n\nA1: We have a theoretical analysis on the generalization error of fine-tuning with pre-training (source) data culminating in Theorem 1, which shows that the generalization error can be further reduced if we select source data to control the gap between the reused source and downstream data during fine-tuning. This theoretical result explains why we need the source data and corroborates our intuition that the abundant image-label pairs from the pre-training data can be useful if an appropriate subset is selected.\n\n**Q2: The insights on how similar the source datasets affect the fine-tuning performance.**\n\nA2: The delta in Theorem 1 means the gap between the source and target data, measured by the difference of loss gradients between the reused source (pre-training) and target (downstream) data. A higher similarity leads to a smaller delta and a lower generalization error bound. As discussed in Line 374-379, our experiment in Fig. 4b corroborates this theoretical finding.\n\n\n**Q3: There is no clear criteria whether the method should be used.**\n\nA3: This is a great question. We use 8 datasets in our experiment including various objects and find that the UOT fine-tuning improves the performance in almost all datasets, indicating that the proposed method is effective in most general image classification tasks. However, for highly specialized tasks such as medical diagnosis (where the image domain is significantly different, e.g., microscope images or CT scans), the reusing the pre-training data from general visual recognition tasks such as ImageNet may not be very helpful. Indeed from Theorem 1, the generalization bound depends on the “delta” between the source and target data. We will try to extend our work to medical data in the future.\n\n**Q4: There are also methods that directly select the data that can benefit the target task.**\n\nA4: In Line 89-107, we discuss several methods for data selection including [18,19,20,21]. We compare with the Co-Tuning in our experiment and discuss the relationship between our work and [18,19,20,21,22] in Line 276-280.\n\n[18] Weifeng Ge and Yizhou Yu. Borrowing treasures from the wealthy: Deep transfer learning through selective joint fine-tuning. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1086–1095, 2017.\n\n[19] Yin Cui, Yang Song, Chen Sun, Andrew Howard, and Serge Belongie. Large scale fine-grained categorization and domain-specific transfer learning. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4109–4118, 2018.\n\n[20] Shuvam Chakraborty, Burak Uzkent, Kumar Ayush, Kumar Tanmay, Evan Sheehan, and Stefano Ermon. Efficient conditional pre-training for transfer learning. arXiv preprint arXiv:2011.10231, 2020.\n\n[21] Kaichao You, Zhi Kou, Mingsheng Long, and Jianmin Wang. Co-tuning for transfer learning. Advances in Neural Information Processing Systems, 33, 2020.\n\n[22] Yunhui Guo, Honghui Shi, Abhishek Kumar, Kristen Grauman, Tajana Rosing, and Rogerio Feris. Spottune: transfer learning through adaptive fine-tuning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4805–4814, 2019.\n\n\n**Q5: What if the training data is a duplicate of the target data?**\n\nA5: If the pre-training data is a duplicate of the target data, then the performance on the target data would be quite strong since the pre-training model generally has a quite low error on the pre-training data. We kindly note that the CUB’s classes overlap with some of ImageNet’s, but the image data are different. Nonetheless, our UOT selection method works as expected on CUB (see Table 1).\n\n**Q6: What if the target label and the source label are semantically similar but not exactly similar. For example, if the target task is to classify dogs vs cats, but the source data have a lot of dog species but not the “dogs” label?**\n\nA6: This is a great question. This is a problem of label-based data selection and we solve this problem by proposing the UOT selection, where the selection is based on pre-trained features (semantics) instead of label text, see Line 51-54.\n\n**Q7: Is the method sensitive to hyperparameter changes? Whether the hyperparameters are correlated with the similarities of added source data?**\n\nA7: Yes, we also observe that the performance is sensitive to the hyperparameters. We attached the hyperparameter result in supplemental materials. We find that on CUB, where the similarity between source and target data is small, a larger lambda generally leads to a better result, indicating that the selected data are quite important for the improved performance.\n\n", " We thank all reviewers for your insightful comments on our paper, based on which we have revised our paper with the following major changes to address your concerns:\n\n* Reviewer **51Vh** and **HBDj**: We add the ablation study of using half of ImageNet in Line 380-385, which shows that even with 50% of ImageNet the UOT fine-tuning is still effective.\n\n* Reviewer **51Vh**: We add the baseline of training from scratch with selected source and target data in Line 615-623 of the full paper in supplemental. The experiment shows the importance of using pre-trained model in the fine-tuning phase.\n\n* Reviewer **718u**, **HBDj** and **51Vh**: The limitation of our method when the pre-training data are not accessible is discussed in Line 393-396. \n\n* Reviewer **718u**: We added the hyperparameter search result in the supplemental material (UOT_hyper_search.xlsx). \n\n* Reviewer **phCA**: We run 5 trials of UOT fine-tuning and add the result to the full version (Line 581-584) and discussed the assumptions in Line 641-642.\n\n* Reviewer **51Vh**: The mentioned typos are fixed in the updated version. \n\nIt is noticed that the novelty of our paper is questioned by Reviewer **HBDj** and **phCA**, here is our response for this issue:\n\n* The novelty of our paper lies in the theoretical analysis and the UOT approach to selection of pre-training (source) data during fine-tuning. There are admittedly existing methods which select source data for a target task and we discuss the fundamental difference between existing methods and ours in Line 89-107. More importantly, the reason why the selected pre-training data are helpful to a downstream task is unveiled by our theoretical analysis (Theorem 1), which is not studied before as far as we know. Informed by Theorem 1, we design the UOT data selection to reduce the gap between source and target domain, which is commented as novel by Reviewer HBDj. In addition, as far as we know, there are few existing methods that target the fine-tuning data selection for self-supervised pre-trained models. Overall, we believe the major contributions of our work have sufficient novelty.\n\n\nWe hope that our response and the updated version address your concerns and our paper can be considered as qualified to be accepted. \n", " The authors investigate whether a pre-trained model can be enhanced when pre-training data are used during fine-tuning. They develop an approach that performs data selection to choose an appropriate portion of pre-training data to enhance the phase of fine-tuning. Specifically, the authors propose a selection algorithm to obtain a subset from pre-training data closest to the target data by solving an unbalanced optimal transport (UOT) problem, which chooses data classes from the pre-training set whose distributional distance to the target data set is small. \n Strength:\n\nThe paper is well written. The author provides both theoretical and empirical investigations. The proposed selection method considers to handle pre-training data with and without labels. The paper has an extensive comparison with other strategies.\n\nWeakness: \n\n- The reason why source data can help for target tasks is not well understood. \n- The theoretical study does not provide clear insights on how similar the source datasets affect the fine-tuning performance. \n- It is not clear whether the target task can always benefit from the techniques. The author discussed “the impact of the domain gap”, however, there is no clear criteria whether the method should be used. For example, will a medical dataset benefit from the ImageNet pre-training data?\n- There are also methods that directly select the data that can benefit the target task, which are not discussed. - What if the training data is a duplicate of the target data? The training data may not further help the target task. For example, CUB has an overlap with ImageNet.\n\n- What if the target label and the source label are semantically similar but not exactly similar. For example, if the target task is to classify dogs vs cats, but the source data have a lot of dog species but not the “dogs” label?\n\n- Fine-tuning is sensitive to hyperparameters [1]. In the paper, the authors performed a large-scale grid search of the optimal hyperparameters for the best performance (5x3x3x3=145 trials per dataset). Is the method sensitive to hyperparameter changes? I am curious if the authors have any observation of whether the hyperparameters are correlated with the similarities of added source data and target data so that the HPO trials can be reduced.\n\n- There are also methods that directly select the data that can benefit the target task (e.g., [2]), which were not discussed or compared.\n\n[1] Li et al, Rethinking the Hyperparameters for Fine-tuning, ICLR 2020\n[2] Dukler et al, DIVA: Dataset Derivative of a Learning Task, ICLR 2022 The limitation is not discussed.", " Pretrained models are widely adopted for various downstream applications and have been demonstrating superior performance. A de-facto technique to utilize such a model is simply fine-tuning the pretrained model to a small downstream task’s dataset. This paper proposes a way to improve this process by selecting a subset of relevant pretraining data and training together with the downstream training data. Strength\n* Employing UOT (unbalanced optimal transport) to select the subset of the pretraining data is novel and was very effective from their empirical evaluation.\n* It is quite surprising that utilizing the pretraining data can improve the fine-tuning performance this much.\n\nWeaknesses\n* Selecting the subset of the pretraining data for the downstream task is not novel (as described in line 92.\n* Authors do not have many baseline methods in their empirical evaluation other than very simple ones. I encourage they compare their work to comparable methods such as [1] or methods that actively prevents catastrophic forgetting [2,3] (3 was not evaluated on the vision but in a similar fashion)\n* (minor) as noted in the limitation, sometimes we do not have the access to the pretraining data. In the contrary [3] does work without the pretraining data.\n\n[1] Chakraborty, Shuvam, et al. \"Efficient conditional pre-training for transfer learning.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022.\n[2] Hayes, Tyler L., et al. \"Remind your neural network to prevent catastrophic forgetting.\" European Conference on Computer Vision. Springer, Cham, 2020.\n[3] Chen, Sanyuan, et al. \"Recall and learn: Fine-tuning deep pretrained language models with less forgetting.\" arXiv preprint arXiv:2004.12651 (2020).\n Q1: Page 6: Is there any reason why the authors chose a small pretrained model? ResNet18 is a bit too small in my opinion. Did they consider larger pretrained models? (e.g. ResNet50 for supervised training or even ResNet101). Is it because larger models may memorize pretraining dataset better and may not benefit from using them?\n\nQ2: Since one of the motivations of using the pretraining data is to prevent “catastrophic forgetting”, I wonder if the authors compared their work to such techniques for example [1,2]. [1] shows it’s much better than simple fine-tuning and contains many baselines on this end. [2] actively prevents catastrophic forgetting even without data.\n\n[2] Hayes, Tyler L., et al. \"Remind your neural network to prevent catastrophic forgetting.\" European Conference on Computer Vision. Springer, Cham, 2020.\n[3] Chen, Sanyuan, et al. \"Recall and learn: Fine-tuning deep pretrained language models with less forgetting.\" arXiv preprint arXiv:2004.12651 (2020).\n Commonly, we do not have access to the pretraining data because of various reasons (c.f. access, storage space, time etc). This limits the use of this method in such scenarios. ", " The paper shows how leveraging some pre-training data during fine-tuning can boost a model's pre-train + fine-tuned performance.\nThe authors suggest a few methods to this end, for both the scenario when pre-training data is unlabeled (i.e. self-supervised learning) as well as labeled -- selecting pre-training data by label, randomly, and via similarity with fine-tuning data by way of optimal transport. The latter is the most innovative and performs the best. With several key assumptions (the most important of which is the bound on the distance between the fine-tuning and pre-training loss gradients), the paper provides bounds for the excess risk under normal fine-tuning as well as under their proposed modified fine-tuning loss. They compare against a single recent baseline (Co-Tuning) and study image classification on 8 datasets using ResNets pre-trained on ImageNet and do several ablation studies. Strengths:\n* Experiments have decent coverage (self-supervised + supervised pre-training ; limited data; 8 datasets) \n* Pretty solid ablation studies\n* Proposed method with UOT selection generally outperforms the other methods.\n* Excess risk bound shown seems semi interesting.\n\nWeaknesses:\n* Novelty is limited -- while I cannot comment extensively of how noteworthy the theoretical analysis is, the suggested approaches for selecting pre-training data seem straightforward.\n* Only co-tuning is compared against (though this method is claimed to be the most competitive recently) and only in the supervised setting. The proposed method with UOT selection loses to co-tuning on 2/8 datasets. Performance is measured as \"the best among 3 trials\" -- running this for more trials and reporting error bars would make the trends more convincing.\n* More experiments would strengthen the paper. Would it be possible to add at least 1-2 NLP experiments as well? Perhaps the same one used in the Co-Tuning paper? The authors do mention limitations in the Conclusion section, which I felt was adequate. However, more discussion around the assumptions made for the theory would be nice -- how strong are the assumptions? Do they hold in practice? ", " This work studies the problem of using data of the pretraining task (pretraining data) for the fine-tuning stage.\n\nThey first analyze the excess risk of the target task when the pretrained model and the pretraining data are used, and show that the proper use of pretraining data can tighten the bound of excess risks. \n\nFor selecting the proper subset of pretraining data, they propose a similarity-based selection method based on the distributional distance between pretraining classes and target data. \n\nTheir empirical results on several image-classification tasks validates the findings of the previous analysis and the several improvements of their method over the conventional fine-tuning without pretraining data. - Problem setting: The use of selected source data to improve target task has been touched before in the transfer learning literatures. This paper studies a seemly new setting: both pretrained model and pretraining data are used in the fine-tuning task. Though it’s new, my question are how important is this setting and under which scenarios is this setting useful? To be specific, I see the overlap of pretrained model and the pretraining data: If the selected pretrained data is more valuable than the pretrained model, why don’t we train the model from pretraining data and the fine-tuning data? Otherwise, as the purpose of the pretrained model is to provide an initially good (and general) representation, if the pretrained model is well-trained, it already well utilized the pretraining data. Also, as training from scratch and pretraining are usually expensive and intensive, does the use of large pretraining data contradict to the purpose of fine-tuning? (In the experiment, the paper use1 up to 100 classes of ImageNet which is approximately 100K samples while the target data (e.g., Stanford Cars) has much less data.\n\n- Analysis: The lemma and theorem are simple but useful to illustrate the idea of this paper. From my understanding, the main contribution of these analyses is to show the usefulness of proper pretraining data selection, rather than study the defined problem in general.\n\n- Similarity-based method: The method is intuitive.\n - One concern is how K-mean on high-dimensional data is useful to provide distinguishable clusters (especially with Euclidean distance)? If these clusters are uniformly sampled from the data, the method is likely to be the random selection.\n - Another question I have is the justification of the real effect of pretraining data. Since the paper simply incorporate the pretraining data via extra regularization term (loss) in the fine-tuning. It’s intuitive that this regularization can at least achieve better performance than the original loss (fine-tuning) with proper regularization parameters. And, the experimental results also show the marginal improvements of the modified loss over the standard fine-tuning and sometimes gets lower performance (table 1b).\n\n- Clarify: the paper is pretty clear to follow and easy to understand.\n\n- Quality:\n - Writing can be improved:\n - In paper 2, the statement “From the perspective …” in lines 60—63 is mostly duplicated with lines 64—66\n - Some statements need to be provided with evidences and more precise contexts. For examples, lines 32—33: “…. training from scratch never matches the performance of fine-tuning …. “\n - Minors: there are some typos, e.g., ‘datausing’ (Figure 3 caption), ‘images’ (line 172) should be ‘samples’.\n\n- Experiments\n - Some results seem to be not representative to me. For example, the Fig.3a shows that 100-class setting provides the best overall performance of method while other settings result in lower performance than the label-based selection. It’ll be better to provide more comparison and robust metrics to the table 1.\n - While table 1 shows the improvement of using proposed method, the improvement is marginal and unclear whether the gain is from the pretraining data or proper parameter tuning?\n - As mentioned above, all considered target tasks have smaller number of data compared to the pretraining data. I think it’s better to show with more settings when the pretraining data is much smaller.\n - Baselines: I suggest the authors to try simple but related baselines: training both pretraining data and target data without pretrained models?\n - Some results in table 1 are far below the best transfer-learning results on the target datasets. For example, on the Stanford Cars, the latest transfer learning may achieve up to 96% accuracy.\n - What happen if we use stronger pretrained models?\n - In figure 3a-2, why don’t we have the label-based line?\n - In figure 3b, what is the accuracy gap? Please see the questions mentioned above. I do not see the limitation and negative societal impact sections. Please see my mentioned limitations above. For the societal impact, the authors may consider the impact of the work on utilizing more pretraining data then standard fine-tuning. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 5, 5, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 2, 3 ]

[ "KYhMYWv3axQ", "8krOTLgLNkF", "dbtiwN1AiEx", "eG17XHYLBjt", "03VdJoPiGWd", "jZ1WxLuWrEx", "jaOKce1QBXd", "jaOKce1QBXd", "4gYIeq9tj3KL", "flvFodYDVAm", "flvFodYDVAm", "fyZd4vGBPBp", "saD2IJIP2W2", "qlnIz_SJbGE", "eG17XHYLBjt", "hCeMBT1lrN5", "mfvjiw2Vpn", "wf7AfZTAaZT", "nips_2022_YTXIIc7cAQ", "nips_2022_YTXIIc7cAQ", "nips_2022_YTXIIc7cAQ", "nips_2022_YTXIIc7cAQ", "nips_2022_YTXIIc7cAQ" ]

[ "7hoTfc2gAyo", "lnVp28VEsCi", "Smp8psilatv", "5wwckMiMQ2N", "ndu1tUMJVku", "4N-CL_8pR09", "9vOAx1JCX0r", "ZIIO_BtU8bA", "iyh5uAQH1sE", "nf3SWnPfY5", "bc26pvVJeJA", "8DMtDBXurHN", "WBmpyaytXL", "jjMUDMTFaxK", "yXth6737L-j", "1mMfRqp4pty" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We sincerely thank you for the review and comments.\n\nAlso thank you for acknowledging the value of our dataset.\n\nAfter discussions in our team, we thought that we should reduce the discussion of metrics and focus on metric that are very familiar to the computer field (such as RMSE).\nWe will add more content to introduce the dataset and benchmark itself so that this paper focuses on our propsed dataset and model.\nMore dataset-related details, as well as model design and training details, will be covered in the main text.\n\nBest, Authors of Paper 690", " I'm sorry for the late response. The authors addressed some of my questions given the limited time. Thanks.\n\nIn the response to Q1, the authors also provide detailed explanation on the necessity of real low-res data and empirical study on the corresponding improvement. The response seems reasonable to me.\n\nAs for Q3 and Q6, the evaluation of performance on precipitation related tasks is still an open problem. E.g., DeepMind's Nature paper resorted to meteorologists for human evaluations due to the discrepancy between evaluations from experts and scores. It's not appropriate to include the intuitive designs of PEM/PDEM as one of the major contributions in this paper.\n\nOverall, the dataset and the corresponding benchmark are valuable. I suggest that the authors focus on them and remove the PEM/PDEM part in the paper. The value of the dataset and benchmark will not be diminished by not proposing \"novel\" metrics. The proposed method does not necessarily have to outperform baselines in all concerned metrics.\n\n[1] Ravuri, Suman, et al. \"Skilfull precipitation nowcasting using deep generative models of radar.\" Nature 597.7878 (2021): 672-677.", " Dear reviewer 5jsP:\n\nWe sincerely thank you for the review and comments. We have provided corresponding responses, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest, Authors of Paper 690", " Dear reviewer WVYT:\n\nWe sincerely thank you for the review and comments. We have provided corresponding responses and results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest, Authors of Paper 690", " Dear reviewer 9mB6:\n\nWe sincerely thank you for the review and comments. We have provided corresponding responses, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest,\nAuthors of Paper 690", " Thanks for your valuable reply!\n\nQ1: Can we get a model that is better at domain specific scores by selecting the candidate models with PEM/PDEM and not MSE?\n\nA1: Thank you for your question. In spatial precipitation downscaling tasks, domain researchers typically use the metrics introduced in our paper to evaluate/select models instead of directly using RMSE [1]. The RMSE here is the pixel-level average error over all frames (i.e. 720 frames in a month), this averaging loses structural and dynamic information [1], which are properties of most interest to domain researchers. \"We could expect better PEM/PDEM performance when better RMSE performance is observed, but it might not always be the case.\" For example, the model can reconstruct some frames very well and others very poorly (this often happens in heavy rain situations, e.g., hurricanes, continuous heavy rain, they occur almost every year), and the model can also get decent RMSE values, in this case, the model exhibits poor temporal consistency and dynamics. However, these issues can be captured by PDE/PDEM, which are more fine-grained metrics.\nIn other words, similar RMSEs may have different PDEs and PDEMs, for example, RCAN (RMSE\\times 100:0.325, PEM: 0.227, PDEM: 0.558) and EDVR (RMSE X100:0.329, PEM: 0.180, PDEM: 0.476) ). So simply using RMSE may cause models selection to fail.\nIn fact, CPMSE has similar functionality to RMSE.\nTherefore, it is entirely feasible to use PDE/PDEM directly for model selection or evaluation.\n\n[1]. Ekström, Marie. \"Metrics to identify meaningful downscaling skill in WRF simulations of intense rainfall events.\" Environmental Modelling & Software 79 (2016): 267-284.\n\nQ2: For example, there might be other domain-specific scores that are missing in the benchmark, how should we incorporate these scores in the PEM / PDEM? \n\nA2: Thank you for your question. It can be added to PEM/PDEM by first normalizing and then weighting the metric to be added.\n", " Thanks for the rebuttal.\n\nRegarding Q1, I can understand the necessity for including a few domain-specific score functions such as MPPE, HRRE, CPMSE, AMMD, HRTS, CMD. However, it is not clear why we need PEM / PDEM at this stage given that they are very consistent with the simpler MSE score. For example, there might be other domain-specific scores that are missing in the benchmark, how should we incorporate these scores in the PEM / PDEM? In fact, people may later adopt these metrics for model selection. Can we get a model that is better at domain specific scores by selecting the candidate models with PEM/PDEM and not MSE?\n\nRegarding Q2, thanks for agreeing to add vision transformers in the benchmark.\n\nRegarding Q3, thanks for the reply. The event types can be useful for further analyzing whether the SR algorithms are robust for different domains (i.e., meteorological events).\n", " Q3: There are no clues about the effectiveness of proposed novel compound metrics PEM and PDEM. It would be much more convincing to conduct empirical studies to prove that models achieving better PEM/PDEM demonstrate better ability on addressing some concerned issues.\n\nA3: Thanks for the comment. Here we are trying to make the metrics more applicable to meteorology society while also containing variables (e.g., RMSE) that are familiar to the computer science society. The metrics Precipitation Error Measure (PEM) and Precipitation Dynamics Error Measure (PDEM) are weighted over a series of metrics with clear physical meaning (reconstruction metrics: MPPE, HRRE, CPMSE, AMMD, and dynamic metrics: HRTS and CMD) and have been applied in downscaling research in meteorology society for a long time (may not in the same abbreviation). We’ve mentioned these in the supplementary (section 3. Metrics) and have added an explanation to the main text. In supplementary section 3, we also discussed how each metric is calculated and what other literature employs the metric. This explains why better PEM/PDEM demonstrates a better ability to address downscaling problems (from a meteorology sense). For example (line 30-33 in supplementary), “The mesoscale peak precipitation error (MPPE; mm/hour) is calculated as the difference of top quantile between the generated/real rainfall dataset which considering both spatial and temporal property of mesoscale meteorological systems, e.g., hurricane, squall. This metric is used in most of these papers (for example [15, 10, 2, 6, 11, 14] (refs in our paper) suggest the quantile analysis to evaluate the downscaling quality)”. To be noticed, in meteorology society, researchers tend to evaluate one downscaling algorithm with not a single variable but multiple variables together. However, it is always important to condense the information when bridging two fields. Here we weighted these variables into two to make comparing machine learning models easier for computer science society. \n\nQ4: Missing training details: Selected baselines are not designed for precipitation data. It is necessary to (at least slightly) modify and tune the models for fair comparison. However, there is no information about these details except for a single statement \"we also adjust the hype parameters of these models for better performance\" in Supl. Sec.5.2.\n\nA4: Thanks for the question. The parts that need to be adjusted for these models include two parts：\n1. The hyperparameters required for training, which we have explained in line 309\\~313 of our paper. It is worth pointing out that typically SR models use a learning rate of 1e-4\\~5e-4, but we found that using 1e-3 is better for our task.\nWe have added more detailed instructions in Section 6.1 of the new version of our paper;\n2. The adjustment of the model, including the adjustment of the input channel and upsampling rate. We adjust the number of channels of input data for SRCNN, SRGAN, EDSR, ESRGAN, DBPN, RCAN, EDVR, RBPN, and our model to 1. We set the input data channel to 5 for SRGAN-V, EDSR-V, and ESRGAN-V. We set the upsampling rate to 3 for all models. \n\n\nQ5: Formatting errors.\n\nA5: Thank you for your thoughtful suggestions. We had corrected \"e.t.c\" to \"etc.\". Careful corrections have been made to the language of our paper. \"L\" denots low-resolution and \"H\" denots the high-resolution. \"T\" represents the frame number. A detailed explanation has been added to Section 5 of the new version of our paper. We have revised the writing of Eq.1. We had highlighted 6 commonly used metrics in Table 1 of the new version of our paper.\n\nQ6: The qualitative results shown in Figure 4 are hard to distinguish. Could the authors provide more evidence to demonstrate that the models achieving better PEM and PDEM generate better predictions?\n\nA6: Thank you for your thoughtful suggestion. For this task, visualization is only an auxiliary means. The field of meteorology directly uses the quantitative metrics mentioned in our paper to measure the quality of model predictions, as described in A3. The two metrics PEM and PDEM describe overall performance over a period of time, while PDEM describes dynamic properties that are difficult to capture in static pictures. PEM and RMSE are usually positively correlated. More reflected in the visualization is the level of RMSE. It is worth mentioning that PSNR/SSIM/LPIPS visual effects are often indistinguishable in image super-resolution tasks. To improve the distinguishability of qualitative analysis results, we marked the PEM and RMSE corresponding to the visualization results to facilitate readers to distinguish. Furthermore, the discriminative regions in the visualization are marked with red boxes.", " Thank you very much for your interest in our work and for your golden suggestions. \n\nQ1: What are the advantages of using the real data collected by two different systems for training super resolution models than using simple downsampling algorithms.\n\nA1: Thanks for the question. When considering real-world meteorological problems, the downscaling algorithm trained on data collected from two different systems will be more helpful. As we mentioned (lines 57-59), “Contrary to image data, the proposed real precipitation dataset … shows the physical characters (e.g., temporal misalignment, temporal sparse and fluid properties, etc., that challenge the downscaling algorithms.” The down-sampled dataset doesn’t reflect these real-world problems. It is necessary to emphasize that the difference between high-resolution observation data and low-resolution observation data in the real downscaling task [1] is not simply the difference in resolution, but the difference in observation methods (e.g., satellite and radar). This situation is like different degenerate kernels (e.g., unknown and bicubic) in image super-resolution. SR models trained on bicubic degenerate datasets (e.g., DIV2K-bicubic) suffer severe performance degradation on the in-the-wild raw data [2,3,4]. On the other hand, many parts of the world are covered by multiple-resolution observations of metrological variables. How to unify them and how to organize them become an important question. When it comes to the two systems mentioned in this dataset, NLDAS (lower-resolution) covers 1980-now, and StageIV (higher-resolution) covers 2002-now. Developing a downscaling algorithm to transfer NLDAS to StageIV allows researchers to extend higher-resolution observations of metrological variables to a longer period, which helps to understand the climate change effect on precipitation. We’ve added further explanations to the main text to explain the advantages of using the real data collected by two different systems.\n\n[1]. Reichstein M, Camps-Valls G, Stevens B, et al. Deep learning and process understanding for data-driven Earth system science[J]. Nature, 2019, 566(7743): 195-204.\n\n[2]. Ji, Xiaozhong, et al. \"Real-world super-resolution via kernel estimation and noise injection.\" proceedings of the IEEE/CVF conference on computer vision and pattern recognition workshops. 2020.\n\n[3]. Hussein, et al. \"Correction filter for single image super-resolution: Robustifying off-the-shelf deep super-resolvers.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2020.\n\n[4]. Xu, Yu-Syuan, et al. \"Unified dynamic convolutional network for super-resolution with variational degradations.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2020.\n\nQ2: The author should compare these two approaches empirically, e.g., demonstrate that models trained with real data are able to reconstruct better high resolution data and hence boost the performance on downstream tasks.\n\nA2: Thank you for your constructive comments. We use the bicubic method (Widely used to synthesize data) to downsample the high-resolution data (624*999) from 2002.7 to 2016.11 to low-resolution data (208 × 333), so that we generate a synthetic dataset. We employ this dataset to train our model from scratch, and use the original data from 2017.7\\~2017.11 as the test set. We report the test results in the table below:\n\n| Approach | MPPE &darr; | HRRE &darr; | AMMD &darr; | CPMSE &darr; | HRTS &darr; | CMD &darr; | PEM &darr; | PDEM &darr; | RMSE X100 &darr; |\n| ---- | ---- | ---- | ---- |---- | ---- | ---- | ---- | ---- | ---- |\n| Ours (real data) | 4.198 | 221.859 | 0.191 | 1.890 | 7.723 | 9.568 | 0.197 | 0.441 | 0.312 |\n| Ours (synthetic data) | 5.187 | 311.212 | 0.232 | 3.121 | 9.953 | 12.282 | 0.259 | 0.568 | 0.399 |\n\nIt can be seen from the table that the performance of the model trained on the bicubic synthetic dataset (row #3) is severely degraded. Therefore, the model trained with the real collected data has a great advantage in the task of spatial precipitation downscaling, and also confirms \"A1\". We have added the above experiment to the Sec.6.1 of the new version of our paper.\n", " Thank you very much for your interest in our work and for your valuable comments. This would be an important work bridging meteorology and computer science. In this paper, we propose the first large-scale dataset for precipitation downscaling that is based on real measured data while the previous models are usually evaluated on synthetic datasets (downsampling the radar maps to generate the synthetic low/high-resolution pairs) and no formal dataset released previously. Under the general trend of the times, it is always good to extend from AI to AI+X. Alphafold's success is such a good example, which tells that deep and well-communicated interaction between AI and other fields could stimulate large scientific breakthroughs. Downscaling is one of the most important tasks in current meteorological research, and the combination with deep learning is also the main research trend [a]. We believe this paper is also a meaningful and successful one and time proves it. To accomplish this work, great and difficult communications between computer science and meteorology side have been done to ensure this precipitation down-scaling is the most important and cutting-edge meteorological task that could be handle by computer science.\n\n[a]. Reichstein M, Camps-Valls G, Stevens B, et al. Deep learning and process understanding for data-driven Earth system science[J]. Nature, 2019, 566(7743): 195-204.\n\nQ1: It seems that RMSE is itself a very good summary metric. Thus, it is not clear why we will still need PEM / PDEM.\n\nA1: Thanks for the comment. We agree RMSE is an excellent summary metric and which is also very familiar to computer science society. For meteorology society, researchers usually use metrics that consider many kinds of meteorological phenomena. The metrics Precipitation Error Measure (PEM) and Precipitation Dynamics Error Measure (PDEM) are weighted over a series of metrics with clear physical meaning (reconstruction metrics: MPPE, HRRE, CPMSE, AMMD, and dynamic metrics: HRTS and CMD) and have been applied in downscaling research in meteorology society for a long time (may not in the same abbreviation). We could expect better PEM/PDEM performance when better RMSE performance is observed, but it might not always be the case. To make this dataset practical for computer scientists and meteorologists, here we introduce both PEM/PDEM and RMSE systems to benchmark the algorithms. \nFor details on calculating PEM/PDEM, we’ve mentioned these in the supplementary (Section 3. Metrics) and have added an explanation to the main text. In supplementary Section 3, we also discussed how each metric is calculated and what other literature employs the metric. This explains why better PEM/PDEM demonstrates a better ability to address downscaling problems (from a meteorology sense). For example (line 30-33 in supplementary), “The mesoscale peak precipitation error (MPPE; mm/hour) is calculated as the difference of top quantile between the generated/real rainfall dataset which considering both spatial and temporal property of mesoscale meteorological systems, e.g., hurricane, squall. This metric is used in most of these papers (for example [15, 10, 2, 6, 11, 14] (refs in our paper) suggest the quantile analysis to evaluate the downscaling quality)”. To be noticed, in meteorology society, researchers tend to evaluate one downscaling algorithm with not a single variable but multiple variables together. However, it is always important to condense the information when bridging two fields. Here we weighted these variables to two to make it easier to compare machine learning models and easier for computer science society to follow.\n\n\nQ2: Currently, the state-of-the-art image super-resolution model is based on vision Transformers (e.g., SwinIR) and the author need to reference the latest progress in this area.\n\nA2: Thank you for your constructive comments. We will definitely add the state-of-the-art transformer-based SR models (e.g., SwinIR) trained on our dataset to the benchmark models.\n\nQ3: The author mentioned that the dataset contains lots of different events such as hurricane, squall. Are the sequences in the dataset marked with the event type?\n\nA3: Thanks for the comment. Yes, we have provided event annotations such as hurricanes, squall lines for relevant frames.\n\n", " Thank you very much for your interest in our work and for your valuable comments. This would be an important work bridging meteorology and computer science. In this paper, we propose the ***first*** large-scale dataset for precipitation downscaling that is based on real measured data while the previous models are usually evaluated on synthetic datasets (downsampling the radar maps to generate the synthetic low/high-resolution pairs) and no formal dataset released previously. Under the general trend of the times, it is always good to extend from AI to AI+X. Alphafold's success is such a good example, which tells that deep and well-communicated interaction between AI and other fields could stimulate large scientific breakthroughs. Downscaling is one of the most important tasks in current meteorological research, and the combination with deep learning is also the main research trend [1]. We believe this paper is also a meaningful and successful one and time proves it. To accomplish this work, great and difficult communications between computer science and meteorology side have been done to ensure this precipitation down-scaling is the most important and cutting-edge meteorological task that could be handle by computer science.\n\n[1]. Reichstein M, Camps-Valls G, Stevens B, et al. Deep learning and process understanding for data-driven Earth system science[J]. Nature, 2019, 566(7743): 195-204.\n\nFor the technical novelty concern. \n\nOur work demonstrates its novelty in two aspects: \n\n1.The first large-scale open-source dataset for precipitation downscaling that is based on real measured data as described above, which will greatly help bridge the DL/ML community with meteorological science, while promoting the development of AI-for-Science.\n\n2.Novel benchmark model structure design and performance. Existing VSR methods generally include motion estimation modules, which are composed of modules (e.g., PCD in EDVR, Projection Module in RBPN, etc.) with strong video dynamics assumptions. As mentioned in our paper, the assumptions do not match precipitation downscaling. Unlike them, our implicit dynamic estimation module (IDEM) is a low inductive-bias module (e.g., transformers outperform CNNs), it only contains N-2 (N is the input adjacent frames, 5 frames in our model setting) weight-sharing small networks, so that IDEM can explore the inherent laws in the precipitation data without constraints/assumptions. In addition, self-attention, as a low inductive-bias operator, has achieved huge performance improvements in computer vision tasks (e.g., image classification, object detection, etc.). The low inductive-bias setting allows self-attention to fully explore the inherent laws within the data without being constrained by data assumptions [2]. At the same time, the self-attention operator also exhibits stronger generalization ability. Analogously, this is also the potential reason why our IDEM works better on the precipitation dataset. The results in Table 1 (in our paper) show the superiority of our model. Furthermore, our IDEM module also shows very competitive performance on the VSR data set: Vid4(4×) Average RGB PSNR 25.85 (EDVR Average RGB PSNR 25.83, DUF Average RGB PSNR 25.79). We will add more details (novelty analysis and performance analysis in VSR task) about the proposed model in Sec.5 and Sec.6.\n\n[2]. Esser P, Rombach R, Ommer B. Taming transformers for high-resolution image synthesis[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2021: 12873-12883.\n\nQ1: Eastern coast of US has been selected for data collections. What about other regions ?\n\nA1: Thank you for your constructive comments. There several reasons for selecting the eastern coast of US. \n1. Compared with other regions in the world, the US has systematic and complete observational data (NLDAS (lower-resolution) covers 1980-now, and StageIV (higher-resolution) covers 2002-now) of various resolutions from different observational systems (e.g., satellite, weather radar, etc.).\n2. Compared to the eastern US, the West Coast has very little precipitation, which is not helpful for our task, so we discarded the West Coast to reduce the redundancy of the dataset.\n3. In our future work, we will expand to more regions of the world.", " Thank you very much for your interest in our work and for your golden suggestions. This would be an important work bridging meteorology and computer science. In this paper, we propose the first large-scale dataset for precipitation downscaling that is based on real measured data while the previous models are usually evaluated on synthetic datasets (downsampling the radar maps to generate the synthetic low/high-resolution pairs) and no formal dataset released previously. Under the general trend of the times, it is always good to extend from AI to AI+X. Alphafold's success is such a good example, which tells that deep and well-communicated interaction between AI and other fields could stimulate large scientific breakthroughs. Downscaling is one of the most important tasks in current meteorological research, and the combination with deep learning is also the main research trend [1]. We believe this paper is also a meaningful and successful one and time proves it. To accomplish this work, great and difficult communications between computer science and meteorology side have been done to ensure this precipitation down-scaling is the most important and cutting-edge meteorological task that could be handle by computer science.\n\n[1]. Reichstein M, Camps-Valls G, Stevens B, et al. Deep learning and process understanding for data-driven Earth system science[J]. Nature, 2019, 566(7743): 195-204.\n\nQ1: SPDnet is not a very good name…\n\nA1: Thank you for your constructive comments. SPDNet is a straightforward name derived from shorthand for \"Spatial Precipitation Downscaling\".\nWe believe a good name is very important to our work, so we will look for a better one.\n\nQ2: \"It says in the checklist that the code and the data are proprietary. This needs to be clarified. What’s the point of publishing a dataset if it cannot be used by others?\"\n\nA2:\nThanks for the comment. \n***All relevant codes and datasets are open-source for research purposes.***\nWe apologize for the error in filling out the checklist, we have changed the item \"Do you include licenses for code and datasets? [No] Code and data are proprietary\" to \"Do you include licenses for code and datasets?[ Yes] see Section 4.2\".\nThe dataset and the code are not proprietary.\nWe will build a dedicated github repository and website for users to easily use our datasets and codes.", " There is not much to say here. The paper organizes a large precipitation dataset from both high res and low res sources and illustrates some baselines. The problem addressed is both interesting to ML (esp. to those interested in mixing physics and ml), and important. The question then, is; given that this data can be obtained directly from the original sources, is a new organization of it necessary and does it warrant a publication in an ML conference. Although I expect other reviewers will disagree, I have a positive view. Publishing this paper will probably increase interest in ML in this set of problems, and some in the community will find the dataset useful. See above SPDnet is not a very good name… It says in the checklist that the code and the data are proprietary. This needs to be clarified. What’s the point of publishing a dataset if it cannot be used by others? ", " This paper presents a large scale dataset for spatial precipitation downscaling which contains more than 62, 400 pairs of high-quality low/high-resolution precipitation maps for over 17 years, ready to help the evolution of deep learning models in precipitation\ndownscaling. The precipitation maps collected in the dataset cover various meteorological phenomena such as hurricane and squall. The data are organised in time series of maps, with 720 maps/month. Comprehensive metrics are also provided to evaluate the performances of models. This paper is well written and brings comprehensive dataset for spatial precipitation. However the technical novelty is low.\n Eastern coast of US has been selected for data collections. What about other regions ? The dataset lacks precipitation maps for several regions", " The paper proposed a large-scale spatial precipitation downscaling dataset named SPDNet. The dataset contains more than 62400 pairs of high-quality low/high-resolution precipitation maps for over 17 years, and covers more than 9 million squre kilometers of land area. The author also introduced 6 metrics that evaluate different aspects of the downscaling models, and 2 summary metrics that combine these 6 individual metrics. The author viewed the task as a video super-resolution problem and compared 14 methods. From the experimental results, the overall performance of the video super-resolution (VSR) models are better than Single-Image Super-Resolution (SISR) models.\n Stengths:\n\n1. The paper proposed the first large-scale precipitation downscaling dataset. This is an important scientific problem and a large-scale dataset can help move the area forward. In addition, the author pointed out the unique characteristics of the task such as temporal misalignment, temporal sparse, and fluid properties.\n2. The paper proposed 6 metrics for evaluating the models, including 4 reconstruction metrics that focuses on evaluating if the predicted high-resolution precipitation map matches the ground-truth, and 2 dynamic metrics that evaluate the dynamics of the predicted precipitation (via first order dynamics).\n3. The paper compared 14 models, including the Kriging method that has been widely used in the geospatial community, and other SISR and VSR methods. The author also extended SRGAN, EDSR, ESRGAN to be VSR methods.\n\nWeaknesses\n1. It seems that RMSE is itself a very good summary metric. Thus, it is not clear why we will still need PEM / PDEM.\n2. Currently, the state-of-the-art image super-resolution model is based on vision Transformers (e.g., SwinIR) and the author need to reference the latest progress in this area.\n 1. The author mentioned that the dataset contains lots of different events such as hurricane, squall. Are the sequences in the dataset marked with the event type?\n 1. The paper will be limited regarding the coverage of the baseline methods. However, it is difficult to cover all the latest image super-resolution methods so it is acceptable.\n\n", " This paper proposed a dataset consists of precipitation image sequences named SPDNet for spatial precipitation downscaling as well as a novel implicit dynamics estimation driven model. The proposed model as well as baseline models are evaluated on SPDNet with task specific metrics. **Strengths**\n1. **Valuable dataset**: The large scale dataset SPDNet is in high resolution and in sequence, which is a valuable contribution to data-driven meteorological research.\n2. **Benchmark**: The authors have evaluate SOTA super resolution models on the proposed dataset ,and thus provide a good benchmark.\n\n**Weaknesses**\n1. **Necessity of low resolution data**: The authors claim in Introduction that the data obtained by simulated degradation is different from the real data collected by two different systems. However, there is no further discussion on it. It is insufficient to argue that their approach is better than obtaining low resolution data by simply downsampling the high resolution data. The author should compare these two approaches empirically, e.g., demonstrate that models trained with real data are able to reconstruct better high resolution data and hence boost the performance on downstream tasks.\n2. **Unconvincing evaluation**: There are no clues about the effectiveness of proposed novel compound metrics PEM and PDEM. It would be much more convincing to conduct empirical studies to prove that models achieving better PEM/PDEM demonstrate better ability on addressing some concerned issues.\n3. **Missing training details**: Selected baselines are not designed for precipitation data. It is necessary to (at least slightly) modify and tune the models for fair comparison. However, there is no information about these details except for a single statement \"we also adjust the hype parameters of these models for better performance\" in Supl. Sec.5.2.\n4. **Formatting errors**: There are some language errors like \"e.t.c.\" $\\rightarrow$ \"etc.\", and misleading notations in mathematical expressions such as missing brackets in Eqn.1, missing description of \"L\", \"H\", \"T\" in line 250. Scores of 6 commonly used metrics in Table 1 should also be highlighted. 1. What are the advantages of using the real data collected by two different systems for training super resolution models than using simple downsampling algorithms? If the two domains need to be similar, directly downsampling the high resolution data is both cheap and effective. If the two domains need to differ a lot from each other, it would be better to categorize the task as domain transferring instead of \"spatial precipitation downscaling\".\n2. The qualitative results shown in Figure 4 are hard to distinguish. Could the authors provide more evidence to demonstrate that the models achieving better PEM and PDEM generate better predictions? Listed in **Weaknesses**" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 6, 6, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 2, 4, 4 ]

[ "lnVp28VEsCi", "iyh5uAQH1sE", "jjMUDMTFaxK", "1mMfRqp4pty", "WBmpyaytXL", "9vOAx1JCX0r", "nf3SWnPfY5", "1mMfRqp4pty", "1mMfRqp4pty", "yXth6737L-j", "jjMUDMTFaxK", "WBmpyaytXL", "nips_2022_0cn6LSqwjUv", "nips_2022_0cn6LSqwjUv", "nips_2022_0cn6LSqwjUv", "nips_2022_0cn6LSqwjUv" ]

[ "PtG45NQpkkJ", "Ply0VluRFTh", "tb0L7U4mSC9", "CQVYb2nxWMh", "BMQYtEixcZa", "KM4jVjaztpu", "8jhUY9VZDme", "e-acn3TDh47", "MnrrwlkBJ9J", "_PGPuyLSGf9n", "j0mKxBWR2X3", "xDl_9vXlFNg", "6ixFh7wv5Z-", "RIp-yQeSiFA", "7Gb3Z_F59BM", "48-nm_Xzd3z", "WjK18NnVFnW", "GaqDNYh_rEb" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " No ethical issues No ethical issues No ethical issues", " The paper is flagged potentially because of bias/discrimination concerns with the output of the algorithm which restores blurred images. There is no discussion in the paper or in the rebuttal on bias properties of the proposed algorithm. The authors did not respond to the Ethics flag being True in the rebuttal. I would suggest that the authors acknowledge the need for a bias analysis of the method e.g. how it performs on facial images of different color tones. The example of such an analysis is in this paper https://arxiv.org/abs/2003.03808 in Section 6 which was critiqued for similar reasons and which addressed the bias concerns. In the interest of clarifying potential negative impacts of the work, the authors should discuss the negative uses of their algorithm for example to de-anonymize images to violate privacy or to assist criminal investigations without proper scrutiny of the algorithm's performance. The paper shows face images from publically available dataset. However, it is not clear if the contributed images can be shown in a paper. It is not discussed if the data contributors provided consent to use their images. After including a discussion of potential negative impacts and clarifying the legitimate use of face images, the paper seems ok. ", " The authors solve my concerns well. I would like to recommend acceptance. ", " Dear reviewers and ACs, \n\nWe noticed that the server of the previous anonymized link (https://anonymous.4open.science/r/ID688/) is down due to unexpected errors. Thus, we replace it with the new anonymous link: https://www.dropbox.com/sh/rqc9lve9h9b0a1s/AACgvj-FbY3Xp1NSaB5-C-URa?dl=0\n\nWe have updated the link in each following response. Sorry for the inconvenience this may cause. \n\nThanks!", " Thank you for giving the final rating as 'Accept'. We are glad that our answer addressed your concerns. Thanks for your time and valuable comments.", " Dear AC Djod, thanks for your valuable comments and suggestions. We evaluated the quantitative results of oracle NN (HQ) on the CelebA-Test dataset, as shown in the following table:\n\n| Methods | LPIPS&darr; | FID&darr; | NIQE&darr; | IDS&uarr; | PSNR&uarr; | SSIM&uarr; |\n| :----- | :-----|:------ |:------ |:------- |:------- |:------ |\n| Input | 0.712 | 295.73| 18.67 |0.32 | 21.53 | 0.623 |\n| CodeFormer(ours) | 0.307 | 57.01 | 4.47 | 0.59 | 21.82 | 0.612 |\n| oracle NN (HQ) | 0.545 | 50.23 | 3.82 | 0.14 | 13.45 | 0.464 |\n| Code GT | 0.124 | 54.31 | 4.33 | 0.89 | 25.43 | 0.749 |\n| GT | 0.00 | 51.40 | 3.84 | 1.00 | ∞ | 1.00 |\n\nIn terms of LPIPS, PSNR, SSIM, and IDS scores, oracle NN (HQ) shows poor quantitative performance, indicating a large disparity between training and testing data, which further demonstrates the good generalization ability of our method.\n\nWe will add both quantitative and qualitative results of oracle NN in the final revised paper, and provide a discussion on the generalization ability of codebook to 'unseen' images. ", " Thanks. The explanations are helpful. It would be better to show the quantitative evaluation results of oracle NN (HQ) in Table 1. This is purely for examining the diversity between training and testing data, not really a competitive comparision. ", " The authors have addressed all my concerns and questions.", " Dear AC DJod, thanks for your question and discussion. \n\nThe proposed CodeFormer actually has a good generalization ability to the unseen faces, even for real-world low-quality (LQ) faces. This is because the learned codebook is able to reconstruct high-quality faces not included in the training dataset. Instead of 'memorizing' the whole face image, the codebook is to learn base code items to store the context-rich visual parts of faces, which are able to represent any HQ faces beyond the training dataset by different code compositions. Theoretically, the representation space of a 1024 codebook with code composition (16x16) could produce $256^{1024}$ different HQ faces, which is much larger than the scale of the training dataset FFHQ (70,000). With such a large representation space, our method exhibits great expressive power and generalizability. In other words, we would like to say that our CodeFormer works by learning to predict the code combinations (sequences) of LQ faces, which are enormous and flexible representations, not 'retrieving' the HQ faces memorized from the training dataset. We list some results to support this statement as follows:\n\n1. In our submission, the HQ versions of all evaluated faces in synthetic and real-world data are not included in the training dataset. (Please note that the real-world test dataset as well as old photos and movie clips do not have the corresponding HQ versions at all.) Nevertheless, the proposed CodeFormer still produced high-quality outputs.\n\n2. To demonstrate the good generalizability of the learned codebook, we provide additional reconstruction results on some 'unseen' HQ faces from the CelebA-HQ dataset. Please find the results in `Response_to_AC_DJod.pdf` (download for the best view) from this anonymous link: https://www.dropbox.com/sh/rqc9lve9h9b0a1s/AACgvj-FbY3Xp1NSaB5-C-URa?dl=0. As shown in Figure A, the learned codebook can reconstruct input HQ face images almost perfectly, even if they are not present in the training data.\n\n3. As suggested by AC DJod, we evaluate the ”oracle Nearest Neighbor“ (oracle NN) on both synthetic LQs and real-world LQs (Note that there is no HQ version for real-world LQ). For each of the test LQ faces, we find the closest HQ face from the training dataset FFHQ in terms of Euclidean distance in the feature domain. We evaluate the oracle NN with different query images for NN retrieval as shown in the following table. The comparisons can be found in `Response_to_AC_DJod.pdf` (download for the best view) from this anonymous link: https://www.dropbox.com/sh/rqc9lve9h9b0a1s/AACgvj-FbY3Xp1NSaB5-C-URa?dl=0. From Figure B (synthetic ) and Figure C (real-world), we can see that oracle NN fails to retrieve a reasonable and matched HQ face, and its results show obvious identity inconsistency. This is expected because the training dataset FFHQ with 70,000 samples is far from being able to cover all faces, in spite of the fact that the FFHQ is the largest HQ face dataset in this field. Hence such a shortcut solution of oracle NN by retrieving faces from the FFHQ is not effective and cannot be applied in practice. Nevertheless, we agree such a comparison and discussion could gain more insight into the characteristics of this method. \n\n | Method | oracle NN (LQ) | oracle NN (HQ)|\n | :-------- | :--- | :----------------- | \n | Query for synthetic data| synthetic LQ face | corresponding HQ face (GT) | \n | Query for real-world data| real-world LQ face | N/A | \n\n\nWe hope this answer could solve your concerns well. Please feel free to give more comments for any concerns or questions. Thanks.", " I have a question regarding the generalization ability of the proposed Codeformer method, which is also related to “[Q5] Wondering if it is possible to extend the proposed method to natural image restoration”. Since the codebook and decoder are all fixed after the training is finished, what if one inputs into the trained network a degraded face whose high-quality version is considerably different from the trained high-quality faces? It would be better if the authors can include for comparison a baseline called “oracle Nearest Neighbor”, which performs restoration by using the most similar high-quality training face with respect to the high-quality version of the degraded testing face.", " Thank you for the positive and insightful comments on the novelty and performance of the proposed method, such as well-organized paper, reasonable design, good writing, promising results, and comprehensive study. The raised concerns are addressed as follows.\n\n**[Q1] Provide some concise discussions about the reconstruction capability of codebook and any potential fidelity issues.**\n\nThe reconstruction capability of codebook is affected by the number of code items. We conducted an ablation study to explore their relationships. As shown in Table 1 of the supplementary, the reconstruction performance (LPIPS and PSNR) is better when more codebook items are activated and learned. To maintain the high fidelity of the reconstructed faces from codebook, we adopt a larger codebook with 1024 items. We also show that a 1024 codebook is sufficient to encode facial details, while more code items over 1024 cannot significantly enhance the reconstruction capability. Please check out [Q1] of Reviewer pfoY.\n\nBesides, we introduced the controllable feature transformation modules to control the information flow from the encoder to decoder, which also helps to complement code composition errors and expression defects. High-fidelity results can be obtained by setting the controllable coefficient *w* to 1.\n\n\n**[Q2] Runtime comparison.**\n\nWe provided the runtime comparison in Table 3 of the supplementary. The proposed CodeFormer has a similar runtime with PSFRGAN and GPEN, inferring one image of 512x512 within 0.1s. Meanwhile, our method achieves the best performance in terms of LPIPS on the Celeb-Test dataset. \n\n**[Q3] Why are Stage II and III trained separately? How about training these two stages together?**\n\nIt is necessary to train Stage II and III separately, since the settings of controllable coefficient *w* are different in these two training stages, i.e., *w* = 0 in Stage II, and *w* = 1 in Stage III. We tried to train these two stages together in an alternate iterative fashion, but cannot get a good performance. The separate training could greatly reduce the difficulty of network learning due to the same coefficient *w* at each stage.\n\n**[Q4] Provide discussions on the choosing of compression rate.**\n\nWe set the compression ratio of 32 in our network design. Smaller compression ratios, such as 16, will destroy robustness to large degradation and result in a longer code sequence (32x32 for the compression ratio of 16), which will significantly increase the difficulty of global modeling of the Transformer and reduce its efficiency. Larger compression ratios, such as 64, cannot maintain the good fidelity of reconstruction results, leading to a serious issue of identity inconsistency. We will add this discussion in the revised version.\n\n**[Q5] Minor typos.**\n\nThanks for your careful reading. We have fixed the typos in the updated manuscript.", " Thank you for the positive and insightful comments about the well-motivated idea, good writing, promising performance, extensive results, and inspiring design. We also appreciate the comments for providing further insightful discussions. Please check out the answers and discussions below.\n\n**[Q1] Further discussion on the number of code items in codebook.**\n\nWe provided an ablation study in Sec. A.1 of the supplementary. Table 1 in suppl. shows that reconstruction performance (LPIPS and PSNR) is better as more codebook items are activated and learned. The CodeFormer adopts a codebook with 1024 items. As suggested by Reviewer pfoY, we also train a large codebook with 2048 items, but it only brings a slight improvement in terms of LPIPS and PSNR, as shown in the following table. The results indicate that 1024 codes are sufficient to encode facial details. We will add this result in the revised supplementary.\n| Num. of Codebook | N=384 | N=1024 (CodeFormer) | N=2048 |\n| :--------------: | :---: | :-----------------: | :----: |\n| LPIPS&darr; | 0.202 | 0.175 | 0.172 |\n| PSNR&uarr; | 22.59 | 23.41 | 23.46 |\n\n\n**[Q2] Provide examples of failure cases.**\n\nWe provide some failure cases via the anonymous link: https://www.dropbox.com/sh/rqc9lve9h9b0a1s/AACgvj-FbY3Xp1NSaB5-C-URa?dl=0 (download the .pdf file for the best view). Although CodeFormer exhibits great robustness in most cases, when it comes to side faces, CodeFormer offers limited superiority to other methods and also cannot produce good results for highly corrupted side faces. This is expected because there are only few side faces in the FFHQ training dataset. As a result, the codebook is unable to learn sufficient codes for the side faces, leading to less effectiveness in reconstruction and restoration. \n\nWe will add some failure cases in our revised supplementary. We hope these failure cases could give some inspiration for future works. For example, one possible research direction is face restoration under different poses (including side faces), which is meaningful and challenging. \n\n**[Q3] The setting of tradeoff weight *w* in Stage III is unclear.**\n\nSorry for confusing you with this training setting. Inspired by network interpolation [a], we only set the *w* to 1 as a marginal value during the training of stage III (Note that stage II was learned under another marginal value of *w* = 0), which then allows network to achieve continuous transitions of results by adjusting *w* in [0, 1] during inference. We have added the clear description in the updated manuscript (Line191).\n\n> [a] Xintao Wang et al. Deep Network Interpolation for Continuous Imagery Effect Transition. In CVPR, 2019.\n\n**[Q4] How to demonstrate the effectiveness of code prediction?**\n\nTo verify the superiority of code prediction for codebook lookup, we conduct the ablation study of two variants, i.e., nearest-neighbour (NN) matching and a CNN-based code prediction module (adopt a Linear layer for prediction following the encoder). The comparison of Exps. (b) and (c) in Table 3 of the manuscript indicates that adopting code prediction for codebook lookup is more effective than NN feature matching.\n\n**[Q5] Wondering if it is possible to extend the proposed method to natural image restoration.**\n\nThis is a good open question. The potential of generalizing the proposed CodeFormer to natural image restoration is also our next investigation. However, a few unique challenges in natural image restoration need to be addressed: 1) An essential and generic codebook for diverse scenes should be learned. 2) More efficient global modeling should be introduced due to the high resolution of natural images. 3) Additional priors such as semantic segmentation map may be needed, as the complexity and variety of textures in natural images will make codebook lookup more difficult and ambiguous.\n\n", " We thank the reviewer for the positive comments on the performance of the proposed method. We will answer your questions as below.\n\n**[Q1] Wondering if VQGAN itself can achieve similar restoration results, except for the code prediction and controllable feature transformation.**\n\nThe original VQGAN performs codebook lookup via Nearest-Neighbor (NN) feature matching. Though it works well on the HQ features, it is not reliable for image restoration since the intrinsic textures of LQ inputs are usually corrupted. The information loss and diverse degradation in LQ images inevitably distort the feature distribution, prohibiting accurate feature matching. As depicted in Fig. 1(b)(right), even after fine-tuning the encoder on LQ images, the LQ features cannot cluster well as the HQ features do, but spread into other nearby code clusters. Hence, VQGAN, which adopts NN matching, is unreliable in such cases. This discovery is also the key motivation of this work.\n\nIn the manuscript, we provided both qualitative and quantitative comparisons to demonstrate the necessity of our method and its advantages over VQGAN. **1)** The qualitative comparisons between VQGAN (NN) and CodeFormer in Fig. 1(f, g), Fig. 6, and Fig.8 demonstrate the superiority of our solution over the original VQGAN, producing much better results on both face restoration and inpainting. **2)** The quantitative comparison of VQGAN (NN) and CodeFormer provided in Table 3 (Exp. b and e) indicates that our method is more effective than NN-matching in VQGAN. In addition, the code lookup accuracy curves presented in Fig. 5 show that CodeFormer achieves more robust code prediction under different degradation levels. **3)** The comparison of Exp. b and f in Table 3 shows that VQGAN produces lower fidelity results (IDS) due to the limited expressiveness of the codebook. Our CodeFormer offers controllable feature transformation modules that complement code composition errors and expression defects.\n\nOverall, the VQGAN (NN) itself cannot achieve similar restoration results as the proposed CodeFormer. In the case of heavy degradation, VQGAN usually produces low-quality results that are accompanied by artifacts due to inaccurate code lookup. In addition, there is a serious issue of inconsistent identity in the outputs of VQGAN, which tends to produce lower fidelity results without any connection between encoder and decoder.\n\n**[Q2] Provide examples of failure cases.**\n\nWe provide some failure cases via the anonymous link: https://www.dropbox.com/sh/rqc9lve9h9b0a1s/AACgvj-FbY3Xp1NSaB5-C-URa?dl=0 (download the .pdf file for the best view). Although CodeFormer exhibits great robustness in most cases, when it comes to side faces, CodeFormer offers limited superiority to other methods and also cannot produce good results for highly corrupted side faces. This is expected because there are only few side faces in the FFHQ training dataset. As a result, the codebook is unable to learn sufficient codes for the side faces, leading to less effectiveness in reconstruction and restoration. \n\nWe will add some failure cases in our revised supplementary. We hope these failure cases could give some inspiration for future works. For example, one possible research direction is face restoration under different poses (including side faces), which is meaningful and challenging. ", " We appreciate the positive and constructive comments about the solid framework, elegant design, ablation study, impressive performance, and clear writing. The raised concerns are addressed as follows.\n\n**[Q1] Missing references and discussion with recent literature [1, 2].**\n\n**Discussion:** There are three key differences between the proposed CodeFormer and the two papers [1, 2]. **1)** The studies [1,2] perform codebook lookup using Nearest-Neighbour (NN) feature matching, which is not reliable for face restoration since the intrinsic textures of LQ inputs are usually corrupted. The information loss in LQ images inevitably distorts accurate feature matching, as depicted in Fig. 1(b) in the main paper. In contrast, our proposed CodeFormer performs codebook lookup via code prediction using a global-modeling Transformer, which shows superior robustness to degradation. The visual comparisons shown in Fig. 1(f, g), Fig. 6, and Fig. 8 support this statement. Besides, the code lookup accuracy comparison in Fig. 5 also demonstrates the superiority of our solution. **2)** Different from the works [1, 2] that fine-tune the decoder $D_H$ in their restoration training stage, we fix the decoder to protect the codebook prior from corruption. Our method emphasizes that the codebook must be used alongside the pre-trained decoder to fully unleash its potential. The ablation study of Exps. (e, g) in Table 3 shows that fine-tuning decoder deteriorates the performance, validating our statement. This is because fine-tuning the decoder destroys the learned prior held by the pre-trained codebook and decoder, resulting in suboptimal performance. **3)** Unlike the fixed fusion connections used in both studies [1, 2], we propose a controllable feature transformation module with an adjustable coefficient to control the information flow from the LQ encoder to decoder. Such a design allows a flexible trade-off between restoration quality and fidelity, achieving robustness against heavy degradation and good identity preservation within a single model. We will add a brief discussion in the revised version and add references [1, 2]. \n\n**Comparison:** As the code of work [2] has not been released yet, we cannot make a comparison with it now. We have provided examples of visual comparisons between CodeFormer and VQFR [1]. Please find the comparison results from this anonymous link: https://www.dropbox.com/sh/rqc9lve9h9b0a1s/AACgvj-FbY3Xp1NSaB5-C-URa?dl=0 (download the .pdf file for the best view). The proposed CodeFormer produces better results than VQFR [1] on both heavy and medium degradation.\n\n> [1] Yuchao Gu et al. VQFR: Blind Face Restoration with Vector-Quantized Dictionary and Parallel Decoder. arXiv preprint arXiv:2205.06803 (2022). \n>\n> [2] Yang Zhao et al. Rethinking Deep Face Restoration. In CVPR, 2022.\n\n\n**[Q2] Provide the detailed network structure of the encoder in CodeFormer and illustrate the design insight.**\n\nWe provide the detailed configurations of network structure in the anonymous link: https://www.dropbox.com/sh/rqc9lve9h9b0a1s/AACgvj-FbY3Xp1NSaB5-C-URa?dl=0, including the structure tables of Encoder, Decoder, Transformer module, and Controllable Feature Transformation module. As described in `Codebook Settings` (Sec. 3.1 in the manuscript), the Encoder mainly consists of 12 residual blocks and 5 downsampling conv layers. \n\nThere is no special layer in Encoder, but we would like to emphasize that the compression ratio of 32 (5 downsampling layers) is critical in our design. Smaller compression ratios such as 16 will destroy robustness to large degradation and result in a longer code sequence (32x32 for the compression ratio of 16), which will significantly increase the difficulty of global modeling of the Transformer and reduce its efficiency. Larger compression ratios such as 64 cannot maintain good fidelity of reconstruction results, leading to a serious issue of identity inconsistency. We will also release our code and models for reference.\n\n**[Q3] Provide examples of failure cases.**\n\nWe provide some failure cases via the anonymous link: https://www.dropbox.com/sh/rqc9lve9h9b0a1s/AACgvj-FbY3Xp1NSaB5-C-URa?dl=0. Although CodeFormer exhibits great robustness in most cases, when it comes to side faces, CodeFormer offers limited superiority to other methods and also cannot produce good results for highly corrupted side faces. This is expected because there are only few side faces in the FFHQ training dataset. As a result, the codebook cannot learn sufficient codes for the side faces, leading to less effectiveness in reconstruction and restoration. \n\nWe will add some failure cases in our revised supplementary. We hope these failure cases could give some inspiration for future works. For example, one possible research direction is face restoration under different poses, which is meaningful and challenging. \n\n**[Q4] Writing typos.**\n\nThanks for your careful reading. We have fixed the typos in the updated manuscript.\n", " This paper presents a vector quantized codebook based method for blind face restoration. Specifically, the face codebook is first learnt from an encoder-decoder convolutional network. To leverage global context, a transformer-structure neural network is designed to better predict code sequence for highly-corrupted LQ faces. At last, a controllable feature transformation module is trained to adjust the relative importance of the input face (fidelity). The proposed method achieves SoTA performance on synthetic dataset CelebA-Test and comparable performance on real-world datasets LFW-Test, WebPhoto-Test, and WIDER-Test. The ablation study also demonstrates the effectiveness of the proposed modules. Strengths:\n1. Solid technical design and framework. The proposed CodeFormer framework is properly and elegantly designed, with supportive ablation studies. Remarkably, the proposed method is able to explicitly control and balance fidelity and quality. \n2. Impressive qualitative performances shown in Figure 3, Figure 4, and the supplementary video. State-of-the-art or comparable quantitative performances shown in Table 1 and Table 2. \n3. Clear writing style. Good technical presentation. \n\nConcerns:\n1. Missing related references and disscusion. I suggest to compare and discuss with some recent codebook-based works, e.g., [1] [2]. \n2. The network structure of the encoder in CodeFormer is unclear. The authors should give detailed description and illustrate the design insight.\n3. Writing typos. (1) L144: Unexpected \"?\". (2) L169, Eq (6). Z_h should be Z_l. \n\n[1] Yuchao Gu et al. VQFR: Blind Face Restoration with Vector-Quantized Dictionary and Parallel Decoder. arXiv preprint arXiv:2205.06803 (2022).\n[2] Yang Zhao et al. Rethinking Deep Face Restoration. In CVPR, 2022. My concerns and questions are:\n\n1. I suggest providing sufficient discussion with some recent literatures, including:\n\n[1] Yuchao Gu et al. VQFR: Blind Face Restoration with Vector-Quantized Dictionary and Parallel Decoder. arXiv preprint arXiv:2205.06803 (2022).\n[2] Yang Zhao et al. Rethinking Deep Face Restoration. In CVPR, 2022.\n\n2. I suggest providing detailed description on the network structure of the encoder and illustrate the design principle. The limitations of the proposed method have been discussed in the submitted manuscript. I suggest providing quantitative examples for cases where the proposed method fails.", " This paper proposes a transformer-based blind face restoration method. Specifically, it follows VQ-GAN to compress the input features and find the nearest code, and performs autoregression and decoder to generate the synthesized images. To handle corrupted input images, they propose to fix the decoder and introduce a code prediction to ensure output fidelity. Extensive evaluations demonstrate the superior performance of the proposed method over existing approaches. Strengths\n- The quantitative and visual results are significantly better than the existing methods.\n\nWeaknesses\n- This paper highly follows the architectural design of VQ-GAN. Although with extensive ablation studies, I am wondering if the VQ-GAN can also achieve similar restoration quality. - The proposed architecture follows VQ-GAN, except for the code prediction and controllable feature transformation. I am wondering if the VQ-GAN itself can also achieve similar restoration results. I do not see any failure cases in the paper. It is essential to show some failure cases for the reader to investigate the failure model to benefit future research.", " To address the task of blind face restoration, this paper designs a novel network by casting restoration task to the code token prediction task. The authors propose a small and finite codebook space to reduce the uncertainty of image restoration. Upon the learned codebook, they exploit the global interaction by a Transformer, and the controllable modules are employed to balance quality and fidelity. The proposed method is evaluated on both synthetic and real-world datasets and extended to other tasks. The experimental results and ablation studies show that the proposed method is able to restore higher-quality results. *Strengths\n1. The design philosophy of this work is well motivated: building a small discrete codebook to reduce the uncertainty of restoration; treating image restoration as a code prediction task; and adopting global-modeling transformer for better prediction.\n2. The writing of this work is pretty good and it is easy to follow how the highlighted contributions are incorporated into the overall network.\n3. The qualitative results are extensive and promising, especially in the provided supplementary and video demo. The proposed method is also evaluated on other tasks, including face inpainting, color enhancement, and old film enhancement. \n4. I like the controllable design to make a trade-off between quality and fidelity, which is inspiring. A good balance between content preservation and generalization ability is achieved.\n*Weaknesses\nIn general, the paper provides promising performance and sufficient experiments. There is no big flaw. Here, just I just provide some suggestions for improving the quality of the paper.\n\n1. The main power seems to be driven by the learned codebook. In this paper, the authors utilize the codebook with 1024 items. Actually, the performance with the more codes in the codebook is also interesting though the 1024 seems sufficient for face image restoration. Discussion on the number of items could further complete this work.\n\n2. Together with limitation discussion, some failure cases could be provided as well for better understanding. *Questions\n1. The training settings of Stage III is unclear, such as, what is $w$ value during training or is it a random value between 0 and 1?\n\n2. The proposed method involves a Transformer to predict the code sequence, and the authors claim that code prediction task by the Transformer could ease the restoration task. But it is unclear if the advantages are introduced by the powerful Transformer. To demonstrate this statement, it would be better to conduct an ablation study that the Transformer predicts the features $\\hat{Z}_c$ directly.\n3. This method is interesting, but I wonder if it has a limitation when applied to generic natural images? From my side, it could be very challenging to learn an essential codebook for a natural image due to diverse scenes and complex textures. What about the authors’ ideas about this? Yes", " This paper deals with blind face restoration in a learned small codebook space. Using a Transformer to model the global composition of LQ faces, the original restoration task is cast into a code prediction task, which is more robust to degradation. To balance the tradeoff between the quality and fidelity of the results, this work proposes to introduce the controllable modules through the connections between encoder and decoder. The proposed CodeFormer outperforms previous methods on multiple datasets and tasks. Strengths:\n1. This paper is well organized and nicely written. The presentation of motivation is clear and smooth.\n\n2. Their practice of transforming the image restoration into a code prediction problem is reasonable.\n\n3. The experiments and study are complete and comprehensive. It is also good to provide an interesting video demo. Besides the blind face restoration, the authors also provide an extension of the proposed idea to other tasks such as image inpainting and colorization. The ablation studies are also sufficient to show the efficacy of key components.\n\n4. The visual results are promising, even on heavy degradations.\n\nWeaknesses:\n\nThe learned codebook has been investigated for image generation, as I understand, it is hard to perfectly reconstruct the original HQ faces, which will lead lower fidelity of results when applied to restoration. It would be helpful to provide some concise discussions about the reconstruction capability of codebook and any potential fidelity issues. 1. The proposed network utilizes a learned codebook as a dictionary, which is similar with the design of DFDNet. As far as I know, DFDNet runs very slowly due to the time-consuming feature matching with its multi-scale dictionaries. Additionally, the proposed method also adopts a Transformer module. How about its runtime?\n\n2. I wonder why the authors train the Stage II and III separately? Is it possible to train them jointly to obtain the final model? \n\n3. This paper adopts a large compression rate of 32 when learn the codebook and autoencoder. However the smaller compression rate, such as 16, could have greater reconstruction capability, which may improve the fidelity of outputs. The discussions or study on the choosing of compression rate could be interesting.\n\nMinor typos:\n- In L100, ‘$\\alpha$’ -> ‘$\\theta$’\n- In Eq. (6), should $Z_h$ be $Z_l$? NA" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 5, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 1, 5, 5 ]

[ "nips_2022_XdDl3bFUNn5", "nips_2022_XdDl3bFUNn5", "xDl_9vXlFNg", "nips_2022_XdDl3bFUNn5", "e-acn3TDh47", "8jhUY9VZDme", "MnrrwlkBJ9J", "j0mKxBWR2X3", "_PGPuyLSGf9n", "xDl_9vXlFNg", "GaqDNYh_rEb", "WjK18NnVFnW", "48-nm_Xzd3z", "7Gb3Z_F59BM", "nips_2022_XdDl3bFUNn5", "nips_2022_XdDl3bFUNn5", "nips_2022_XdDl3bFUNn5", "nips_2022_XdDl3bFUNn5" ]

[ "w0PCNKJrV_P", "HTqs_LbvBQl", "5EGfdb3OAxw", "5Vgw8y8hHd5", "RiKd1VhyYBj", "TemxPtrwDWP", "ur9CcokaJ_W", "nvCNi8OTHKh", "k7JsXSVSNJy", "6ZzXvXflBt", "L9iob09rkhe", "sWyDy-hr2Vh", "QktqnbbVZke", "jteJqdcYkXK", "yjLmL3o0eF_", "_NSBEaUxNWI", "qZkpfsJO1vW", "ElKklpTWxVs", "clAaUW6Aup4", "Og0Hc7y55hl" ]

[ "author", "official_reviewer", "author", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " \n\n\nWe thank the reviewer for raising the score. To address the reviewer's last concern regarding the effectiveness of FedSim on identifiers like \"names\", we conduct experiments on an **additional real-world dataset \"_company_\"**, the identifiers in which are \"**company names**\". Our experimental results demonstrate that **FedSim has significant (5+%) improvement on some datasets linked on 'names'**.\n\n## Task and Dataset Description\n\n### Dataset A (Primary Party)\n**Public Link**: https://www.kaggle.com/datasets/mirbektoktogaraev/should-this-loan-be-approved-or-denied\n\n**Description**: A dataset of loan transactions between companies and banks from the U.S. Small Business Administration (SBA).\n\n**Size**: 77225 x 91 (We use a subset of the original dataset due to time constraint)\n\n**Labels**: SBA’s guaranteed amount of approved loan **ranging from 500 to 3,675,000**.\n\n### Dataset B (Secondary Party)\n**Public Link**: https://www.kaggle.com/datasets/peopledatalabssf/free-7-million-company-dataset\n\n**Description**: A dataset of companies across 237 countries. The features include company size from 1-10,000+, company location, number of employees, etc.\n\n**Size**: 220583 x 157 (We use a subset of the original dataset due to time constraint)\n\n### Task\nThe task is to predict SBA’s guaranteed amount of approved loan in each transaction (**regression**) according to the historical transactions and company information. Two datasets are linked on the **company names**. We list some examples of such identifiers below.\n> (Examples from dataset A)\n> \n>ANASTASIA CONFECTIONS, INC.\n>\n>TRIANGLE MACHINE & MFG., INC.\n>\n>STEPHANIE DEVELOPMENT, L.L.C.\n>\n> (Examples from dataset B)\n> \n>bright futures, a college and career management company\n>\n>new york life insurance company\n>\n>intercontinental hotels group (ihg)\n\n\n## Experimental Setting\n### Preprocessing\nWe preprocess the original dataset for training by \n\n- Converting all characters to lower case\n- Removing all rows with NaN\n- Converting categorical features to one-hot\n- Removing all rows with duplicate company names\n\nFor Exact, we directly compare the **lower-case string identifiers** and get **77k exactly matched** pairs. For all other models (Top1Sim, AvgSim, FeatureSim, FedSim), we generate Bloom filters from strings and compare the Hamming similarity between Bloom filters. The generating of Bloom filters follows FEDERAL [28] (see Appendix H in the revision).\n\n### Results\nThe RMSE scores of each baseline and FedSim are presented in the table below. We seek the reviewer's understanding that we are unable to present the variance due to the time constraint of the author-reviewer discussion. \n\n| Models | RMSE |\n|------------|-------|\n| Top1Sim | 42210 |\n| Exact | 41875 |\n| AvgSim | 37598 |\n| FeatureSim | 37618 |\n| **FedSim** | **35737** |\n\nWe observe from the table that **FedSim improves on all the baselines by at least 5%**, which demonstrates the efficacy of FedSim on datasets linked by 'names'. Notably, these large RMSE scores are reasonable because of the large range of labels (500 to 3,675,000). We validate this fact by observing that the **R2 scores of all the models are above 0.9**, which indicates the prediction is **highly related** to real labels.\n\nAnother observation is that **similarity-based models** (FedSim, FeatureSim, AvgSim) **outperforms Exact despite the noise introduced by generating Bloom filters**. This result further implies that exact linkage is not suitable for many real-world applications. Moreover, in the applications that require Bloom filters to preserve privacy, Exact is also ineligible to compare these Bloom filters.\n\nUnfortunately, we do not have enough time to update another version of the revision or conduct comprehensive experiments on this dataset before the due of the author-reviewer discussion. These contents will be added in future revisions. Nonetheless, **we believe that these preliminary results have already demonstrated the effectiveness of FedSim on datasets linked by \"names\"**. We sincerely hope to have the opportunity to update these experimental results in the final revision.", " Although I still have doubts on the general effectiveness of the proposed methods (especially when the identifiers are names), I am still grateful that the authors justify part of their assumptions (general availability of common attributes, and common lack of unique keys). I am willing to raise from 3 to 4.", " Dear reviewers,\n\nThank you for your efforts in reviewing our paper. We specially thank Reviewer W2LK and 8KCf for their prompt response and meaningful discussion. We will appreciate it if we can receive more feedback from you before the Author-Reviewer discussion due. Any comments will be welcomed. We also hope you could reconsider your ratings if appropriate.\n\nBest Wishes,\n\nAuthors of Submission 685", " We thank the feedback from the reviewer.\n\n1. We appreciate the reviewer's advice. We had mentioned the training time in lines 206-207 in our draft. We have added the dimension in line 285 in our revision.\n\n3. We apologize for the mistake of using the traditional Gaussian mechanism that requires $\\varepsilon\\in (0,1)$. This result can be extended to $\\varepsilon >0$ in [1] by adding more noise (larger $\\sigma$). **We have revised the theorem, proof, and figure in the updated revision**. This mistake does not affect our previous conclusion because the larger $\\sigma$ makes differential privacy **even more impractical**. In summary, differential privacy that protects against all possible attacks is impractical in this scenario; as an alternative, our analysis suggests that the privacy risk against certain attacks can be significantly reduced by adding Gaussian noise.\n\n[1] Balle, Borja, and Yu-Xiang Wang. \"Improving the gaussian mechanism for differential privacy: Analytical calibration and optimal denoising.\" International Conference on Machine Learning. PMLR, 2018.", " I thank the authors for their response.\n\n1. (for Q2, Q3) I appreciate the authors providing experiment details in the Appendix. By only reading the main Sections before seeing the response, I had no idea that this information was provided in the Appendix. I understand that due to the page limitation, it would be difficult to provide all this information in the experiment section. I recommend having a brief introduction in Section 6.1 (for example, see Appendix for training time and dimensions).\n\n2. (for W1, Q1) I appreciate the authors' introducing more backgrounds about PPRL and FEDERAL [19] in the revised version of the paper.\n\n3. (for W2) Similarity-based training paradigm design seems a challenging problem under the federated learning setting. However, in its current form, the solution to this problem seems somewhat straightforward (without concrete privacy analysis). The privacy analysis can also be an important contribution. I read Appendix E.2 and find it hard to follow. For example, Theorem 2 shows that Procedure G is differential privacy when ε, δ ∈ (0,1), while line 782 of page 22 shows that the value of ε is very large and not in range (0,1), thus does not follow Theorem 2. I think a more concrete discussion on privacy risks related to differential privacy would be necessary.", " We thank the reviewer's prompt clarification and respond as below.\n\nThe assumption \"similar shared attributes leading to similar records\" is **generally true** according to our application study in GRLC. We demonstrate this point as follows. First, this assumption holds if the identifier **contains only \"address\"** as shown in our experiments, leading to a clear improvement. Therefore, this assumption also holds if the identifier **contains \"address\"** because the similarity of one attribute affects the similarity of the quasi-identifier containing this attribute. Second, this assumption potentially holds if the identifier **contains other attributes excluding \"name\" and \"address\"** because our experiments indicate that FedSim has improvement (though maybe marginal) when identifiers are \"game title\" or \"time\". Third, FedSim has no improvement only when the assumption does not hold on **all the shared attributes**. We summarize the eight applications with shared attributes in the table below. Please refer to Table 11 in Appendix I of the revision for the references.\n\n| Identifier category | #projects in the category | References | Percentage | Improvement of FedSim |\n|------------------------------------------------------------------|---------------------------|------------------|------------|-----------------------|\n| Identifier contains \"address\" | 5 | [15,29,39,44,45] | 62.5% | Clear Improvement |\n| Identifier contains \"name\" and other attributes except \"address\" | 1 | [19] | 12.5% | Potential Improvement |\n| Identifier contains neither \"name\" nor \"address\" | 1 | [29] | 12.5% | Potential Improvement |\n| Identifier contains \"name\" only | 1 | [3] | 12.5% | No Improvement |\n\nFrom the table, it can be observed that **FedSim can have a clear improvement on the majority (62.5%) of applications with shared features**. On the contrary, the applications whose identifiers contain only \"name\" are relatively rare (12.5%).\n\nWe also highlight that FedSim produces close performance to baselines even when the identifier is \"name\" or unique ID, i.e., **FedSim $\\ge$ baselines under all the identifiers** with a modest $K$. This is demonstrated by an experiment in Appendix D.6. This lack of improvement is because of the nature of the identifier instead of the technical design of FedSim. We present these marginal-improvement cases to demonstrate the limitation of FedSim, which is also requested by _Reviewer ddh8_.\n\nAlthough our experiments have covered geolocations, time, and titles, we appreciate the reviewer's advice to conduct experiments on more real-world applications. Since the data of most linkage applications in GRLC are not publically available, we are trying to find real-world data linked on quasi-identifiers. If we can complete experiments before the revision due, we will add them to the revision.\n\n### Comment on the example of dblp\nThe example of dblp is not wholely against our assumption. Considering a linkage between dblp and other websites on the \"name\" attribute only, although there are indeed numerous \"Wei Wang\" in different fields, \"Wei Wang\" and \"Wei Wang\" are **possibly** to be in the same field, whereas \"Wei Wang\" and \"Chermaine Deepa Antony\" are **unlikely** to be in the same field because no \"Wei Wang\" works in skeletal age assessment (the field of Chermaine). In addition, we may also need to consider similar names in the linkage since \"Wei Wang\" can be referred to as \"Wang Wei\" on other websites. In summary, this example implies that **the similarity of names indicates the possibility of being the same user**, thus indicating the similarity of data records. Nonetheless, this indication can be weak (i.e., $\\Delta$ is small in our metric), thus the improvement of FedSim could be small in this case. The improvement on \"game\" and \"song\" also illustrate this weak indication. The indication is more evident when considering not only \"name\" but a quasi-identifier with other attributes, especially the fuzzy ones like \"address\".\n\n", " I would like to clarify my exact meaning regarding the \"lack of general effectiveness\". \n\nFrom my perspective, the intuition or the foundation of your work is that, \"samples with similar shared attributes are similar in general and may help VFL modeling\". To show the validity of your foundation, you have to demonstrate two facts. \n\n1. Shared attributes widely exist for non-exact record matching. The authors have made a good job in demonstrating this point using examples of German Record Linkage Center. \n2. The shared attributes are generally helpful for better VFL modeling, or similarly, similar shared attributes lead to similar records in general. My doubt primarily lies in this point. In the experiments, the authors use two types of shared attributes, the first being geospatial information (house, bike, hdb), and the second being names (song, game). It is intuitive that geospatial information will be helpful. However, I find it hard to believe that similar names (song and game titles) may be helpful. In fact, the experiments also show this point, as the improvements on song and game are very marginal. In practice, when we talk about users, it is also not true that people with similar names have similar properties (e.g. there are numerous 'Wei Wang' on dblp (https://dblp.org/pid/35/7092.html), many of whom have wildly different research topics.) \n3. Finally, I would like to make it clear that, what I am doubtful is the general effectiveness of similar 'names' rather than similar 'strings'. Strings may be helpful, but names may not. Sorry for the confusion.\n\nTo summarize, it seems that, as far as the experiments show, the effectiveness of FedSim is prominent only when the shared attributes are geospatial locations. More justification is needed to verify its general effectiveness. ", " \nIn the beginning, we would like to correct that we **did not** claim that \"_in most cases, quasi-identifiers of users (address, name, birth date, postal code) are strings_\". Instead, we claimed that \"_the similarity of some fields can reflect the similarity of the property, such as **address** (**5/11** projects) in **GPS or string** format_\". This implies that **the address existing in almost half of projects is a common identifier in practice**. Our experiments show **significant improvement** of FedSim on 'house' and 'hdb' dataset with **geo-encoded address** as identifiers.\n\n**Using geo-encoded address is a common practice in record linkage**. Among the five applications using addresses, one explicitly claims that they use geocoded addresses instead of strings.\n\n> \"_Second, individual addresses were geocoded and geographically clustered ..._\" - [4]\n\nTwo have geolocations in the dataset but do not claim the usage in the linkage.\n\n> \"_It may be possible to assign establishments to these companies, in principle, by including geo-information on companies’ and establishments’ addresses._\" - [2]\n> \"_Microm provides geomarketing data at the street level and was added to the PIAAC data based on respondents’ addresses._\" - [5]\n\n**The geolocation and string can be transferred to each other given a map.** Even if the original addresses are strings, we can easily transfer these strings to the geolocations if it brings better accuracy. Intuitively, geolocation contains more spatial information than strings. Thus, geolocation is more suitable for the VFL applications that consider spatial information.\n\nIn addition, **the data type is not a limitation by design in FedSim**. FedSim focuses on _learning useful information from similarities_, while _designing linkage functions to calculate similarities_ is an orthogonal topic studied in PPRL. No matter what data type the identifier is, given a linkage function that can obtain useful similarities, FedSim can improve based on the similarities. We highlight that the reason why \"game\" and \"song\" has smaller improvement is **their similarity distribution benefiting Top1Sim** (i.e., $\\Delta(Top1Sim)$ is small) instead of their identifiers being strings.\n\n", " I acknowledge the author response. \n\n1. I appreciate the authors' case study on real world record linkage. The results provide justification on real-world data linkage processes and offer insights about when FedSim can be applied. This partially addresses my concerns. \n\n2. Given the results, I still consider the assumption \"shared features are useful\" strong. As you have made clear in the German Record Linkage Center case, in most cases, quasi-identifiers of users (address, name, birth date, postal code) are strings. However, in your evaluation, on 'game' and 'song' data whose shared attributes are strings, the improvements are quite marginal (0.17% on game, 0.01 on song). Therefore, in the existing form, FedSim does not seem to be widely effective. \n\n3. I appreciate the authors clarifying the inference process and removing the overclaiming. \n\nHowever, in its current form, the paper still suffers from problems such as limited insights and lack of general effectiveness. I thus cannot recommend this paper or change my rating to a more positive side. ", " ## Response to Weakness\n\n3. ___\"Biased evaluation\"___\n\n \n\nAs we have explained in \"the response to Weakness 2\", our experiments are based on two assumptions that **commonly exist in real-world applications**. For example, address (in house and hdb dataset) is used for linkage in five out of 13 applications.\n\n \n\nBesides those datasets where FedSim outperforms baselines, **we have also conducted a study on when FedSim fails in Appendix D.6**. We generate a synthetic dataset \"sklean-random\" with unique pure random identifiers. Our results in Table 9 show that FedSim has a close performance to Exact/Top1Sim only when $K=30$. If we increase $K$ to 50, the accuracy of FedSim significantly drops below Exact/Top1Sim due to overfitting. In addition, song dataset linked with song titles is another good example. FedSim has little improvement on song because the similarity of titles is little related to the similarity of content.\n\n \n\nIn summary, FedSim has a close performance to Exact on meaningless shared features, which has already been shown in our experiments.\n\n \n\n \n\n4. ___\"Inference procedure not discussed\"___\n\n \n\nDuring the inference, for each data record in the primary party, $K$ most similar data records in secondary parties are linked. These linked data records are fed into the FedSim model to derive the final prediction. We have clarified this point in paragraph 5 of Section 4.2.\n\n \n\n5. ___\"Minor issues: coloring of figures\"___\n\n \n\nWe appreciate the reviewer's advice and have set a different marker for each line in our figures.\n\n \n\n## Response to Questions\n\n \n\n1. Please refer to our response to \"Weakness 4\" for details.\n\n \n\n2. We will add experiments on both datasets once completed. As we have elaborated in \"Response to Weakness 3\", **we would expect FedSim to have a similar performance to Exact on the datasets with meaningless shared features**.\n\n \n\n3. We appreciate the reviewer's advice and have removed the initial claim in our revision.", " ## Response to Weakness\n\n1. ___\"The insight seems to be overclaiming.\"___\n\nWe appreciate the reviewer's advice and have removed this claim in our revision.\n\n2. ___\"Strong and not realistic assumptions on the 'common features'.\"___\n\nSince VFL is a rather recent paradigm with fewer real applications, we investigate the applications of a traditional area \"record linkage\" which has many existing applications. The application scope of record linkage reflects the application scope of VFL, because all the VFL algorithms require the data to be linked (either on ID or other features) before training.\n\nGerman Record Linkage Center (GRLC) published an article [1] to summarize its completed linkage projects since 2011. We list the information of identifiers in these eight applications as follows.\n\n- \"_Since there was no common identifier available to make such an assignment, the record linkage had to be conducted using alternative identifiers, such as establishment names and addresses._\" - [2]\n\n- \"_We use the Merge ToolBox (MTB) software (Schnell et al., 2004) to perform distancebased record linkage of the two address data files. The fields street and city name were compared with N-grams throughout._\" - [3]\n\n- \"_Data is stored in spells that are linked to persons. The spells come along with a variety of socio-demographic variables such as gender, age, or nationality as well as spatial information such as addresses, municipality, and region type._\" - [4]\n\n- \"_Microm provides geomarketing data at the street level and was added to the PIAAC data based on respondents’ addresses._\" - [5]\n\n- \"_Regarding their partners, given the lack of a unique identifier key, it was necessary to link the individuals by using non-unique and error-prone identifiers, such as names and addresses._\" - [6]\n\n- \"_In the first exact linkage step, the complete agreement in all other linkage-relevant fields was decisive, i.e. first and last name, date of birth, gender, street, house number, postal code and city._\" (Translated from German) - [7]\n\n- \"_to link the data rows in which there is exact match of characteristics (e.g. spins in the name initials or in the date of birth, deviations by one or a few days in different dates)_\" (Translated from German) - [8]\n\n- \"_We link establishments to transactions based on company names, because there are no common company identifiers that would easily link our PE buyout sample to the Establishment History Panel (BHP)._\" - [9]\n\nTwo observations can be made from these projects. First, among the 11 completed projects, eight projects require linking datasets without user ID. **This implies that, in the majority (around 8/11) of real applications, there does not exist a shared user ID, which supports our first assumption**. Second, the similarity of some fields can reflect the similarity of the property, such as address (5/11 projects) in GPS or string format. Even for the field whose own similarity does not reflect record property, such as name, birth date, and postal code, the similarity of the quasi-identifier containing these fields (2/11 projects) can reflect the property. This is because records with more matched fields are more likely to belong to the same user, especially when considering typos that widely exist in practice [2-9]. Therefore, **the similarity of shared features is related to the property of records in many (around 7/11) real-world cases, which supports our second assumption.** We have included the evidence in the introduction and Appendix I of our revision.\n\n[1] Antoni, Manfred, and Rainer Schnell. \"The past, present and future of the German Record Linkage Center (GRLC).\" Jahrbücher für Nationalökonomie und Statistik (2019)\n\n[2] Schild, Christopher-Johannes. \"Linking'Orbis' Company Data with Establishment Data from the German Federal Employment Agency.\" (2016).\n\n[3] Eberle, Johanna, and Michael Weinhardt. \"Record linkage of the linked employer-employee survey of the socio-economic panel study (SOEP-LEE) and the establishment history panel (BHP).\" (2016).\n\n[4] Kroh, Martin, et al. The 2013 IAB-SOEP Migration Sample (M1): Sampling design and weighting adjustment. No. 271. SOEP Survey Papers, 2015.\n\n[5] Perry, Anja, and Beatrice Rammstedt. \"The research data center PIAAC at GESIS.\" Jahrbücher für Nationalökonomie und Statistik 236.5 (2016).\n\n[6] Schild, Christopher-Johannes, and Manfred Antoni. \"Linking Survey Data with Administrative Social Security Data-the Project'Interactions Between Capabilities in Work and Private Life'.\" German Record Linkage Center, Working Paper Series (2014).\n\n[7] Antoni, Manfred, and Arne Bethmann. \"PASS-Befragungsdaten verknüpft mit administrativen Daten des IAB.\" (2014).\n\n[8] Gramlich, Tobias. \"’STROKES’–Record Linkage der Schlaganfälle in Hessen 2007-2010 (Strokes-Record Linkage of Stroke Cases in Hesse 2007-2010).\" (2014).\n\n[9] Antoni, Manfred, Ernst Maug, and Stefan Obernberger. \"Private equity and human capital risk.\" Journal of Financial Economics 133.3 (2019).", " \n## Response to Weakness\n\n1. We appreciate the reviewer's advice and have removed this claim in the revision.\n\n \n\n2. **Only on the five real-world datasets without privacy protection, does FedSim consistently outperform baselines.** There are some cases in that FedSim has similar or lower accuracy in our experiments. These cases include\n\n \n\n- In Figure 5(a), on boone (synthetic) dataset, **FedSim always has almost the same accuracy as Top1Sim** under different $\\sigma_{cf}$.\n\n- In Figure 5(a), on frog (synthetic) dataset, **FedSim is outperformed by AvgSim under large scale of noise ($\\sigma_{cf}=0.2$)**, because the similarities is no longer meaningful.\n\n- In Figure 6, on house, taxi dataset, **FedSim is outperformed by AvgSim** under small $\\tau$ (large noise on similarities).\n\n- In Figure 6, on game dataset, **FedSim is outperformed by Top1Sim** under large $\\tau$ (small noise on similarities).\n\n- In Figure 8, on song dataset, **FedSim has a close performance to AvgSim and FeatureSim**.\n\n \n\nFurthermore, **we have conducted a study on when FedSim fails in Appendix D.6**. We generate a synthetic dataset \"sklean-random\" with unique pure random identifiers. Our results in Table 9 show that FedSim has **close performance to Exact/Top1Sim** only when $K=30$. If we increase $K$ to 50, **the accuracy of FedSim significantly drops below Exact/Top1Sim** due to overfitting.\n\n \n\nIn summary, **our experimental results have already shown that FedSim fails in certain cases as we elaborate above**. We add more discussions on the assumption and limitations of FedSim in Appendix I of the revision.\n\n \n\n3. The framework of FedSim cannot be directly applied to other VFL algorithms, e.g., logistic regression and tree-based algorithms. This is because FedSim requires the similarity model and merge model to be trained together with the main VFL model, which requires the VFL algorithm to be neural-network-based. To adapt FedSim to other VFL algorithms, a possible direction is to exchange the intermediate information in these algorithms like exchanging gradients in SplitNN. We leave this topic as our future work. We discuss these future directions in Appendix F of the revision.\n\n \n\n## Response to Questions\n\n We add a detailed discussion of the limitation (assumption) and application scope of FedSim in Appendix I of the revision. In brief, we assume that the similarity between identifiers is related to the similarity between data records. We also demonstrate that this assumption commonly holds in practice.\n\nIn addition, in Section 4.3, we have proposed a data-linkage-based metric to estimate the improvement of FedSim over baselines (i.e., AvgSim, Top1Sim, Exact) without training. In brief, we calculate a score $\\Delta$ based on the similarity distribution to estimate the potential improvement of FedSim. This metric has also been validated in our experiments (Figure 5(b)). From the figure, we observe that **$\\Delta(Top1Sim)$ is positively correlated with real improvement on Top1Sim**, indicating that the metric can be effectively used to estimate the improvement of FedSim without training.", " \n## Response to Weakness\n\nW1: We include a brief introduction of FEDERAL [19] in **Appendix H of the revision** due to the page constraint.\n\n \n\nW2: Besides considering PPRL in VFL, the main challenges are similarity-based training paradigm design and privacy risk analysis.\n\n \n\nW3: We formulate the perturbation under differential privacy in **Appendix E.2 of the revision**. Specifically, we demonstrate that __differential privacy that protects against all possible attacks is impractical in this scenario__; as an alternative, our analysis suggests that the privacy risk against certain attacks can be significantly reduced by adding Gaussian noise. Taking house dataset as an example, $\\mu_0=-46237.78, \\sigma_0=21178.86$. Letting $\\delta=10^{-5}$, we can derive the values of $\\tau$ and $\\varepsilon$ under different noise scales $\\sigma$. When setting $\\sigma=1$, the differential privacy parameter $\\varepsilon=1.5\\times 10^6$ implies that there is almost no privacy guarantee at all. Nonetheless, the attacking success rate $\\tau=2.7\\times 10^{-5}$ suggests that the privacy risk from certain attacks can be quite low.\n\n \n\n## Response to Questions\n\nQ1: We follow the reviewer's advice by highlighting our contributions to training paradigm design and privacy analysis in the introduction of our revision. Meanwhile, we **analyze the noise under differential privacy and compare differential privacy with our metric in Appendix E.2 of the revision**. Please refer to the \"Response to W3\" for our main findings.\n\n \n\nQ2: For the training process, **we have compared the training time of FedSim with baselines in Appendix D.4**. The results indicate that FedSim requires **longer but acceptable training time** compared to baselines. In addition, we also present the **number of parameters of each model in Appendix D.4 in the revision**. For the linkage process, the computational complexity has been analyzed in FEDERAL [19]. We also empirically **present the linkage time in Appendix D.4 in the revision**. The results indicate that linking Bloom filters for privacy is more time-consuming than linking raw float/string features. This indicates that a more efficient PPRL approach is desired.\n\n \n\nQ3: The dimension of identifiers in each dataset is presented in Table 3 in Appendix C. **Most datasets contain multi-dimensional identifiers with dimensions ranging from 2 to 30.** For the datasets with multi-dimensional identifiers, we simply **calculate a similarity value between two identifier vectors** to improve efficiency and avoid overfitting. This might cause some information loss, but we find **the accuracy loss is negligible in our experiments**. In addition, we highlight that $\\sigma_{cf}$ is only for generating synthetic datasets. **The noise $\\sigma$ for privacy is added to a similarity value instead of each dimension.**\n\n \n\nQ4: We have introduced more backgrounds of PPRL in Appendix H in the revision. For both numeric and nominal identifiers, we generate a Bloom filter for each identifier by following [19]. The Hamming distances ($\\text{dist}(k^P_i,k^S_j)$) between these Bloom filters are calculated. Then, we perform normalization (Equation 1) and noise addition (Equation 2) to obtain $s_{ij}$.", " \n## Response to Questions\n\nQ1: \"___Can you describe how the presented work can be further improved?___\"\n\n \n\nResponse to Q1: Regarding the performance, the CNN merge gate still introduces many additional parameters. The sort gate and merge gate can be potentially replaced by attention; thus, further performance improvement is possible. Regarding privacy, more advanced attacks and stronger privacy metrics are desired.\n\n \n\nQ2: \"___What are the potential privacy implications when choosing a large K value for the number of soft linkages during training?___\"\n\n \n\nResponse to Q2: Increasing $K$ enlarges the possibility of different $k_i^A$ matching the same $k_j^B$, thus increasing $|Q|$ in Equation 12 in Appendix A. As explained in the last paragraph of Appendix A, increasing |Q| leads to a lower success rate of the intuitive attack due to the noise added to similarities. In summary, **increasing $K$ potentially leads to higher privacy risk, but the success rate of the intuitive attack remains unchanged.**\n\n", " \n## Response to Weakness\n\n1. Our contribution includes two parts: the framework of FedSim and the privacy concerns of FedSim. For the first part, FedSim only modifies the model structure of SplitNN, while following the training process of SplitNN. Therefore, the analysis of convergence in FedSim also follows the analysis on SplitNN, which is orthogonal to this paper. For the second part, we theoretically prove the success rate of our proposed attack, and theoretically demonstrate the impracticability of differential privacy in this scenario.\n\n \n\n2. In **Appendix E.2 of our revision**, we demonstrate that **differential privacy that protects against all possible attacks is impractical in this scenario**; as an alternative, our analysis suggests that the privacy risk against certain attacks can be significantly reduced by adding Gaussian noise. Taking house dataset as an example, $\\mu_0=-46237.78, \\sigma_0=21178.86$. Letting $\\delta=10^{-5}$, we can derive the values of $\\tau$ and $\\varepsilon$ under different noise scales $\\sigma$. When setting $\\sigma=1$, the differential privacy parameter $\\varepsilon=1.5\\times 10^6$ implies that there is almost no privacy guarantee at all. Nonetheless, the attacking success rate $\\tau=2.7\\times 10^{-5}$ suggests that the privacy risk from certain attacks can be quite low.\n\n \n\n3. The main distinction in the soft linkage is the similarity metric. As explained in the second paragraph of Appendix C, our experiments already covered different similarity metrics including Euclidean similarity, edit similarity, and Hamming similarity. We further add **an ablation study of similarity metrics in Appendix D.7 in the revision**. The results indicate that the similarity metric does not significantly affect the performance.\n\n \n\n4. For the training process, **we have compared the training time of FedSim with baselines in Appendix D.4**. The results indicate that FedSim requires **longer but acceptable training time** compared to baselines. In addition, we also present the **number of parameters of each model in Appendix D.4 in the revision**. For the linkage process, the computational complexity has been analyzed in FEDERAL [19]. We also empirically **present the linkage time in Appendix D.4 in the revision**. The results indicate that linking Bloom filters for privacy is more time-consuming than linking raw float/string features. This indicates that a more efficient PPRL approach is desired.\n\n \n\n## Response to Questions\n\nQ1: According to a survey [40], most linkage approaches contain three steps: blocking, comparison, and classification. Our soft linkage approach, following traditional PPRL in \"blocking\" and \"comparison\" steps, **directly outputs the similarities with normalization and noise addition** without performing the \"classification\" step. We have highlighted this point in the first paragraph of Section 4.1 in our revision.\n\n \n\nQ2: The output of sort gate $\\mathbf{o}_i'$, containing $K$ output vectors with $l_m$ dimensions, is regarded as a 2D input of size $K\\times l_m$ for the CNN merge gate. Then, the merge gate effectively merges these output vectors with close similarities and outputs the final prediction. We have clarified this point the the \"merge gate\" paragraph in Section 4.2 in the revision.\n\n \n\nQ3: Please refer to \"Response to Weakness 2\"\n\n \n\nQ4: Yes, FedSim requires **longer but acceptable training time** compared to baselines. Please refer to \"Response to Weakness (4)\" for details.", " This paper introduces a novel FedSim approach which leverages the record similarity for soft linkage on top of the SplitNN. It is an improvement over the existing Vertical Federated Learning, which is mainly based on the Exact and Top1Sim. The paper also consider the privacy risk caused by similarity. The experimental results show the performance improvements of FedSim against some existing benchmarks. Pros: \n1. The problem is interesting and timely\n2. The idea is simple and the results demonstrate its power\n3. The paper is easy to read\n\nCons: \n1. Lack of theoretical analysis of the proposed method\n2. The privacy analysis seems to be weak; can it be linked to differential privacy? \n3. The experimental results are not convincing; lack of detailed ablation study. For instance, it will be interesting to know how different soft linkage approaches can help with the task. \n4. The computational complexity is not discussed (and comparing with other method) Q1: There are many soft linkage research, i.e., matching pairs between different parties. Can you briefly explain what is the significance/novelty/difference between your approach and other approaches on record linkage?\n \nQ2: The merge gate is not clear; can you provide a formal description?\n\nQ3: How the privacy guarantee relates to differential privacy?\n\nQ4: Computationally, will the approach introduce additional cost?\n No ", " This paper describes a framework for enabling VFL while addressing records linkage as a part of the training process. \nThe authors motivated their work by applications where existing VFL record linkage solutions were insufficient. For instance, if the linking data include GPS coordinates or names it would make sense to perform fuzzy matching. Additionally, the authors buckled the trend when instead of dividing record linkage and training into separate phases they combined them into one coupled phase where the weight or top K similarities would also be discovered during training. \nEven through the paper is primary focuses on 2 parties VFL the authors also describe how to extend their framework to multiple parties.\n This paper is well-written and addresses an important issue. It is well motivated and supported by strong results on multiple synthetic and real-world datasets. The authors attached source code and instructions on how to build the framework and how to run tests. So it appears that their work can be replicated.\n Can you describe how the presented work can be further improved? \nWhat are the potential privacy implications when choosing large K value for the number of soft linkages during training? I believe the authors have sufficiently addressed the limitations of their work related to scalability and privacy.", " Federated Learning (FL) is a collaborative learning framework for training a model from datasets owned by different parties. A commonly used paradigm for FL is Vertical Federated Learning (VFL), where parities share different features of the same set of samples. Before actually doing the privacy-preserving training process, parties need to first link features with the same or similar identifiers. Existing VFL solutions focus more on exact identifier linkage (one-to-one linkage) by leveraging hashing methods or cryptographic protocols like Private Set Intersection (PSI). However, in some scenarios, linking identifiers with high (but not top) similarity benefits the training. \n\nThis paper designed a coupled training paradigm, FedSim, that introduced Privacy-Preserving Record Linkage (PPRL) that supports high similarity linkage into VFL. Under the SplitNN framework, this paper introduced a new model structure that can take the advantage of the additional similarity information to train a better SplitNN model. The experiments show that the proposed framework can train a better model in a vertical federated manner with little additional cost. Strengths:\n\nS1: Identify a good topic that needs to be addressed in VFL. \n\nS2: Give a reasonable and lightweight solution for the problem. The solution can provide some privacy guarantees under the weak security model (without formally provable security).\n\nS3: Provide sufficient experiments.\n\nWeaknesses:\n\nW1: Lack of brief introduction for the PPRL method, making the proposal somewhat hard to understand without seeing [19].\n\nW2: Limited contribution to introducing PPRL into VFL. \n\nW3: The privacy guarantees provided by perturbing identifiers using Gaussian noises need to be further discussed. Q1: Introducing PPRL into VFL seems a limited contribution.\nAlthough this paper identified a good topic in VFL (Similarity linkage), directly introducing PPRL into VFL seems a straightforward way of solving the problem. I found the main contribution of the paper is not introducing PPRL into VFL, but a new framework (shown in Section 4.2) that leverages the additional similarity information for benefiting VFL. Also, this paper in fact introduced a new way of securing PPRL, i.e., adding Gaussian noises during the PPRL step. To the best of my knowledge, this method can be formalized using Gaussian Differential Privacy or related techniques. I strongly recommend the authors have further analysis and discussions on these two parts, instead of only highlighting the (somewhat limited) contribution of introducing PPRL into VFL.\n\nQ2: About performance comparisons.\nAlthough there are some methods that support similarity linkage, most of which introduce cryptographic tools (e.g., homomorphic encryption, public-key encryption). Such cryptographic tools would introduce high computation costs, making the VFL inefficient and hard to be deployed in practice. This paper introduced a lightweight solution to this problem, namely, the Bloom Filter method proposed in [19]. Even though the Bloom Filter method is lightweight compared with heavy cryptographic operations, it would still introduce some additional symmetric cryptographic operations (like hashes) and some additional communications (like sending Bloom Filters to the server and sharing the similarities). I am wondering if the authors can provide time consumption and communication costs for each phase of FedSim. I personally think these experimental results would further show the efficiency of FedSim.\n\nQ3: About the high-dimensional identifier case\nIn Section 6.1, the authors stated that the experiments used a perturbed identifier for linkage, which is generated by adding Gaussian noises with the same variance (\\sigma_{cf}) to each dimension (See P7, line 288). However, it seems that all experiments use only one dimension as the identifier. It would be better if the authors provide additional discussion on the high-dimensional identifier case.\n\nQ4: About the background of the Bloom Filter PPRL method\nBloom Filter is a well-known technique that has been used in many situations. The Bloom Filter PPRL method used in this paper is a modified one introduced in [19], which does not only support similarity computation between nominal inputs but also numeric inputs. Without the necessary background introduction about the Bloom Filter method proposed in [19], it seems hard for the reader to understand how to calculate the similarity for numeric identifier in FedSim. The authors provided limitations adequately in the Appendix. ", " The paper proposes FedSim, a new VFL training paradigm. FedSim explicitly explores the similarity information between the non-matched pairs and couples the correspond module into SplitNN (an existing VFL training model). The authors also provide privacy guarantee to a greedy attack algorithm. Finally, they verify the effectiveness of their algorithm on synthetic and real datasets. Strengths: \n1. The paper is easy to follow: the motivation is sound, the flow is smooth and the presentation is clear.\n2. The paper makes solid contribution by witnessing the potential information loss in the process of exact-match record linkage, and coupling the similarity information with the existing SplitNN model to improve the performance of VFL. Overall this feels like a simple-but-effective idea to me and is the major factor that reflects my rating.\n\nWeaknesses:\n1. The author emphasize that 'non-matched pairs can also benefit VFL with a properly designed training method', and they see it as a 'counterintuitive' conclusion. While I agree that this is indeed a nice and novel observation, I would like to point out that in contrast to being 'counterintuitive', this feels most natural to me. Placing it in a broader context of machine learning, an analogy would be 'data-augmentation will benefit supervised learning'. I think the tone needs to be revised here --- it is ok to acknowledge that your approach is 'simple' --- this will actually serve as a plus if it is also 'effective'. \n2. Following the point above, while I believe that a specific type of data augmentation will be effective in **some** learning tasks, there **must** exist other scenarios where it won't work. Similarly, I don't think it is the case that FedSim **always** outperforms its counterparts. Sometimes exact-match is more favorable, for example, top-K record linkage based on the similarity of phone numbers does not make too much sense to me. The authors do **not** discuss the limitations of their approach at all, and specifically, the experiment results demonstrate that FedSim consistently beats other baselines in all **selected** tasks, which actually downgrades my overall rating of this paper --- I tend to believe that the experimental evaluations are 'crafted'.\n3. I also do not see enough discussions on the reliance of the training framework. Can the similarity-based module be easily incorporated into other VFL protocols (e.g., logistic regression based on homomorphic encryption)? I would like to see a **detailed** discussion of the limitations, application scope (beyond listing two positive examples) and comparison to existing approaches of FedSim. This will greatly benefit the practitioners. Say if two financial institutions want to vertically train a machine learning model, should they consider your algorithm or not and why? The authors only point out a few extensions (e.g., generalization to multiple parties, other attack methods). ", " This paper proposes a framework for vertical federated learning (VFL), called FedSim. \n\nIn general, VFL contains two steps, the first being the record linkage, the second being the model learning. FedSim is based on the observation that existing methods separate these two steps and focus solely on the model learning step. For the record linkage step, existing works use simple exact/one-to-one matching, and thus fail to exploit information from non-matched entities. \n\nFedSim proposes a method to exploit similar records in VFL. It matches samples across parties according to similarity, and further uses the similarity information to adaptively fuse features from the other party. Further, a simple way to estimate the performance improvement is proposed, and a theoretically grounded method to ensure privacy is proposed. Experiments on several datasets show the effectiveness of FedSim. ## Originality\nThe main idea of the paper is to use similar but not exactly matched samples to assist vertical federated learning. \n\n+ **Pros** The idea is somewhat new in VFL. The common practice of VFL is that training is only performed on exactly matched samples. \n\n- **Cons** The authors seem to be overclaiming on the originality and insights of the idea. The authors highlight the insight that \"non-matched pairs can also benefit VFL\" in line 68, Introduction, and regard it as 'counter-intuitive'. However, although the insight is indeed not explored in VFL, I would not consider the insight highly novel or counter-intuitive. Specifically, in the sense of general machine learning, the insight that \"similar but not the same samples can boost machine learning performance\" has been well recognized and exploited. For example, Graph Neural Networks (GNN) [1, 2] are perfect illustrations of this insight. The primary idea of graph neural networks is to aggregate features from neighboring nodes of the central node, which is basically using similar samples to improve feature learning for the central node. Furthermore, even though there may not be explicit links (e.g. friends in social networks, citations in academic networks), using general feature similarity to build implicit graphs is also a common idea. For example, [3] builds a nearest neighbor graph on latent features to facilitate deep semi-supervised learning. Therefore, the insight the authors claim has been known and used in a larger area and may not be \"counter-intuitive\" or \"new\". The authors indeed made a valid observation, but they should not over-claim. \n\n## Quality\nThe designed method to exploit record similarity contains a merge gate, a weight gate, and a sort gate. Similar but non-exactly matched samples are weighted by the sort gate and the weight gate to assist VFL. The authors also propose a method based on histogram to estimate performance gains. Further, the authors discuss the potential privacy leakage caused by the record similarity, and propose a method to protect data privacy with theoretical analysis. Experimental results show that FedSim outperforms simple baselines that utilize record similarity (Top1Sim, AvgSim). Also, the impact of privacy protection on accuracy is studied, and the improvement estimation method is shown to have positive correlation with the actual performance improvement. \n \n- **Pro**. I appreciate the authors' discussion and method about privacy leakage caused by the record similarity. As FL puts emphasis on data privacy, such discussion is necessary. Also, it is good to see the experiments on the tradeoff between privacy and accuracy. I also consider the improvement estimation method interesting. Experiments also validate the effectiveness of the estimation. \n\n- **Con**. The authors made two important assumptions in this paper, that some features are shared between the primary and the secondary parties, and that similarity of the shared features are indicative of the common information (Section 4.3). However, in practice, I would like to raise my doubts on both assumptions. \n 1. **Shared features**. In practical VFL applications where each sample corresponds to a user, the common features held by different parties are often limited [4]. Specifically, in most cases, the only shared feature may be the user ID, and practitioners apply private set intersection (PSI). In this case, FedSim cannot apply. \n 2. **Usefulness of shared features**. Even if such features do exist, it is non-trivial to determine whether the similarities between them are useful. For example, suppose there exist several quasi-identifiers regarding a user, e.g. name, phone number, email, and so on. It is generally hard to say that people with similar names/phone numbers/email service providers have similar properties. \n 3. **Experiments are biased towards the two assumptions**. Continuing from the unrealistic assumptions, I would like to point out that the authors have manually chosen datasets with indicative common features. For example, in the bike dataset, the shared features are longitudes and latitudes of start/end points, and the task is to predict the travel time. It is clear that routes with similar start/end points will have similar travel time, which leads to a bias that favors similarity-based methods against exact-matching-based ones. It is not clear how FedSim compares against exact-matching-based methods when no such indicative common features are present, e.g. the only common features are quasi-identifiers such as names. \n\n## Clarity\nThe presentation of this paper is well-organized. I find it easy to follow the paper. \n\n## Significance. \nI find the paper to be marginally significant. As said in the \"originality\" part, the paper builds on a known idea to improve the performance of VFL. Thus, while the idea and the techniques are sound, it may not bring much insight to the community. \n\n## Overall Strengths: \n- **Good Presentation**. The paper is well-presented and generally easy to follow. \n- **Discussion on privacy**. See 'quality'. \n- **Improvement estimation method is interesting**. See 'quality'. \n\n## Overall Weaknesses:\n- **The insight seems to be overclaiming.**. See \"originality\". \n- **Strong and not realistic assumptions on the \"common features\"**. See 'quality'. \n- **Biased evaluation**. See \"quality\"\n- **Inference procedure not discussed** The authors fail to discuss how the primary party does inference for new samples. Does it need to query similar samples from the secondary party? I would like to see a discussion on the extra procedures and extra costs of the inference phase. \n- **Minor issues**: Please use a better coloring to plot the figures. The current coloring is not friendly to black-and-white printers and color-blind readers. \n\n[1] Hamilton et al. Inductive Representation Learning in Large Graphs. NIPS 2017\n\n[2] Kipf et al. Semi-supervised Classification using Graph Convolutional Networks. ICLR 2017\n\n[3] Iscen et al. Label Propagation for Deep Semi-supervised Learning. CVPR 2019\n\n[4] Sun et al. Vertical Federated Learning without Revealing Intersection Membership. Arxiv 2021.\n 1. How does a model learned by FedSim perform inference? Any additional procedures/overhead?\n\n2. I would like to see how FedSim performs on other datasets commonly used in VFL, e.g. Criteo and Avazu [4]. In these cases, no strong priors about indicative common features (e.g. longitude/latitude) exist. \n\n3. Please justify how the insights learned from FedSim differs from the insights learned from existing works on GNN and graph-based semi-supervised learning ([1-3]). Otherwise, you should tone down the claims in the Introduction. I don't see anything that raises ethical concerns. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 5, 6, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 2, 3, 3, 4 ]

[ "HTqs_LbvBQl", "TemxPtrwDWP", "nips_2022_fiBnhdazkyx", "RiKd1VhyYBj", "QktqnbbVZke", "ur9CcokaJ_W", "nvCNi8OTHKh", "k7JsXSVSNJy", "6ZzXvXflBt", "Og0Hc7y55hl", "Og0Hc7y55hl", "clAaUW6Aup4", "ElKklpTWxVs", "qZkpfsJO1vW", "_NSBEaUxNWI", "nips_2022_fiBnhdazkyx", "nips_2022_fiBnhdazkyx", "nips_2022_fiBnhdazkyx", "nips_2022_fiBnhdazkyx", "nips_2022_fiBnhdazkyx" ]

[ "klfd30Ta0X1", "OA0FbNEl-I1", "nLOPqHm_Gd5", "hJunvw7KtVN", "njEsyOZMxCh", "MhSPWfvg_Dr", "YUJw4qR7uch", "WKUsCo819J4", "rsjnTR1m-px", "PRS1t0Gr8t", "nGiVEgz1q_E" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank reviewer *mvcT* for the constructive comments and for raising the score. We have uploaded a slightly edited revision which incorporates the follow-up comment.\n\nThe main change is to replace the requirement (4) in Assumption 2.5 by $N\\log^{8} N=o(n_{L-2}n_{L-1})$. This last expression does not contain the parameter $\\alpha$ anymore and, after carefully tracking the logarithms, we have also been able to improve upon the requirement mentioned in our previous response ($N\\log^{12} N=o(n_{L-2}n_{L-1})$). \n\nThe changes to the arguments are minor and we summarize them below:\n\n* We have changed (22) and (25) in Lemma B.1, and updated the proof of this lemma since it uses the new over-parameterization requirement $N\\log^{8} N=o(n_{L-2}n_{L-1})$.\n\n* Lemma B.1 is used twice in the proof of Lemma D.1 (l. 1066 and l. 1075) and once in the proof of Lemma D.2 (l. 1107). These parts do not require any change since we can simply apply the new version of Lemma B.1.\n\n* Lemma B.1 is used in the proof of Theorem 3.4 contained in Appendix E.3, and the lines 1173-1175 have been slightly edited to reflect the change in Lemma B.1. \n\nThe rest of the argument is not affected by our change in the requirement (4).\n\nAs regards the body of the paper, we have followed the reviewer’s suggestion and we have substituted the vague statements (containing “roughly”) with rigorous ones. In particular, we have edited l. 11-12 of the abstract, l. 52-54 in the introduction, l. 165-166 in the notation, and l. 179-180 after Theorem 3.1. Following the reviewer’s suggestion, we have also moved the discussion on the assumption $N=\\tilde o(d^2)$ directly after Assumption 2.5, see l. 149-154, instead of having it after the statement of Theorem 3.1. \n\nWe hope that the reviewer is fully satisfied with this revision, and that all concerns have been resolved. If this is not the case, we are happy to answer follow-up questions. \n", " Thanks to the reviewers for the detailed response. I am satisfied with the author's comments on the classification problem and agree with the reviewer that achieving memorization (and, similarly, performing optimization) for regression is harder than for classification. Therefore, I will increase my score from 4 to 5. \n\n1. I am convinced that most of the standard datasets satisfy the condition $n < d^{2/(1+\\alpha)}$. However, since the $n > d^{2}$ case is a more challenging problem for memorization, I would like to suggest the author make it clear in the assumption section rather than after the theorem. \n\n2. \"Roughly\" make the statements in the paper vague and hard to follow. I think the authors should replace them with rigorous conditions. It would be great if the authors could avoid introducing the term $\\alpha$. In that case, the authors can claim that the total number of neurons in the network can be as little as $\\tilde{\\Omega}(\\sqrt{N})$.\n \n\n", " We would like to thank the reviewers for their numerous valuable comments. We are glad that the reviewers recognize that our “proofs are solid” (*Rev. 5UpM*) and “the theoretical contributions are clear” (*Rev. mnfH*). We are also thankful to *Rev. mnfH* for acknowledging the technical innovations of our argument. \n\nNext, we provide separate replies to the four reviewers, in which we address all their points. We have uploaded a revision of the body of the paper and of the supplementary material as well. In our responses, we point to the parts of the paper that have been modified. The numbering of lines, equations and references refers to the revised version, and the main changes are highlighted in blue color. We have tried to keep such changes to a minimum in the body, in consideration of the strict 9-page limit holding also for the revision.\n\nFinally, we remark that we have been able to remove the following assumption on the activation function: $\\mathbb E_{\\rho} [ \\phi(\\gamma \\rho) ] \\neq 0$ for all $\\gamma \\neq 0$, where $\\rho$ is a standard Gaussian random variable. This was the third part of Assumption 2.3 in the submitted version and we had already pointed out that this “last condition is purely technical and simplifies the part of the argument concerning the centering of the feature maps”. In fact, after the submission deadline, we have found a bug in the proofs of Appendix D and, after writing down a simple way to fix the bug, it became apparent to us that the assumption above was unnecessary. As a result, we have removed the extra assumption, updated the discussion on the centering part (see l. 223 and l. 233 of the revision) and also the proofs in Appendix D.\n", " We thank the reviewer for the detailed comments. We reply below to the three questions posed by the reviewer, and we are happy to answer additional follow-up questions. We hope that our response solves the concerns about the significance of our work. If this is the case, we also hope that the reviewer will consider raising the rating.\n\n----\n\n**Question 1.** \n\nWe believe there is a misunderstanding here, and we would like to clarify this point. The first requirement of Assumption 2.5 is that there exists $\\alpha>0$ such that (4) holds. First, notice that choosing a *larger* $\\alpha$ leads to a *more restrictive* condition (4). As (4) is required to hold only *for some* $\\alpha>0$, we are allowed to pick this $\\alpha$ to be very small, e.g. $\\alpha=0.001$. \n\nIn fact, the *tight* over-parameterization condition would be $N=o(n_{L-2}n_{L-1})$. The point of (4) is to allow a small slack in the exponent via the additional parameter $\\alpha$, in order to take care of extra logarithmic factors appearing in the argument. More specifically, by tracking such logarithmic factors, the requirement (4) in Assumption 2.5 can be replaced by $N\\log^{12} N=o(n_{L-2}n_{L-1})$ (which now does not contain $\\alpha$ anymore). We have refrained from doing that in the submitted version, since we deemed (4) as written more clean and clear. However, we acknowledge that the current writing has led to a question by both this reviewer and reviewer *UvzJ* (see also the first point in the corresponding response). Hence, if the reviewers find it useful, we are happy to replace the requirement $N^{1+\\alpha}=o(n_{L-2}n_{L-1})$ with the slightly less restrictive requirement $N\\log^{12} N=o(n_{L-2}n_{L-1})$ and perform the necessary (very minor) edits to the proofs in the appendix.\n\nAs a final note, in the revision, we have changed the statement\n\n“This means that the total number of neurons of the network can be as little as $\\Omega(\\sqrt{N})$\"\n\ninto\n\n“This means that the total number of neurons of the network can be *roughly* as little as $\\Omega(\\sqrt{N})$”,\n\nwhere the *roughly* captures the extra logarithmic factors (or small slack in the exponent), see l. 176 of the revision. \n\n----\n\n**Question 2.**\n\nFollowing our response to the previous point, we can take $\\alpha$ to be arbitrarily small and, hence, the condition mentioned by the reviewer is that $N=o(d^2)$ (up to extra logarithmic factors). We would like to make two comments about this condition. \n\nThe first comment is theoretical in nature. When all the widths have the same scaling, then having that $N$ scales at most as $d^2$ is **necessary** for the results of our paper to hold. In fact, if $N$ scales faster than $d^2$, the NTK is a low-rank matrix and, therefore, its smallest eigenvalue is $0$. The two consequences of our main result (Corollary 4.1 about memorization and Theorem 4.2 about optimization) are also not true in general when $N$ scales faster than $d^2$. In fact, in this setting, there are more data points to fit than parameters to help with the fitting. This argument can be made formal by bounding the VC dimension, see e.g. [10].\n\nThe second comment is more linked to the practice of neural networks trained on standard datasets. Most practical datasets are high-dimensional and this is also true for some of the most ‘standard’ ones: for MNIST, $N=60000$ and $d=784$, hence $N\\ll d^2 \\approx 6\\cdot 10^5$; for CIFAR-10, $N=5\\cdot 10^4$ and $d=3\\cdot 32^2$, hence $N\\ll d^2 \\approx 10^7$; for ImageNet, $N=1.4\\cdot 10^7$ and $d=2\\cdot 10^5$, hence $N\\ll d^2 \\approx 4\\cdot 10^{10}$. Thus, it is reasonable to say that the condition $N=o(d^2)$ is satisfied in (some) realistic settings. We have added this observation in l. 180-185 of the revision.\n \nFor another discussion about the significance of our work, we refer the reviewer to our answer to the first question of reviewer *5UpM*.\n\n----\n \n**Question 3.** \n\nThis is an excellent suggestion. Let us point out that achieving memorization (and, similarly, performing optimization) for regression is harder than for classification. In fact, achieving memorization for regression means to satisfy *exact equalities*, while for classification it suffices to satisfy *inequality constraints*. This is the fundamental reason why the number of parameters has to be at least linear in the number of data points for regression, while polylogarithmic widths are sufficient for classification. We have clarified this point and we have added the two references suggested by the reviewer at the end of Section 5 of the revision. ", " We would like to thank the reviewer for the comments and for acknowledging the technical innovations introduced by our contribution. We reply below to the three (minor) concerns raised in the review, and we are happy to answer additional follow-up questions. In case the reviewer is satisfied with our response, we hope that raising the rating will be considered.\n\n----\n\n**Concern 1**\n\nThis is an excellent question. Let us discuss how the “hidden constants” affect the lower bound (6), which constitutes the key result of this paper, and the crucial over-parameterization requirement (4) needed for such a result to hold.\n\nAs for the lower bound in (6), the $\\Omega$ in the LHS does not hide any terms depending on the network topology. To see this, note that the smallest eigenvalue of the NTK is lower bounded by the smallest eigenvalue of the centered NTK via Theorem 3.2, and the difference between these two quantities is $o(n_{L-2}n_{L-1})$. Furthermore, by examining (213) in Appendix E.3, we have that the lower bound on the smallest eigenvalue of the centered NTK comes from the $\\ell_2$ norm of the rows of the centered Jacobian minus some terms which are again $o(n_{L-2}n_{L-1})$ (the quantity $\\Delta$ is bounded in Eq. (212)). As the $\\ell_2$ norm of the rows of the centered Jacobian does not depend on the network topology with the practical initialization considered in Theorem 3.1, also the lower bound (6) is not affected by the topology. We remark that this $\\ell_2$ norm and, therefore, the lower bound (6) both depend on the Lipschitz constant of the activation function. \n\nAs for the over-parameterization requirement (Eq. (4) in Assumption 2.5), we note that this would include a term of the form $(\\prod_l \\max(1, n_l/n_{l-1}))^{16}$. This can be noticed by examining Eq. (212) in Appendix E.3. In fact, in order to ensure that $\\Delta$ is $o(n_{L-2}n_{L-1})$, it suffices that $N$ scales with the sub-exponential norm of the rows of the centered Jacobian raised to the 8-th power. The sub-exponential norm of the rows of the centered Jacobian scales as the square of the Lipschitz constant of the feature map, and this Lipschitz constant scales as $\\prod_l \\max(1, n_l/n_{l-1})$. We remark that this dependence on the network topology is not tight, and we believe it could be improved. We have not pursued this direction so far, in order to make our assumptions easier to grasp and the proofs easier to follow. \n\n----\n\n**Concern 2**\n\nAfter the edits in the argument in Appendix D, the probability appearing in Theorem 3.1 has been changed to $1 - C N e^{-c \\log^2 n_{L-1}} - C e^{-c \\log^2 N}$. However, this change should not impact the concern of the reviewer, which is about the term $C N e^{-c \\log^2 n_{L-1}}$. In fact, it is clear that the term $C e^{-c \\log^2 N}$ vanishes for large $N$.\n\nLet us recall that, by Eq. (5) in Assumption 2.5, $n_{L-1}$ cannot be exponentially smaller than $N$. In particular, we require the existence of $\\gamma>0$ such that $N^\\gamma = \\mathcal O(n_{L-1})$. This assumption avoids exponential bottlenecks in the neural network and, as a consequence, it also ensures that the term considered by the reviewer vanishes. In fact, this term can be bounded as follows:\n\n$CN e^{-c \\log^2 n_{L-1}} \\leq CN e^{−\\gamma^2 c \\log^2 ⁡N} = C e^{\\log N − \\gamma^2 c \\log^2 ⁡N},$\nwhich goes to $0$ as $N$ grows.\n\nIn general, the term $CN e^{-c \\log^2 n_{L-1}}$ vanishes as long as the width $n_{L-1}$ is not exponentially small when compared to the dataset size $N$. This last assumption is mild and, for concreteness, we also consider a simple numerical example. Consider the ImageNet dataset ($N=1.4\\cdot 10^7$), assume all layer widths to be equal to the input dimension ($n_{L-1} = d = 2\\cdot 10^5$), and set all constants to 1. Then, we obtain $N e^{ - \\log^2 n_{L-1}}=1.4 \\cdot 10^7 e^{- (\\log(2 \\cdot 10^ 5))^2} \\approx 10^{-58}$, which is very small, as predicted.\n\n----\n\n\n**Concern 3**\n\nWe agree with the reviewer that any curve looks linear in a sufficiently small neighborhood of any given point. However, we would like to remark that the smallest eigenvalue of the NTK exhibits a linear behavior in $d^2$ for a rather large interval of values of $d^2$. In fact, we have repeated the same experiment for $N=3000$ after increasing by a factor $4$ the values in the x-axis of the previous plot, and we have obtained very similar results. The new version of the plot with larger values on the x-axis is contained in the file `scaling_wider.pdf` that can be found in the supplementary material of the revision. \n", " We thank the reviewer for the comments. We clarify below the two points raised as ‘Weaknesses’, and we are happy to answer additional follow-up questions. \n\n----\n\n**Question about $\\alpha \\ge 1$**\n\nWe believe there is a misunderstanding here, and we would like to clarify this point. The first requirement of Assumption 2.5 is that *there exists* $\\alpha>0$ such that (4) holds. First, notice that choosing a *larger* $\\alpha$ leads to a *more restrictive* condition (4). As (4) is required to hold only *for some* $\\alpha>0$, we are allowed to pick this $\\alpha$ to be very small, e.g. $\\alpha=0.001$. Thus, the case $\\alpha\\ge 1$ does not lead to the desired minimum over-parameterization requirement. \n\nIn fact, the *tight* over-parameterization condition would be $N=o(n_{L-2}n_{L-1})$. The point of (4) is to allow a small slack in the exponent via the additional parameter $\\alpha$, in order to take care of extra logarithmic factors appearing in the argument. More specifically, by tracking such logarithmic factors, the requirement (4) in Assumption 2.5 can be replaced by $N\\log^{12} N=o(n_{L-2}n_{L-1})$ (which now does not contain $\\alpha$ anymore). We have refrained from doing that in the submitted version, since we deemed (4) as written more clean and clear. However, we acknowledge that the current writing has led to a question by both this reviewer and reviewer *mvcT* (see also the first point in the corresponding response). Hence, if the reviewers find it useful, we are happy to replace the requirement $N^{1+\\alpha}=o(n_{L-2}n_{L-1})$ with the slightly less restrictive requirement $N\\log^{12} N=o(n_{L-2}n_{L-1})$ and perform the necessary (very minor) edits to the proofs in the appendix. \n\n**[EDIT]** After the follow-up comment of reviewer *mvcT*, we have implemented this change and further improved the over-parameterisation requirement to $N\\log^{8} N=o(n_{L-2}n_{L-1})$. The changes to the arguments in the appendix and to the body of the paper are minor, and they are detailed in the follow-up response to reviewer *mvcT*.\n\n----\n\n**Question regarding the optimization**\n\nWe think the reviewer is referring to the optimization result (Theorem 4.2). If this is not the case and we misinterpreted the comment, please let us know and we are happy to clarify this point further.\nThe reviewer is correct when mentioning that the NTK changes as the parameters get updated and, hence, one needs to make sure that such parameters do not grow unbounded. In fact, this is precisely our proof strategy for Theorem 4.2. The core of the argument consists in controlling how the NTK changes along the optimization trajectory. More specifically, we bound the radius of a ball that contains the whole trajectory of gradient descent (from initialization until a point with 0 loss is reached), and we also bound the NTK spectrum inside this ball. The detailed proof is provided in Appendix H, and there are no hidden additional assumptions. \n", " We thank the reviewer for the feedback. As for the minor writing suggestion on the PSD acronym, we have corrected the paper accordingly. We reply below to the three questions posed by the reviewer, and we are happy to answer additional follow-up questions. In case the reviewer is satisfied with our response (especially the discussion about the significance of proving guarantees under minimum over-paramerization), we hope that raising the rating will be considered.\n\n----\n\n**Question 1**\n\nWhile it is certainly true that modern deep learning models are vastly over-parameterized, in the era of “big data” the sizes of datasets have also exploded. This means that it is not really realistic for the widths of the layers of a deep network to scale polynomially with the number of training data. For example, the CIFAR-10 training dataset contains 50000 images. Thus, if the layer widths were to scale *only linearly* with the number of data samples, the total number of parameters would be roughly $2.5 \\cdot 10^8$. This is way more than what it suffices to completely fit random labels on CIFAR-10, namely $N \\approx 10^6$ [72]. ImageNet is even bigger: even if we consider a subset of $1.2 \\cdot 10^6$ images as in [72] (out of the total $1.4\\cdot 10^7$ training data samples), a similar back-of-the-envelope computation leads to a model with more than $10^{12}$ parameters, which surpasses in size the largest model ever released. Again, in [72], it is shown that $2.4 \\cdot 10^7$ parameters are enough to fit random labels for this subset of $1.2 \\cdot 10^6$ training data points.\n\nThe numerical evidence presented above suggests that having a number of parameters of the same order as the dataset size is much closer to practice than having a number of neurons of that order. The main result of our paper gives a **rigorous justification to this phenomenon**, showing that memorization and optimization are in fact possible as soon as the number of parameters (and *not* the number of neurons) scales at least linearly in the dataset size. Such a result can be regarded as the end point of a popular line of research in the theoretical deep learning literature, which has provided optimization guarantees under milder and milder over-parameterization requirements. More specifically, [5] requires the layer widths to be $\\Omega(N^{24})$, [73] requires $\\Omega (N^{14})$ neurons, [74] requires $\\Omega (N^{8})$ neurons, [21] requires $\\Omega (N^{4})$ neurons, and finally [47] requires $\\Omega (N)$ neurons. Furthermore, there is increasing evidence that, in the challenging setup in which the layer widths are *sub-linear* in $N$, neural networks still memorize the training data [14, 71, 66], reach zero loss under gradient descent training in the two-layer setting [61, 50, 42], and in the deep case, gradient descent explores a nicely behaved region of the loss landscape [44]. We also remark that in some of the existing work (e.g., [44]), it is explicitly left as an open problem to prove that gradient descent is able to optimize neural networks with sublinear layers.\n\nIn summary, **our work addresses this open problem, and it is the first to show that a class of deep networks with minimum over-parameterization can memorize and optimize**. To achieve this goal, we need to develop a novel analysis, as also acknowledged by *Rev. mnfH*, who recognized our technical innovations. \n\nIn order to address this point, we have added a clarification in l. 36-40 of the revised version.\n\n----\n\n**Question 2**\n\nIn the body of the paper, we mention several times that the NTK is shown to be “well conditioned”. When we do that, we refer to the conditioning number of the matrix, given by the ratio between its largest and smallest eigenvalues. Since we prove a lower bound on the smallest eigenvalue of the NTK, this automatically gives an upper bound on its condition number, thus showing that the NTK is in fact well conditioned. \n\nWe hope that this clarifies the concern of the reviewer, and we remain at disposal in case further clarifications are needed. \n\n----\n\n**Question 3**\n\nThis is an excellent point. As correctly guessed by the reviewer, the labels used in Figure 2 are in fact random. However, similar results can be obtained using ‘low-complexity’ labels. In particular, we have repeated the experiment using as labels $y_i = v^\\top x_i$, where $v$ is a random unitary vector in $\\mathbb R^d$. The results are very similar and they are provided in the file `optimization_labels.pdf` in the supplementary material of the revised version.\n\n", " This manuscript analyses the neural tangent kernel in the regime of minimum over-parameterization. In detail, the authors prove the lower bound about the NTK eigenvalue for deep nets with minimum over-parameterization. Then, they apply the theorems to the aspects of networks' memorization and training. Pros:\n\nThis manuscript deeply investigate the question of minimum over-parameterization;\n\nThe proofs are solid;\n\nTwo application are proposed based on theorems.\n\nCons:\n\nThis paper is very theoretical and focuses on the minimum over-parameterization in deep learning. I am not an expert about the NTK research, so I mainly give some comments and suggestion on writting. For me, it is neccesary to clearly and comprehensively illustrate the backgroud and significance on investigating the problem of minium over-parameterizatio, please see Questions below.\n\nSome minor writing suggestions:\n\n1. Line 60: the full name of PSD should be proposed; 1. The modern deep learning foucses on \"super\" over-parameterization, why do the paper research the minimum over-parameterization? For completing the NTK theorem? How the research on the minimum over-parameterization help understand the success of deep nets?\n\n2. What is the mean of \"to be conditioned\"?\n\n3. About the experiments of Figure 2, are the used labels random? If yes, Can we get the similar results with normal label (or normal dataset with low complexity, compared to the complex random datasets)? \n Please the Questions.", " This submission studies the problem of minimum over-parameterization in deep neural networks. More specifically, the authors investigated the settings with sublinear layer width and provides the lower bound in terms of the smallest NTK eigenvalue. I must first say that this paper is much beyond my expertise, and the evaluation of this submission should depend on other reviewers with necessary background.\n\nStrength:\nAs the authors claimed, this paper gives an affirmative answer regarding whether NTK is well-conditioned in the sublinear setting. The theoretical results from Theorem 3.1 match the claim. The authors also provide details proof to cover the main steps.\n\nWeakness:\nSome clarification regarding the assumptions would be helpful to understand the major conclusion. For example, if \\alpha >= 1 in Eq. (4), does it mean that the number of neurons would exceed the sublinear case? \n\nAnother case is regarding the proof for the smallest NTK eigenvalue: how does it depend on the optimizer? Since NTK changes with updated parameters (which may explode if optimization failed), does the proof depend on any hidden assumptions for the optimizer? See above Yes", " For an $L$-layer (loosely) pyramidal network, this paper gives a probabilistic lower bound on the smallest eigenvalue of the empirical neural tangent kernel Gram matrix, which is proportional to the product of the width of the last two hidden layers. When combined with known results on NTK, this lower bound implies that $\\sim \\sqrt{N}$ neurons are enough to learn a solution (via GD) that memorizes $N$ copies of data. I do not have anything major against the acceptance of this paper. The paper is well written and the theoretical contributions are clear (up to my knowledge). I especially appreciate the proof-technical innovation in the paper---the three-stage centering argument may be quite useful for the future works in this direction.\n\nNevertheless, I do have some minor concerns:\n\n- Assumption 2.4 restricts the setup to neural networks with \"loose pyramidal topology,\" which seems to be much weaker than the strict pyramidal topology in the sense that the layer width need only be smaller than a constant times the preceding layer's width. While this looks very easy to satisfy, this also suggests that actually many \"constants\" are being hidden inside the big-O notation of Theorem 3.1. Could you briefly describe the what the hidden terms of Theorem 3.1 are, and how they behave with respect to the assumption?\n\n- The probability of event at Theorem 3.1. is $1 - C \\exp(-c\\sqrt{N}) - CN\\exp(-c\\log^2 n_{L-1})$. I am particularly worried about the last term, which is proportional to the sample size $N$. Could you explain in more detail, why, and under what condition such $N$-proportionality does not really make the probabilistic bound meaningless?\n\n- I do not find Figure 1 to be very meaningful---any curve can look linear when we select a nice interval. My questions are basically the same as the weaknesses described above:\n\n- Could you describe what the hidden terms of Theorem 3.1. are?\n\n- Please explain when and why $CN\\exp(-c\\log^2 n_{L-1})$ would be small enough for event in Theorem 3.1 would happen with a sufficiently large probability. Limitations are well-addressed.", " This paper shows that NTK can be well-conditioned in a sub-linear setup. In particular, they proved that roughly $\\Omega (N)$ parameters are needed to get a good NTK matrix, and also $O(N)$ parameters are enough to memorize the training data. Based on those NTK bounds, they further provide results on the memorization capacity and the optimization via gradient descent and square loss. It is interesting to study the neural network in a sub-linear setup. For square loss, the authors provided valuable sight for the training data memorization as well as the optimization. This paper is well-written and clear for the technique part. However, I have several concerns about the significance and the limitation of the results. Besides, I think this paper can improve the clarity of their results by making a comparison with the setting for the classification. 1. Requirement 4 in Assumption 2.5 implies that the total number of neurons should be larger than $\\Omega(N^{(1+\\alpha)/2})$. This violates the statement after Theorem 3.1 in line 175. \n\n2. The authors argue that when all the widths have the same scaling, the upper bound matches the lower bound. In this case, the training data size $N$ should be smaller than $d^{2/(1+\\alpha)}$ according to Assumption 2.5, where d is the dimension of the input. This is a fairly strong condition for the training data set, which may limit the significance of the results. \n\n3. Under certain margin assumptions on the training data, [1] showed that a polylogarithmic width condition suffices for two-layer ReLU networks to converge and generalize. Later [2] studied how much over-parameterization is sufficient to learn deep ReLU networks and showed that under certain assumptions on the training data, polylogarithmic width is sufficient. Since these papers have milder overparameterization conditions of the NNs, the authors may want to make a comparison with those results. \n\n[1] Ji, Ziwei, and Matus Telgarsky. \"Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networks.\" International Conference on Learning Representations. 2019.\n\n[2] Chen, Zixiang, et al. \"How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?.\" International Conference on Learning Representations. 2020. The authors have addressed their work's limitations and potential negative social impact." ]

[ -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, 2, 1, 2, 4 ]

[ "OA0FbNEl-I1", "hJunvw7KtVN", "nips_2022_x8DNliTBSYY", "nGiVEgz1q_E", "PRS1t0Gr8t", "rsjnTR1m-px", "WKUsCo819J4", "nips_2022_x8DNliTBSYY", "nips_2022_x8DNliTBSYY", "nips_2022_x8DNliTBSYY", "nips_2022_x8DNliTBSYY" ]

[ "K8eh7afAiuM", "I4ezJh56Djb", "U0viBC3-xxB", "iuBZcc_z88T", "VwYPH4wq3N", "G83cKZmT7yo", "HhTZvAl58Ue", "mSAKjTuIyh", "DQQ3B1w4RWK", "IcHtlTVZkh", "geJ2vc6yJya", "re7MRekgf5O", "3d3Spev6GfS", "X4oAlc_pgbp", "HgnMuTsdWp1" ]

[ "author", "author", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear reviewer,\n Do you have any further concerns or suggestions? We are very delighted to discuss them with you.", " Dear Reviewer,\n\nSince the rebuttal discussion is about to end soon, we are wondering if our response and revision have cleared your concerns. We would appreciate it if you could kindly let us know whether you have any other questions. We are looking forward to comments that can further improve our current manuscript. Thanks!\n\nBest regards,\n\nThe Authors", " Dear Reviewer,\n\nWe have updated our related works and further discussed the limitations. We are wondering if our response and revision have cleared your concerns. We would appreciate it if you could kindly let us know whether you have any other questions. We are looking forward to comments that can further improve our current manuscript. Thanks!\n\nBest regards,\n\nThe Authors", " Thanks for the response. My concerns are addressed.", " Dear Reviewers,\n\nWe were wondering if our response and revision have cleared all your concerns. In the previous responses, we have tried to address all the points you have raised. In the remaining 1 day of the rebuttal period, we would appreciate it if you could re-evaluate our submission, or kindly let us know whether you have any other questions, so that we can still have time to respond and address them. We are looking forward to discussions that can further improve our current manuscript. Thanks!\n\nBest regards,\n\nThe Authors", " Ok, thank you for the clarifications", " Dear Reviewers,\n\nWe were wondering if our response and revision have cleared all your concerns. In the previous responses, we have tried to address all the points you have raised. In the remaining 3 days of the rebuttal period, we would appreciate it if you could re-evaluate our submission, or kindly let us know whether you have any other questions, so that we can still have time to respond and address them. We are looking forward to discussions that can further improve our current manuscript. Thanks!\n\nBest regards,\n\nThe Authors", " Thank you, your comments are valuable and helpful for revising and improving our paper and providing necessary guidance for our research.\n\nQ1-2. A: Although we do not explicitly capture the causation structure, the regularization terms to the polynomial coefficients and matrix basis help TPGNN to eliminate redundant dependence. According to the experimental results, the learned structure is highly sparse, with a Frobenius norm of $16.12 \\pm 1.31$ (the matrix size is $288\\times 288$). Besides, if we replace the learned structure with the prior structure, i.e., the physical distance graph, then the performance declines by $13.13$%, $13.94$%, and $12.23$% on the three metrics. We discussed the limitations in Section 6.\n\nQ3 & Q5. A: We updated the related works for discussing the research you mentioned. Besides, we merged the discussion on GCNs and PGFs into one paragraph.\n\nQ4. A: These works model dynamic correlation among variables based on self-attention. For self-attention, the input sequence decides the constructed structure. However, the input length on the PEMSD7 dataset is 12, but the whole training sequence has a size of over 8000. Therefore, the dynamic structure captured by self-attention is sometimes misleading, especially when the input sequence is noisy. Besides, the main motivation of these works for using self-attention is providing input for the GNNs. In our work, we explicitly point out the challenge and propose a practical method that accurately models dynamic dependence.\n\nQ6. A: a) N and c are small in practice. In Appendix 4, we list the parameter scale of different methods. As a snapshot, TPGNN: 0.31M, MTGNN: 0.44M, Graph Wavenet: 0.25M, STGCN: 0.33M. Therefore, our method TPGNN is lightweight in parameter scale.\n\nb) According to Eq (7) of [R14] and Eq (13) of [R16]. The two works do not actually adapt the coefficients according to the time, they share a set of polynomial coefficients across different sliding windows.\n\nc) In Table 3 of the ablation study, we investigate the influence of the average coefficients on the model performance. w/o overview is the version that does not use average coefficients. The results indicate that TPGNN outperforms the w/o overview's accuracy by 3.60% on average, and the w/o overview has a significant accuracy variance. Besides, predicting with $T$ groups of polynomial coefficients increases the space complexity. \n\nd) According the Equation (5) and (6), we have $\\mathbf{\\bar{a}}=(\\mathbf{e}^{(t)},\\dots,\\mathbf{e}^{(t+T-1)})\\mathbf{W}_c\\mathbf{W}_a$. Clearly, $\\mathbf{\\bar{a}}$ is decided by $t$, i.e., the average coefficients are still time-varying. $\\mathbf{\\bar{a}}$ changes with the movement of the sliding window according to the equation. \n\ne) We further implement a graph-based-decoder version of our method, the experimental results on PEMSD7 (horizon 12) are (MAE/MAPE/RMSE): $3.349\\pm0.137/8.461\\pm0.133/6.680\\pm0.330$. The change impairs the performance by 2.92%. Due to the auto-regressive process, we have to train a recurrent GNN if we use a graph-based decoder. The over-smoothing problem of GNN is unavoidable because we share an identical GNN across the iterations. \n\nQ7: Theorem 1 is used to address the 2nd challenge. It points out the ability boundaries of the TPG module, which gives the requirements to achieve perfect approximation. Otherwise, the approximation ability of our method is unknown for general cases. We have carefully checked R[9] and R[19], but they do not have a result like Theorem 1 to specify the bound of the TPG module under the Frobenius norm. We further generate synthetic MTS datasets with ground-truth variable dependence to solve the second challenge. Theorem 1 and the synthetic datasets experiments are indispensable to validate the TPGNN's effectiveness.\n\nQ8: At time step $t-1$, we define a temporal graph structure $\\mathbf{W}^{(t-1)}\\in\\mathbb{R}^{N\\times N}$as the ground-truth dependence. We then aggregate $\\mathbf{X}^{(t-1)}\\in\\mathbb{R}^{N\\times 1}$ based on $\\mathbf{W}^{(t-1)}\\in\\mathbb{R}^{N\\times N}$, i.e., $\\mathbf{W}^{(t-1)}\\mathbf{X}^{(t-1)}$. We set $\\mathbf{W}^{(t-1)}\\mathbf{X}^{(t-1)}\\in\\mathbb{R}^{N\\times 1}$ as the mean, $\\sigma$ as the standard deviation, and produce $\\mathbf{X}^{(t)}$by sampling from the normal distribution $\\mathcal{N}(\\mathbf{W}^{(t-1)}\\mathbf{X}^{(t-1)},\\sigma)$. The detailed algorithm is shown in Appendix A.3.3. There are two reasons to use the method. 1) The method enables us to access the ground-truth variable dependence. 2) The method is easy to implement, and the resultant MTS data has complex behavior. We have visualized some examples in Appendix A.3.3.\n\nMinor comments.1-3) A: Thanks for your suggestions. We update Section 3.1 to clarify some misleading concepts. (4) They have no connections. 5) the latter represents the ground-truth laplacians. 6) Solar-energy has 10512 test samples, the sample numbers are listed in Table1.", " Thank you, your comments are valuable and helpful for revising and improving our paper, as well as providing important guidance for our research.\n\nWe have noticed that our work has similarities to GPR-GNN [1]. In the related work, we thoroughly discuss the difference between GPR-GNN and our work. The main difference is that our method can capture variable dependence of multivariate time-series (MTS) data by representing the dependence as a temporal matrix polynomial. It is crucial for the GNNs-based MTS forecasting method since MTS data commonly do not have an explicit graph structure, which is different from typical graph datasets like Cora and DBLP. \n\nFurthermore, we generate six synthetic MTS datasets that have ground-truth variable dependence. We then compare the dependence capturing ability of several baselines with our method. The results demonstrate that our approach outperforms GPR-GNN by 53.47% in approximating the dependence structure.\n\nQ: Self-attention might be the simplest way to learn dynamic graph structures. How does it perform compared to TPGNN?\n\nA: We have compared our method with self-attention in Table 4, the results demonstrate that our method outperforms self-attention by 23.41% in capturing the variable dependence. Furthermore, we implement a self-attention version of our method and test it on the PeMSD7 dataset. The results for horizon 12 are (MAE/MAPE/RMSE): $4.325\\pm 0.063/10.553\\pm 0.204/8.040\\pm0.146$, which impairs the accuracy by 28.42% on average. As a result, self-attention is impractical for capturing the dynamic graph structures.\n\nQ: What's the time complexity of TPGNN?\n\nA: Suppose that the input MTS data has $N$ variables, the input sequence length is $T$, the feature dimension is $D_e$, and the polynomial order is $K$. The TPGNN is composed of self-attention and the TPG module, and it is known that self-attention has a time complexity as follows:\n$$\n\\mathcal{O}(NT^2D_e+NTD_e^2)\n$$\n\nAs for the TPG module, the time complexity for constructing the initial adjacency matrix is $\\mathcal{O}(N^2)$, and the time complexity of Equation (7) is $\\mathcal{O}(KT(ND_e^2+N^2D_e))$. As a result, The overall time complexity of TPGNN is $\\mathcal{O}(KTN^2D_e+KTND_e^2+NT^2D_e)$. Since the $K, D_E$ is small in practice, the efficiency of TPGNN is mainly decided by $N$ and $T$. We add a section in Appendix A.2 to comprehensively illustrate the time complexity of our method. Besides, Appendix A.2 also contains numerical results of TPGNN's efficiency. The results show that TPGNN has competitive efficiency with SOTA methods like MTGNN [39]/Graph Wavenet [40], though these methods do not have self-attention modules.", " Thank you, your comments are valuable and helpful for revising and improving our paper, as well as providing important guidance for our research. \n\nQ: From what I understand, the initial adjacency matrix is computed from embeddings that are not related to the learning process. It is correct? Do think it is possible to learn it in an end-to-end way?\n\nA: In the equation(2) and (3), we construct the initial adjacency matrix with embeddings $\\mathbf{E}$：\n$$\n\\begin{equation}\n\\mathbf{A}=\\operatorname{SoftMax}(\\operatorname{ReLU}(\\mathbf{EE^T}))\n\\end{equation}\\tag{2}\n$$\n$$\n\\begin{equation}\n\\mathbf{A}=\\operatorname{SoftMax}(\\operatorname{ReLU}(\\mathbf{EE^T}))+\\mathbf{L}\n\\end{equation}\\tag{3}\n$$\n\nFollowing the end-to-end fashion, these embeddings are also learnable parameters. As a result, we optimize the resultant adjacency matrix in the learning process (end-to-end).", " Thank you, your comments are valuable and helpful for revising and improving our paper, as well as providing important guidance for our research. As for your concerns about the autoregressive (AR) strategy, the AR strategy has been proven effective across various areas. The strategy is still applied in frontier research like Denoising Diffusion Probabilistic Model (DDPM) [R1], and the most famous generation models like DALLE 2 [R2] and Imagen [R3] are based on DDPM. Although the prediction errors are accumulated over time, the strategy provides a powerful inductive bias to enforce the model to utilize the context information, improving the long-term prediction performance. As for the efficiency issue, we can reduce the computation cost by lowering the sample rate of data, e.g., increasing the time interval between two successive forecasts. Furthermore, we add a comprehensive time complexity analysis of TPGNN in Appendix 2.\n \nQ: Many recent studies (such as Informer, Autoformer, FEDFormer, and N-HiTS, among others) use the Electricity, Traffic, and Exchange datasets for the long-horizon multi-step forecasting setting. Why didn't the authors consider these datasets as benchmarks for this task?\n\nA: Thank you for your suggestion. The benchmark selections are mainly based on related works like MTGNN [39] and StemGNN[4]. They use the Electricity, Traffic, and Exchange datasets for evaluating model performance on the single-step forecasting. For the multi-step forecasting task, the evaluation is conducted on the traffic datasets. The two traffic datasets are essential for our evaluation since they have prior structures, i.e., the physical distance among sensors. The experimental results illustrate that the learned structure captures valid dependence that does not record by the prior structure. Furthermore, we compare our method with Informer [46] on the two traffic datasets. The results validate that the complexity of the two datasets and TPGNN outperforms other baselines significantly.\n\nQ: How does the choice of T_p affect the performance? Would it be beneficial to match the cycle to known seasonalities of the data?\n\nA: We commonly set $T_p$ as one day/week/season according to the sample rate of datasets. To answer your question, we conduct several experiments on PeMSD7 to investigate the influence of $T_p$. We set the $T_p$ as 16hour, 24hour (one day), 32hour, and the horizon is 12. \n\nThe results for $Tp=16hour$ are (MAE/MAPE/RMSE): $3.241\\pm0.021/8.248\\pm0.089/6.547\\pm0.016$\n\nThe results for $Tp=24hour$ are (MAE/MAPE/RMSE): $3.215\\pm0.014/8.221\\pm0.035/6.559\\pm0.023$\n\nThe results for $Tp=32hour$ are (MAE/MAPE/RMSE): $3.234\\pm0.024/8.230\\pm0.077/6.536\\pm0.052$\n\nThe results illustrate that our method is robust to the $T_p$'s selection. Therefore, a roughly correct selection is enough to get a good result. As for the inferior performance on Exchange, we think the main reason is the small sample size, which causes difficulties in capturing the dynamic variable dependence.\n\nQ: Adding simpler univariate baselines to the experiments (classic models such as ARIMA, SeasonalNaive, and DL methods such as N-BEATS) will help better measure the complexity/accuracy tradeoff of TPGNN.\n\nA: Thanks for your suggestion. VARMLP [43] is one of the representative univariate baselines based on ARIMA. For the multi-step forecasting task, the FC-LSTM is a univariate baseline; Furthermore, we add ARIMA to the baselines according to your advice (Table 2).\n\n[R1] Nichol, Alex and Prafulla Dhariwal. “Improved Denoising Diffusion Probabilistic Models.” ArXiv abs/2102.09672 (2021): n. pag.\n[R2] Ramesh, Aditya et al. “Hierarchical Text-Conditional Image Generation with CLIP Latents.” ArXiv abs/2204.06125 (2022): n. pag.\n[R3] Saharia, Chitwan et al. “Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding.” ArXiv abs/2205.11487 (2022): n. pag.", " The paper proposes TPGNN, a novel graph model for multivariate time-series forecasting. The most significant improvement of TPGNN is the ability to learn dynamic correlations between nodes. TPGNN models a dynamic graph with a novel component, TPG, based on matrix polynomials. The paper demonstrates how the proposed model can learn actual correlations in a simulated setting and provide theoretical guarantees for the approximation. TPGNN achieves SoTA performance on 6 benchmark datasets, on both single-step and multi-step settings. Strengths:\n- The paper proposes a novel module, TPG, to model dynamic correlations between time series.\n- Authors provide theoretical approximation guarantees and empirical results on simulated data.\n- Ablation studies demonstrate the gains in performance of each component.\n- TPGNN achieved SoTA performance on 6 benchmark datasets, on both single-step and multi-step settings. \n- The paper is well written and clear.\n\nWeaknesses:\n- The model can only learn periodic correlations, as the coefficients of the polynomials are fixed between cycles. This potentially limits the model's advantages to settings with distinct periodic patterns. This might explain why TPGNN performs worst in Exchange, a dataset without clear seasonalities. \n- To produce multi-step forecasts, TPGNN uses an auto-regressive strategy. This strategy performance is worst than other methods (such as the direct strategy) on long-horizon forecasting, as 1. errors accumulate over time, leading to worse performance, and 2. longer inference times.\n- The paper claims the model achieves SoTA performance on the long-horizon setting; however, the horizons considered in the paper are far lower than most recent studies. For example, the Informer paper (and a whole body of literature) considers a multi-step forecast of 720 timestamps.\n- The paper does not present any time complexity analysis.\n - Many recent studies (such as Informer, Autoformer, FEDFormer, and N-HiTS, among others) use the Electricity, Traffic, and Exchange datasets for the long-horizon multi-step forecasting setting. Why didn't the authors consider these datasets as benchmarks for this task?\n- How does the choice of T_p affects the performance? Would it be beneficial to match the cycle to known seasonalities of the data?\n- Adding simpler univariate baselines to the experiments (classic models such as ARIMA, SeasonalNaive, and DL methods such as N-BEATS) will help better measure the complexity/accuracy tradeoff of TPGNN. Limitations are discussed, and I do not identify potential negative social impacts.", " The paper presents a novel framework for multivariate time series forecasting in the context of Graph Neural Networks (GNN). The aim of the work is to take into account the variable dependence which can evolve temporally. To tackle the issue, the authors propose to use a dynamic adjacency matrix inside the GNN process. This matrix corresponds to a polynom of an initial adjacency matrix where the coefficients are learned from the data and depend on the timestamp. The initial adjacency matrix is computed from the data following previous works and can integrate previous knowledge. A hypothesis of periodicity is considered in order to obtain a finite number of polynomial coefficients. The computed dynamic adjacency matrix is then used in a Graph Convolutional network to obtain the encoding module. The decoder uses a self-attention mechanism to forecast in a auto-regressive way the future of the time series. The authors propose a theorem to prove the correctness of the estimation of the adjacency matrix. An extensive experimental part compares the proposed approach to several SOTA baselines and presents a complete ablation study. Finally, experiments on artificial (and real) data show the effectiveness of the proposed module to learn the graph correlation structure. \n\n Strengths:\n* The paper is well written, the SOTA is clearly stated and the work is well positioned wrt to previous works. \n* The model is clearly presented and illustrated\n* The experimental part is very well designed, with exhaustive experiments (comparison to SOTA models, ablation study wrt all the aspects of the model, analysis of the captured correlation,..).\n\nWeaknesses :\n* The novelty is not great (but sufficient in my opinion)\n* The experimental section is quite overfilled, maybe some results can be put to the appendix to give more space to introduce the datasets for instances. From what I understand, the initial adjacency matrix is computed from embeddings that are not related to the learning process. It is correct? Do think it is possible to learn it in an end-to-end way? NA", " This paper introduces a Temporal Polynomial Graph Neural Network (TPGNN) for multivariate time series forecasting. TPGNN first models the overall correlation with a static matrix basis, and then constructs a matrix polynomial for each time step by a set of learnable time-varying coefficients and the matrix basis. The experimental results on several benchmark datasets show that TPGNN could outperform the baseline methods. Strengths:\n1. The experimental results on PEMS datasets show that the proposed TPGNN could achieve state-of-the-art performance. \n2. The experimental results on the synthetic dataset show that TPGNN could approximate the underlying graph structure.\n3. The paper is clear and easy to follow.\n\n\nWeakness:\n1. The novelty of using matrix polynomial to approximate graph structure is limited, as it is quite similar to [1]. \n2. The experimental results on the single future step forecasting task show that the improvements are not significant for many metrics.\n3. Other weaknesses: please refer to the questions.\n\n[1] Chien, Eli, et al. \"Adaptive universal generalized pagerank graph neural network.\" arXiv preprint arXiv:2006.07988 (2020). 1. Self-attention might be the simplest way to learn dynamic graph structures. How does it perform compared to TPGNN?\n2. What's the time complexity of TPGNN?\n N/A", " This paper focuses on multivariate time series forecasting based on correlation graphs between such data. The main motivation is that dynamic correlation can avoid the bias in the solution that approaches focusing on the static correlation graph operate. Leveraging this dynamic correlation graph, a GNN-based model is leveraged to find higher-order representations of the data. One key aspect of the paper is that is uses time-varying coefficients (later, I argue that it is not explicitly the case). Some theoretical comparisons on the graph-based component of the paper are given. Numerical result on several datasets show a good performance and a thorough abolition study supports the role of the different components. Strengths:\n+ Works on dynamic graphs for forecasting rather than static, which is a less exposed area;\n+ Establishes links between;\n+ Numerical results are quite strong and support the method;\n+ Some theoretical results about the role of the graph filter (not of all the method) are given;\n\nWeaknesses\n- The paper over claims its contribution as proposing learning solutions over time varying graphs; while later on discusses that there exist prior work on learning over time-varying graphs;\n- Related work are rather limited and discusses mainly some baseline methods in GNN but misses several recent works on polynomial filtering for MTS; hence, the specific contribution of the paper is unclear and not well positioned, consequently, its novelty is lower than claimed.\n- The paper focuses entirely on correlation as the main argument to aid forecasting, bypassing any discussion related to causation; hence, limitations of the approach are not thoroughly discussed;\n- The provided theoretical result are tangential to the method developed and rather focused on the graph filter but not of the overall solution; \n- It is unclear if the benefits comes from the graph-based encoder with all the dynamics or from the non-graph based decoder.\n\n\n\n 1- All work is based on correlation graphs to support forecasting. But in real multivariate time series, causation is often more important than correlation, especially in traffic networks. And since the correlation does not imply causation, the model presents a limitation in this regard. The authors should discuss this aspect int he paper and provide guidelines about it.\n\n2- Regarding the challenges of related works in the introduction. Point 1) about no variable dependence and using physical distance graphs. This is one approach to build the graph as the physical graph may provide additional information to aid the forecasting. But those methods could apply to any graph, even a similarity (KNN graph, correlation) and the likes. However, working with correlation graphs (or in general data-graphs) may not necessarily be beneficial. This is because both the graph and the model parameters are estimated from the same data, hence there is redundancy in the model. In this regard, the graph structure does not bring any additional information that is not present in the data themselves (as a road network would do) but it rather acts as bias (the type of graph) we choose to model the data. In this regard, the scientific challenge of current approaches are not well positioned.\n\n3- Following the above point, the fact that temporal data may be better represented by time-varying graphs is of more importance. The paper should however acknowledge and contrast the contribution also with alternatives coming from non-GNN but graph-based methods such as [R1, R2, R3] and references therein. Also there are also works on GNNs over dynamic graphs, e.g., [R4] and following works that refer to it. The same remark applies here as well. \n\n4-Wrt works [36, 35, 4] it is claimed that those models also work with a dynamic correlation among variables. And it is also claimed that their issues is that the learned graph is sensitive to the observation. Can you elaborate more on this, why it is the case. And also why in the proposed model does not suffer from it as the graph is also build from the observation. In my view, this is needed as the proposed approach is related to these works and this may entail the key contribution.\n\t4a) In general, it I given the impression in the introduction that one of the key novelties of this paper is to work with time varying graphs. But as acknowledged here and in comment 2 other works have already proposed this. In this regard, the paper introduction does not give merit to existing literature and does not detail entirely the key contribution of the paper wrt those alternatives.\n\n5- Related works on GNNs and PGFs. \n\t5a) The division of GNNs into spectral and spatial methods is misleading. While there is a track of record within the CS community to do so, recent works have indeed realised that all GNN approaches are spatial—maybe the only spectral one is the early work in [R5]. In fact, the GCN mentioned as a spectral method is actually spatial. It can be seen as a particular case of GraphSage or message passing where the aggregation is dictated by multiplying nodal features with the graph Laplacian.\n\t5b) The GCN is a particular case of [R6] that claimed to use Chebyshev polynomials but as realised recently they often learn coefficients not respecting the coefficient rules in the Chebyshev polynomials [R8]. In turn, since the GCN is just an order one polynomial, and a particular case of [R6], it is more appropriate to give as an example [R6].\n\t5c) Polynomial graph filters have been initially formalised in the field of graph signal processing [R9, R10]. Also GCN [12] and ChebNet [R6, R8] use polynomial graph filters in the form of Chebyshev polynomials [R11]. The work in [30] instead is a very particular case of polynomial filtering. The link between polynomial filtering and GNNs has been discussed in [R12] including the expression of GCNs and SGCs as such polynomials. Another broader category casting the aforementioned GNNs are particular instances of graph filtering can be found in [R13] and their use for spatiotemporal learning has been discussed in [R14, R15, R16].\n\t5d) Some encoder decoder structure for GNN-based learning in multivariate time series have been discussed in [R17, R18]. The paper should highlight the contribution wrt these works as they also focus on dynamic graphs within the encoder-decoder solution.\n\nWhile some of this discussion may not be central to the developed method, I feel it is propagating misleading information about the GNN architecture. The authors are in this regard requested to reorganise this part and highlight the differences in using PGFs wrt to alternatives that have used them for multi-variate time series forecasting.\n\n6- Method\n\n6a) Learning matrices E in (2) has a number of parameters Nc. Isn’t this too much and suffering the curse of dimensionality?\n\n6b) The graph filter with time-varying coefficients has been discussed for forecasting in [R14, R16]. Here the difference stems mainly on using a (partially) learnable matrix A as well. Please highlight the differences.\n\n6c) After (5): the use of “average result” yields a smoothing (or low pass filtering) of the spatiotemporal data; hence, while it can play a role in robustness it also affects performance. Limitations of this choice should be discussed. \n\n6d) From eq. (7), it is shown that the average coefficients are used. So the final model in the end is not strictly a time varying model. This comes as a surprise as up to this point is has been build up towards a method that was time varying. It is therefore needed to highlight this properly not only in the introduction but also when contrasting with related works. The model is basically some engineered form of a PGF applied per time stamp, where the coefficients are the same (they only differ in the embedding). This to some extent contradicts the motivation and the theme of the paper in the earlier parts, which should be re-organised to make this part explicit.\n\n6e) Why the decoder is not made graph-based? Can one then attribute the benefits to the graph-based solution proposed in the paper or to this non graph-based decoder? The motivation behind such a choice and role of the different components is unclear.\n\n7- Theoretical properties - Thm1 is not about the TPGNN but it is rather the ability of a graph filter wrt the adjacency matrix A to approximate a user-defined operator. Similar results have been already discussed in the field of graph signal processing; see e.g., [R9, R19]. This result instead is applied to every operator (G^t) and errors are summed. The polynomial order in fact does not have to be large enough, but should satisfy the Cayley-Hamilton theorem (see [R19]).\n\nWhile we could argue this result differs so some extend form that in the aforementioned works, I feel it is tangential to the method (TPGNN) as it does not account for several aspects of the method, e.g., (7) and the diffusion convolutional layer where these are embedded. Consequently, it is unclear if the TPGNN can indeed achieve perfect approximation and the provided theoretical properties reported do not support it.\n\n8- In Sec. 5.5. the definition of the normal distribution, \\sigma be a covariance matrix. Also it is said that the matrix signal X^(t) but the dimensions are those of a vector. I’m a bit confused here. In the same sentence it is also said that X^(t) depends on W^(t) but in the normal distribution it appears W^{(t-1)}. Are all these typos? If not considering the entries of X^(t) independent and identically distributed seems like a bit limitation to me. Can the authors elaborate why it makes sense considering this way of generating the data?\n\nMinor comments\n- Sec. 3.1: The MTS data is a graph signal \\mathcal{G}… is a wrong statement as the symbol represents a set (i.e., the graph), while the graph signal is defined as the data on this graph [R9-R10]-R14-R16-R11.\n- Sec. 3.1.-If W^t is time varying, shouldn’t also \\mathcal{E} be a time varying set of edges? Or do you mean a set of fixed edges exist and only their weights changes?\n- “not independent“ -> dependent\n- Is any link between the embedding vectors e_ts in the paragraph after (4) and the embedding matrix E in (3)? Either way, please make this explicit.\n- In 3.2, Laplacians are indicated with bold L; in Thm.1 with bold G;\n- There is a typo in the body of Lemma 2: “mathbfG” \n- Are there enough data in the test set to have a significant fourth decimal digit (e.g., Tab2)\n\n\n[R1] Natali, Alberto, et al. \"Learning Time-Varying Graphs from Online Data.\" arXiv preprint arXiv:2110.11017 (2021).\n\n[R2] Shafipour, Rasoul, et al. \"Identifying the topology of undirected networks from diffused non-stationary graph signals.\" IEEE Open Journal of Signal Processing 2 (2021): 171-189.\n\n[R3] \t.\tB.Zaman,L.M.L.Ramos,D.Romero,andB.Beferull-Lozano,“Online 
topology identification from vector autoregressive time series,” IEEE Transactions on Signal Processing, vol. 69, pp. 210–225, 2021. \n\n[R4] Rossi, E., Chamberlain, B., Frasca, F., Eynard, D., Monti, F., & Bronstein, M. (2020). Temporal graph networks for deep learning on dynamic graphs. arXiv preprint arXiv:2006.10637.\n\n[R5] Bruna, J., Zaremba, W., Szlam, A., & LeCun, Y. (2013). Spectral networks and locally connected networks on graphs. arXiv preprint arXiv:1312.6203.\n\n[R6] Defferrard, Michaël, Xavier Bresson, and Pierre Vandergheynst. \"Convolutional neural networks on graphs with fast localized spectral filtering.\" Advances in neural information processing systems 29 (2016).\n\n[R8] He, Mingguo, Zhewei Wei, and Ji-Rong Wen. \"Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited.\" arXiv preprint arXiv:2202.03580 (2022).\n\n[R9] Sandryhaila, Aliaksei, and José MF Moura. \"Discrete signal processing on graphs.\" IEEE transactions on signal processing 61.7 (2013): 1644-1656.\n\n[R10] Shuman, David I., et al. \"The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains.\" IEEE signal processing magazine 30.3 (2013): 83-98.\n\n[R11] Shuman, David I., et al. \"Distributed signal processing via Chebyshev polynomial approximation.\" IEEE Transactions on Signal and Information Processing over Networks 4.4 (2018): 736-751.\n\n[R12] Gama, Fernando, et al. \"Graphs, convolutions, and neural networks: From graph filters to graph neural networks.\" IEEE Signal Processing Magazine 37.6 (2020): 128-138.\n\n[R13] Isufi, Elvin, Fernando Gama, and Alejandro Ribeiro. \"EdgeNets: Edge varying graph neural networks.\" IEEE Transactions on Pattern Analysis and Machine Intelligence (2021).\n\n[R14] Isufi, Elvin, and Gabriele Mazzola. \"Graph-time convolutional neural networks.\" 2021 IEEE Data Science and Learning Workshop (DSLW). IEEE, 2021.\n\n[R15] Hadou, Samar, Charilaos I. Kanatsoulis, and Alejandro Ribeiro. \"Space-time graph neural networks.\" arXiv preprint arXiv:2110.02880 (2021).\n\n[R16] Isufi, Elvin, et al. \"Forecasting time series with varma recursions on graphs.\" IEEE Transactions on Signal Processing 67.18 (2019): 4870-4885.\n\n[R17] Sanchez-Gonzalez, Alvaro, et al. \"Learning to simulate complex physics with graph networks.\" International Conference on Machine Learning. PMLR, 2020.\n\n[R18] Pfaff, Tobias, et al. \"Learning mesh-based simulation with graph networks.\" arXiv preprint arXiv:2010.03409 (2020).\n\n[R19] Segarra, Santiago, Antonio G. Marques, and Alejandro Ribeiro. \"Optimal graph-filter design and applications to distributed linear network operators.\" IEEE Transactions on Signal Processing 65.15 (2017): 4117-4131. see above in the questions" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 5, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 4, 4, 5 ]

[ "U0viBC3-xxB", "re7MRekgf5O", "HgnMuTsdWp1", "DQQ3B1w4RWK", "nips_2022_pMumil2EJh", "IcHtlTVZkh", "nips_2022_pMumil2EJh", "HgnMuTsdWp1", "X4oAlc_pgbp", "3d3Spev6GfS", "re7MRekgf5O", "nips_2022_pMumil2EJh", "nips_2022_pMumil2EJh", "nips_2022_pMumil2EJh", "nips_2022_pMumil2EJh" ]

[ "03IiqkZjlB9", "78SDO689yZ-", "S9-4xxO3nWC", "Cus5jFCq4g-", "4gfdso1EgDra", "LfnRz9JQuJ8", "0qgbUOiUo9", "D5IoKk3FvYy", "yu4PIur3o7C", "HstKp2gbBx", "yGSKYtZJF2V", "yJFla3eoT8D", "1-cSaYl7JhN", "4NmaW94cdwi" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Yes the appendix was originally in the supplementary.zip but we have included the updated Appendix directly in the main paper so that it was easier for reviewers to have access to all the modifications in a single document. Sorry for the confusion this has created.\n\n- __\"Prediction of diverse and plausible futures and Image resolution.\"__ As stated in L251 we have tested our models (including in the experiments on image resolution) in the new town 05 as it is the most complex town. We will make that clearer in the captions of Table 4 and 5. Thank you for pointing us to the average log-likelihood to measure diversity of the predicted futures. We will include a few sentences to describe the difficulty of quantitatively evaluating prediction diversity, and specify that we only qualitatively show the diversity of predicted futures.\n- __\"Comparison.\"__ That is a good point, we will change the experiment name from \"no segmentation\" to \"only actions\".\n\nThank you for this discussion, we believe that the additional experiments and insights helped us improve the paper.", " Thank you, I am able to see the revisions at the end of the main paper. I looked in the supplementary .zip for the appendix, as that's where I found it previously. After considering these revisions altogether, I believe the weaknesses I stated were mostly addressed, although a few things should still be improved. I will increase my score to weak accept.\n\n- **\"Prediction of diverse and plausible futures and Image resolution**. The image ablations are included, thank you, although the appendix section doesn't describe the scale of evaluation (how many new towns were used?). The open-loop prediction results present quantitative evidence of the degree of plausibility of the predicted rollouts w.r.t. the action quality and the segmentation forecasting quality. As noted in your response, a measure of the diversity is more difficult. One potential metric is the average log-likelihood of different potential futures in situations known to have diverse outcomes from the expert (e.g. running the expert with different goals at an intersection with the same dynamic and static configuration). It's okay that this evidence is missing, it just means that the paper should replace \"diverse\" with \"qualitatively diverse\", altogether remove it, or dedicate a few sentences to describing the difficulties with evaluating the diversity evaluation and caveating the claims that they are qualitative.\n- **Comparison**, OK, I now understand that no high-dimensional reconstruction loss was used in that experiment. However, it should be clear from Table 2 alone that that is true (instead of a small clarification in the appendix), because that's quite a different experiment (predicting only the actions is quite different from predicting the actions and the images). Perhaps change it to \"only actions\" instead of \"no segmentation\".\n\n", " Thank you for the additional comments. The appendix has been updated in the 02/08 revision in the submission history. From the discussion above, it seems like Reviewer FfUk could see Appendix B. However if the 02/08 version still doesn’t appear for you we can try to upload the paper again, but we’re not sure whether we can do that during the discussion period ?\n\n- The section about __\"Prediction of diverse and plausible futures\"__ is on page 19-21 Appendix B.1, and the section about __\"Image resolution\"__ is on page 22-23 Appendix B.2.\n- __Comparison with “Deep Imitative Models for Flexible Inference, Planning, and Control”.__ That makes sense. Actually, since we set the image reconstruction loss to zero in our experiments (as specified in Appendix A.2 L531), the added “No segmentation” row in Table 2 is exactly what you are describing. This ablation only regresses future actions and does not reconstruct to high dimensional bird’s-eye view segmentation. We observe a decrease in both cumulative reward (7621 -> 7085) and driving score (61.1 -> 53.6). This result seems to indicate that modelling high-dimensional observations improves driving performance.\n- __Deterministic temporal baseline__: we will include a description of this baseline in the paper.\n", " Thank you for your response. I respond to your responses below:\n\n- *3D inductive bias*: The inclusion of evidence for the geometry claim is good. \n- *Prediction of diverse and plausible futures*: From what I can tell, the Appendix has not been updated. I see no Appendix Section B or B.1\n- *Comparison with “Deep Imitative Models for Flexible Inference, Planning, and Control”*: The comparison that would have satisfied my concern on this point is something that models _only_ the future actions (or positions) of the ego-agent in a model-based way. From what I can tell, there's no ablation of the high-dimensional observation targets (both $\\hat o$ and $\\hat y$ simultaneously) from the learning objective. The main difference between [A] and the proposed paper is that the learning objective includes the high-dimensional predictions, basically, both are \"Model-Based Imitation Learning for Urban Driving\", but the submitted paper presents a model of high-dimensional predictions, rather than just the low-dimensional information. Therefore, it would be very informative to run that ablation.\n- *Image resolution*: From what I can tell, the Appendix has not been updated. I see no Appendix Section B or B.2 Table 4.\n- *Deterministic temporal baseline*: Please include the exact learning objective for this baseline somewhere in the paper. It's unclear without it.", " __Evaluation method__\n\nOur evaluation method is actually not new and has been used by recent works [5-7]. It consists of evaluating the driving agent on a town never seen during training and in new weather conditions. Similarly to [5-7], the routes in the evaluation are those specified by the CARLA challenge (https://leaderboard.carla.org/get_started/). There are also advantages in this evaluation method compared to the public leaderboard:\n\n- It is possible to test generalisation capabilities. We can evaluate the model in a town never seen during training and weather conditions never seen during training. In the public leaderboard, it is standard practice to train the model on all the towns and weathers the model will be evaluated on. \n- We can have full control over the training data and sensor inputs of the model for fair comparison. Iteration speed is also much faster - submissions in the leaderboard take 80-300 hours to complete and are limited to a single model at a time (with a compute budget of 200 hours per month). In our evaluation setting, there are no restrictions in the number of models we can evaluate, and a single evaluation takes under 12 hours on a GTX 1080Ti.\n- The data collection, model training, and evaluation scripts are all available in the supplementary material, and we plan to publicly release the code. It will therefore be possible for researchers who would like to build up on this work or compare their method to ours to do so.\n\n__Supplementary__\n\n- Table A.2.3. was indeed overflowing, thank you for pointing us to this.\n\n- In Table 7 (Section B.3), the route score for 8h of training data is actually 100.0. The “1.0” was a typo due to the fact that the simulator returns the route score and infraction penalty in decimal values ([0, 1]), but it is standard practice to report these metrics in [0, 100] by multiplying by 100 for readability. \n\n[5] “Multi-Modal Fusion Transformer for End-to-End Autonomous Driving”, Prakash et al., CVPR 2021.\n\n[6] “End-to-End Urban Driving by Imitating a Reinforcement Learning Coach”, Zhang et al., ICCV 2021.\n\n[7] “Learning from All Vehicles”, Chen and Krähenbühl, CVPR 2022.\n", " ### Related Works\nParagraph looks good\n\n### No Leaderboard Submission\nThanks for clarifying, I understand the challenges of submitting to the leaderboard. \nUnfortunately this makes me a bit worried that if future works want to compare with MILE, they'll have to reproduce your experimental setting.\n\n### Supplementary\n* Table A.2.3 - table overflowing\n* Table 7 (Section B.3) - why is the route score for 8h of training data \"1.0\" and bolded?", " We thank the reviewer for pointing us to the environment prediction line of work [1-6]. We will include these in the related works.\n\n__[1-4]__ predict future static and dynamic occupancy grid maps (OGMs) from past OGMs in urban driving scenes. They frame environment prediction as a video prediction problem. The static and dynamic OGMs are obtained by processing LiDAR measurements and 3D object detections. \n\nAlthough the output space between [1-4] and our proposed approach is similar (BeV representation), there are three key differences:\n\n1. Both the inputs and outputs of their model are OGMs. This means the static scene can be predicted perfectly by simply estimating ego-motion from past inputs. The motion prediction of dynamic agents is also made easier as the vehicles are already represented in a metric BeV space. In contrast, our proposed model operates on high-dimensional camera images and has to do all the heavy lifting to reason about 3D geometry and semantics from images in order to predict BeV outputs.\n2. Their methods are deterministic, whereas our approach is probabilistic and can predict multimodal futures.\n3. They do not model ego-behaviour. We jointly predict future states and actions, and demonstrate the efficacy of the learned policy in the CARLA driving simulator. \n\n\n__[5]__ also predict future static and dynamic OGMs but use 3D LiDAR point clouds as inputs. They show preliminary results of a non-learned navigation system that can control a robot in a simulated Gazebo environment to avoid obstacles using the predicted OGMs. In comparison, our proposed model can jointly reason on future states and actions probabilistically. As shown in the supplementary video, it can predict diverse and plausible future states, consistent with predicted actions.\n\n__[6]__ focus on dynamic scene modelling in dense urban driving scenes. In addition to future occupancy maps of dynamic objects, and contrary to [1-4], they also predict future flow fields. A flow field indicates the 2D BeV velocity of each moving object. This allows them to use the chain of flow predictions to trace back the identity of detected moving objects back to the present time. The inputs of their model are: (i) past agent states (position, velocity, bounding box), (ii) road structure (points sampled uniformly along the line segments and curves), and (iii) traffic light states. These input points are placed in a BeV grid and processed with an encoder-decoder architecture to output future occupancy maps and future flow fields. However, similarly to [1-4], their approach is deterministic and does not model ego-behaviour.\n\n\n__Questions__\n\n3 - Yes, the RL expert uses BeV segmentation as input during inference, which is not the case of our camera-only model.\n\n5 - We will give a more precise description of how the infraction penalty is calculated.", " Thank you for the clarifications and the related works additions! Below are some of my follow-up thoughts.\n\n> \"While trajectory forecasting methods only model the dynamic scene, world models jointly reason on static and dynamic scenes.\" \n\nThis reasoning makes sense. In this case, I think it would be pertinent to discuss the environment prediction line of work (e.g., [1-6]) that make predictions and reason about both the static and dynamic environments.\n\n[1] Itkina, Masha, Katherine Driggs-Campbell, and Mykel J. Kochenderfer. \"Dynamic environment prediction in urban scenes using recurrent representation learning.\" 2019 IEEE Intelligent Transportation Systems Conference (ITSC). IEEE, 2019.\n\n[2] Toyungyernsub, Maneekwan, et al. \"Double-prong ConvLSTM for spatiotemporal occupancy prediction in dynamic environments.\" 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2021.\n\n[3] Lange, Bernard, Masha Itkina, and Mykel J. Kochenderfer. \"Attention Augmented ConvLSTM for Environment Prediction.\" 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2021.\n\n[4] Mohajerin, Nima, and Mohsen Rohani. \"Multi-step prediction of occupancy grid maps with recurrent neural networks.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2019.\n\n[5] Thomas, Hugues, et al. \"Learning Spatiotemporal Occupancy Grid Maps for Lifelong Navigation in Dynamic Scenes.\" 2022 International Conference on Robotics and Automation (ICRA). IEEE, 2022.\n\n[6] Mahjourian, Reza, et al. \"Occupancy flow fields for motion forecasting in autonomous driving.\" IEEE Robotics and Automation Letters 7.2 (2022): 5639-5646.\n\n1. This is good insight, thank you!\n2. Thank you! \n3. Does the RL expert use BeV segmentations during inference?\n4. Noted.\n5. This would be good to highlight in the paper for clarity.\n6. Thank you for the clarification!", " We thank the reviewer for their thorough feedback and comments. We are pleased to see they appreciated the novelty of our visual world model for urban driving, as well as how our ablations illustrate the importance of 3D geometry, semantic segmentation, and probabilistic modelling.\n\nThe reviewer’s main concern was that some claims made in the paper lacked quantitative evidence. We have updated the paper to include additional quantitative results. \n\n__3D inductive bias__\n\nWe have ablated the 3D lifting from the main method, and similarly to the single frame model, this resulted in a large performance drop as shown in Table 2. The cumulative reward decreased by 41% from 7621 to 4522. This is additional evidence that modelling 3D geometry is important for urban driving.\n\n__Prediction of diverse and plausible futures__\n\nWe have added an experiment in Appendix B.1 to evaluate the plausibility of the predicted states and actions from our model. We deployed the model in the simulator in the fully recurrent setting (i.e. the recurrent state is updated continuously with new observations and never reset). At regular intervals, we make our model “dream” and predict future states and actions without having access to new image observations, and execute those actions in the simulator. After this episode of dreaming, the model observes a few frames to update its knowledge of the world, and then dreams again. We repeat this procedure over the whole evaluation, with different dreaming time windows (see Appendix B.1 for more details).\nFigure 4 shows that our model can dream for up to 30% of the time without any performance degradation in either driving performance or segmentation prediction accuracy. This experiment quantitatively shows that MILE can predict plausible future states and actions.\n\nWe agree with the reviewer that quantitatively evaluating whether the predicted futures are diverse is an important problem. However, this task is hard as we only have access to a single future. It could be possible to do so in simulation by randomising seeds and creating different futures from the same starting point.\n\n__Comparison with “Deep Imitative Models for Flexible Inference, Planning, and Control”__\n\nOverall the approach of [A] is different because they do not model the world/environment. They inferred future trajectories of the ego-agent from expert demonstrations, and conditioned on some specified goal to perform new tasks. \n[A] models the probability distribution of actions rather than the states of the world. Our model can jointly predict static scene, dynamic scene, and ego-actions. \n\nA direct comparison is not possible without running their model. However the public implementation runs on an older version of CARLA, which makes comparison difficult. We thank the reviewer for the reference and have added this method to the related works.\n\n__Image resolution__\n\nWe evaluated the importance of image resolution by training MILE at different resolutions: 75x120, 150x240, 300x480, and 600x960 (our proposed resolution). We reported the results in Appendix B.2 Table 4 and observed a significant decrease in both driving score and cumulative reward. The performance drop is most severe in the infraction penalty metric. To get a better understanding of what is happening, we detailed in Table 5 the breakdown of the infractions. We reported the number of red lights run, the number of vehicle collisions, and the number of pedestrian collisions, all per kilometre driven. As the resolution of the image lowers, the number of infractions increases across all modalities (red lights, vehicles, and pedestrians). These results highlight the importance of high resolution images to reliably detect traffic lights, vehicles, and pedestrians. Figure 7 and 8 illustrate how traffic lights and pedestrians become much harder to distinguish in lower image resolutions.\n\n__Observation dropout and semantic segmentation labels__\n\nWe have ablated the observation dropout and semantic segmentation labels in Table 2, resulting in, respectively, a 29% and 7% decrease in cumulative reward. \n\n__Deterministic temporal baseline__\n\nIn this baseline, we have removed the probabilistic modelling. There is no longer a prior and posterior networks and a Kullback-Leibler divergence loss to match the two distributions. The temporal information is aggregated through the same recurrent neural network f. The purpose of this experiment was to investigate the effect of probabilistic modelling.\n", " We thank the reviewer for their insightful feedback and comments. We are pleased to see they found the idea of learning a world model while incorporating 3D geometry well-motivated and intuitive. We are glad they found the empirical evaluation, analysis and discussion thoughtfully constructed and convincing.\n\n__Trajectory prediction, imitation learning and world models__\n\n_“There has been lots of work in the trajectory prediction setting that builds world models in dynamic environments (e.g., [1,2]).”_\n\nTrajectory forecasting aims at estimating the future trajectories of dynamic agents using past physical states (e.g. position, velocity), and scene context (e.g. as an offline HD map). World models build a latent representation of the environment that explains the observations from the sensory inputs of the ego-agent (e.g. camera images) conditioned on their actions. While trajectory forecasting methods only model the dynamic scene, world models jointly reason on static and dynamic scenes. The future trajectories of moving agents is implicitly encoded in the learned latent representation of the world model, and could be explicitly decoded given we have access to future trajectory labels.\n\nMore importantly, trajectory forecasting methods assume access to past physical states of dynamic agents, and to scene context through an offline HD map. World models have to infer these quantities from image observations only, in order to accurately predict future states.\nFor these reasons, even though [1,2] model the dynamic environment, they cannot be considered as world models.\n\n\n_“The related works section is missing a discussion of trajectory prediction methods which are closely related to imitation learning as presented in the paper.”_\n\nWe have added a section in the related works to discuss how trajectory forecasting methods are related to imitation learning and world models.\n\n\n__Comparison with an RL baseline__\n\n_“The considered baselines do not seem to include an RL approach with access to the same input information as MILE.”_\n\n\nTo our knowledge, [3] is the only camera-based RL model evaluated on CARLA. We could not compare our model with their method as their public code repository did not have the training script, but only the inference script of a model trained on an older version of CARLA.\n\n__Typos__\n\nWe thank the reviewer for pointing out the typos, which are now corrected. We have also fully proofread the paper.\n\n__Questions__\n\n1. Labels in non-simulated settings could be obtained using a combination of manual labelling and labels from a teacher model, such as BEVFormer [4] that recently won first prize in the “Waymo Open Dataset challenge”. Teacher labels will be of high quality but not as perfect as the ones obtained from the simulator. \nIt would be possible to evaluate the effect of replacing perfect simulator labels with imperfect labels from a teacher model the following way. (i) We train a teacher BeV model on a small subset of annotated data, (ii) we label the whole dataset with the teacher, (iii) we train MILE using the teacher labels and evaluate the impact on performance.\n2. We have included a description of the “lift” operation in Appendix A.2.\n3. The RL expert used to collect expert demonstrations was trained using privileged BeV segmentation as an input to the model. Our proposed model does not assume access to BeV segmentation during inference, but only to camera inputs. The BeV labels are only used during training.\n4. See paragraph above “Comparison with an RL baseline”.\n5. Yes, higher is better for the infraction penalty. At the beginning of an evaluation run, the infraction penalty is set to 100. A multiplicative penalty is applied for each infraction. For example hitting two cars would result in an infraction penalty of 100*0.6^2=36.\n6. The exact same model was used in the two evaluation methods (reset state and fully recurrent). The difference is that in “reset state”, every time a new observation comes in, the hidden state of the world model is reset, and the whole past sequence of observations (o_1,...,o_T) has to be processed to compute the new latent state (h_T, s_T). \nIn the fully recurrent approach, the hidden state of the world model is never reset, but continuously updated in a recursive manner for each new observation. For example if a new frame o_{t+1} is observed, then the latent state [h_t, s_t] is updated using the deterministic and stochastic updates defined in L135-136. \nThe difference in inference speed comes from the fact that only a single observation is processed in the “fully recurrent” approach, whereas the whole sequence of past observations has to be processed in the “reset state” approach.\n\n\n[3] “End-to-End Model-Free Reinforcement Learning for Urban Driving using Implicit Affordances”, Toromanoff et al., CVPR 2020.\n\n[4] “BEVFormer: Learning Bird's-Eye-View Representation from Multi-Camera Images via Spatiotemporal Transformers”, Li et al., ECCV 2022.\n", " We thank the reviewer for their suggestions and comments. We are glad they appreciated how this work showed the effectiveness of world models in urban driving simulators, as well as the quality of the predicted futures.\n\n__Trajectory forecasting and word models__\n\n_“I would like to see a bit of discussion or related works on trajectory forecasting”_\n\nTrajectory forecasting aims at predicting the future positions of dynamic agents, given their past trajectory and scene context. The methods in trajectory forecasting operate on physical states (e.g. position, velocity), and scene context is given as an offline map or inferred from LiDAR inputs [1, 2, 3, 4].\n\nWorld models learn latent states that model the dynamics of the environment conditioned on the actions of the ego-agent. Both the static scene and the dynamic scene are modelled. The world model does not have access to past physical states and scene context in the form of an offline map, but only to observations from the sensory inputs of the ego-actor. It has to learn latent dynamics that explain the observations of the ego-agent. \n\nThe static scene and motion of dynamic agents is thus modelled implicitly in the latent state, but can be decoded into interpretable outputs (e.g. bird’s-eye view semantic segmentation, future trajectories of agents). Joint modelling of static scene and dynamic scene can be helpful for planning and acting. For instance, interactions between traffic lights and other dynamic agents are better modelled jointly.\n\nWe have added a section in the related works to discuss how trajectory forecasting methods are related to world models.\n\n\n\n\n__Comments__\n\n- _“Adding dataset size to Table 1 would be helpful for comparison.”_\n\nWe have added the dataset size of prior works in Appendix Table 6. We found that most recent methods (including ours) have a similar dataset size of around 20-30 hours of driving data.\n- _“It seems like a few important experiments refer solely to the supplementary”_\n\nWe have edited the paper to include more experiments from the supplementary in the main paper.\n- _“Does this work have a submission to https://leaderboard.carla.org/leaderboard/?”_\n\nThis work does not yet have a public submission on the leaderboard, but it is a task we are actively working on.\n\n__On BeV labels instead of 3D bounding boxes__\n\n_“Is there any particular reason why rasterized BEV labels were used for future prediction rather than detections (i.e. boxes)?”_\n\n- If the decoder to BeV segmentation was replaced with a decoder to 3D bounding boxes, the static and dynamic components would be decoupled (assuming there is an additional decoder for static scene). This decoupling is not advantageous since the dynamic agents’ actions are conditioned on the static scene in which they operate.\n- We chose to represent the scene in the ground plane because driving happens on the 2D road, which is an effective inductive bias for the network.\n- BeV segmentation makes the architecture simpler since it allows us to not limit the maximum number of agents in the scene and not use a recurrent-style decoder from the latent state. Instead, we simply use a convolutional network to decode to BeV.\n\n__How much data is needed?__\n\n_“How much driving data is needed for a \"good enough\" world model?”_\n\nWe investigated how performance scales with data. We trained our proposed model with a fraction of the full dataset (1/2, 1/4, 1/8, 1/16 and 1/32) and reported the results in Appendix Table 7. We observe similar performance across all metrics for a dataset size of 8 to 32 hours (which is the full training set). Performance however degrades monotonically starting from 4 hours of training data. We conclude that on the CARLA simulator, around 8 hours of data collected by our expert driver is sufficient.\n\n\n[1] “DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents”, Lee et al., CVPR 2017.\n\n[2] “PRECOG: PREdiction Conditioned On Goals in Visual Multi-Agent Settings”, Rhinehart et al., ICCV 2019.\n\n[3] \"TNT: Target-driveN Trajectory Prediction\", Zhao et al., CoRL 2020. \n\n[4] \"Trajectron++: Dynamically-Feasible Trajectory Forecasting with Heterogeneous Data\", Salzmann et al., ECCV 2020.", " This work develops an model-based imitation learning pipeline for autonomous driving.\nTheir observation network encodes multi-view camera images and route information into a latent embedding which is then used in a variational generative model to predict future BEV semantic segmentation and expert actions.\nTo my knowledge, this is the first work to show the effectiveness of world models in autonomous driving simulators. ### Strengths\n* Clear writing, technical portion + model architecture easy to understand, since this work seems like FIERY but instead predicts driving actions.\n* Their model, which uses cameras only, shows significant improvements over even lidar-based methods.\n* Supplementary video shows fairly good short-term predictions.\n* I agree with and am glad to see the discussion of driving score - the score is definitely biased towards certain types of routes and adding the reward/normalized reward as another source of quantitative evaluation is useful.\n\n### Weaknesses\n* The architecture figure looks more complicated than the architecture actually is. I would suggest adding a simpler toy figure in place of Figure 1, moving the current figure to the technical section.\n* I would like to see a bit of discussion or related works on trajectory forecasting. It would be beneficial to discuss some of the difference between world models and trajectory forecasting since there are many recurring themes between these two areas.\n* Adding dataset size to Table 1 would be helpful for comparison.\n* It seems like a few important experiments refer solely to the supplementary - I'd suggest some spacing edits to try to fit these into the main paper. * Does this work have a submission to https://leaderboard.carla.org/leaderboard/? This is important to my final rating.\n* Related to the trajectory forecasting point - is there any particular reason why rasterized BEV labels were used for future prediction rather than detections (i.e. boxes)?\n* BEV labels would require auto-labeling or human annotations - how much driving data is needed for a \"good enough\" world model? yes", " The paper presents an offline imitation learning approach that simultaneously predicts the evolution of the environment and imitates the expert driver. The proposed approach uses camera-based observations and a semantic segmentation map to build a world representation. The camera images are lifted to 3D and combined into a BeV representation. The environment evolution is performed in a compact latent space. The proposed method achieves better performance and generalization than prior work on a CARLA benchmark. Strengths:\n* The paper is well written and the ideas are easy to follow.\n* The problem is well-motivated and the literature review does a good job at contextualizing the paper in prior work.\n* The idea behind end-to-end feature learning, while incorporating geometric bias is intuitive.\n* Overall, the empirical evaluation of the method is extensive and convincing. The analysis and discussion is thoughtfully constructed, and the different components of the architecture were thoroughly ablated.\n* The figures are informative and effectively illustrate the proposed approach and results.\n\nWeaknesses:\n* The sentence in the abstract is a bit strong 'So far, such world models have been shown to be highly effective at solving games, but only in simple visual environments with little interaction among agents.'. There has been lots of work in the trajectory prediction setting that builds world models in dynamic environments (e.g., [1,2]).\n* The related works section is missing a discussion of trajectory prediction methods which are closely related to imitation learning as presented in the paper.\n* One of the motivations for the imitation learning approach over RL is the difficulty in constructing rewards. However, in the evaluation, the most effective metric is determined to be cumulative reward. The considered baselines do not seem to include an RL approach with access to the same input information as MILE.\n\n[1] Zhao, Hang, et al. \"TNT: Target-driven Trajectory Prediction.\" Conference on Robot Learning. PMLR, 2021.\n[2] Salzmann, Tim, et al. \"Trajectron++: Dynamically-feasible trajectory forecasting with heterogeneous data.\" European Conference on Computer Vision. Springer, Cham, 2020.\n\nThe paper needs to be proofread for typos. The following is a non-exhaustive list of the typos I found:\n\n1. The BeV acronym is defined in line 30, but not consistently used after that.\n2. Line 106: 'a the full description' should read 'the full description'.\n3. Line 168: 'indicating the agent where to navigate' should read 'indicating to the agent where to navigate'.\n4. Line 234: 'as it obtained' should read 'as it is obtained'.\n5. The references should be proofread (e.g., to ensure the year is not entered twice in a citation, the conference venue is listed instead of ArXiv when available, etc.). In addition to addressing the above listed weaknesses, I have the following questions for the authors. Assuming these questions and concerns are addressed, I am currently inclined to raise the score to an accept.\n\n1. How would the BeV semantic segmentation labels be achieved without LiDAR in a non-simulated setting?\n2. What is the explicit definition of the lift operation in line 157?\n3. In lines 209 and 210, it is stated that the RL expert was trained using privileged information (e.g., BeV semantic segmentation). However, my understanding was that the proposed model is also trained on BeV semantic segmentation. What is the privileged information available to the RL expert, but not the proposed model?\n4. Are any of the considered baselines RL agents outside the expert? One of the motivations behind the proposed method is the ability to avoid constructing a reward. However, the cumulative reward is a key metric of evaluation for the proposed method, thus a comparison to an RL agent trained with this reward while having access to the same input information as MILE would be worthwhile.\n5. Is higher better for the infraction penalty?\n6. What makes the recurrent approach faster in Sec. 5.4? Were the models for the two evaluation methods trained differently? The authors have listed some limitations as part of future work. Some potential additional limitations to include are: imitation learning methods can be subject to adversarial attacks and the model does not have safety guarantees.", " This paper proposes a predictive model of visual data for the task of imitation learning in CARLA. The model is trained to forecast RGB images, semantic segmentation images, and expert actions in the variational inference framework. The proposed method incorporates several new components, including a 3D geometry inductive bias that leverages camera intrinsics and extrinsics, as well as a variation on training called “observation dropout”. Experiments illustrate the effectiveness of the proposed approach on several towns in CARLA, relative to other recent approaches. The proposed approach is overall the most performant. Ablations also illustrate the importance of the 3D inductive bias in the single frame prediction setting, the importance of multi-frame prediction, the importance of the semantic segmentation modeling, and the importance of stochasticity. # Strengths\n- The presents the first evaluation of a visual world model on the task of offline imitation learning for urban driving in simulation\n- The paper demonstrates compelling performance results of the main method\n- The paper presents an interesting approach for “lifting” the representation into 3D using the camera intrinsics and extrinsics was incorporated into the model.
\n\n# Weaknesses\nOverall, there are many proposed components and claims of the method that lack quantitative evidence.\n\n- In the main claims of the introduction, L35 claims that the method “scales … by leveraging 3D geometry as an inductive bias”. However, the 3D inductive bias was not ablated from the main method (only from the single-frame prediction). Therefore, the claim has no evidence. Quantitative proof of this claim is needed in order me to agree with the inclusion of this claim, and thus I must weaken my evaluation of the paper's soundness and contributions.\n- In the main claims of the introduction, L59 claims that “Our model predicts a distribution of diverse and plausible futures that can be decoded”. However, there is no quantitative evaluation on the diversity or the plausibility of the forecasted futures. This claim also appears in the conclusion. Quantitative proof of this claim is needed in order me to agree with the inclusion of this claim, and thus I must weaken my evaluation of the paper's soundness and contributions.\n- A missing point of comparison is an existing model-based imitation learning approach that has been applied to CARLA [A]. This approach models only the future positional trajectory of the ego-vehicle. Although it would require a bit of experimentation, it would be informative to compare against it, or something like it, that purely models the future motion of the ego-vehicle, as opposed to the entire image. I suspect the current approach might perform quite well just by modeling the future positions, as opposed to the future semantic segmentation and RGB observations. I would at least like to see the proposed approach evaluated against itself when just trained to forecast the future positions of the vehicle.\n- L100 The high resolution input is quite interesting, but it was not ablated (relative to the standard Dreamer model, which uses 64x64x3 images). The evaluation would be improved if a comparison to simply resizing the larger dimension of the input image to be 64 and running that as a comparison. This would enable us to understand the effect of using a higher resolution image. It is possible there is no effect, or that there is a significant effect. The results are important and relevant in either case.\n- “Observation dropout” in S3.5 was a new method that was proposed but not ablated. The proposed approach should ablate this proposed component in order to highlight its efficacy.\n- The ablation of the semantic segmentation targets for the main method is missing. The conclusion mentions “another exciting avenue is self-supervision in order to relax the dependency on the bird’s-eye view segmentation labels”. However, this should have been already investigated by simply removing this supervision from the main model and investigating its effect.\n\n## Post-rebuttal update\nThe weaknesses I described were more-or-less addressed in the revised version and the authors' responses. \n\n[A] Deep Imitative Models for Flexible Inference, Planning, and Control, ICLR 2020. https://openreview.net/forum?id=Skl4mRNYDr\n Aside from addressing the main points in the weaknesses (the two regarding the 'main claims' are the most important)\n\n- The “deterministic temporal” baseline needs more explanation. Is it using the same architecture? What is the precise training objective? No, there is no clear \"limitations\" section. The paper requires some discussion of limitations relative to (a) scalability w.r.t. availability of training data (b) feasibility w.r.t. existing model-free imitation learning methods, among others." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 7, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 3, 4 ]

[ "78SDO689yZ-", "S9-4xxO3nWC", "Cus5jFCq4g-", "yu4PIur3o7C", "LfnRz9JQuJ8", "yGSKYtZJF2V", "D5IoKk3FvYy", "HstKp2gbBx", "4NmaW94cdwi", "1-cSaYl7JhN", "yJFla3eoT8D", "nips_2022_Zk1SbbdZwS", "nips_2022_Zk1SbbdZwS", "nips_2022_Zk1SbbdZwS" ]

[ "9yr2kl4am0L", "Jif9NygUN3p", "YAdHHLw7kG_", "XSjwVfUckYo", "J_qVE1RrTq6", "8UNbYB8J2z", "Jw6aTZ6qBFDx", "YiVsKoQK5PO", "magoZYwGwlP", "uzOlryqTcR-", "r0XtbfdqFum", "PM3oDztoQJ_", "On4k4-3Y2zb" ]

[ "author", "official_reviewer", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We thank the reviewer for the positive feedback. We will, for sure, include all the clarifications and the additional experiments in our paper.", " I would like thank the authors for their hard work to address my comments (including performing additional experiments). After reading authors' response as well as other reviews + responses, I would like to change my decision to weak accept. \nI would strongly recommend the authors to include all the clarifications and the additional experiments in the main paper (e.g., I have not seen KPConv experiment in the paper).", " We would like to thank the reviewer for the positive feedback, and for the follow-up comments, which we address below.\n\n**Q1**. We will, for sure, clarify the incorporation of area elements in our paper to avoid misunderstanding. We thank the reviewer for the careful check and the suggestion on the writing.\n\n**Q2**. We indeed compute the eigendecomposition of the Laplacian matrix $\\mathbf{L}$ at the highest resolution (say, $k$). The resulting $k$ eigenfunctions are ordered by the corresponding eigenvalues. For a functional map of resolution $i \\times i$, where $i < k$, we directly reuse the first $i$ eigenfunctions in the computation. We will make this point clear in the paper.", " I want to thank the authors for their extensive replies.\n\nQ1: Good to know that you do take area elements into account, but it could be made clearer in the text (I did double check before posting and couldn't find any explicit reference and several places that lead to the misunderstanding)\n\nQ2: How do you compute only one decomposition and use it at all scales? do you compute it only at the highest resolution and use that for all scales assuming the implicit mapping given by the uspcaling? If so, again it is not very clear from the text.\n", " We would like to thank the reviewer for the positive feedback, and for the follow-up comments, which we address below.\n\n**Q6-1.** Attention analysis.\n\nWe fully agree with the reviewer that the attention analysis is a crucial aspect of our work. We will, for sure, clarify and expand the discussion on this in our paper. We thank the reviewer for the suggestion on the writing.\n\n**Q6-2.** The independent experiment w.r.t ZoomOut.\n\nAs suggested by the reviewer, we include the results of directly using the initial 200X200 functional map, labeled as id-3 in the table below (id-1 and id-2 are reported in a consistent way as in our previous response). We observe that id-3 has slightly better performance on FAUST and SCAPE consisting of near-isometric shapes, but it has significantly worse performance on SHREC'19 and SMAL, which are composed of non-isometric shapes never seen during descriptor training. We remark that the descriptors in this experiment are extracted by the same feature extractor as in Ours-Fast model trained in the supervised setting. Nevertheless, the result also echoes our attention analysis (**Q1**) and the utility of data-driven choice for spectral resolution.\n\n| id | FAUST | SCAPE | SHREC'19 | SMAL |\n|---|---|---|---|---|\n| 1. | 1.8 | 2.4 | 7.2 | 5.9 |\n| 2. | 1.8 | 2.4 | 6.9 | 6.1 |\n| 3. | 1.3 | 1.8 | 9.1 | 8.3 |\n\n**Q6-3.** Comparison with Trappolini et al.\n\nThank you for the remark. We agree that comparing methods designed for different scenarios is not always straightforward. For fairness, we will provide in our paper, a fully detailed description on the training data size and input data type for the method by Trappolini et al.\n\nTo clarify, for the comparison in the table of **Q5-4**, we obtained the results of the method by Trappolini et al. by initializing their network with their released trained weights and then fine-tuning on our used benchmarks. In our experiments, the results obtained by training their network from scratch on our used benchmarks (which are much smaller-scale than considered in that work) were not competitive. For the pre-trained weights, as mentioned in their paper, Trappolini et al. trained their network on the SURREAL dataset consisting of 10,000 shapes. Note that we do not pre-train our network on SURREAL, and we train from scratch on each dataset. We will make these points clear in our paper, and will be happy to include additional comparisons, if deemed appropriate by the reviewer.\n", " Thanks to the authors for clarifying my previous doubts.\nI just have a few more questions/consideration I would like to be addressed:\n1 - I think the attention analysis is a crucial aspect of the analysis, I have to admit that I somehow missed it. Nevertheless, I would expand a bit its discussion on the main paper (and adjust the font size in fig 3).\n2 - It is interesting (and somehow unexpected) your analysis of the ZoomOut upsampling. To better understand the analysis, it would be useful to show also the correspondence results directly using the 200x200 original FM.\n3 - For the comparison with Trappolini et al., it would be fair to mention that you are putting yourself in the best conditions for your method (as you already noted, a small training set using the original architecture thought for a much larger training set). Further, Trappolini et al., similarly to 3D-CODED, work on PC and do not require connectivity as input.", " We would like to thank the reviewer for the constructive comments and acknowledging that\n1. The proposed method learns the soft thresholding weights to combine functional maps obtained from matching at different spectral resolutions, which allows the network to optimize the spectral resolution.\n2. Extensive experiments show the effectiveness of the combination on various benchmarks, on which it achieves state-of-the-art or comparable performance.\n\nBelow we respond to the specific comments raised by the reviewer in detail.\n\n**Q1. Technical novelty.**\n\nWe agree that intuitively a learned combination of weights should work better. Please note, however, that in order to enable this, we had to introduce multiple novel contributions such as, in-network spectral upsampling, which allows to compare and combine different spectral resolution functional maps. Furthermore, predicting the attention weights from the residuals of spectral alignment is also novel, and has not been considered before, to the best of our knowledge. All of these novel components are important for the performance and accuracy of our approach. Our technical contributions are appreciated by the reviewers **PHU8** and **6wTY**, who find our proposal sound and interesting.\n\n**Q2. Generality with other architectures.**\n\nWe thank the reviewer for the suggestion. To demonstrate the generality of our approach, we performed a quick test replacing DiffusionNet (Fig. 2) with KPConv, which is another advanced feature extraction backbone, with supervised training. The table below shows that our method brings consistent improvement across different architectures in various testing settings, including the generalization stress-test on SHREC'19 and SMAL consisting of non-isometric shape pairs and unseen shape classes. Thus our approach is generic and *not* an extension of one specific approach.\n\n| Train on / Test on | FAUST+SCAPE / FAUST | FAUST+SCAPE / SCAPE | FAUST+SCAPE / SHREC'19 | SMAL / SMAL |\n|---|---|---|---|---|\n| GeomFmaps + DiffusionNet | 2.6 | 2.9 | 7.9 | 8.4 |\n| Ours-Fast + DiffusionNet | **1.3** | **1.8** | **7.1** | **5.8** |\n| GeomFmaps + KPConv | 2.7 | 6.6 | 13.3 | 9.4 |\n| Ours-Fast + KPConv | 1.4 | 5.5 | 8.1 | 6.8 |\n\nReferences:\n\nH. Thomas, et al. \"*KPConv: Flexible and deformable convolution for point clouds.*\" ICCV 2019.\n\n**Q3. Ours-Fast results.**\n\nWhile this behavior can indeed be counter-intuitive, we attribute it partly to the fact that Ours-FAST avoids solving many linear systems inside the network. While the full method (Ours) is more principled, it also relies on solving $k$ linear systems with differentiable matrix inversion for *each* intermediate functional map. Numerically this can lead to more instabilities, especially at the early training stage when descriptors are not fully trained. While Ours-FAST leverages principal submatrices to simplify the computation, we have the loss $L_{inter}$ to supervise all the intermediate functional maps at training time to ensure approximation accuracy (Sec. 4.3). Comparatively the full method can be more prone to numerical issues, which ultimately can lead to a drop in performance in certain cases.\n\n**Q4. Partial shapes.**\n\nOur work does not have an explicit component for overlap mask prediction between partial shapes, which needs to be considered in partial functional correspondence [24,10]. The Laplacian basis used in the functional map framework [13] has global support. When shapes are partially overlapped, a direct application of the functional map framework would not produce reasonable results, and special architecture designs like [10] are required for the overlap mask prediction. While this is possible, it is orthogonal to the scope of our work. We also remark that in [10], attention is learned in the feature domain. In contrast, our work learns attention in the spectral domain for functional maps, which has not been studied in existing literature. \n\nWe hope to have addressed the reviewer's concerns in detail and would thus kindly ask the reviewer to reconsider their rating.", " **Q5. Minor issues.**\n\n**Q5-1.** Point-wise correspondence computation.\n\nTo compute the point-wise correspondences from a functional map $\\mathbf{C}$, we perform nearest neighbor search between the aligned spectral embeddings $\\Phi_{1}\\mathbf{C}^{\\top}$ and $\\Phi_{2}$, as mentioned in L153. We note that we did *not* perform any post-refinement for the results of our method (Tab. 1, 2, and 3).\n\n**Q5-2.** Reference of deep functional map.\n\nWe will add references to the deep functional map works, including [7,8,9,5], in Sec. 3. \n\n**Q5-3.** The ablation of $\\tau$.\n\nThe reviewer's understanding of the ablation of $\\tau$ is correct. We mean that $\\tau=10$ is a balanced choice for both Ours-Fast and Ours to produce good performance. We will fix the misused words.\n\n**Q5-4.** Comparison with other methods.\n\nWe will clarify the input data types of the compared methods. Specifically, 3D-CODED [53] works on point clouds but requires a template, and the other methods use meshes in the benchmarks.\n\nIn the table below, we compare our work with the recent transformer-based method by Trappolini et al in the supervised setting. Our method has significantly better performance. In particular, this transformer-based method struggles on SCAPE and SHREC'19, which have more challenging human poses, and on SMAL, which stress-tests generalization to unseen shape classes. Besides, the small-scale training sets in these benchmarks may also pose challenges to this transformer-based method that requires voluminous training data. In contrast, our method works well with limited training data.\n\n| Train on / Test on | FAUST+SCAPE / FAUST | FAUST+SCAPE / SCAPE | FAUST+SCAPE / SHREC'19 | SMAL / SMAL |\n|---|---|---|---|---|\n| Trappolini et al. 2021 | 2.7 | 18.6 | 16.7 | 26.1 |\n| Trappolini et al. 2021 + Refinement | 1.6 | 11.7 | 10.9 | 23.7 |\n| Ours-Fast | **1.3** | **1.8** | 7.1 | 5.8 |\n| Ours | **1.3** | **1.8** | **6.2** | **5.3** |\n", " We would like to thank the reviewer for the constructive comments and acknowledging that\n1. The paper proposes a neural network architecture that exploits multi-resolution functional maps to predict a pointwise correspondence between two shapes.\n2. The proposed data-driven approach is for sure an interesting solution to address the choice of suitable size of the truncated eigenbasis, a common problem in functional map-based methods.\n3. The method is validated on common 3D non-rigid datasets composed of humanoid and animal shapes.\n\nBelow we respond to the specific comments raised by the reviewer in detail.\n\n**Q1. Attention score analysis.**\n\nPlease note that we have provided analysis on the obtained attention scores in Sec. 5.3 (L330), in Fig. 3-rightmost of the paper, and in Fig. 5-rightmost of the supplementary material. The plots of the learned spectral attention show that, for near-isometric (intra-class) shape pairs, the network puts most of the weights on functional maps of resolution in [150, 200]; while for more difficult non-isometric (inter-class) shape pairs, the network assigns more weights to functional maps of resolution in [50, 150]. For the non-isometric case, this suggests that the smaller functional maps are more reliable and can be more accurately estimated than the larger ones. In contrast, for near-isometric shapes, higher-resolution maps can be estimated directly (and thus, lower-resolution ones as well, since those are given as principal submatrices of the larger functional maps). These results highlight the necessity of making the spectral resolution decision in a data-dependent manner, and our work presents the first study and an effective solution for this problem.\n\n**Q2. Fast version of the network.**\n\nThe upsampled functional maps indeed improve the final result in the fast version of the network. As shown in Fig. 5-rightmost of the supplementary material, the fast version of the network learns to put attention weights on lower-resolution maps, especially in the inter-class setting. We remark that in Fig. 5, the text label \"Ours\" should be \"*Ours-Fast*\", and we will fix this typo in the final version. For the principal submatrices, we stress that, in addition to refinement by the upsampling strategy, they are also supervised by the $L_{inter}$ loss. Please refer to our response to **Q3** below.\n\nWe performed an independent experiment w.r.t ZoomOut, according to the suggestion. Specifically, given a pair of shapes with extracted descriptors and the FMReg solver [5], we test the following two settings individually:\n1. Compute an initial functional map of size 30X30 and then use ZoomOut to upsample it to a map of 200X200 as output.\n2. Compute an initial functional map of size 200X200, take the principal submatrix of size 30X30, and then use ZoomOut to upsample it to a map of 200X200 as output.\n\nThe table below shows that these two strategies lead to comparable results, further confirming the effectiveness of our principal submatrix-based idea.\n\n| id | FAUST | SCAPE | SHREC'19 | SMAL |\n|---|---|---|---|---|\n| 1. | 1.8 | 2.4 | 7.2 | 5.9 |\n| 2. | 1.8 | 2.4 | 6.9 | 6.1 |\n\nFinally, we stress that our method does *not* rely on the original ZoomOut method for post-refinement. Our differentiable spectral upsampling is an integral component of our network learning, and what is more important is that we apply it consistently in both training and testing stages.\n\n**Q3. $L_{inter}$ loss.**\n\n$L_{inter}$ is applied to *all* intermediate multi-resolution functional maps {$\\mathbf{C}^{i}$} in both the fast and normal versions of the network, as shown in Eq. (6). The ablation study in Tab. 3 (Full model vs. w/o $L_{inter}$) shows that imposing $L_{inter}$ can help the network to produce better intermediate functional maps, which significantly improves the accuracy of the final output map. The results also show that $L_{inter}$ has similar effects on both Ours-Fast and Ours.\n\n**Q4. Implementation details.**\n\nWe kindly refer the reviewer to the supplementary material (Sec. A & B) for more implementation details. We will be happy to provide clarifications on the implementation if requested. We will also make our code and data publicly available upon publication, to ensure full reproducibility of our work.", " We would like to thank the reviewer for the constructive comments and acknowledging that\n1. The multi-resolution functional map representation is sound and interesting, and the spectral attention mechanism provides a smart data-driven way to select the resolutions.\n2. The approach can work both in the supervised and unsupervised settings.\n\nBelow we respond to the specific comments raised by the reviewer in detail.\n\n**Q1. Shape sampling.**\n\nWe clarify that our approach does *not* assume uniform sampling of the input shapes. \n\nFirst, we have taken into account the area elements of vertices of the input shape in the spectral decomposition of the Laplace-Beltrami operator (Sec. 3). Specifically, we follow the standard practice in existing literature to represent the Laplace-Beltrami operator as an $n \\times n$ matrix $\\mathbf{L} = \\mathbf{S}^{-1} \\mathbf{W}$. Here $\\mathbf{S}$ is the diagonal matrix of lumped area elements for the $n$ vertices, and $\\mathbf{W}$ is the cotangent weight matrix.\n\nSecond, we use DiffusionNet [14] as the feature backbone, which also takes into account the area elements and is agnostic to varying mesh samplings.\n\nTherefore our approach is adaptive to non-uniform sampling by design. We will make these points clear in the paper.\n\n**Q2. Limitations of spectral decomposition.**\n\nWe agree with the reviewer that the eigenfunctions of the Laplace-Beltrami operator, used in the classical functional map framework [13] and our work, are known to have certain limitations, such as lacking locality and being less robust to partiality and topological changes. In this way, we inherit the limitations of the works that we build upon, such as [5,7,9,8], etc.\n\nPlease note, however, that the functional map framework in itself does not rely on a specific spectral basis. Thus regarding locality, our method can potentially be extended to other spectral bases that have more local support, such as the Compressed Manifold Modes proposed by T. Neumann et al., which are independent of mesh sampling and would be an interesting avenue for future work.\n\nWe also clarify that our method does *not* need to compute multiple spectral decompositions. Indeed, for an input shape, we perform only a one-time eigendecomposition of the Laplacian matrix $\\mathbf{L}$ defined above and take the first $k$ eigenfunctions, where $k$ corresponds to the *largest* functional map size (Sec. 4.1). These $k$ eigenfunctions are reused in the computation of multi-resolution functional maps (Sec. 4.1). Thus our method is *not more* affected by the above limitations than other spectral approaches. \n\nNevertheless, we followed the evaluation protocols of existing non-rigid shape matching works [13,55,7,5,9], and our experiments (Tab. 1 & 2) show that our method robustly handles near-isometric and non-isometric shapes and generalizes well to unseen shape classes.\n\nReferences:\n\nT. Neumann, et al. \"*Compressed manifold modes for mesh processing.*\" CGF 2014.\n\n**Q3. Map supervision.**\n\nIn the supervised setting, the ground-truth functional map can be obtained by projecting the ground-truth point-to-point map onto the reduced spectral basis. Note that a functional map of size $k \\times k$ is fully determined by $k$ pointwise correspondences, i.e., a small number of precise landmarks on each shape. Such ground-truth labelings are readily available in the benchmarks tested in Sec. 5 and have been used in existing supervised methods [5,7]. The experiments (Sec. 5) show that our method can work well in the supervised setting in practice.\n\nNevertheless, we agree that the unsupervised version of our method is particularly interesting as it can be applied in settings without any explicit supervision.", " The manuscript introduces shape matching framework based on multi-resolution functional maps. the idea is that the Laplace-Beltrami operators and their spectra are computed for shapes at various resolution, and for each resolution the corresponding functional map is computed. In order to make eigenfunctions and functional maps at various resolution comparable, a spectral upscaling scheme is adopted.\nWith he functional maps to hand, an attention mechanism based on mapped-point residual is adopted. The output of the attention network is a set of weight used to linearly combine the the maps. The addition of the multi-resolution aspect o functional maps is sound and interesting, and the attention mechanism provides a smart data-driven way to select the resolutions. However, what it lacks is locality: different scales can behave differently in different regions of the shape, especially in conjunction to non-uniform sampling.\n\nI quite like the fact that the approach can work both in a supervised and unsupervised setting, but I believe that a supervised setting where the map is known is a bit unrealistic. Perhaps a setting where known corresponding functions over the two shapes are given would form a better use-case (incidentally, that was the original use-case for functional maps). Does the approach assume uniform (possibly unequal) sampling of the shapes? I see no indication of the use of the area elements in the spectral decomposition and the multi-resolution approach would probably need to adapt to non-uniform sampling.\n\n I believe that the negative societal impacts have been assessed correctly. As for Limitations, the performance issue with spectral decomposition is common to all spectral approaches, but they also incur other, arguably more severe limitations regarding their robustness to noise, extreme partiality, and topological deformation. That being said, the present proposal is affected by those limitations more than other spectral approaches because it needs to compute multiple spectral decomposition (one per scale) and then perform the upscaling since in the end it needs to work at the highest resolution.", " The paper proposes a neural network architecture that exploits multi-resolution functional maps to predict a pointwise correspondence between two shapes. The architecture is composed of two blocks. The first block follows the idea of Deep Functional Maps (REF) and consists of multiple networks each predicting a functional map at a different resolution. The second block takes as input these functional maps and the residual (i.e. the eigenbases alignment error per each point of the two shapes) and computes an attention score with which to derive the final functional map as a weighted sum of all the functional maps. To make it possible to sum the maps at different resolutions, the authors propose to adopt a differentiable upsampling scheme inspired by ZoomOut. The method is validated on common 3D non-rigid datasets composed of humanoid and animal shapes. The paper addresses a common problem in the design and application of Functional Map-based methods, which consists of the choice of suitable size of the truncated eigenbasis for the problem at hand. The proposed data-driven approach is for sure an interesting solution. \n\nUnfortunately, an analysis of the obtained attention scores in different scenarios (e.g. near-isometric vs non-isometric) is missing and would have been a strong contribution to the paper. Indeed, as a motivation for this work, the authors suggest that few basis functions are prefered for highly non-isometric shapes while near-isometric shapes can benefit from the use of a wider eigenbasis that includes also higher frequencies. Even if this sounds like a reasonable premise, there isn’t any analysis supporting this claim.\n\nAs a last note, I found the paper generally well written, but some details on the method implementation are missing, or at least not perfectly clear.\n I’m a bit confused about the use of this attention scheme with the fast version of the network, where lower resolutions are derived as submatrices. In this case, it seems to me that the only difference between the different resolution FMs is given solely by the upsampling strategy. Are the upsampled matrices improving the final result or is most of the attention put on the larger FM? If for ZoomOut it is reasonable that, with few corresponding functions, solving for a smaller optimization problem and then upsampling can lead to better results, in this case, the method solves the least-square problem for the wider basis-function and then takes a submatrix. It is not obvious to me that this leads to the same result.\n\nAlso, following the previous point, is L_{inter} for the fast version computed only for the wider FM? If so, why the huge difference in tab 3?\n\nMinor:\n- Maybe I missed it in the paper, but how are the point-wise correspondences computed?\n- Description of deep functional map refers to a course. Isn’t there any reference to the original paper proposing this method?\n- I’m also not sure of understanding the ablation of \\tau. In tab 3 results with 5 and 20 are reported, while the full model should use 10, justifying this choice as a trade-off between speed and performance. Looking at the results I do not see this trend, in fact, both 5 and 20 are way worse than the Full model (with tau=10). Am I missing something?\n- In the comparison with other methods, it is worth mentioning which kind of date each method works. Some of the methods take as input point clouds, while the proposed method requires triangular meshes (at least in the shown experiments). Also, even if not critical, it would be worth adding recent SOTA methods for shape registration with transformers (Trappolini et al., Shape registration in the time of transformers, NeurIPS 2021).\n The paper clearly states the main limitations of the proposed approach, including the need for triangled meshes and the lack of experiments on partial ones. (eg. SHREC’16: Partial matching of deformable shapes, Matching deformable objects in clutter)", " The paper proposes a learning-based framework for non-rigid shape matching by building upon the functional map representation, and especially its learning-based variant GeomFmaps. The major contribution of the paper is learning the soft thresholding weights to combine functional maps obtained from matching at different spectral resolutions, which allows the network to optimize the spectral resolution. The paper illustrates the effectiveness of the combination on various benchmarks, on which it achieves state-of-the-art or comparable performance. Strengths:\nExtensive experiments and state-of-the-art performance - the authors perform evaluations on widely adopted human shape matching datasets such as FAUST and SCAPE and a non-isometric dataset SHREC’19. Table 1 shows that on these datasets the paper outperforms the GeoFmaps (the method extended in this paper) and also outperforms all the other methods (presented), with a few exceptions. \nThe authors further evaluate on an animal shape matching dataset SMAL and show (Table 2) considerable improvement on GeomFmaps (e.g., in supervised setting: 5.3 vs. 8.4 mean geodesic error X 100) and DeepShells (unsupervised setting 5.3 vs. 29.3 ). Additional evaluation is provided on the challenging humanoid shape dataset from DeformingThings4D for both near-isometric and\nhighly non-isometric correspondence. The authors show improved performance intra-class in supervised setting and intra and inter- class in unsupervised setting (Table 2). The authors also provide an ablation study Table 3, that shows the importance of learned spectral attention (linear combination weights of the functional maps).\n\n\nWeaknesses:\n1) Limited novelty of the idea: lines (54 - 57) \"Finally, to train our network, we propose to impose penalties on the intermediate multi-resolution functional maps as well as the final map. This is different from existing approaches [7, 9, 5, 10], to name a few, that penalize a single hand-picked spectral resolution\" --Essentially the only novelty of this paper is learning of the soft-thresholding of the / best weighted combination of functional maps obtained from matching at different spectral resolutions. While the benefit to the performance is substantial, the idea is not essentially novel (it makes sense that a learned combination of weights would work better).\n2) Extension of an existing work: The authors claim that their method is generic enough to directly benefit from other advances in deep functional map training, such as improved architectures or regularization. Note that this claim seems reasonable based on the architecture introduced in Figure 2 (the blue block can be probably replaced with a different architecture), however it is not supported by experiments. This makes their work seem like an extensions of one specific approach. \n3) There is little deep dive into the results, for example the authors do not elaborate on why the more efficient technique named \"Ours-FAST\" sometimes outperforms \"Ours\", which is not intuitive. The authors only say lines 293 - 295: \"Besides, the fast version of our method gives almost the same results as the complete approach, and even better results in some cases. This underlines the fact that the approximation made in this version of our model works well in practice.\". There is no insight as to why this happens. 1) line 47 - \"our framework consists **in** two novel..\" -- Did you mean \"consists in\" or \"consists of\"? \n2) \"Shape 40 in SHREC’19 is a partial shape and removed from the dataset, since it is outside the scope of this work\" - it is not clear why partial shape is out of scope of this work, please explain (line 123 actually mentions that attention has been previously applied to partial shape matching) \n3) Please explain why the fast method yields improved results in many cases (Tables 1 and 2). To the best of my understanding there is no negative societal impact to the paper. The authors mention human surveillance, which does not seem to be a direct application of the shape matching.\nOtherwise the authors discuss general limitations - computationally non-efficient computation of spectral decomposition for each input shape. (lines 360 - 363 \"While the pre-computation is efficient for moderately sized shapes, down-sampling or remeshing may be needed for large-size input\"). " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 7, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 4 ]

[ "Jif9NygUN3p", "Jw6aTZ6qBFDx", "XSjwVfUckYo", "uzOlryqTcR-", "8UNbYB8J2z", "YiVsKoQK5PO", "On4k4-3Y2zb", "magoZYwGwlP", "PM3oDztoQJ_", "r0XtbfdqFum", "nips_2022_2EwEWrNADpT", "nips_2022_2EwEWrNADpT", "nips_2022_2EwEWrNADpT" ]

[ "uiXX1Tysm4", "lZuEbZxdsdM", "6Zx9D0g6hxQ", "c0dzrDsKDabk", "vpxEq7O9IBH", "VySn_DM_qj3", "5xWzcTZVB9q", "AEX3uX3wU87", "SMOEh_fQxk", "JMaXyxyiibv", "OSLHuaIcuO6", "DJ_59eLceC9" ]

[ "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for your efforts on the additional experiments and detailed response. They have resolved most of my concerns. Therefore, I will increase my rating to 6. Great work :)", " We really appreciate your positive comments, which means a lot to us!\\\nWe will definitely follow all reviewers' comments to improve our work and keep up explorations in the community!", " Thank you for the metric explanation, and sorry for the lack of familiarity with them. A short explanation is enough and greatly appreciated to avoid going through another link for a quick understanding. So thank you for considering adding it to the revised paper. \nThe failure case added to the supplementary material is very informative and really encapsulates the grouping mechanism problem. Looking forward for future work to see how to handle such cases.\n\nThank you for the information and performance comparisons. It really shows the benefits of the authors method!\n\nFor the shorted range and KITTI comparison, the modified table is really informative and appreciated. Of course, the time limit doesn't allow more comparisons to be done, but the short range information still gives an idea of FSD performances. Thank you for the added information.\n\nConcerning the multi-scale grouping, these are some very interesting findings. Of course investigating the implications of modifying the grouping algorithms to perform better on pedestrians and small object, is out of the scope of the paper and would be a paper on its own. \nBut the experiment is greatly appreciated, and I am very curious to read future work on the matter. \n\nThank you again to the authors for the extra experiments and details added and explained. A very interesting paper and with a good analysis.\n\n\n", " Dear all,\\\nThanks again for the very constructive comments and spending your valuable time reading our responses!\\\nWe are open to any further discussions during the author-reviewer discussion period (Aug 2-9). ", " We really appreciate your affirmation of our work and the constructive advice.\n## Q1: Metrics and Qualitative Results.\nWe are sorry for the lack of explanation for some metrics.\nWe guess some readers may be unfamiliar with the metrics used in Argoverse 2 dataset.\nHere we provide the detailed official explanations ([link](https://github.com/argoai/av2-api/blob/main/src/av2/evaluation/detection/eval.py)).\nAnd we will make a quick explanation in the revised version as the reviewer kindly suggested.\nAs for failure cases, a common one is that two close objects are grouped together by the CCL (Sec. 3.2) if the distance threshold in CCL is not suitable, leading to a false negative.\nWe provide a rare case in the **Section C of our revised supplementary materials** for illustration. Fortunately, it could be solved with a different grouping method. \n\n\n## Q2: More Comparisons on Memory and Latency\nIt is a valuable suggestion, and we discuss this in two aspects.\n\n(1) The compared method CenterPoint is one of the most efficient SOTA methods.\nBesides, the official reported latency of top-performing PVRCNN++ is around 100ms (10 FPS), which is still slower than FSD (~ 60ms). Due to the time limit to training PVRCNN++ (no released model weights), we will make a stricter comparison in the future.\n\n(2) Almost all other SOTA methods (e.g., CenterPoint, PVRCNN++) adopt dense feature maps in their backbone, and the computational costs on dense feature maps are quadratic to the perception range.\nSo it could be expected that FSD will be more efficient than these SOTA methods in the long-range setting.\n\n## Q3: Short-range Performance\nWe appreciate this very thoughtful consideration.\nWe first humbly clarify that the range in the KITTI dataset is only a little shorter than Waymo Open Dataset ( $70m$ v.s. $75m$).\nTo resolve the reviewer's concern, we re-benchmark the performance in different range intervals with the official Waymo evaluation tool.\nAnd the performances are shown in the following table.\n\n| Method | Veh. L1 AP (0m-30m) | Veh. L1 AP (30m-50m) | Ped. L1 AP (0m-30m) | Ped. L1 AP (30m-50m) | Cyc. L1 AP (0m-30m) | Cyc. L1 AP (30m-50m) |\n| --- | --- | --- | --- | --- |--- | --- |\n| PVRCNN++(center) | 93.3 | 78.1 | 84.9 | 79.7 | 83.7 | 68.9 |\n| FSD | 93.3 | 78.4 | 87.0 | 82.6 | 86.1 | 70.9 |\n\nCompared with the top-performing PVRCNN++(center), FSD shows comparable or better performance in the shorter range.\n\n## Q4: Other Grouping Methods\nWe agree with the reviewer that adopting other grouping methods would be interesting. However, the multi-scale grouping causes overlaps between different scale, which is incompatible with our current pipeline. Due to the time limit, we follow the suggestion of the reviewer, while simplifying the multi-scale grouping to single-scale grouping (SSG). \nThe basic idea is to apply Farthest Point Sampling in voted centers and then use ball query in these sampled centers to discover the groups. The results are shown in the following table.\n\n| Method | Veh. L1 AP/APH | Veh. L2 AP/APH | Ped. L1 AP/APH | Ped. L2 AP/APH |Cyc. L1 AP/APH | Cyc. L2 AP/APH |\n| --- | --- | --- | --- | --- |--- | --- |\n| FSD (CCL, 6 epochs) | 77.3/76.9 | 69.8/69.3 | 81.4/76.0 | 73.8/68.7 | 75.8/74.5 | 73.8/72.5 |\n| FSD (SSG, 6 epochs) | 79.0/78.5 | 69.9/69.5 | 75.2/70.0 | 66.1/61.7 | 75.6/74.5 | 73.6/72.5 |\n| FSD (SSG on Veh, CCL on Ped and Cyc, 6 epochs) | 79.0/78.5 | 69.9/69.5 | 81.5/76.0 | 73.8/68.8 | 75.7/74.4 | 73.6/72.4 |\n\nThe result above is very interesting.\nSSG achieves a better performance in vehicle class.\nHowever, the performance of the pedestrian class has severe drop. We speculate that the performance drop may be caused by the improper radius of the ball query, which is sensitive in small object detection. Multi-scale grouping might alleviate this problem. We have to leave it for future work due to time limit of rebuttal.\nThen we only adopt SSG for vehicle class, then FSD achieves better overall performance (the last row).\nWe will figure out the reasons behind this phenomenon and find a better way for grouping.\nThanks again for such a constructive suggestion!", " ## Q4: Speedup with Highly-optimized Engines\nAs can be seen from Q2, the main source of latency is the commonly-used sparse encoder (backbone).\nWe believe there will be better support for sparse operations with the development of infrastructure.\nFor example, sparse matrix multiplication is supported in the recent version of TensorRT ([link](https://developer.nvidia.com/blog/accelerating-inference-with-sparsity-using-ampere-and-tensorrt/)).\n\nSome highly optimized implementations of sparse convolution are already available, like TorchSparse and Spconv2.\nWith float16 quantization, the sparse encoder could have around 45% inference speed improvement (see spconv2 [benchmark](https://github.com/traveller59/spconv/blob/master/docs/BENCHMARK.md)).\n\nNote that the costs of dynamic pooling and broadcast are very small.\nThe optimization of other parts is well explored since they are commonly used in many algorithms.\nWe are trying to deploy FSD in real-world applications and the speedup should be considerable.\n\n## Q5: SST on Argoverse 2\nOur devices (RTX 3090) can not afford the training memory consumption of SST on AV2 (See Fig. 5 in our paper).\nSo we adopt gradient checkpointing to save memory (leading to a very slow training speed).\nWe list the results in the **shared response**.\nThe accuracy of SST_center is lightly lower than CenterPoint mainly due to the poor performance on large objects (e.g., School Bus), caused by the center feature missing.", " We sincerely thank you for the very professional comments. We are inspired and hope our discussion brings more insights.\n\n\n## Q1: SIR v.s. DETR-like Head\nBefore working on FSD, we have spent much time building fully sparse detector by replacing the dense head of SST with a DETR-like sparse head. Here we share some experiences and thoughts.\n\n(1) Directly adopting existing DETR-like heads can not make the detector fully sparse because almost all of them rely on dense feature maps. For example, in Object DGCNN and TransFusion, the sparse object queries need to gather information from dense LiDAR BEV feature maps (serve as values and keys).\n\n(2) Global cross attention on the whole scene is expensive. So the mainstream transformer-based detectors (e.g., DETR3D, Object DGCNN, BEVFormer) adopt the local deformable attention instead. However, the deformable attention requires interpolation in dense feature maps. It is not a trivial thing to do efficient differentiable interpolation in the unstructured sparse voxel features.\n\n(3) Another potential way we have tried is to apply local attention between sparse queries and their sparse neighborhood features.\nHowever, this raises three problems.\n(i) Due to varied object sizes, it is non-trivial to set a suitable local attention range for each query.\n(ii) The positions of queries often vary in different layers like in the deformable attention.\nThe implementation of such attention between sparse features and queries with changeable positions is very tricky and hard to optimize.\n(iii) In some crowded scenes (e.g., many pedestrians), it is difficult for the queries to match objects stably and exhaustively, leading to slow convergence or a high false negative rate.\nDue to these challenges, our SST-based DETR-like detector obtains much worse performance than FSD.\n\n(4) However, the schemes proposed in (2) or (3) still have potential advantages.\n(i) Attention mechanism can be viewed as a differentiable soft grouping, which is potentially better than the grouping in FSD. We will try to adopt some learnable soft grouping strategies in future work.\n(ii) Ｔheoretically, the attention mechanism has a larger capacity than the PointNet-like SIR.\n(iii) The end-to-end manner makes it NMS-free. However, in FSD, removing NMS leads to 2 AP drops in the vehicle class.\n\nWe will keep up to explore more possibilities in the future.\n\n## Q2: Detailed Runtime Evaluation\nThe evaluation is conducted on 2000 random samples from Waymo Open Dataset with 3090 GPU. We do not apply any test time optimizations. The lighter version is explained in **Q3**.\n| Component | Latency(ms, 1 frame) | Latency (ms, 3 frames)| Latency (ms, lighter, 3 frames)\n| --- | --- | --- | --- |\n| voxel feature extraction (a.k.a, VFE)| 4.0 | **16.1** | 7.0\n| Sparse Voxel Encoder (backbone)| 21.0 | 25.2 | 25.0\n| Point segmentation & voting (segmentor head)| 1.8 | **10** | 3.0\n| CCL (CPU version)| 5.3 | 7.0 | 7.0\n| Linear layer in SIR| 5.1 | 7.6 | 4.8\n| Dynamic pooling in SIR| 1.9 | 3.2 | 2.0\n| Dynamic broadcasting in SIR| 0.5 | 1.1 | 0.6\n| Group Correction| 2.6 | 5.1 | 5.0\n| Linear layer in SIR2| 4.7 | 7.5 | 5.3\n| Dynamic pooling in SIR2| 1.7 | 3.3 | 1.9\n| Dynamic broadcasting in SIR2| 0.4 | 0.9 | 0.6\n| NMS and box decoding | 7.7 | 10.2 | 8.4\n| Others | 4.1 | 6.0 | 4.7\n| Total | 60.8 | 103.1 | 75.3\n\nWe also want to humbly clarify that we do not emphasize the absolute inference latency of FSD. Instead, we focus on the scalibity of FSD in the long range setting.\n\n## Q3: Multi-frame Model\nWe conduct 3-frame experiments on WOD, and we list all the results in the **shared response** to all reviewers.\nAnd the detailed latency is shown in **Q2**.\n\nThe main latency increases from the 1-frame model to the 3-frame model lie in the widely-used VFE and segmentor head, which contain point-wise operation.\nSIR module is only applied on the foreground points, so its latency increase is acceptable.\n\nFor optimization, we first use a lighter VFE and segmentation head by decreasing their channels from 64 to 32. As we discussed in Sec. 4.6 of paper, SIR could also adopt voxelization for some classes with normal or large sizes. So we apply voxelization of $ 0.3m \\times 0.3m \\times 0.3m $ for vehicle class for further acceleration. The performance and latency of this **lighter FSD** are shown in the **shared response** and **Q2**, respectively. The performance loss of the lighter FSD is minor.", " We are grateful for your valuable comments and constructive advice, which helps us a lot to make the paper better.\n## Q1: Writing of Methodology Part\nThanks for reminding! Our motivation to propose some new names is to make the concept more general and easy to describe. We will adopt plain expressions in the revision for easier understanding.\n## Q2: Comparison with PV-RCNN++\nIn the initial submission, we simply adopted the CopyPaste augmentation in previous methods (CenterPoint, SST), where the number of maximum pasted instances in each frame is 15/10/10 for Vehicle/Pedestrian/Cyclist, respectively.\nReaders could refer to the standard [config](https://github.com/open-mmlab/mmdetection3d/blob/master/configs/_base_/datasets/waymoD5-3d-3class.py#L24) in MMDetection3D.\nThe SIR and SIR2 modules are trained with all foreground instances without background, which indicates FSD is sensitive to the number of pasted instances.\nAs expected, we find the standard CopyPaste setting (15/10/10) is too heavy for FSD and causes overfitting in short-range vehicles and cyclists with a longer schedule.\nFSD achieves much better results after we decrease the number of pasted instances in CopyPaste augmentation (5/5/3 for vehicle/pedestrian/cyclist) and apply a longer schedule (12 epochs). For a fair comparison, we also decrease the number of pasted instances in the SST baseline, while there are no significant improvements. All the results are shown in the **shared response**.\n\nFor small objects, their superior performances come from the fine-grained feature extraction in SIR. Table 6 in our paper shows that coarser representation degrades the performance of small objects.\n\n## Q3: Analysis of Center Feature Missing\nWe truly appreciate this valuable comment. We address the reviewer's concern in the following aspects.\n\n(1) First we want to humbly explain that SIR is not trying to directly overcome the center feature missing, but is a workaround for the issue. Specifically, SIR makes predictions from features of the whole instance instead of the single center feature, which might be missing or weak. We wish this intuitive explanation could help readers better understand how SIR works.\n\n(2) To compare the center accuracy as the reviewer suggested, we calculate the average center translation error (ATE) of true positives for FSD and SST_center under different vehicle length breakdowns. \n\n| Method | ATE (0m-4m) | ATE (4m-8m) | ATE (8m-12m) | ATE (12m-INF) |\n| --- | --- | --- | --- | --- |\n| SST_center| 0.144m | 0.123m | 0.323m | 0.401m | \n| FSD | 0.145m | 0.113m | 0.225m | 0.300m | \n\n(3) Following your kindly suggestions, we show extensive qualitative analysis in the **Section A of our revised supplementary materials**. Let us know if you have better suggestions, and we are happy to provide more explanations.\n\n## Q4: Fast Convergence\nThe reason is that positive samples dominate the training of SIR and SIR2 due to we segment the instances at first.", " We decrease the number of pasted objects in the CopyPaste augmentation to prevent FSD from overfitting, then we adopted a longer schedule (6 epochs -> 12 epochs) and now FSD achieves new state-of-the-art performance. We present the detailed modification in the Q2 of response to R#1.\\\nIn the following tables, `before update` means adopting the old CopyPaste setting and `after update` means adopting the new setting.\n\n## Waymo Open Dataset\nThe following table shows the updated performance as well as the results in multi-frame settings. We mark the best single-frame results in **bold**.\n\nFor a fair comparison, we also decrease the number of pasted objects for SST to update its performance. However, this strategy causes performance loss for SST, especially for the Pedestrian and Cyclist classes.\n\n| Method | Veh. L1 AP/APH | Veh. L2 AP/APH | Ped. L1 AP/APH | Ped. L2 AP/APH |Cyc. L1 AP/APH | Cyc. L2 AP/APH |\n| --- | --- | --- | --- | --- |--- | --- |\n| SST_center (24 epochs, before update) | 75.4/74.9 | 66.8/66.3 | 80.3/72.3 | 72.6/65.2 | 71.6/70.3 | 68.9/67.7 |\n| SST_center (24 epochs, after update) | 75.0/74.6 | 66.6/66.2 | 79.1/71.3 | 71.1/64.0 | 69.0/68.2 | 66.6/65.8 |\n| PVRCNN++ (30 epochs) | 78.8/78.2 | 70.3/69.7 | 76.7/67.2 | 68.5/59.7 | 69.0/67.6 | 66.5/65.2 |\n| PVRCNN++(center, 30 epochs) | 79.3/78.8 | **70.6/70.2** | 81.3/76.3 | 73.2/68.0 | 73.7/72.7 | 71.2/70.2 |\n| FSD (6 epochs, before update) | 77.3/76.9 | 69.8/69.3 | 83.3/77.7 | 74.4/69.3 |73.2/71.9 | 70.8/69.6 |\n| FSD (12 epochs, after update) | **79.5/79.0** | 70.3/69.9 | **83.6/78.2** | **74.4/69.4** |**75.3/74.1** | **73.3/72.1** |\n| FSD (3 frames) | 80.6/80.1 | 71.5/71.1 | 85.3/81.9 | 78.5/75.2 | 80.6/79.5 | 78.4/77.4 |\n| FSD (3 frames, lighter) | 80.4/80.0 | 71.4/70.9 | 85.2/81.9 | 78.3/75.1 | 80.7/79.5 | 78.5/77.6 |\n\nWe present the details of lighter FSD (the last row) in the **Q3** of response to R#2.\n\n## Argoverse 2 Dataset\nSimilarly, we weaken the CopyPaste augmentation for the AV2 dataset. For clarity and simplicity, here we report the mean AP of all classes and AP of several main classes.\n| Method | mean AP | Vehicle | Bus | Pedestrian | Motorcyclist | Motorcycle | Bicyclist |C-Barrel | A-Bus | School Bus | \n| --- | --- | --- | --- | --- |--- | --- | --- | --- | ---| ---|\n| CenterPoint (before update) | 22.0 | 67.6 | 38.9 | 46.5 | 28.6 | 33.4 | 20.1 | 32.2 | 8.7 | 25.8\n| CenterPoint (after update) | 22.9 | 67.1 | 39.9 | 44.5 | 33.3 | 36.9 | 23.0 | 33.0 | 10.1 | 27.8\n| SST_center (before update) | 21.4 | 65.2 | 23.3 | 50.5 | 29.4 | 37.9 | 23.9 | 34.8 | 7.0 | 20.0\n| SST_center (after update) | 22.2 | 65.0 | 24.1 | 49.3 | 33.7 | 39.4 | 24.0 | 33.2 | 8.8 | 21.0\n| FSD (before update) | 24.0 | 67.1 | 39.8 | 57.4 | 30.0 | 38.1 | 27.0 | 38.1 | 15.6| 30.0\n| FSD (after update) | 28.2 | 68.1 | 40.9 | 59.0 | 39.7 | 49.0 | 33.4 | 42.6 | 20.4| 30.5\n\nC-Barrel: Construction Barrel. A-Bus: Articulated Bus \\\nThe updated performance on rare classes (e.g., Motorcyclist, Motorcycle) is significantly improved by alleviating overfitting.\n\n## Qualitative Analysis\nWe provide extensive visualization and analysis in **Section A of our revised supplementary materials**. Let us know if reviewers have better suggestions, and we are happy to add more content!", " This paper targets the problem of high computational complexity in LiDAR-based long-range 3D object detection. It proposes a fully sparse 3D object detection paradigm, i.e., from the feature extraction to the proposal generation and bounding box prediction, all are conducted based on sparse voxels or points. Specifically, built upon the commonly used sparse voxel encoder, it devises a novel sparse instance recognition (SIR) module to perform 3D detection based on local points, which is efficient in implementation and resolves the \"center feature missing\" problem. Experiments demonstrate the efficacy of this proposed method, especially for large vehicles/tiny objects and long-range cases. Strengths:\n- The studied problem is valuable for practical use. The motivation that dense prediction can bring high computational complexity for long-range cases is reasonable. A fully sparse 3D object detector is suitable given the sparse property of LiDAR points distribution.\n- The analysis of the difference between the proposed method and voxel-based semi-dense detectors/conventional voting in VoteNet makes the contribution of this paper clear.\n- Illustrations are clear and concise, making the proposed method much easier to understand.\n- Experiments support the main claims in this paper. The improvement in the detection performance of small objects/huge vehicles is impressive.\n- The efficiency analysis in terms of different perception ranges shows the main advantage of the proposed paradigm.\n\nWeaknesses:\n- The methodology part is hard to follow. In particular, so many new concepts are unnecessarily defined in the presentation, for example, dynamic broadcast/pooling, sparse instance recognition, group feature aggregation, integration, sparse prediction, etc. For some of them, the author would have better expressions/names to explain them for easier understanding. There is no need to package some easy operations or commonly used modules with totally new names, which can only make the implementation hard to understand.\n\nIn contrast, the illustration is clear and concise to represent the overall pipeline and main modules of the proposed framework.\n\n- Experiments: Although the proposed method can address the center feature missing problem to some extent and improve the detection performance of huge vehicles, it still performs a little worse than state-of-the-art methods (e.g., PV-RCNN++) on the vehicle detection of Waymo. The better mAP over 3 classes is mainly contributed by better performance on small objects. Maybe need some analysis on this phenomenon.\n\n- The analysis of the center feature missing problem is a little vague. Specifically, is there any way that we can observe the effect of addressing this problem more straightforwardly? From my perspective, the detection performance of huge vehicles can not directly support the claim strongly, maybe at least we need a more detailed analysis of the center localization accuracy or some qualitative analysis. (Minor) I notice the model converges faster than SST and wonder whether there is any potential reason/discussion about it. The author discusses the limitations and societal impact adequately in the paper.", " This paper studies efficient long-range LiDAR-based 3D object detection. The authors propose a fully sparse 3D object detector (FSD) to eliminate the dense BEV feature map that scales poorly with the perception range. Similar to VoteNet, FSD first applies the sparse encoder to extract point/voxel-wise features, then groups the points into instances, and finally predicts the boxes based on the instance-wise features. The authors have evaluated their proposed FSD on Waymo and Argoverse 2. FSD achieves superior performance on both benchmarks, especially Argoverse 2 where the perception range is much larger. **[Strengths]**\n\nThis paper is well-written and easy to follow. The authors clearly explain the missing center feature problem with a good illustration (Figure 1). Generally, the figures in this paper have pretty good quality and clarity, which helps readers understand the proposed algorithm easily.\n\nThe problem studied in this paper is very important as long-range perception is very critical in high-speed driving scenarios. The proposed FSD is technically sound and achieves good empirical results on large-scale benchmark datasets.\n\n**[Weaknesses]**\n\nThe technical novelty of this paper is a bit limited as the proposed FSD is very similar to VoteNet. The authors have clarified the differences between FSD and VoteNet in Section 3.5. However, both of them are more of engineering improvements than technical contributions. That said, the authors apply this idea to solve an important real-world problem, which could still provide valuable insights to other researchers in the community.\n\nResearchers have spent considerable efforts on transformer-based detection heads (DETR) besides anchor-based and center-based heads. Lately, there have been several follow-ups in 3D object detection, such as Object DGCNN, DETR3D, and TransFusion. DETR head provides a potential workaround for large dense BEV feature maps. The authors could discuss the pros and cons of DETR and SIR in their rebuttal.\n\nAlthough the computational cost of FSD does not grow with the perception range, it does scale linearly with the point cloud density. This could be problematic for denser point clouds (either with temporal fusion or simply with more laser beams). In contrast, dense detectors suffer less from this since the BEV feature map will always have the same resolution regardless of the point cloud size. In all experiments, the authors use single-frame point clouds for evaluation. It would be necessary to conduct experiments (or at least measure the memory footprints and inference latency) with denser multi-frame point clouds.\n\nAs this paper focuses on efficiency, it would be essential to understand where the efficiency boost comes from. For example, the authors could provide a detailed latency breakdown of different components in FSD. Besides, different inference backends could lead to very different latency results. The dense BEV encoder is composed of regular 2D convolutions, which can be easily accelerated by existing inference libraries (such as TensorRT and TVM), while the proposed SIR module is harder to be optimized. Therefore, it is unclear whether FSD could still achieve such significant speedups with highly-optimized inference engines.\n\nFinally, there are a few aspects that could potentially be improved in the experimental evaluation:\n* As FSD is based on SST, it would be necessary to report the accuracy of SST on Argoverse 2 for an apples-to-apples comparison.\n* The authors could consider conducting experiments on nuScenes, where there are many competitive LiDAR baselines. I would love to see the answer to the following questions in the rebuttal:\n* What are the pros and cons of DETR and SIR in dealing with long-range perception?\n* How well does FSD scale with denser point clouds (*e.g.*, from temporal fusion)?\n* Where does the efficiency boost of FSD come from?\n* Could FSD still achieve the same level of speedup with highly-optimized inference engines (*e.g.*, TensorRT, TVM)?\n* What is the accuracy of SST on Argoverse 2?\n\nThe authors could refer to the previous section for more detailed comments. The authors have addressed the limitations and potential negative societal impact of their work.", " The authors propose a novel 3D lidar point cloud detection method. the method is based on \na sparse instance recognition module which groups points into features, making the feature\nextraction and bounding boxes regression for detection more efficient than other point-based\nmethods. The motivation and goals of the work are well explained and clear. \nThe experimentation section is good and the ablation study brings interesting conclusions.\n\nThe paper has some little missing information listed in the questions below. However, it would be nice to have a quick explanation for the metric used as well as some qualitative\nvisual results, especially for the \"failing\"/less good results compared to other methods.\nAlso perhaps for the memory and latency performances, having more of the SOTA methods for comparison\nwould bring more value to the discussion.\nFinally, even if the paper is more focused on long and sparse lidar data compared to other methods.\nIt would be interesting for a small comparison on the KITTI dataset, to see if the method\nstill performs correctly on shorter-range point clouds. The limitation mentioned by the authors is found in the grouping strategy employed. \nI agree that a comparison with another grouping method would be out of the scope of the paper, but then perhaps an extra comparison with the grouping method used by another method would be interesting? (pointnet++ multi-scale grouping module for example)." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 3 ]

[ "VySn_DM_qj3", "6Zx9D0g6hxQ", "vpxEq7O9IBH", "SMOEh_fQxk", "DJ_59eLceC9", "5xWzcTZVB9q", "OSLHuaIcuO6", "JMaXyxyiibv", "nips_2022_evWx_rWWJuG", "nips_2022_evWx_rWWJuG", "nips_2022_evWx_rWWJuG", "nips_2022_evWx_rWWJuG" ]

[ "OsAkyTVB652", "ziXmX5YZ5GA", "7HTGJj32uVQ", "UgoGjslx21b", "9fvDUWTvgV3", "6sXRlFMDV1t", "-omq-dVGfjw", "g7epMkrpr86", "dsvR1RjL0i0", "Vnz70NEln7j", "nXSVVIc-GgW" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks again for your valuable time and constructive comments in reviewing our paper. We will further revise and polish our final version towards publication.", " I have read all the reviews and author response, the authors made significant efforts to address all the raised concerns. I would keep my decision as accept.", " We would like to sincerely thank the ACs and all reviewers for the positive comments and valuable suggestions. We have carefully addressed all comment point to point in the following. We have rearranged our manuscript and supplementary material according to the comments Newly added or modified texts are highlighted in blue in the revised manuscript. We wish our revision can satisfy the requirements of all Reviewers.", " Thanks for your constructive comments and support. The concern is addresssed point to point below.\n\n**Q1**: When the deterministic quantization function is applied to quantized ViT, such objective is equivalent to maximizing the information entropy. The reason is not clearly described.\n\n**A1**: As described in Line 14-18 of [1], *it is shown that, for a class of signal distributions, which includes the Gaussian, the quantizers with maximum output entropy (MOE) and minimum average error (MAE) are approximately the same within a multiplicative constant.* Thus the process of minimizing the error between full-precision values and quantized values is equivalent to maximizing the information entropy of the quantized values. We update the relevant part of our paper and highlight them in blue in the new version. \n\n**Q2**: The experiments are sufficient but the proof of these two techniques is a bit weak.\n\n**A2**: Following [1], given a quantizer with $a$ bits by quantizing full-precision values ${\\bf x}$ into a set $\\mathcal{Q} = \\{[Q_1 = -2^{a-1}, Q_2, \\cdots, Q_{N - 1}, Q_N = 2^{a-1}-1]\\}, N = 2^a$, where the quantized value $Q({\\bf x})$ is in the set $\\mathcal{Q}$. The average mutual information $I({\\bf x}; Q({\\bf x}))$ is\n\n&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;$I({\\bf x}; Q({\\bf x})) = H(Q({\\bf x})) - H(Q({\\bf x}) | {\\bf x}) = H(Q({\\bf x})).$\n\nFor fixed bit width $a$, $I({\\bf x}; Q({\\bf x}))$ is maximized by choosing\n\n&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;$p_k = Pr\\{Q({\\bf x} = Q_k)\\} = \\frac{1}{2^a}, k \\in {1, \\cdots, N},$\n\nwhere $Pr\\{\\cdot\\}$ denotes the probability. \nThe process of minimizing the average error (MAE) between full-precision values and quantized values is written as \n\n&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;$E_{\\theta} = \\sum_{k=1}^N \\int_{Q_k}^{Q_{k+1}}p_k \\cdot |{\\bf x} - Q({\\bf X}) |^{\\theta} d{\\bf x}.$\n\nAnd as mentioned in [1,2], an approximate relationship for the MAE objective with Gaussian distribution is\n\n&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;$\\int_{Q_k}^{Q_{k+1}} p_k^* d{\\bf x} \\cong \\frac{1}{N},$ &emsp;&emsp;&emsp;&emsp;$p_k^* = A p_k^{\\frac{1}{1 + \\theta}},$\n\nwhere $A$ is a constant. Thus the quantization process of minimizing quantization error is approximately the same as maximizing the information entropy. We propose IRM for modifying the information entropy and distributions of the quantized representations in the forward process, and DGD for minimizing the information gap between full-precision representations and quantized counterparts in the backward process. In this case, we prove that our method improves the performance of quantized ViT through maximizing the information entropy of the quantized representations.\nWe add these proof according to your comments in the new version of Supplementary file and highlight them in blue.\n\n**Q3**: Please prove why maximizing the mutual information between quantized and full-precision representations is equivalent to maximizing the information entropy $H(Q_x)$, there is nothing new in the the discussion of supplementary material.\n\n**A3**: Following [1], we prove that maximizing the mutual information between quantized and full-precision representations is equivalent to maximizing the information entropy $H(Q_x)$. Please refer to **A2** above. \n\n**Q4**: The learnable parameters $\\gamma_q$, $\\beta_q$ and $\\gamma_k$ and $\\beta_k$ are updated with the total loss, they could get a better information as Figure 4, but how to prove that they could achieve the state of information maximization. The Information Rectification Module (IRM) seems a loss-aware method instead a strong constrain to keep the max information.\n\n**A4**: We first change the information entropy of ${\\bf q}$ and ${\\bf k}$ in quantized ViT into $\\frac{1}{2}\\log 2 \\pi e [\\gamma^2_{\\bf q}(\\sigma^2_{\\bf q} + \\epsilon_{\\bf q})]$ and $\\frac{1}{2}\\log 2 \\pi e [\\gamma^2_{\\bf k} (\\sigma^2_{\\bf k} + \\epsilon_{\\bf k})]$ through IRM, as described in Eq. (8) and Eq. (9) in the paper. Then we distill the $\\tilde{\\bf q}$ and $\\tilde{\\bf k}$ for minimizing the information gap between full-precision attention and quantized counterparts through DGD *i.e.,* the gap between $\\mathcal{H}(Q_a({\\bf x}))$ and $\\mathcal{H}({\\bf x})$), which maximizes the information entropy of quantized representations to approximation the information entropy of full-precision counterparts. \n\n[1] Messerschmitt. Quantizing for maximum output entropy (corresp.). IEEE Transactions on Information Theory, 17(5):612–612, 1971.\n\n[2] Bernard Smith. Instantaneous companding of quantized signals. Bell System Technical Journal, 36(3):653–709, 1957.\n", " Thanks for your feedback. We address your concern point by point below.\n\n**Q1(a)**: this paper argues that `a direct quantization method leads to the information distortion’ in Line 45. The approach proposed in this paper does not improve this phenomenon either (e.g. 1.2268 in Fig. 1(b) v.s. 1.3672 in Fig. 5(b) for Block.3. The variance difference is even larger with the proposed approach).\n\n**A1(a)**: Sorry for the confusion, the variance difference might not mean that the information distortion phenomenon has not been improved. As shown in Fig. 5, the distribution in Q-ViT with IRM follows a distribution closer to Gaussian distribution compared to the vanilla baseline, although the difference of variance is larger. Differently, the distribution of baseline is different from the Gaussian distribution generated from the mean and variance of corresponding values (red line vs. blue shadow in Fig. 1(b)). With the Gaussian distribution hypothesis (supported by [1]), our Q-ViT with IRM mitigate the information distortion phenomenon through re-distributing attention module in the Q-ViT towards Gaussian distribution of the full-precision counterparts.\n\n**Q1(b)**: The quantization of MHSA introduces a large loss of precision, which has been found in transformer quantization in the NLP (such as Q-BERT, Q8BERT, BinaryBERT, FullyBinaryBert, etc.) and is not unique to the ViT model. \n\n**A1(b)**: This phenomenon is not unique to the ViT model, however previous quantization methods in the NLP *e.g.*, Q-BERT, Q8BERT, BinaryBERT and FullyBinaryBert fail to effectively address such bottleneck. Differently, our work improves the quantized ViTs from a new perspective. The IRM and DGD can also be used for BERT-based models on NLP, which will be further explored in our future work.\n\n**Q2**: Some minor problems: (a) In Fig2, the tilde hat of k is too small. It should be inconsistent with q’s hat. (b) In Equation 9, $Q_k$ might be $Q(k)$ to be consistent with $Q(q)$.\n\n**A2**: We correct these typos in the new version highlight them in blue.\n\n**Q3**: This paper alleviates the problem of accuracy loss caused by ViT quantization to some extent by two improvement measures. However, I expect that the author dig deeper into the differences between ViT and CNN quantization and the differences between transformer quantization in vision and NLP.\n\n**A3**: (1) *Differences between ViT and CNN quantization*: \n\nCNNs calculate features from local regions based on convolution, while ViT calculate features based on global information via inner product. That means that local feature quantization error will only affect part of CNN features, but affect more on the global feature extraction of ViT. Also, previous CNN quantization methods fail to address the severe performance degeneration problem on ViT.\n\n(2) *Differences between ViT and BERT-based NLP models quantization*: \n\nInformation density is different between language and vision. Texts are highly semantic and information-dense, while images are natural signals with heavy spatial redundancy. As a result, existing quantization methods in NLP are generally different from those in vision.\n\nWe add these discussion according to your comments in the new version of Supplementary file and highlight them in blue.\n\n**Q4**: I notice that this work applies Adam optimizer with weight decay set as 0, which is not a regular setting. I suggest the author add extra ablation studies on it to make the paper more complete. \n\n**A4**: We set weight decay as 0 for a better performance. The more detailed ablation experiments are listed in the table below. We update the description in the new version of our Supplementary file and highlight them in blue. \n\n|&emsp;&emsp;Weight decay&emsp;| Bits | Top-1 | Bits | Top-1 | Bits | Top-1 |\n|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n|0|4-4|**80.9**|3-3|**79.0**|2-2|**72.0**|\n|1e-4|4-4|80.4|3-3|78.6|2-2|71.5|\n|2.5e-5|4-4|80.6|3-3|78.7|2-2|71.6|\n|1e-5|4-4|80.6|3-3|78.7|2-2|71.8|\n|1e-6|4-4|**80.9**|3-3|78.9|2-2|71.8|\n\n[1] Haotong Qin, Yifu Ding, Mingyuan Zhang, Qinghua Yan, Aishan Liu, Qingqing Dang, Ziwei Liu, and Xianglong Liu. Bibert: Accurate fully binarized bert. In Proc. of ICLR, pages 1–24, 2022. \n", " Thanks for your feedback. We address your concern point by point below.\n\n**Q1**: How is the “6.14x”in Abstract calculated?\n\n**A1**: We calculated the acceleration rate through FLOPs. Tthe FLOPs of 4-bit Q-DeiT-S is 0.7, while the FLOPs of full-precision model is 4.3 (6.14 $\\times$ of 0.7). \n\n**Q2**: In L155, how is the distance between each attention weight calculated?\n\n**A2**: We calculate the distance between each attention weight matrix through l2 distance. We update the description in the new version and highlight them in blue. \n\n**Q3**: In L191, learning rates of learnable gamma and beta are not clarified, are they the same as the learning rate of the whole network?\n\n**A3**: The learning rates of learnable $\\gamma$ and $\\beta$ are same as the whole network. We update the description in the new version and highlight them in blue. \n\n**Q4**: In Eq. 10, why just query and key are distilled, instead of query, key and value?\n\n**A4**: In Supplementary file, we conduct the ablation experiments of distilling different parts of query, key and value. Thus, we distill query and key only for better performance in the main results. \n\n**Q5**: How are $\\alpha_x$ and $\\alpha_w$ learned through training? Are the training settings the same as other learnable parameters?\n\n**A5**: $\\alpha_x$ and $\\alpha_w$ are updated through back propagation and the training settings are same as other parameters. \n\n**Q6**: In Eq. 7, after maximizing the information entropy, $q_x$ should follow an uniform distribution, however, in the aforementioned figure 4, the query and key may follow a Gaussian distribution. This seems to be conflicting.\n\n**A6**: As described in Line 15-18 in Supplementary file, $q_{\\bf x}$ is the possible values of $Q_a({\\bf x})$ (which is $Q_a({\\bf q})$ or $Q_a({\\bf k})$ in different conditions) with probability $p(\\cdot)$. Note that when the information entropy maximizing, all possible quantized values $q_{\\bf x} \\in \\{-Q_n^a, -Q_n^a + 1, \\cdots, Q_p^a\\}$ intend to follow an uniform distribution, while the reconstructed $\\hat{\\bf x}$ roughly follow a Gaussian distribution. \n\n**Q7**: In Eq. 8, how are the mu and sigma calculated? Are they channel-wise or layer-wise?\n\n**A7**: In Eq. 8, the mean and the variance of ${\\bf q}$ and ${\\bf k}$ are calculated based on the whole query or key matrix, *i.e.*, layer-wise. \n\n**Q8**: How is Eq. 9 derived? Especially the part “$\\frac{1}{2} \\log 2\\pi e[\\gamma^2(\\sigma^2 + \\epsilon)]$”?\n\n**A8**: ${\\bf q}$ and ${\\bf k}$ follow Gaussian distribution, according to the Gaussian hypothesis in \\cite{qin2022bibert}. Thus, the information entropy of $\\mathcal{H}(Q({\\tilde{\\bf q}}))$ and $\\mathcal{H}(Q({\\tilde{\\bf k}}))$ is derived based on the information entropy of Gaussian distribution. ", " Thanks for your constructive and supportive comments.\n\n**Q1**: In Line 61, what is the actual meaning of “quantified representations”?\n\n**A1**: \"quantized representations\" in Line 61 represents the quantized query and key *i.e.*, $Q_a({\\bf q})$ and $Q_a({\\bf k})$ in our MHSA module of each layer in a ViT model. \n\n**Q2**: In section 4.1 “Architecture bottleneck”, how are these experiments trained? the same as the main experiments settings?\n\n**A2**: These ablation experiments are conducted the same as experiments in Tab. 2. We added this description in the new version and highlight them in blue. \n\n**Q3**: In Line 155, “distance”should be “distances”.\n\n**A3**: We revise the typo and highlight in blue.\n\n**Q4**: Font sizes of the legend in Figure 4 are inconsistent and should be larger.\n\n**A4**: We update the figure in the new version.\n\n**Q5**: Are the IRM applied before quantizing attention module, or after quantizing? Such two situations may lead to different results.\n\n**A5**: The IRM is applied before quantizing the query and key in each MHSA module, which modifying the information entropy and distributions of the query and key for minimizing the information gap between full-precision representations and quantized counterparts. If IRM is applied after quantizing the query and key, the information distortion already exists and cause the essential global information to be distorted by the quantization operation. Thus, we appliy IRM before quantizing the attention module. \n\n**Q6**: In section 5.1, authors mentioned that the Q-ViT is initialized from pertained full-precision counterparts. However, how are the alpha and zero point initialized?\n\n**A6**: $\\alpha$ and $z$ are initialized as random parameters in our implementation. \n\n**Q7**:: In Eq. 7, what does “$q_x$ is the random quantized variables in $Q_a(x)$” mean? What are the possible values of “$q_x$”?\n\n**A7**: As described in our Supplementary file, $q_{\\bf x}$ is the possible values of $Q_a({\\bf x})$ (which is $Q_a({\\bf q})$ or $Q_a({\\bf k})$ in different conditions) with probability $p(\\cdot)$. For example, if quantizing ${\\bf x}$ into $a$ bits, the possible discrete values of $q_x$ are $[-2^a, -2^a + 1, \\cdots, 2^{a-1} - 1, 2^{a-1}]$. \n\n**Q8**: In Eq. 8, after introducing IRM, the module calculate the mean and variance of Q and K in each block for each forward process, will this affect the speed of inference?\n\n**A8**: The IRM operation will not be involved into the inference process, thus it will not affect the speed of inference. ", " This paper proposed a novel and efficient quantization method for Vision Transformers. The authors first identify the bottleneck low-bit quantized Vision Transformers which comes from the information distortion of the low-bit quantized self-attention map. The authors then develop an IRM and a DGD scheme for fully quantized Vision Transformers based on the aforementioned bottleneck, which leads to a fully quantized Vision Transformers. 1.In Line 61, what is the actual meaning of “quantified representations”?\n\n2.In section 4.1 “Architecture bottleneck”, how are these experiments trained? the same as the main experiments settings?\n\n3.In Line 155, “distance”should be “distances”. \n\n4.Font sizes of the legend in Figure 4 are inconsistent and should be larger. \n\n5.Are the IRM applied before quantizing attention module, or after quantizing? Such two situations may lead to different results. \n\n6.In section 5.1, authors mentioned that the Q-ViT is initialized from pertained full-precision counterparts. However, how are the alpha and zero point initialized?\n\n7.In Eq. 7, what does “q_x is the random quantized variables in Q_a(x)” mean? What are the possible values of “q_x”?\n\n8.In Eq. 8, after introducing IRM, the module calculate the mean and variance of Q and K in each block for each forward process, will this affect the speed of inference?\n Please see above. Please see above.", " This paper studies the quantization of the Vision Transformer model, especially in the low-bit case. For the problem of large quantization accuracy loss at low bits, two improvements, IRM and DGD, are proposed in this paper, respectively. Concretely, IRM maximizes the information entropy of the quantized representation. DGD supervises the model with other patch-based similarity pattern matrices. Strengths:\n1.\tThe quantization of ViT models is an important research topic. In this paper, the accuracy loss caused by ViT quantization is mitigated to some extent.\n2.\tThe article is well written and well finished. It is easy to follow.\n\nWeaknesses:\n1.\tThe analysis of vit quantification could be explained in depth:\n(a) this paper argues that `a direct quantization method leads to the information distortion’ in Line 45. The approach proposed in this paper does not improve this phenomenon either (e.g. 1.2268 in Fig1(b) v.s. 1.3672 in Fig5(b) for Block.3. The variance difference is even larger with the proposed approach). \n(b) The quantization of MHSA introduces a large loss of precision, which has been found in transformer quantization in the NLP (such as Q-BERT, Q8BERT, BinaryBERT, FullyBinaryBert, etc.) and is not unique to the ViT model. \n2.\tSome minor problems:\n(a)\tIn Fig2, the tilde hat of k is too small. It should be inconsistent with q’s hat. \n(b)\tIn Equation 9, $Q_k$ might be $Q(k)$ to be consistent with $Q(q)$.\n 1.\tThis paper alleviates the problem of accuracy loss caused by ViT quantization to some extent by two improvement measures. However, I expect that the author dig deeper into the differences between ViT and CNN quantization and the differences between transformer quantization in vision and NLP.\n2.\tI notice that this work applies Adam optimizer with weight decay set as 0, which is not a regular setting. I suggest the author add extra ablation studies on it to make the paper more complete.\n The limitations have been well addressed.", " This paper focused on Vision Transformers quantization aware training methods. In this paper, the bottleneck of QAT for ViT are firstly studied which are mainly caused by the information distortion in MHSA. This paper thus propose IRM and DGD scheme to solve such bottleneck which retains the performance of quantized ViT from full-precision counterparts. Strength:\n\n1. The paper is technically sound and easy to understand.\n\n2. The experiments show that the proposed method is effctive.\n\nWeakness:\n\n1. How is the “6.14x”in Abstract calculated?\n\n2. In L155, how is the distance between each attention weight calculated?\n\n3. In L191, learning rates of learnable gamma and beta are not clarified, are they the same as the learning rate of the whole network? \n\n4. In Eq. 10, why just query and key are distilled, instead of query, key and value?\n\n5. How are alpha_x and alpha_w learned through training? Are the training settings the same as other learnable parameters?\n\n6. In Eq. 7, after maximizing the information entropy, q_x should follow an uniform distribution, however, in the aforementioned figure 4, the query and key may follow a Gaussian distribution. This seems to be conflicting. \n\n7. In Eq. 8, how are the mu and sigma calculated? Are they channel-wise or layer-wise?\n\n8. How is Eq. 9 derived? Especially the part“1/2 log2πe[gamma^2(sigma^2 + epsilon)]”?\n See weakness above. -", " In this paper, Q-ViT is proposed, an effective fully quantized scheme for vision transformer. This paper first introduces the bottleneck for severe performance drop and then present the Information Rectification Module (IRM) and Distribution Guided Distillation (DGD) to bulld a high-performance fully quantized vision transformers. And the experimental results demonstrate the superiority of Q-ViT. Strengths\n1. The analysis of the bottleneck for severe performance drop is clear.\n2. The experimetal results are state-of -the-art.\n3. The paper is well-written and easy to understand.\n4. The code and checkpoints are open sourced.\n\nWeaknesses\n1. When the deterministic quantization function is applied to quantized ViT, such objective is equivalent to maximizing the information entropy. The reason is not clearly described.\n2. The experiments are sufficient but the proof of these two techniques is a bit weak. 1. Please prove why maximizing the mutual information between quantized and full-precision representations is equivalent to maximizing the information entropy $H(Q_x)$, there is nothing new in the the disussion of supplementary material.\n\n2. The learnable parameters $\\gamma_q$, $\\beta_q$ and $\\gamma_k$ and $\\beta_k$ are updated with the total loss, they could get a better information as Figure 4, but how to prove that they could achieve the state of information maximization. The Information Rectification Module (IRM) seems a loss-aware method instead a strong constrain to keep the max information.\n\n Yes" ]

[ -1, -1, -1, -1, -1, -1, -1, 6, 8, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, 4, 5, 4, 5 ]

[ "ziXmX5YZ5GA", "UgoGjslx21b", "nips_2022_fU-m9kQe0ke", "nXSVVIc-GgW", "dsvR1RjL0i0", "Vnz70NEln7j", "g7epMkrpr86", "nips_2022_fU-m9kQe0ke", "nips_2022_fU-m9kQe0ke", "nips_2022_fU-m9kQe0ke", "nips_2022_fU-m9kQe0ke" ]

[ "6XwF0V8K9AW", "XJVYFvgmzsN", "rukZFYrwHyF", "zVf86OiBd-J", "SdzGInVSzN_", "vtm_sCsFqQAc", "sePpVVAhPwl", "qpXTN14FIYe", "0dlkQasAO3r", "ViyP9R4pdxl" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for the explanations. I have read the author's feedback. I would like to keep my review unchanged, and continue to support acceptance for this paper!", " The author-rebuttal phase closes today. Please acknowledge the author rebuttal and state if your position has changed. Thanks!", " The author-rebuttal phase closes today. Please acknowledge the author rebuttal and state if your position has changed. Thanks!", " Thanks for the responses. My concerns have been addressed, and I'd like to keep my initial rating.", " Thanks for your inspiring comments. The detailed replies are as follows.\n\n---\n\nQ1: The paper only discusses uniform sampling as the selected method of landmarks. Other sampling strategies (e.g., leverage score [2]) could be tried to further improve the performance of the algorithm.\n\nA1: The methods such as leverage score sampling and ridge leverage score sampling have been used to improve the Nyström method in kernel $k$-means. However, there lacks relevant researches about the selection of landmarks in multiple kernel clustering (MKC). This is still an open problem in MKC. We will try to study the effect of sampling strategy of the proposed method in our future work.\n\n---\n\nQ2: The authors haven’t analyzed the optimal number of landmarks. In the experiments, the number of landmarks is regarded as a hyper-parameter, which seems to require more effort to select the best one.\n\nA2: The authors in [1] give a theoretical research about the optimal number of landmarks of Nyström method for kernel $k$-means. The optimal number is given as $\\mathcal{O}(\\sqrt{n})$, where $n$ is the sample number. However, in our experiments, we find that $\\mathcal{O}(\\sqrt{n})$ may be too many for MKC. In most datasets, the used landmarks are far less than $\\mathcal{O}(\\sqrt{n})$. Because the empirical clustering risk will vary greatly with different kernel weights, it may be very difficult to study the optimal number of MKC in theory. We will try to address this issue in the future research.\n\n---\n\nQ3: The authors only provide the theoretical and empirical results about SimpleMKKM. Some classic MKC algorithms are not discussed.\n\nA3: We conduct additional experiments on three classic algorithms, i.e., average multiple kernel $k$-means (AMKKM), multiple kernel $k$-means (MKKM) [3] and multiple kernel k-means clustering with matrix-induced regularization (MKKMMR) [2]. The results are reported in Section B5 of the appendix. As seen from the first two tables, our method achieve comparable clustering performance in the comparison with the standard AMKKM and MKKM, while the running time is far less. However, the results of our method fluctuates more dramatically when we apply it on MKKMMR. It is caused by two main reasons: 1) The hyper-parameter of MKKMMR makes the kernel weights be instable; 2) The optimal hyper-parameter of MKKMMR on landmarks is different to the whole training dataset. Through the experimental results and our empirical analysis, we find that our method would be more effective on the parameter-free multiple kernel clustering algorithms.\n\n---\n\n[1] Calandriello D, Rosasco L. Statistical and computational trade-offs in kernel k-means. In NeurIPS 2018.\n\n[2] Liu X, Dou Y, Yin J, et al. Multiple kernel k-means clustering with matrix-induced regularization. In AAAI 2016.\n\n[3] Huang H C, Chuang Y Y, Chen C S. Multiple kernel fuzzy clustering. In TFS 2011.", " Thanks a lot for your valuable feedback! We will answer your questions point by point.\n\n---\n\nQ1: In the paper, only SimpleMKKM is used as an example to verify the effectiveness of the out-of-sample method. As a consequence, the experimental support of the paper is relatively weak. It will be better if more state-of-the-art multiple kernel clustering algorithms, such as [1][2], can be analyzed.\n\n\nA1: The algorithm in [2] needs to calculate the weight for each sample of each view, thus the proposed method can't be performed on it. We conduct additional experiments on three classic algorithms, i.e., average multiple kernel $k$-means (AMKKM), multiple kernel $k$-means (MKKM) [3] and multiple kernel k-means clustering with matrix-induced regularization (MKKMMR) [1]. The results are reported in Section B5 of the appendix. As seen from the first two tables, our method achieves comparable clustering performance in the comparison with the standard AMKKM and MKKM, while the running time is far less. However, the results of our method fluctuates more dramatically when we apply it on MKKMMR. It is caused by two main reasons: 1) The hyper-parameter of MKKMMR makes the kernel weights be instable; 2) The optimal hyper-parameter of MKKMMR on landmarks is different to the whole training dataset. Through the experimental results and our empirical analysis, we find that our method would be more effective on the parameter-free multiple kernel clustering algorithms.\n\n---\n\nQ2: Some minor issues are in the manuscript.\n\nA2: Thank you for pointing out these issues. We have addressed them in the revised manuscript.\n\n---\n\nQ3: Why do the authors select SimpleMKKM as a baseline for the implementation of the proposed method?\n\nA3: The reasons why we select SimpleMKKM as the baseline are as follows.\n1) SimpleMKKM is one of the state-of-the-art algorithms which has promising clustering performance and efficiency. Moreover, SimpleMKKM has no hyper-parameter, and is more practical for application.\n2) Through experimental observation, we find that the kernel weights of SimpleMKKM is stable against the training sample. In the theoretical analysis, because the optimization method is gradient descent, we can prove the stability of SimpleMKKM by studying the variation of kernel weights in each iteration. Other MKC algorithms may also have stability, but it's difficult to analyse in theory.\n\n---\n\nQ4: The proposed method for construction of the approximated indicator functions is inspired by [4]. However, the contribution over the mentioned method is not clearly described in the manuscript. More information should be given.\n\nA4: We extend the method in [4] from single kernel to multiple kernel, and successfully apply it in the fields of clustering algorithms. Denote the integral operator $L_{\\kappa}$ associated with the kernel function $\\kappa$ as\n$\n(L_{k}f)(\\mathbf{x}) = \\int_{\\mathcal{X}}k(\\mathbf{x},\\mathbf{y})f(\\mathbf{y})d\\rho(\\mathbf{y}).\n$\nThe empirical kernel matrix is $\\frac{1}{n}\\mathbf{K}$, whose element is $K_{ij} = \\kappa(\\mathbf{x_i},\\mathbf{x_j})$. $L_{\\kappa}$ can be seen as the expected form of $\\frac{1}{n}\\mathbf{K}$. $L_{\\kappa}$ and $\\frac{1}{n}\\mathbf{K}$ operate on different space. To study the relation of above two operators, the authors in [4] define two operators $T_{\\mathcal{H}},T_n: \\mathcal{H} \\rightarrow \\mathcal{H}$ as\n$\nT_{\\mathcal{H}} = \\int_{\\mathcal{X}} \\langle\\cdot,\\kappa_\\mathbf{x} \\rangle \\kappa_\\mathbf{x} d\\rho(\\mathbf{x})$ and $T_{n} = \\frac{1}{n} \\sum_{i=1}^n \\langle\\cdot,\\kappa_{\\mathbf{x_i}} \\rangle \\kappa_{\\mathbf{x_i}},\n$\nwhere $\\kappa_\\mathbf{x} = \\kappa(\\cdot,\\mathbf{x})$ and $\\kappa_{\\mathbf{x_i}} = \\kappa(\\cdot,{\\mathbf{x_i}})$. By Proposition 9 of [4], the eigenvector and eigenfunction of $\\frac{1}{n}\\mathbf{K}$ and $T_n$ are as follows:\n$\n\\mathbf{h_k} = \\frac{1}{\\sqrt{\\lambda_k}} (u_k(\\mathbf{x_1}),\\cdots,u_k(\\mathbf{x_n})), \\quad u_k(\\mathbf{x}) = \\frac{1}{\\sqrt{\\lambda_k}} \\left(\\frac{1}{n} \\sum_{i=1}^n h_{ik}\\kappa(\\mathbf{x},\\mathbf{x_i}) \\right),\n$\nwhere $\\lambda_k$ is the $k$-th eigenvalue of $\\frac{1}{n}\\mathbf{K}$. It is easy to check that for any point $\\mathbf{x}$ on the sample space, the embedding vector can be approximated as $[h_1(\\mathbf{x}),\\cdots,h_K(\\mathbf{x})]$, where $h_k(\\mathbf{x}) = \\frac{1}{n\\lambda_k} \\left( \\sum_{i=1}^n h_{ik}\\kappa(\\mathbf{x},\\mathbf{x_i}) \\right)$. In the setting of multiple kernel, kernel function is $\\kappa_{\\boldsymbol{\\alpha}}$, thus we can approximate the embedding of $\\mathbf{x}$ by Eq.(8) of the manuscript.\n\n---\n\n[1] Liu X, Dou Y, Yin J, et al. Multiple kernel k-means clustering with matrix-induced regularization. In AAAI 2016.\n\n[2] Gönen M, Margolin A A. Localized data fusion for kernel k-means clustering with application to cancer biology. In NeurIPS 2014.\n\n[3] Huang H C, Chuang Y Y, Chen C S. Multiple kernel fuzzy clustering. In TFS 2011.\n\n[4] Rosasco L, Belkin M, De Vito E. On learning with integral operators. In JMLR 2010.\n", " Thanks for constructive comments to improve the paper. We address the points you raised one by one.\n\n---\n\nQ1: Some other methods for large-scale implementation of kernel clustering algorithms should be referred, e.g., Nyström [1] and random Fourier feature [2].\n\nA1: Thanks, we discuss the mentioned methods as follows. \"To improve the scalability of kernel clustering algorithms, methods such as Nyström [1] approximation and random Fourier feature (RFF) [2] are proposed. These two methods acquire the non-linear feature of samples in real space through the approximating the kernel matrix. However, Nyström method can't be implemented on out-of-sample points directly. RFF can fill this gap, but the dimension of the learned embedding is comparably large such that the subsequent clustering process is time consuming. More seriously, because it's difficult to bound the difference of the kernel weights before and after the approximation, these two methods are rarely implemented on MKC algorithms.\" We will add the above contents to the introduction section to make the point clear.\n\n---\n\nQ2: The proposed clustering risk bound should be compared with other relevant works.\n\nA2: In existing literature, the authors in [3] propose the excess risk bound of kernel $k$-means as $\\mathcal{O}\\left(\\frac{K}{\\sqrt{n}}\\right)$, where $K$ is the cluster number and $n$ is the number of samples. As an improvement of the above result, the authors in [4] bound the excess risk as $\\mathcal{O}\\left(\\sqrt{\\frac{K}{n}}\\right)$, which matches with the\nstated lower bound and is nearly optimal. In this paper, the proposed excess risk bound of single kernel is $\\widetilde{\\mathcal{O}}\\left(\\frac{K}{n\\sqrt{n}}+\\frac{1}{\\sqrt{n}}\\right)$ with two mild assumptions, which is tighter than $\\mathcal{O}\\left(\\sqrt{\\frac{K}{n}}\\right)$. In multiple kernel clustering, the proposed bound is $\\tilde{\\mathcal{O}}\\left(\\frac{(m+1)K}{n\\sqrt{n}}+\\frac{1}{\\sqrt{n}}\\right)$, which is tighter than the existing results $\\mathcal{O}(\\frac{mK}{\\sqrt{n}})$ proposed in [5].\n\n---\n\nQ3: Experiments are not sufficient. In Section 5.1, the authors provide theoretical analysis of clustering on single kernel. However, the paper lacks corresponding experiments.\n\n\nA3: To give empirical evidence of our theoretical results, we conduct experiments on single kernel, and the results are reported in Section B5 of the revised manuscript. All experimental setting and datasets are the same as Section 6.1. The used kernel matrix is constructed by the average summation of all base kernel matrices. As seen from the Table 7 in the appendix, we can find that our method achieve comparable clustering performance in comparison with the standard kernel $k$-means. As stated in Section 4.2, the proposed method sharply reduces the running time. It shows that our method is effective to clustering algorithm on single kernel, i.e., kernel $k$-means.\n\n---\n\nQ4: The codes of experiments are not available.\n\nA4: The code is now available in an anonymous website. Please refer to https://anonymous.4open.science/r/MKC_approximation-6091/.\n\n---\n\nQ5: In experiments, the clustering performance of SimpleMKKM with the proposed method on some datasets is superior to the original one. I think that the authors should give more discussions about this phenomenon.\n\nA5: Our method aims to approximate the exact embedding $\\mathbf{H}$ which is obtained by original multiple kernel clustering (MKC) algorithm. As shown in [5], when the objective value of original MKC algorithm converges to optima, the exact $\\mathbf{H}$ may not obtain the best clustering performance. Thus, in some datasets, the approximation embedding can obtain better but similar clustering performance comparing with the exact one.\n\n---\n\n[1] Musco C, Musco C. Recursive sampling for the nyström method. In NeurIPS 2017.\n\n[2] Chitta R, Jin R, Jain A K. Efficient kernel clustering using random fourier features. In ICDM 2012.\n\n[3] Biau G, Devroye L, Lugosi G. On the performance of clustering in Hilbert spaces. In TIT 2008.\n\n[4] Liu Y. Refined Learning Bounds for Kernel and Approximate $ k $-Means. In NeurIPS 2021.\n\n[5] Liu X, Zhu E, Liu J, et al. SimpleMKKM: Simple multiple kernel k-means. arXiv preprint 2020.\n", " The paper studies the problem of clustering out-of-sample data over multiple kernel clustering dataset. The authors of the paper seek to solve the problem by learning the embedding functions with a novel approximation strategy by take advantage of the relation between empirical kernel matrix and integral operator of the kernel function. Then, the generalization ability of the method is studied with valuable depth from single kernel setting to multiple kernel setting. Finally, numerical experiments are conducted to verify the superiority of the proposed algorithm. Strengths:\n1. The proposed method can greatly accelerate MKC on handling out-of-sample problem. Though the method is simple, it can reduce the time complexity from $\\mathcal{O}(N^3)$ to $\\mathcal{O}(N)$. Consequently, the method can enable MKC to be performed on large-scale dataset.\n2. The authors offer theoretical analysis about the proposed method. It is the first time the stability of clustering algorithm is analyzed. The paper is technically sound, and the proofs are strict.\n3. The paper establishes a connection between the stability of MKC algorithm and the output kernel weights, which enlightens a design principle for this type of algorithms.\nWeakness:\n1. Some other methods for large-scale implementation of kernel clustering algorithms should be referred, e.g., Nystr\\\"om [1] and random Fourier feature [2].\n\n2. The proposed clustering risk bound should be compared with other relevant works.\n\n[1] Cameron Musco and Christopher Musco. Recursive sampling for the Nystr\\\"om method. In NeurIPS 2017.\n\n[2] Radha Chitta, Rong Jin, and Anil K. Jain. Efficient Kernel Clustering Using Random Fourier Features. In ICDM 2012.\n\n3. Experiments are not sufficient. In Section 5.1, the authors provide theoretical analysis of clustering on single kernel. However, the paper lacks corresponding experiments.\n\n4. The codes of experiments are not available.\n In experiments, the clustering performance of SimpleMKKM with the proposed method on some datasets is superior to the original one. I think that the authors should give more discussions about this phenomenon. None.", " The paper provides a general method that enables multiple kernel clustering algorithms to compute the embedding of out-of-sample points efficiently. Instead of re-computing the sample embedding of the unseen samples with the support of the whole data matrix, the authors directly obtain the embedding by constructing the embedding functions through approximating the eigen function of the integral operator defined by the optimal kernel function. With these functions, the embedding of the out-of-sample data can be easily and accurately calculated. Moreover, the upper bound of excess clustering risk is established based on the studying of stability of the proposed method. Experimental results demonstrate the effectiveness and efficiency of the proposed method. Strengths\n\n1. The out-of-sample problem of MKC studied by this paper is important and challenging. The idea of enabling kernel clustering algorithms to obtain the embedding of out-of-sample data is novel and interesting. \n\n2. The conducted generalization study of clustering algorithms is an important theoretical contribution. \n(1) The paper for the first time establishes the excess risk bound of kernel k-means by the analysis of its algorithmic stability. \n(2) The analysis is extended to multiple kernel setting. The proposed theoretical results enlighten a new way to study the generalization ability of multiple kernel clustering algorithms. \n\n3. The paper is well written with clear and rational motivation. It presents a novel way of scaling the method to large scale multiple kernel clustering scenario and a new perspective of generalization analysis of MKC. These are valuable for AI researchers in this field. \n\n\nWeakness\n\n1. In the paper, only SimpleMKKM is used as an example to verify the effectiveness of the out-of-sample method. As a consequence, the experimental support of the paper is relatively weak. It will be better if more state-of-the-art multiple kernel clustering algorithms, such as [1][2], can be analyzed.\n\n[1] Liu, X.; Dou, Y.; Yin, J.; Wang, L.; and Zhu, E. 2016. Multiple kernel k-means clustering with matrix-induced regularization. In AAAI, 1888–1894.\n\n[2] Gonen, M., and Margolin, A. A. 2014. Localized data fusion for kernel k-means clustering with application to cancer biology. In NIPS, 1305–1313.\n\n2. Some minor issues are as follows.\n\nI. In the proof of Proposition 4.1, $R(H)$ should be written as $R(H,P)$ as its definition in the main text.\n\nII. “Denote the k-th eigenvalue/vector pairs” in Line 483. 1. Why do the authors select SimpleMKKM as a baseline for the implementation of the proposed method? \n\n2. The proposed method for construction of the approximated indicator functions is inspired by [3]. However, the contribution over the mentioned method is not clearly described in the manuscript. More information should be given.\n\n[3] Rosasco L, Belkin M, De Vito E., On learning with integral operators. In JMLR, page 905–934, 2010. The limitation of the proposed method is considered in the conclusions. The societal impact is not discussed, and this will not cause any potential negative societal impact.", " The paper proposes a new method for efficient multiple kernel clustering (MKC) over out-of-sample data. This method has the potential to scale the existing MKC algorithms to handle large-scale datasets. Then, the generalization ability of the method is studied from the single kernel setting to the multiple kernel setting, which provides valuable insight of the algorithm. Finally, numerical experiments are conducted to verify the superiority of the proposed algorithm. Some strengths:\n1. This work studies the generalization ability of the clustering algorithm based on algorithmic stability, which is a significant and interesting research topic. By selecting $n$ samples as landmarks, the approximation embedding of the remaining samples can be computed with $O(N)$ time complexity, where $N$ is the sample number. Thus, the method can make existing MKC scalable to large-scale datasets.\n2. The theoretical analysis of the paper is novel and sound. Theoretical analysis has proved that the proposed method has desirable generalization ability ($\\mathcal{O}((m+1)Kn^{-3/2}+n^{-1/2})$), which provides a tighter bound than the one ($\\mathcal{O}(mKn^{-1/2})$) provided in [1]. It guarantees the effectiveness of the proposed method. Moreover, the analysis can be scalable to multiple kernel clustering and the proofs are correct.\n3. The paper is easy to follow and well-written.\n\nSome weaknesses:\n1. The paper only discusses uniform sampling as the selected method of landmarks. Other sampling strategies (e.g., leverage score [2]) could be tried to further improve the performance of the algorithm.\n2. The authors haven’t analyzed the optimal number of landmarks. In the experiments, the number of landmarks is regarded as a hyper-parameter, which seems to require more effort to select the best one.\n3. The authors only provide the theoretical and empirical results about SimpleMKKM. Some classic MKC algorithms are not discussed.\n\n[1] Xinwang Liu, En Zhu, Jiyuan Liu, Timothy Hospedales, Yang Wang, and Meng Wang. Simplemkkm: Simple multiple kernel k-means. In arXiv preprint arXiv:2005.04975, 2020.\n\n[2] Petros Drineas, Malik Magdon-Ismail, Michael W. Mahoney, and David P. Woodruff. Fast approximation of matrix coherence and statistical leverage. Journal of Machine Learning Research, 13:3441–3472, 2012. Please check the Weakness box. None." ]

[ -1, -1, -1, -1, -1, -1, -1, 6, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, 4, 4, 5 ]

[ "sePpVVAhPwl", "0dlkQasAO3r", "qpXTN14FIYe", "SdzGInVSzN_", "ViyP9R4pdxl", "0dlkQasAO3r", "qpXTN14FIYe", "nips_2022_QYD9bDWR3R_", "nips_2022_QYD9bDWR3R_", "nips_2022_QYD9bDWR3R_" ]

[ "hYE8X_oSC4w", "tTcqaF7RjHl", "yQ1JpaeSwax", "qIFHCTq5Hd0", "m-9mshDqJBI", "vthQM_yYTv", "RUnMpC_AQCW", "blo9WDS4f-n", "hWuBNAvhq5U", "7d7DzWlXxt2", "1mOZnBje3CF", "PQP9Ewfs2gk", "sukZ66QsCY", "2wHsr1CHoxp", "AyWDbSRAUBv" ]

[ "official_reviewer", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for addressing my concerns. After reading the rebuttal, I have adjusted my rating accordingly. ", " Dear Reviewer,\n\nWe are wondering whether your concerns have been properly addressed.\nIf you have further questions after reading the answers, it would be great to let us know. \n\nBest regards, \nThe authors.", " Thank you fro your explanation and responses.\n\nNot having the validation group labels cause a much smaller effect than I would have thought, which is promising. Overall I think this method is interesting and useful so I will adjust my score accordingly.", " The authors have properly addressed my concerns and questions. The code is also made publicly available, which I appreciate much.\n\nI went through the other reviewers' comments and corresponding replies. Overall, I regard this paper to be a nice work that can be impactful in this area. The combination of mixup and importance weighting is novel, insightful theoretical analysis is provided, and SOTA performance is achieved. \n\nCurrently I will keep my score fixed. Although I would like this paper to be accepted, I am also willing to listen to the opinions of the other reviewers, especially reviewer ptj2, whose score is divergent from the other reviewers. ", " \nWe thank the reviewer for the encouraging comments and insightful feedback. We address the concerns below.\n\n***Q1. What is a 'reasonable' importance weight, and on what basis can this assumption be made?***\n\nR1. First, we assume the samples with high uncertainty can be given a higher weight and vice versa. This assumption is reasonable since samples in the majority group have low uncertainties with high probability as shown in Fig. 1. Holding this assumption, we chose a simple yet effective implementation, i.e., set importance weight that is linearly correlated to the uncertainty. As shown by our extensive results, this strategy can achieve satisfactory performance. \n\n***Q2. How does UMIX perform without the group labels in the validation set?***\n\nR2. First, we added the evaluation on the Waterbirds and CelebA dataset without using the validation set group label information. Specifically, after each training epoch, we evaluate the performance of the current model on the validation set and save the model with the best average accuracy. Finally, we test the performance of the saved model on the testset. The experimental results are shown in the following tables. From the experimental results, we have the following observations: 1. When the validation set group information is not used, the worst-case ACC of our method drops a little while the average ACC improves a little. 2. Compared with JTT using validation set group information, our method still achieves excellent performance, such as on the Waterbirds dataset, which is still 2.9% higher than JTT in terms of worst-case accuracy.\n\n| Dataset | Metric | ERM | JTT | Ours | Ours (without validation group label) |\n|------------|----------------|-------|-------|-------|---------------------------------------------|\n| Waterbirds | Average ACC | 97.0% | 93.6% | 93.0% | 93.6% |\n| Waterbirds | Worst-case ACC | 63.7% | 86.0% | 90.0% | 88.9% |\n| CelebA | Average ACC | 94.0% | 88.0% | 90.1% | 90.4% |\n| CelebA | Worst-case ACC | 47.8% | 81.1% | 85.3% | 84.6% |\n\nSecond, we agree that it is an oracle strategy since it requires additional group information of validation set. However, as shown in some related works [1,2], the model selection with no group labels during validation is a very hard and ill-posed problem. Model selection always has a huge impact on the performance of the final model. Under our framework, this problem could be better solved. For example, we can estimate the uncertainty of the validation set samples and construct a pseudo-worst-case group based on the uncertainty of the validation set. Finally, we can reduce the impact of model selection by selecting the best model based on pseudo-worst-case accuracy.\n\n***Q3. Section 5 states \"Thus our bound can be tighter when the intrinsic dimension of data is small (i.e., rank($\\Sigma$) $\\ll d$).\" Is this really useful? Can you point to some intuition or concrete examples of when this would usefully lower the bound? When can we reasonably expect that to not be full rank? On the same note, is this referring to the dimension in the input space, the output space before the loss function, or something else entirely?***\n\nR3. This is a very good question. \n\n```\n\"Is this referring to the dimension in the input space?\"\n```\nYes, the intrinsic dimension of data refers to the input space's intrinsic dimension. \n\n```\n\"When can we reasonably expect that to not be full rank?\"\n```\nWhen the features are highly correlated, e.g., some variables are relevant to the existing ones, which is prevalent in practice, rank($\\Sigma$) would be much smaller than the input space dimension. \n\n```\n\"Is this really useful? Can you point to some intuition or concrete examples of when this would usefully lower the bound?\"\n```\nLiterature from statistical learning has shown that redundant features may do serious harm to the generalization capability of the ERM [3]. Instead, this issue can be alleviated by our proposed UMIX framework, which smartly introduces data augmentation by inherently imposing an implicit regularization. Specifically, the data augmentation takes the subpopulation shift into account by leveraging the knowledge from the heterogeneity between different subpopulations to improve the generalization. Therefore, our theoretical bound is exactly the analysis of the above intuitive consideration. We will add some concrete, synthetic examples in the revision. \n", " ***Q4. Are you actually MC sampling the saved SWAG models by building the Gaussian posterior throughout the training process in order to get the importance weights? OR are you just using the snapshots to get the model disagreement?***\n\nR4. Unlike SWAG, we didn't build the Gaussian posterior, since our method aims to obtain the uncertainty of the training samples. We employ a more efficient way to avoid the high computational and memory-storage overhead during sampling from the model posterior distribution. Specifically, compared with SWAG or other uncertainty estimation methods, our method is more efficient from two perspectives. First, we do not need to estimate the posterior distribution of the model parameters. Second, we do not need to sample lots of models from the estimated posterior distribution again to obtain uncertainty. Therefore, in practice, our model is much more efficient compared SWAG.\n\n***Q5. Section 3.1 says that the $N$ training examples are i.i.d. and sampled from $P$, but then immediately says that the subpopulation $g$ follows the distribution $P_g$. Shouldn't the assumption then be that the dataset is not i.i.d. and only conditionally i.i.d. given $P_g$?***\n\nR5. Thanks for the suggestion. For clarification, we will revise it to \"The setting can be considered as that the training distribution $P$ to be a mixture of $G$ groups $P_g$.\" in the revision.\n\n***Other minor concerns***\n\nWe also thank the reviewers for their other detailed suggestions, which helped us a lot. We will revise the paper based on the comments.\n\n**Reference**\n\n[1] Zhai R, Dan C, Kolter Z, et al. Doro: Distributional and outlier robust optimization[C]//International Conference on Machine Learning. PMLR, 2021: 12345-12355.\n\n[2] Liu, Evan Z., et al. \"Just train twice: Improving group robustness without training group information.\" International Conference on Machine Learning. PMLR, 2021.\n\n[3] Shen, Zheyan, et al. \"Stable learning via sample reweighting.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 34. No. 04. 2020.\n", " We thank the reviewer for their very thorough read of the paper and their extensive feedback. We will consider their many suggestions with great care. We only respond to the most salient points below, but we will follow up on the unresolved suggestion in the future.\n\n***Q1. Comparison with existing works.***\n\nR1. In the paper (L68 to L82), we have briefly described the differences between JTT and LISA. Here we explain it in more detail.\n\n---\n**Comparison with JTT.** JTT obtains and employs importance weights which is quite different from our method. \n* First, the importance weights are obtained in different ways. The proposed algorithm introduces uncertainty-based importance weights constructed by sampling multiple prediction results from the historical training trajectory, while JTT obtains importance weights by building an error set from a single prediction result. Therefore JTT can be seen as a special case of our method. \n* Second, the importance weights are employed in different ways. JTT just reweights the training samples during training, while we introduce sample weights into the vanilla mixup strategy to improve the importance weighting.\n\n\n---\n**Comparison with LISA.** The settings and motivations of LISA and the proposed method are different from our paper. \n* First, LISA assumed that the group label is available during training, which may limit its application in scenarios where group labels are inaccessible (e.g., anonymous samples for privacy protection [1]). Our paper studies the group-oblivious setting, i.e., without dependence on the group information, which enjoys wider applicability. \n* Second, LISA aims to improve the generalization of the model by mixing samples from the same subpopulation or the same label, while our method tries to improve the traditional importance reweighting through uncertainty-aware mixup. \n\nTherefore, our work is orthogonal to LISA, i.e., we can use our weight-building strategy to improve LISA. \n\n***Q2. Why can SWAG not be used directly in this method?***\n\nR2. Thanks for your suggestions. We will add the following discussions in revision. In the proposed method, we perform a prediction ensemble using the historical model snapshots for uncertainty quantification. This is for both efficiency, implementation, and accuracy reasons. \n\n* For efficiency, in contrast to SWAG, our method can significantly reduce the computational and memory-storage cost, since SWAG needs to sample multiple DNN models and performs inference computations on them. \n* For implementation, our uncertainty estimation method is agnostic to the optimization algorithm and backbone network. SWAG or some other methods may be limited to the optimization algorithm and backbone network. For example, an SGD optimizer is required in SWAG to estimate the posterior while other more suitable optimizers may be required when using some backbone networks (e.g., an AdamW optimizer is often required in a Bert-based backbone). \n* For accuracy, our method has achieved quite promising final accuracy in contrast to other methods. \n\nIn summary, we choose an uncertainty score that can achieve satisfactory performance while being more memory and computationally efficient. Further, we highlight that the main contribution of our paper is not focusing on specific uncertainty measures and the SWAG can be also naturally integrated into the UMIX framework. \n\n***Q3. Would it be more ideal to weight based on epistemic uncertainty only?***\n\nR3. This is a very insightful question. In fact, in our proposed method, the samples are indeed weighted only based on epistemic uncertainty, which can be understood from the following two perspectives. \n* First, our uncertainty is obtained by sampling from the model on the training trajectory, which can be seen as sampling from the model posterior in a more efficient way. \n* Second, as discussed in the limitation (L109 in the appendix), we consider that the training samples do not contain the inherent noise (aleatoric uncertainty) since it is usually intractable to distinguish between noisy samples and minority samples from data with subpopulation shifts. We leave this problem for future work. \n\nWe will add these discussions in the revision.", " \n***Q4. How the uncertainty measure changes over time during the process?***\n\nR4. We show the empirical results on the CelebA dataset in the following table and other details will be plotted as line charts to add to the revision. From the experimental results, we observe that during training, easy groups with sufficient samples can be fitted well in the earlier training stage. Conversely, the harder group is learned more slowly by the model. \n\nFor example, on the CelebA dataset, Group-0 and Group-1 with about 72K and 67K training samples quickly achieved over 95% accuracy. The accuracy rate on Group-2, which has about 23K training samples, increased more slowly and finally reached around 84%. The accuracy on Group-3, which has only about 1K training samples, is the lowest.\n\n| Training epoch | Group-0 ACC | Group-1 ACC | Group-2 ACC | Group-3 ACC |\n|:-----------------------:|:--------------------:|:--------------------:|:--------------------:|:--------------------:|\n| 1 | 99.6% | 100.0% | 15.7% | 0.0% |\n| 5 | 95.9% | 99.7% | 72.1% | 14.8% |\n| 10 | 95.9% | 99.5% | 78.9% | 26.1% |\n| 15 | 95.9% | 99.5% | 81.4% | 30.4% |\n| 30 | 96.1% | 99.5% | 84.3% | 36.6% |\n\n***Q5. Performance on the source domain test set along with the target domain results on Camelyon17.***\n\nR5. We present the experimental results on the source domain of our method and some comparison methods in the following table. From the experimental results, we can see that our method is more competitive on source domain data compared to JTT.\n\n| ERM | JTT | Ours |\n|--------------|--------------|--------------|\n| 95.2% | 92.5% | 93.7% |\n\n***Q6. It would be ideal if the authors could test on a couple more domain generalization datasets, as this seems relatively unexplored (only Camelyon-17), and many of the baseline methods are targeted towards the domain generalization setting.***\n\nR6. Thanks for your suggestion. In this paper, we mainly focus on the task of the subpopulation shift rather than domain generalization. Although we have shown that our method can improve the model robustness against out-of-domain settings on the Camelyon-17 dataset, we think this is just a preliminary exploration to validate its effectiveness on the domain generalization tasks. In practice, our method could achieve leading performance by focusing on these difficult samples with higher uncertainty in the training set. However, the task of domain generalization is more challenging than the sub-population shift and can be seen as an ill-posed problem [2]. We think that combining the invariant feature learning [3] with an importance-weighting-based mixup may be a promising way to handle the domain generalization task. Therefore, we leave this idea as a possible future direction. \n\n**Reference**\n\n[1] Hashimoto, Tatsunori, et al. \"Fairness without demographics in repeated loss minimization.\" International Conference on Machine Learning. PMLR, 2018.\n\n[2] Koh P W, Sagawa S, Marklund H, et al. Wilds: A benchmark of in-the-wild distribution shifts[C]//International Conference on Machine Learning. PMLR, 2021: 5637-5664.\n\n[3] Arjovsky M, Bottou L, Gulrajani I, et al. Invariant risk minimization[J]. arXiv preprint arXiv:1907.02893, 2019.\n", " \nWe thank the reviewer for the positive feedback and address the concerns point-by-point.\n\n***Q1. Training procedure details.***\n\nR1. Thanks for your suggestions. The training procedure is the same as vanilla ERM except for the proposed UMIX augmentation method/loss function, making our model more simple and general. More specifically, as shown in Algorithm 1, we first obtain the training samples from the training dataset, then perform the proposed method to augment the training samples and calculate the loss, and finally update the model parameters with an optimization algorithm. Moreover, the complete code has been released at https://anonymous.4open.science/r/UMIX-64ED to help readers to understand more training details. \n\n***Q2. Choices of hyperparameters.***\n\nR2. Thank you for your suggestions. Limited by space, the detailed hyperparameters setting for Algorithm 1 and Algorithm 2 is in Appendix B.3. For example, on the Waterbirds dataset, $T_s$ and $T$ are 50 and 10, respectively. For better clarification, we will move some main settings of hyperparameters to the main text in the next version. \n\n***Q3. Why is there hardly any samples with uncertainty from 0.3 to 0.8?***\n\nR3. The strict concentration around 0.3 and 0.8 is due to the attributes of the training datasets with imbalanced subpopulation distributions. Specifically, the majority groups tend to have smaller uncertainties (less than 0.3) due to sufficient training samples. On the other hand, minority groups often have higher uncertainties (greater than 0.8) due to less attention during training. Actually, it also shows the effectiveness of the employed uncertainty estimation strategy since the sharpness of uncertainty distribution is good.", " We appreciate the reviewer's comments and efforts sincerely. We believe the following point-to-point response can address all the concerns and misunderstandings.\n\n***Q1. Clarify the originality and significance.***\n\nR1. In short, the proposed method explores a novel and smart way to combine the superiorities of both mixup and importance-weighting strategies. We found the combination can bring both empirical improvements and theoretical insights. \n\nSpecificifically, the originality, and significance of our method are four-fold.\n\n* First, from the method perspective, as pointed out by the introduction and prior theoretical analysis [1, 2, 3, 4, 5], previous importance-weighting-based methods suffer an intrinsic limitation that their weighting effects will diminish along with the training proceeds, especially when they are applied to over-parameterized NNs. In this paper, motivated by the mixup strategy which can always produce \"reasonable\" novel samples, we propose a novel and smart way to combine the superiorities of both mixup and IW strategies. Given the high-level idea, we further instantiate it as a general learning framework with effective engineering implementations and the use of high-quality uncertainty quantification. We found the combination can bring both empirical improvements and theoretical insights as shown below. To the best of our knowledge, we are the first to explore the above idea and have successfully validated its effectiveness to tackle the issue of subpopulation shift.\n\n* Second, from the theoretical perspective, we provide insightful analysis that the employment of mixup can achieve a distribution-dependent generalization bound in the subpopulation shift setting and the bound can be tighter than the one achieved by conventional importance weighting methods. This interesting theoretical finding can motivate the research community to explore the usage of the mixup for obtaining a more explainable and tight generalization bound. \n\n* Third, from the empirical perspective, we have validated that the proposed UMIX achieves excellent performance in both group-oblivious and group-aware settings. Specifically, in the group-oblivious setting, our method achieves state-of-the-art performance in terms of worst-case accuracy on three datasets with subpopulation shifts. Further, we can still achieve competitive performance without using group information compared with group-aware algorithms.\n\n* At last, from the application side, given the broad usage of importance-weighting methods in distribution shift, fair machine learning, and long-tailed classification [6, 7], the proposed technique can be applied to a wide range of scenarios to improve the generalization ability of IW-based methods. \n\n***Q2. Other choices of this \"uncertainty score\".***\n\nR2. Thanks for your suggestions and we will add the following discussions in revision. At a high level, we perform a prediction ensemble using the historical model snapshots for uncertainty quantification. This is for both efficiency and accuracy reasons. \n\n* For efficiency, in contrast to other typical uncertainty quantification methods such as Bayesian learning or model ensemble [8,9], our method can significantly reduce the computational and memory-storage cost by employing the information from the historical training trajectory, since Bayesian learning or model ensemble needs to sample/save multiple DNN models and performs inference computations on them. \n\n* For accuracy, our method has achieved quite promising final accuracy in contrast to other methods. \n\nIn summary, we choose an uncertainty score that can achieve satisfactory performance while being more memory and computationally efficient. \n\nFurther, we highlight that the main contribution of our paper is not focusing on specific uncertainty measures and other measures (e.g., Bayesian-based or ensemble-based methods) can also be naturally integrated into the UMIX framework. \n\n***Q3. Significance of worst-case accuracy.***\n\nR3. On the one hand, the worst-case accuracy is a standard metric in this research community. As we can see, many recent papers [2,10,11,12] in this line also employ the worst-case accuracy as an evaluation metric. \n\nOn the other hand, the trade-off between the average and worst-case accuracy is a well-known challenge [6]. Different scenarios and applications will lay different emphasis on these two measures. For example, in fairness-related applications, we should pay more attention to the performance of the minority groups to reduce the gap between the majority groups and ensure the fairness of the machine learning decision system. \n\nIt's worth noting that even though the proposed method focus on worst-case accuracy, it also achieves competitive performance in terms of average accuracy compared with recent methods. ", " ***Q4. How to obtain the uncertainty $u_i$?***\n\nR4. As shown in the manuscript (Line 158-161 and Algorithm 1), the uncertainty score $u_i$ and importance weights are fixed as input for all the epochs during training in Algorithm 1. We restate the basic procedure of the proposed method here. \n\nOur method is mainly composed of two steps, including obtaining training importance weights and uncertainty-based mixup training. \n* Firstly, we employ Algorithm 2 to obtain the uncertainty-based training importance weights. \n* Then, the training importance weights are fixed as static weights to conduct uncertainty-based mixup training, i.e., Algorithm 1.\n\n***Q5. A suggestion about more memory-efficient implementation.***\n\nR5. This is a very useful suggestion and we will add this modification in the revision. In the current version, it has little impact on the training procedure because it only takes about $N*T$ floating points number of extra memory costs to save these results, where $N$ and $T$ are the number of training samples and epochs, respectively.\n\n**Reference**\n\n[1] Byrd J, Lipton Z. What is the effect of importance weighting in deep learning?[C]//International Conference on Machine Learning. PMLR, 2019: 872-881.\n\n[2] Sagawa S, Koh P W, Hashimoto T B, et al. Distributionally Robust Neural Networks[C]//International Conference on Learning Representations. 2020.\n\n[3] Zhai R, Dan C, Kolter Z, et al. Understanding Why Generalized Reweighting Does Not Improve Over ERM[J]. arXiv preprint arXiv:2201.12293, 2022.\n\n[4] Sagawa S, Raghunathan A, Koh P W, et al. An investigation of why overparameterization exacerbates spurious correlations[C]//International Conference on Machine Learning. PMLR, 2020: 8346-8356.\n\n[5] Xu D, Ye Y, Ruan C. Understanding the role of importance weighting for deep learning[C]//International Conference on Learning Representations. 2021.\n\n[6] Hashimoto T, Srivastava M, Namkoong H, et al. Fairness without demographics in repeated loss minimization[C]//International Conference on Machine Learning. PMLR, 2018: 1929-1938.\n\n[7] Japkowicz N. The class imbalance problem: Significance and strategies[C]//Proc. of the Int’l Conf. on Artificial Intelligence. 2000, 56: 111-117.\n\n[8] Gal Y, Ghahramani Z. Dropout as a bayesian approximation: Representing model uncertainty in deep learning[C]//international conference on machine learning. PMLR, 2016: 1050-1059.\n\n[9] Lakshminarayanan B, Pritzel A, Blundell C. Simple and scalable predictive uncertainty estimation using deep ensembles[J]. Advances in neural information processing systems, 2017, 30.\n\n[10] Liu E Z, Haghgoo B, Chen A S, et al. Just train twice: Improving group robustness without training group information[C]//International Conference on Machine Learning. PMLR, 2021: 6781-6792.\n\n[11] Michel P, Hashimoto T, Neubig G. Distributionally Robust Models with Parametric Likelihood Ratios[C]//International Conference on Learning Representations. 2022.\n\n[12] Piratla V, Netrapalli P, Sarawagi S. Focus on the Common Good: Group Distributional Robustness Follows[C]//International Conference on Learning Representations. 2022.", " The paper extends the Mixup method by utilizing a dynamic uncertainty score as importance weight for Mixup samples. The uncertainty score (for a given x_i) is obtained by tracking the average prediction error of x_i through out the training trajectory, as an indication of how \"hard\" it is to learn this example.\n\nThe method is evaluated on 4 datasets with subpopulation shift. The proposed method outperforms others on \"worst case\" accuracy, but under-performs the baseline (ERM) on average accuracy. The overall writing is clear and easy to follow. However, I feel the originality and significance of the proposed method is thin. It is a straightforward extension of Mixup by combining importance weight and uncertainty score. The paper didn't explore or discuss other choices of this \"uncertainty score\" as importance weight. There's a whole literature on influence score (how influential is an example to the learning process), which can also play a similar role here.\n\nThe evaluation results are ok but not impressive. I'm not convinced that a better \"worst\" accuracy but degraded avg accuracy is a significant contribution, given all the extra compute required by UMix. Perhaps other reviewers could convince me how this is important and relevant to the research community.\n The uncertainty score u_i is updated every epoch, right? i.e. as the training epoch (T) progresses, you will get updated value of u_i(T). If so, please reflect that in Algorithm 1.\n\nIn Algorithm 2, you don't have to \"save\" all the predictions for every example at every epoch. Keeping a running average of $\\kappa(y_i, f_{\\theta_t}(x_i))$ over epoch t for each $x_i$ would be more memory efficient, right? NA", " The paper proposes a new mixup method (UMIX) based on uncertainty estimation and importance weighting for subpopulation shift. The authors also prove theoretically that UMIX can achieve better generalization error bounds over IW methods without mixup. **Strengths**\n\nOriginality: Though the ideas of uncertainty estimation, importance weighting and mixup are not new, the combination of these ideas are novel and intriguing.\n\nQuality: The authors proved empirically and theoretically that their method is better than other baselines. The results are rather solid.\n\nClarity: The paper is well-written and easy to follow.\n\nSignificance: The paper provides a new method for augmenting mixup via uncertainty.\n\n**Weaknesses**\n\nI have not identified major weaknesses of this paper. However, I do have some concerns and listed them in the “Questions” part below. \n1. While the idea proposed by the paper is straightforward, there are some missing details that are essential to justify the method’s effectiveness. For example, UMIX can be seen as a new data augmentation method/loss function, but how is the training procedure like? Is it similar as ERM, or is it adopted from some other algorithm. Adding this discussion would help to verify whether the comparisons are fair or not.\n\n2. The choices of parameters are missing and including them (such as T_{s} and T in Algorithm 2) would be nice.\n\n3. In Figure1, why is there hardly any samples with uncertainty from 0.3 to 0.8? Is it an effect of KDE, or is it due to the attributes of the datasets?\n\nMinor questions:\n\n1. Line59: contirbution $\\rightarrow$ contributions The authors have thouroughly discussed the limitations and social impacts of their work in the appendix. ", " The authors tackle the problem of subpopulation shift without subpopulation labels. They propose a method called uncertainty-aware mixup (UMIX), which augments regular mixup with importance weights computed based on predictive uncertainty. The authors benchmark their method against a large set of group aware and group unaware baselines on standard datasets, finding that their method shows competitive worst-case accuracy. Finally, the authors provide theoretical insight into why their method outperforms traditional importance weighting-based methods. Strengths:\n- The paper is generally well-written and easy to follow.\n- The authors compare against a wide range of methods on the standard datasets, and report their results with standard deviations (in the appendix).\n- The method performs competitively relative to the baselines.\n\nWeaknesses:\n1. Though the method is novel, is it only an incremental change from what is proposed in JTT and LISA.\n2. The authors should provide more empirical justification for the uncertainty measure that they use. Though it is inspired by SWAG, it does seem quite different from SWAG. How does the measure of uncertainty compare with SWAG, and why can SWAG not be used directly in this method (by sampling from the posterior over weights)?\n3. It seems that the uncertainty measure takes both epistemic and aleatoric uncertainty into account. Would it be more ideal to weight based on epistemic uncertainty only, as some groups may inherently have more error than others?\n4. It would be interesting to explore how the uncertainty measure (Fig. 1) changes over time during the process of running Algorithm 2. Does this empirically support the intuition from Lines 195-198? \n5. For Camelyon-17, I would suggest showing performance on the source domain test set along with the target domain results.\n6. It would be ideal if the authors could test on a couple more domain generalization datasets, as this seems relatively unexplored (only Camelyon-17), and many of the baseline methods are targeted towards the domain generalization setting. \n7. The authors should state the range of hyperparameters tuned, as well as the total tuning budget, in Appendix B3.\n Please comment on points 2-6 from above. The authors adequately address the limitations in the appendix.", " The authors propose a importance reweighting scheme for mixup which promotes a fair training balance between subgroups in the data. The does not require group\nlabels during training. # Strengths\n\n- The paper is well placed among recent works in both mixup, and importance reweighting methods.\n- The method performs well without group information during training which is impressive\n- The theoretical analysis provides a nice\n- Overall I think this is a solid work, but I some clarification on the issues raised in the following sections.\n\n# Weaknesses\n\n- L190 says that you assume a reasonable importance weight is linearly\npositively correlated to the corresponding uncertainty. What is a 'reasonable'\nimportance weight, and on what basis can this assumption be made? I realize\nthis is shown in Figure 1, but there should be some provided justification or\nreference to the fact that this will be empirically tested later.\n\n- How does UMIX perform without the group labels in the validation set? If the\nmethod is assumed to be oblivious to the group information, then it may not be\nreasonable to assume that they are always in the validation set.\n\n# Minor\n\n- L113: BNN's is proposed --> BNN's have been proposed.\n- L115: Performing ensembles --> ensembling them.\n- L122: upweight mixed samples thus can encourage --> upweight mixed samples, and thus can encourage.\n- L158: weights of UMIX are posed --> What does this mean?\n- L178: $p(theta; \\mathcal{D})$ --> shouldn't this be $p(\\theta | \\mathcal{D})$?\n- L180: with $T$ Monte Carlo Sampling --> with $T$ Monte Carlo samples\n- L193: in practice we could set $c = 1$ --> Does this mean that you do set $c=1$ in practice? It should be clearly stated if that is the case.\n- L295: proportion is --> proportion being\n- L296: in specific --> specifically\n - Section 5 states \"Thus our bound can be tighter when\n315 the intrinsic dimension of data is small (i.e., rank(Σ) ≪ d).\" Is this really useful? Can you point to some intuition or concrete examples of when this would usefully lower the bound? When can we reasonably expect that to not be full rank? On the same note, is this referring to the dimension in the input space, the output space before the loss function, or something else entirely?\n\n- Are you actually MC sampling the saved SWAG models by building the Gaussian\nposterior throughout the training process in order to get the importance\nweights? OR are you just using the snapshots to get the model disagreement?\n\n- Section 3.1 says that the $N$ training examples are i.i.d. and sampled from\n$P$, but then immediately says that the subpopulation $g$ follows the\ndistribution $P_g$. Shouldn't the assumption then be that the dataset is not\ni.i.d. and only conditionally i.i.d. given $P_g$? The authors have addressed both in the appendix. " ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 6, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 3, 4, 3 ]

[ "PQP9Ewfs2gk", "PQP9Ewfs2gk", "vthQM_yYTv", "hWuBNAvhq5U", "AyWDbSRAUBv", "AyWDbSRAUBv", "2wHsr1CHoxp", "2wHsr1CHoxp", "sukZ66QsCY", "PQP9Ewfs2gk", "PQP9Ewfs2gk", "nips_2022_IzpgGB5pC_s", "nips_2022_IzpgGB5pC_s", "nips_2022_IzpgGB5pC_s", "nips_2022_IzpgGB5pC_s" ]

[ "KNAqEeAI90Z", "lhctoqmb57V", "-2Oj-Qfks6", "39FzGQaoPiR", "3xHEkG9x1Ff", "S15M6yBlnpqM", "Ao9lBGTqIQI", "USWN_okhorXn", "gH1VnGI2z60P", "dZitzt40BMW", "a1eRTqP6kjn", "48EMTfdxkFn", "y2m7LMIYV8", "Y8H7Sm1dyq9", "vrUEweqH-qi", "CVnvpNtK0an", "X5qdsAAacNE", "ucMAUxUaK2d", "GG1KR1m9ylv" ]

[ "author", "author", "official_reviewer", "author", "official_reviewer", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Dear Reviewer h3Wy,\n\nThank you for acknowledging that our research problem is *\"extremely important\"* and *\"scale of the experiments conducted is large\"*.\nWe also thank you for pointing out the computational neuroscience papers. After reading them carefully, we find that they *do not* perform large-scale quantitative analysis as we do to show the relationship between invariance and network performance. In our revised paper, we have included these works and discussed their differences from our work (Lines 23-31 in the main paper).\n\nFurthermore, we have highlighted the essential difference between our network-level EI and neuron-level invariance measures (please see Q2-Q4 in the response and Lines 110-111 in the main paper).\n\nIn addition, we have clarified that the relationship between out-of-distribution generalization and invariance is *not* discussed in referenced works (please see Q5 and Q6).\n\nWe believe ***our claims are correct in the context of the referenced works***. We hope our response has addressed your initial concerns. Please let us know if you have any other questions.\n\nBest,\n\nAuthors", " Dear Reviewer NZba\n\nWe appreciate your constructive suggestions and thank you for raising your score. We believe it would be interesting and promising to consider more special cases in the definition of invariance. We have highlighted this research point in our revised paper.\n\nKind Regards,\n\nAuthors", " Most of my concerns are addressed. While the design of EI still seems unnatural to me, the empirical results are compelling. I have updated my score accordingly.", " Dear Reviewer qWbK,\n\nThank you for your valuable comments and constructive suggestions! We are happy to hear that your concerns have been resolved.\n\nKind Regards,\n\nAuthors", " Rebuttal has solved all my concerns. I will maintain my initial score. ", " Dear Reviewers,\n\nThank you for your detailed and thoughtful feedback. Inspired by your valuable suggestions, we have added more experimental analyses and included the suggested related works. We have also updated the main paper and supplementary material. We summarize the major changes below:\n\n- **Correlation study under the iWildCam-WILDS setup**. We show that under this new setup, rotational invariance (EI) is also correlated with accuracy (*Q4/Reviewer G2Vw, Section D.2 in the Supp.*).\n\n\n- **More research on EI**. ***First***, we compare our EI with existing measures (*e.g.*, JS and L2) on the CIFAR-10 and iWildCam-WILDS setups (*Q1/Reviewer NZba, Section A.2 in the Supp.*). We show that other measures lead to very unstable correlations under different setups. In contrast, EI strongly correlates with accuracy on all test sets under the three setups. ***Second***, inspired by the suggestions of Reviewers NZba and G2Vw, we discuss a modified version of EI that considers the prediction consistency in the \"otherwise\" case of EI. We show that EI is more stable than this modified version on the ImageNet setup (*Q4/Reviewer NZba, Section E in the Supp.*).\n\n- **More experimental analyses**. ***First***, we show that model invariance and generalization exhibit a strong correlation on ObjectNet (*Q4/Reviewer qWbK, Section D.1 in Supp.*).\n ***Second***, we show that using more rotation angles to measure rotation invariance does show higher correlations (*Q1/Reviewer G2Vw, Section E in Supp.*). ***Third***, we show that the accuracy and invariance of randomly initialized models are very low and cluttered (no linear relationship) (*Q5/Reviewer G2Vw*).\n\n- **More related works**. ***First***, we include computational neuroscience works (*suggested by Reviewer h3Wy*). ***Second***, two theoretical studies (*suggested by Reviewer qWbK*) are also included. We also highlight our work's differences (*Lines 23-28 in the main paper*).\n\nWe hope our response has addressed the initial concerns. Please let us know if you have any other questions.\n\nKind Regards,\n\nAuthors", " Dear Reviewer G2Vw,\n\nThank you for your positive assessment and constructive feedback on our work. We gratefully acknowledge that your suggestions helped us to improve our manuscript.\n\nBest,\n\nAuthors", " I thank the authors for a clear and concise rebuttal, where the main issues raised in the review were addressed. I believe the paper is of great interest, particularly the thorough evaluation, which is even more complete after rebuttal.\nFor these reasons, and those mentioned in my review, I maintain my initial score.", " \n**Q1: Authors incorrectly claim “existing works are qualitative”, but “there is a very long list of existing works which study this relationship quantitatively” [1-8].**\n\nThank you for pointing out these works, which we carefully read during rebuttal. We find there is no quantitative analysis of the relationship between invariance and generalization: these works only quantitatively study invariance itself. We therefore believe our claim is correct. \n\n**Q2: Authors incorrectly claim existing works are “not taking into account confidence”, but “Invariance has been long measured in neuroscience with metrics that take into account confidence.” [1-4].**\n\nWe respectfully disagree. The suggested papers ***do not really discuss the confidence*** as we know it in deep neural networks [a]. Specifically, the suggested papers [1-4] study ***response values of an individual neuron*** for the input stimulus, where such response values are at the local neuron level. In comparison, “confidence” in our work refers to ***class prediction score*** given by the classifier for an input image, and such confidence value is on the global network level. This definition of confidence is widely adopted in the community [a]. Therefore, we believe our claim is correct. \n\n*[a] Goodfellow, Ian, Yoshua Bengio, and Aaron Courville. Deep learning. MIT press, 2016.*\n\n**Q3. Theoretical investigations [7,8] have also presented much more articulate representations of invariance measurement.**\n\nGreat comment. We agree both works give interesting insights of invariance measurement on the ***representation level***. Specifically, they define that a representation map is invariant if it gives the same representation on the original and transformed data.\nHowever, this representation-level invariance measurement ***cannot be applied*** under this paper’s context: analyzing different models of their invariance vs. generalization ability. The reason is that different models have very different representations (*e.g.*, dimensionality). In comparison, EI does not work on the feature level: the proposed usage of confidence score allows us to compare different models effectively. \n\n**Q4: No novel contribution: The formulation of EI is very similar to those proposed in [1], and the specialization score presented in [2].\nThank you for this comment. We would like to emphasize that EI is very different from fractional task variance (FTV) [1] and specialization score [2].**\n\nFirst, ***FTV [1] does not*** measure invariance. Instead, FTV describes which tasks a neuron tends to learn.\n\nSecond, ***specialization score [2]*** measures a neuron’s certain property which is a ***combination*** of selectivity and invariance instead of invariance itself. Specifically, in its formula, the specialization score is computed by an invariance score and a selectivity score: the latter two have different physical meanings, and their geometric mean no longer measures invariance itself. \n\n\nThird, the invariance score considered in [2] is computed on the ***neuron level***: the invariance score of a neuron is calculated according to its response/activity changes on the transformed stimulus. In comparison, our EI is on the ***network level***: we measure how consistent the network's class predictions are on transformed test data.\n\n\nWe will add the above discussions to the revised paper. \n", " **Q5: Authors incorrectly claim “existing works are in-distribution”, but “In [7,8,2] authors have studied specifically the problem of out-of-distribution and invariance. In fact, [2] presents new, complex datasets to study specifically this particular problem.”**\n\nThanks for this comment. We would like to point out that ***[7,8] does not*** use out-of-distribution data or study the relationship of OOD and invariance: they only study invariance. On the other hand, ***[2] studies a very specific OOD problem***: recognizing objects under new viewpoints, while the OOD generalization we study is much more general (much more beyond viewpoint variation) and widely acknowledged in the community [b,c]. Further, as mentioned in our reply to *the above Q4*, ***[2] does not study pure invariance vs. OOD***, but a mixed property, and this investigation is on the neuron level instead of the network level as we do. In addition, the scale of the experiments in [2] is limited: it only studies a few network structures.\n\n*[b] Taori, Rohan, et al. \"Measuring robustness to natural distribution shifts in image classification.\" In NeurIPS, 2020*\n\n*[c] Hendrycks, Dan, et al. \"The many faces of robustness: A critical analysis of out-of-distribution generalization.\" In ICCV, 2021*\n\n\n**Q6: Authors incorrectly claim “no strong quantitative correlation shown on OOD data”, but “both [1,2] show quantitatively that generalization positively correlates with invariance. This has also been discussed at length in previous works including [7,8]”**\n\nThanks for the comment. We find that ***OOD generalization is not discussed in the studies of [1,7,8]***, so there is no report of the quantitative relationship between OOD and invariance of [1,7,8]. In fact, there is even no mention of invariance in [1]. \n\nRegarding [2], it only studies the relationship between specialization score and a specific OOD problem (*i.e.*, unseen category-viewpoint combination). As mentioned above, the specialization score ***is not equal to*** the invariance score, and this specific OOD problem ***is not representative*** of the general OOD generalization problem the machine learning community is studying. \n\nAs such, we feel that there is no obvious error in our claim. \n\n**Reference**\n\n*[1] Yang, Guangyu Robert, et al. \"Task representations in neural networks trained to perform many cognitive tasks.\" Nature neuroscience, 2019*\n\n*[2] Madan, Spandan, et al. \"When and how convolutional neural networks generalize to out-of-distribution category–viewpoint combinations.\" Nature Machine Intelligence, 2022*\n\n*[3] Goodfellow, Ian, et al. \"Measuring invariances in deep networks.\" In NIPS, 2009*\n\n*[4] Riesenhuber, Maximilian, and Tomaso Poggio. \"Just one view: Invariances in inferotemporal cell tuning.\" In NIPS, 1997*\n\n*[5] Achille, Alessandro, and Stefano Soatto. \"Emergence of invariance and disentanglement in deep representations.\" The Journal of Machine Learning Research, 2018*\n\n*[6] Bricolo, Emanuela, Tomaso Poggio, and Nikos K. Logothetis. \"3D object recognition: A model of view-tuned neurons.\" In NIPS, 1996*\n\n*[7] Poggio, Tomaso A., and Fabio Anselmi. Visual cortex and deep networks: learning invariant representations. MIT Press, 2016*\n\n*[8] Anselmi, Fabio, Lorenzo Rosasco, and Tomaso Poggio. \"On invariance and selectivity in representation learning.\" Information and Inference: A Journal of the IMA, 2016*\n\n", " **Q1: The method could benefit from using multiple transformed versions of x (eg. randomly sampled rotations). However, the proposed 3-way rotation is enough to prove the validity of EI in this work.**\n\nGood idea. During rebuttal, we performed a correlation study under the ImageNet setup using more randomly sampled rotations. Specifically, we use 5 rotations (two new angles [40.1, 215.0] plus the original three 90-degree rotation angles) and 7 rotations (four new angles [38.4, 134.2, 194.0, 340.7] plus the original three 90-degree rotation angles). Results are presented below.\n\n|Test Set|ImageNet-Val|ImageNet-R|ImageNet-A|\n|:-|:-:|:-:|:-:|\n| 3 rotations | 0.927 | 0.846 | 0.778 |\n| 5 rotations | 0.936 | 0.860 | 0.807|\n| 7 rotations | **0.948** |**0.874**| **0.814**|\n\nWe observe that using more rotation angles does yield higher correlations (measured by Spearman's rank correlation). We will add these results in the revised version.\n\n**Q2: Could you comment on the use of three 90 degree rotations per sample to compute EI. Could this be missing many cases where the model is invariant (or not)? I believe EI could be used to \"map\" the invariance of a CNN in the full transformation domain, which could be extremely important to guide machine learning practitioners to improve their models.**\n\nInsightful idea. We would like to share our thoughts from the following aspects. First, for rotation invariance, using three 90-degree angles satisfies our basic needs, as illustrated in the experiment. During rebuttal, we further find that using more rotation angles is beneficial (see our reply to Q1). It likely means using more angles captures finer details of a model’s invariance property. \n\nSecond, rotation invariance measured in our work may not be sufficient to reflect invariance to other transformations (*e.g.*, shear and illumination change). If we could analyze the invariance of a CNN in the full transformation domain, we would probably be able to gain a more comprehensive understanding of model generalization / invariance capacities. \n\n**Q3: It is reasonable to discard all cases where both predictions disagree, but many times they might mildly disagree, even within the expected standard deviation. The \"otherwise\" case in EI (Eq. 1) could be further refined accounting for those cases.**\n\nA: Good suggestion. In our work, we mainly discuss four representative cases and explain the limitations of existing measures (*e.g.*, JS and L2) for correlation studies. In light of your question, during rebuttal we modify the proposed EI to consider predictions that \"slightly disagree\". More details can be viewed in our response to ***Q4/Reviewer NZba***. \n\nWe show that the modified EI gives a stronger correlation only on ImageNet-Val and a weaker correlation on other test sets. From this trial, we think it is not easy to improve EI that covers some unconsidered cases, especially in this short period. The proposed method can thus serve as a starting point to inspire new research in the long run. \n\n**Q4: I missed at least one dataset that is strongly OOD: train on Imagenet and finetune for a dataset that is completely unrelated to Imagenet. Please take this as a suggestion to further improve the paper.**\n\nGood suggestion. In the light of this suggestion, we newly use iWildCam-WILDS [a] for correlation study during rebuttal. iWildCam-WILDS is an animal species classification dataset, where the distribution shift arises due to variations in camera angle, lighting, and background.\n\n*[a] Koh, P. W., Sagawa, S., Marklund, H., Xie, S. M., Zhang, M., Balsubramani, A., Hu, W., Yasunaga, M., Phillips, R. L., Beery, S., et al. WILDS: A benchmark of in-the-wild distribution shifts. In ICML, 2021*\n\nFollowing the practice in [3], we finetune 30 classifiers that are pretrained on ImageNet using the codes provided by [a]. Then, we report the correlation results on its out-of-distribution test set (OOD Test). \nWe show that under the iWildCam-WILDS setup, rotation invariance (EI) also correlates with accuracy (measured by the macro F1 score). Please refer to the table below. \n\n|Test Set|Pearson’s Correlation ($r$)|Spearman’s Rank Correlation ($\\rho$)|\n|-----|:------:|:------:|\n|OOD Test | 0.902 | 0.915|\n\n", " \n**Q5: I would suggest including randomly initialized networks (not trained) in the study. These networks could also be invariant, but do they follow the same trend shown in the plots? Or training till convergence is a condition for EI to work? The study of randomly initialized networks could also shed some light on the invariance induced by the architectural design alone.**\n\nInteresting suggestion. First, during rebuttal we tested 20 randomly initialized networks (e.g., ViT and EfficientNet) on 7 ImageNet test sets. We observe that both their rotation invariance and classification accuracy *are very low* and cluttered (no linear relationship) and conclude that these networks do not have good invariance capacity. So for EI to work we cannot use randomly initialized models. \n\nFurthermore, we also tested 10 CIFAR-10 classifiers that are not trained till convergence. Specifically, the classifiers are only trained with a few epochs. We observe that they still follow a similar linear trend. Therefore, training till convergence is not a necessary condition for EI to work.\n\n**Q6: What is the correlation between EI (grayscale) and EI (rotation). Intuitively, they are strongly correlated; if so, which of the two is the most important source of invariance for generalization?**\n\nInteresting point. We observe that they are indeed strongly correlated. In our new experiment, the Spearman's rank correlation $\\rho$ is 0.947, 0.950, and 0.965 on ImageNet-Val, ImageNet-S, ImageNet-R, respectively. It suggests that the network simultaneously gains rotation and grayscale invariance.\n\nRegarding which invariance is more important for generalization, our correlation studies (Figures 2 and 3) show that rotation invariance generally has a stronger correlation with accuracy than grayscale invariance (5 out of 6 test sets). The only case for grayscale to have a stronger correlation is ImageNet-R, which is featured by style shift. We think under style shift, the model probably has more incentives to be invariant to color changes. \n\nIn the real world, images often exhibit diverse geometric and color variations. To measure generalization in these scenarios, we think both rotation and grayscale invariance are critical.\n", " **Q1: Using \"Drawback of existing invariance measures\" to summarize the paragraph (lines 97-105) is not very coherent and is a bit confusing.**\n\nA: Thank you for pointing this out. To avoid confusion, we will use “limitations of some commonly used invariance measures”.\n\n**Q2: Additional techniques such as confidence [48] and sharpness [49] are used when KL [50, 51] or L2 are used for maintaining consistency. It can also be mentioned these techniques to help illustrate why KL and L2 are not suitable for correlation study.**\n\nA: Good idea. We fully agree that these techniques (confidence [48] and sharpness [49]) can be used to discard samples (e.g., case d) with flat softmax outputs when computing the consistency loss. This will avoid scenarios where KL and L2 mistake them as samples with high prediction consistency. We will discuss these techniques in Lines 103-105.\n\n**Q3: Correlation study on ObjectNet would be interesting.**\n\nA: Great suggestion. Following the practice in [2], we evaluate classifiers on the 113 ObjectNet classes that overlap with ImageNet and report correlation study results.\n\n|Type|Pearson’s Correlation ($r$)|Spearman’s Rank Correlation ($\\rho$)|\n|-----|:------:|:------:|\n|Rotation | 0.982 | 0.975|\n|Grayscale | 0.964 | 0.951|\n\n***On ObjectNet, we observe that model invariance and generalization exhibit a strong correlation***: when using rotation invariance, Pearson's correlation ($r$) is 0.982, and Spearman’s Rank correlation ($\\rho$) is 0.975. Under grayscale invariance, $r$ is 0.964, and $\\rho$ is 0.951.\n\n[2] Miller, John P., et al. \"Accuracy on the line: on the strong correlation between out-of-distribution and in-distribution generalization.\" International Conference on Machine Learning. PMLR, 2021.\n\n**Q4: Related works ( [a,b]) should be included.**\n\nA: Thanks. Work [a] derives model complexity bounds based on the sample cover induced by data transformations. Work [b] develops a new generalization error bound using the proposed quotient feature space for invariant and equivariant deep neural networks. Both works qualitatively suggest that learning invariant features benefits generalization. Different from them, we perform a large-scale quantitative correlation study using various models and different test sets and empirically report that model invariance and generalization exhibit a strong linear correlation on both in- and out-of-distribution test sets. We will update Lines 23-29 to discuss both works.\n\n*[a] Zhu Sicheng, Bang An, Huang Furong. \"Understanding the generalization advantage of model invariance from a data perspective.\" In NeurIPS, 2021*\n\n*[b] Sannei, Akiyoshi, Masaki Imaizumi, and Makoto Kawano. \"Improving generalization bounds for group-invariant/equivariant deep networks through quotient feature spaces.\" Uncertainty in Artificial Intelligence, 2021*\n\n\n**Q5: Differences or new contributions should be further highlighted in Section 2.**\n\nA: Thanks. Lines 59-75 of Section 2 introduce works of predicting generalization in deep learning (PGDL). These works generally assume an in-distribution test set and study limited types of networks. In comparison, we conduct a much more comprehensive study on both in-distribution and out-of-distribution test sets, using various network architectures. We will update Lines 68-75 to highlight the difference between our work and PDGL.\n\n\n**Q6: Section 5.7 should be highlighted as it presents another key observation.**\n\nThanks. We will make Section 5.7 a separate section and integrate the correlation results (Figure A-3) in the main paper.\n", " **Q1: For CIFAR-10 the authors do not do any comparison of measures. Using more datasets for comparing invariance measures.**\n\nGood suggestion. To more comprehensively compare EI with existing measures, we newly report the correlation results under the **CIFAR-10 setup**. We report the Spearman’s rank correlation ($\\rho$) between classification accuracy and rotation invariance. From the results (see table below), we find when EI is used, there is a stronger correlation on the three test sets under the CIFAR-10 setup.\n\n|Test Set|L2|JS| acc. difference| consistency|consist.+conf.|EI|\n|:-|:-:|:-:|:-:|:-:|:-:|:-:|\n|CIFAR-10|-0.164|0.088|0.006|0.848|**0.934**|**0.934**|\n|CIFAR10.1|0.190|0.270|0.625|0.787|0.910|**0.927**|\n|CINIC |0.265 |0.334|0.550|0.637|0.883|**0.905**|\n\nTo further demonstrate the usefulness of EI for correlation studies, we newly use **iWildCam-WILDS** setup (see ***Q4/Reviewer G2Vw*** for more details) to compare EI with other measurements. Results are presented below. Under this setup, our method still has a high correlation ($\\rho$=0.915). \n\nWhile correlation strength computed with \"accuracy difference\" is higher than EI, we emphasize that this measure gives much lower correlations under other setups. For example, under the CIFAR-10 setup, the correlation strength ($\\rho$) computed by \"accuracy difference\" and EI is 0.625 and 0.550 on CIFAR10.1 and CINIC, respectively. These experiments indicate that EI has very strong and stable correlations with models’ OOD accuracy.\n\n|Test Set| L2|JS|acc. difference |consistency|consist.+conf.|EI|\n|:-|:-:|:-:|:-:|:-:|:-:|:-:|\n|OOD Test |0.819| 0.665 |**0.934** | 0.158 | 0.420 | 0.915|\n\n**Q2: Evaluate the Spearman’s rank correlation for JS-divergence on ImageNet-S and ImageNet-A.**\n\nThanks for the suggestion. During rebuttal we evaluate Spearman’s rank correlation for other measures including JS-divergence on a series of benchmarks including ImageNet-S and ImageNet-A. Results are summarized in the table below.\nWe observe that JS only shows a strong correlation on ImageNet-Val while EI exhibits a strong correlation in all the five datasets.\nWe will update Table 1 with the additional Spearman’s rank correlation metric.\n\n|Test Set|ImageNet-Val|ImageNet-R|ImageNet-S|ImageNet-A|ObjectNet|\n|:-|:-:|:-:|:-:|:-:|:-:|\n| JS | -0.905 | -0.172 | 0.148| -0.257 | -0.468 |\n|L2| -0.834 | -0.053 |0.462|0.001| -0.262 |\n|acc. difference| -0.904| -0.172 | -0.147 | -0.257 | 0.421 |\n|consist.| 0.973 | 0.870 | 0.801 | 0.765 | 0.955|\n|consist.+conf.| **0.980** | **0.856** | 0.745 | 0.722|0.950|\n| EI | 0.927 | 0.846 | **0.897** | **0.778** | **0.975** |\n\n**Q3: If we focus on Spearman’s rank correlation, EI is no longer superior in predicting generalization among other measures like the prediction consistency.**\n\nGreat question. It is true EI gives a lower Spearman's rank correlation than a few other measures (*e.g.*, \"prediction consistency\") on ImageNet-S and ImageNet-Val. However, we would like to emphasize these measures lead to very unstable correlations under different setups. For example, while “prediction consistency” presents a strong correlation ($\\rho$ = 0.973) on ImageNet-Val, it exhibits a much weaker correlation ($\\rho$ = 0.158) on iWildCam-Wilds. \n\nIn comparison, EI has strong correlations on all the test sets under the three setups (CIFAR-10, ImageNet, and iWildCam-Wilds). Thus, we think EI generally is more indicative of model generalization ability than other measures.", " **Q4: Why does a model making confident mistakes have the same invariance as a model making unconfident mistakes (Figure 1 (c) and (d))? If we look at the invariance from the loss perspective, the former model usually incurs a higher consistency loss than the latter one, hence less invariant.**\n\nGreat question. We intuitively define the EI score as 0 if the network gives different class predictions on the original and transformed image (the \"otherwise\" case in Eq.1). Inspired by the question, we further consider the consistency of the softmax outputs when defining the \"otherwise\" case in EI. Specifically, we use the *negative JS* in the “otherwise” case. Under this modification, the EI scores are -0.665 and -0.029 in case (c) and case (d), respectively. Using this modified EI, we report the correlation studies on a series of benchmarks below (using the ImageNet models). \n\n|Test Set|ImageNet-Val|ImageNet-R|ImageNet-S|ImageNet-A|ObjectNet|\n|:-|:-:|:-:|:-:|:-:|:-:|\n| EI | 0.927 | **0.846** | **0.897** | **0.778**|**0.975**|\n|Modified EI|**0.972**|0.764|0.422|0.575|0.937|\n\nCompared with EI, the modified EI gives a higher Spearman’s rank correlation ($\\rho$) on ImageNet-Val (0.972 vs. 0.927). However, on harder OOD test sets (*e.g.*, ImageNet-S), the modified EI usually has a weaker correlation (0.422 vs. 0.897). \n\nIn designing EI, we mainly study four representative cases and explain the limitations of some commonly used measures (*e.g.*, JS and L2). We also acknowledge that considering more special cases would be beneficial for refining the \"other\" cases of EI, but considering the complexity of this problem, this is unlikely to be achieved in the short run. As such, we would like to view the current work as a starting point that could inspire new research in the long run.\n", " The paper starts with three claims in existing works that motivate their work---(1) the relationship between generalization and invariance are largely qualitative in existing work, (2) they are restricted to in-distribution datasets, and that (3) existing quantitative methodologies to quantify invariance do not take into account confidence of predictions. To address these, the authors propose a metric for invariance (EI), which uses both consistency and confidence of model predictions. Then, they conduct an evaluation of how generalization and invariance are correlated across a variety of architectures. Strengths:\n\n1. The problem is extremely important. Understanding the mechanisms driving generalization is a fundamental problem in ML. Invariance has been proposed as one potential mechanism generalization could be achieved. And so, studying their relationship in deep models is important.\n\n2. Scale of the experiments conducted is large.\n\nWeaknesses:\n\n1. Severely incorrect claims: Unfortunately, there are serious flaws at in the claims made in this work. Below I list them with reasoning/citations:\n\na) Existing works are qualitative: There is a very long list of existing works which study this relationship quantitatively, and have reported it before [1-8]\nb) Existing works are in-distribution: In [7,8,2] authors have studied specifically the problem of out-of-distribution and invariance. In fact, [2] presents new, complex datasets to study specifically this particular problem.\nc) Not taking into account confidence: Invariance has been long measured in neuroscience with metrics that take into account confidence. Adaptations of this metric can be seen in [1,2,3,4]. Theoretical investigations [7,8] have also presented much more articulate representations of invariance measurement.\nd) No strong quantitative correlation shown on OOD data: Both [1,2] show quantitatively that generalization positively correlates with invariance. This has also been discussed at length in previous works including [7,8].\n \n2. Completely missing a large portion of literature on invariance and generalization: There is a large body of literature on invariance and generalization (beyond the ones cited below), which this paper has completely ignored. It is not placed in the context of these works, and that may be partly why the paper has made incorrect claims due to being unaware of existing works. \n\n3. No novel contribution: The formulation of EI is very similar to those proposed in [1], and the specialization score presented in [2]. It is what EI adds beyond existing work, as the problems mentioned in this paper as motivations are not true, and have been already addressed by past work which the paper has not referred to.\n\nIn summary: This paper seems unaware of a large subfield of existing literature in neuroscience and AI, which has led to incorrect claims about existing works. It is unclear how EI adds beyond existing works. All in all, the paper needs a major rethinking and reevaluation of the contributions in light of a thorough literature review on generalization and invariance.\n\nReferences\n\n1. https://www.nature.com/articles/s41593-018-0310-2\n2. https://www.nature.com/articles/s42256-021-00437-5\n3. https://papers.nips.cc/paper/2009/file/428fca9bc1921c25c5121f9da7815cde-Paper.pdf\n4. https://papers.nips.cc/paper/1997/file/792c7b5aae4a79e78aaeda80516ae2ac-Paper.pdf\n5. https://arxiv.org/pdf/1706.01350.pdf\n6. https://papers.nips.cc/paper/1996/hash/2812e5cf6d8f21d69c91dddeefb792a7-Abstract.html\n7. Poggio, T.A. and Anselmi, F., 2016. Visual cortex and deep networks: learning invariant representations. MIT Press.\n8. https://academic.oup.com/imaiai/article-abstract/5/2/134/2363483?redirectedFrom=fulltext\n N/A Yes.", " This work proposes a very simple to implement, yet effective, metric (effective invariance or EI) to assess the invariance of a model with respect to some input transformation. The main novelty of the proposed method is that it does not rely on the true label, but rather on the agreement between the predictions given an image and its transformed version.\n\nThe main findings of the paper are about the role of invariance in multi-class classification problems. The authors find that invariance (as measured by EI) is strongly correlated with accuracy for a large set of models and datasets. Moreover, it is empirically proven that EI is much better than Jensen-Shannon Divergence at capturing invariance for OOD datasets, showing that EI is a more robust metric for invariance.\n\nAn additional (and important) observation included in the paper is that training with additional data is more effective (in terms of invariance) than any of the augmentation strategies tried. \n\nThe experimental setup is very solid, with a large breadth of models and datasets being evaluated. Moreover, the paper is well written and the language used is clear and concise. **Strengths:**\n\n* The proposed measure for invariance is extremely simple to implement, and well backed up by examples and experimental results.\n* The experimental setup is very solid, with a large amount of state of the art models being analyzed. The distinction between fully-supervised, semi-supervised and models trained with more data is smart, and allowed the authors to reach some conclusions in terms of the use of more data in training wrt. augmentations.\nThe comparison with other measures for invariance in Fig. 6, Table 1 and Appendix A is very interesting, and also clearly favorable for EI.\n* The paper's language is clear, I enjoyed the reading. The experimental setup is very well described, with links to all models used and datasets. I believe one of the major strengths of this paper is the experimental setup itself.\n\n**Weaknesses:**\n\n* Although the metric proposed is evaluated using 3 rotations of 90 degrees per image, I believe the method could benefit from using multiple transformed versions of $x$ (eg. randomly sampled rotations), and then measuring the agreement similarly to Eq. (1). However, I believe the proposed 3-way rotation is enough to prove the validity of EI in this work.\n\n* The EI proposed in Eq. (1) is always 0 when there is a disagreement between the prediction of the unaugmented $x$ and the augmented $x^\\prime$. It is reasonable to discard all cases where both predictions disagree, but many times they might mildly disagree, even within the expected standard deviation. I think that the \"otherwise\" case in Eq. (1) could be further refined accounting for those cases where it is not clear whether the model is invariant or not.\n\n* All the OOD datasets analyzed are modifications of Imagenet, which was used for training. I really appreciated the breadth of OOD datasets tested, but I missed at least one dataset that is strongly OOD, for example train on Imagenet and finetune for a dataset that is completely unrelated to Imagenet. I expect EI to perform well in those cases too, so please take this as a suggestion to further improve the paper. * DNNs are known to be very sensitive to specific translations [1] even if they are \"hard-wired\" to be translation invariant. This sensitiveness is much stronger for other transformations for which the DNN has learnt the invariance. Could you comment on the use of three 90 degree rotations per sample to compute EI. Could this be missing many cases where the model is invariant (or not)? I believe EI could be used to \"map\" the invariance of a CNN in the full transformation domain, which could be extremely important to guide machine learning practitioners to improve their models.\n\n* I would suggest including randomly initialized networks (not trained) in the study. These networks could also be invariant, but do they follow the same trend shown in the plots? Or training till convergence is a condition for EI to work? The study of randomly initialized networks could also shed some light on the invariance induced by the architectural design alone.\n\n* What is the correlation between EI(grayscale) and EI(rotation). Intuitively, they are strongly correlated; if so, have the authors thought about understanding which of the two is the most important source of invariance for generalization?\n\n\n[1] Biscione and Bowers, Convolutional Neural Networks Are Not Invariant to Translation, but They Can Learn to Be, JMLR 2021. I believe the authors have addressed the limitations of their work correctly, pointing out:\n* The scope of the paper is on multi-class classification. The study (and maybe new formulations of EI) could be extended to regression, detection, etc.\n* The inherent invariances in some architectures (eg. hard-wired rotation invariance), which are not included in this study.\n* The impact of *geographic shift*, not included in this work.\n\nAdditionally, the authors comment on the societal impact, which is limited since this work uses already pre-trained models. The major impact is inherited from the impact of each of these models themselves.", " This work considers generalization and invariance, two key properties of machine learning models. Specifically, this work conducts a large-scale quantitative correlation study between generalization and invariance on ImageNet and CIFAR setups. To help the correlation study, this work introduces the Effective Invariance Score (EI). It is more suitable for measuring model invariance than other measures such as KL and L2. Two key observations are reported: 1) generalization and invariance exhibit strong linear relationships on both in-distribution and out-of-distribution test sets; 2) when tested on different test sets, the accuracy of the model is linearly related to its invariance ability. [Strengths]\n[1] Overall, the work is well written. Motivation, focus, experimental setup, and key observations are clearly presented. Related work is well organized.\n\n[2] The proposed Invariance Score (EI) is reasonable and well-discussed. The authors give an intuitive illustration in Figure 1. Furthermore, comparisons with other measures in the Supplementary file help to understand why EI is more suitable for correlation studies.\n\n[3] Existing work mainly gives qualitative hints on the relationship between invariance and generalization. The main contribution of this work is it provides quantitative analysis. Furthermore, observations are presented on both in-distribution and out-of-distribution test sets. This is another contribution compared with the existing works. The results on the ImageNet testbed are comprehensive and systematic.\n\n[4] Another interesting observation is that model invariance and accuracy also exhibit strong linear correlations on various test sets (Section 5.7). The results are reported on ImageNet-C with several models, which are helpful.\n\n[5] In addition to the two main observations, this work investigates other points, including how the correlation on the hard test set varies (Section 5.3), and why JS is not suitable for correlation studies (Section 5.5 and in Supplementary Material). These points help to understand the relationship between model invariance and generalization.\n\n[Weaknesses]\n[1] This work quantitatively investigates the relationship between model invariance and generalization. This work points out that previous work [11-13, 15, 28] gave some qualitative hints about the positive correlation between them (Lines 23-29, 68-75). However, some recent works such as [a] and [b] are missing. They should be included and discussed.\n\n[a] Zhu Sicheng, Bang An, Huang Furong. \"Understanding the generalization advantage of model invariance from a data perspective.\" Advances in Neural Information Processing Systems 34 (2021): 4328-4341.\n[b] Sannei, Akiyoshi, Masaki Imaizumi, and Makoto Kawano. \"Improving generalization bounds for group-invariant/equivariant deep networks through quotient feature spaces.\" Uncertainty in Artificial Intelligence. PMLR, 2021.\n\n[2] Continuing the above point, existing works mainly focus on the in-distribution generalization. In contrast, this work investigates both in- and out-of-distribution test sets. Differences or new contributions should be further highlighted in Section 2. The current version (lines 68-75) is not very clear.\n\n[3] This work conducts correlation studies on the ImageNet testbed, which includes several test sets. These test sets are diverse and come from different distributions (Lines 154-157). It is good and convincing. Another test set is ObjectNet, where object backgrounds, rotations, and viewpoints are diverse. It would be better if this work could include this test set in the correlation study.\n\n[4] Section 5.7 should be highlighted as it presents another key observation. However, it is not heightened in the current version. In addition, the results in the Supplementary Materials (Figure A-3) should be included in the main paper, which helps illustrate the observations. The following questions and suggestions are expected to be addressed in the rebuttal.\n\n[1] First, lines 97-105 explain why KL is not used for correlation studies. I understand why KL and other measures are not suitable. However, using \"Drawback of existing invariance measures\" to summarize the paragraph is not very coherent and is a bit confusing.\n\n[2] Also, in semi-supervised learning, other additional techniques such as confidence [48] and sharpness [49] are used when KL [50, 51] or L2 are used for maintaining consistency. These techniques may avoid the problems illustrated in case (c) and case (d) in Figure 1. It can also be mentioned on lines 97-105 to help illustrate why KL and L2 are not suitable for correlation studies at work.\n\n[3] As illustrated in the weaknesses, a correlation study on ObjectNet would be interesting.\n\n[4] In addition, related works (eg, [a,b]) should be included in this work. Section 5.7 should be highlighted (see Weaknesses above).\n In Section 6, the authors clearly discuss potential limitations and propose possible solutions and potential research directions. Potential negative social impacts are also discussed.", " The authors design an empirical measure of model invariance based on prediction consistency and invariance. With this measure they evaluate the correlation between model invariance (to rotation and grayscale) and generalization on several in-distribution and out-of-distribution ImageNet variants. They show that the model’s accuracy and invariance are linearly correlated, and that such correlation is better captured by their designed measure than other existing measures. ### Strengths:\n1. The linear relationship between model generalization and the invariance captured by the introduced measure is interesting, especially considering that the measure is handcrafted to have a specific form. \n\n2. The evaluation covers the most recent model architectures, including several vision transformers.\n\n### Weaknesses:\n1. Current evaluation datasets are not comprehensive enough to draw convincing conclusions about the introduced measure. Most of the results are based on ImageNet variants, whereas for CIFAR-10 the authors do not do any comparison of measures. For such a handcrafted measure, readers may need similar observations on more diverse datasets, including some existing OOD benchmarks.\n\n2. To make fair comparisons among different invariance measures, Spearman’s rank correlation is arguably a better choice than Pearson’s correlation, since different measures have different algebraic forms so a simple linear correlation may be too restrictive. I’m glad to see the authors use both correlation measures for evaluation. Nevertheless, some results are missing, including Spearman’s rank correlation for JS-divergence on ImageNet-S and ImageNet-A. Also, if we focus on Spearman’s rank correlation, the introduced measure is no longer superior in predicting generalization among other measures like the prediction consistency.\n\n3. The motivation for designing the EI measure is subjective — why does a model making confident mistakes have the same invariance as a model making unconfident mistakes (Figure 1 (c) and (d))? If we look at the invariance from the loss perspective, the former model usually incurs a higher consistency loss than the latter one, hence less invariant. I recommend the authors to elaborate more on this motivation.\n Could you also evaluate the Spearman’s rank correlation for JS-divergence on ImageNet-S and ImageNet-A? This could make the comparison fairer. Yes, the authors addressed the limitations and potential negative societal impact of their work." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 7, 7, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 5, 4, 3 ]

[ "CVnvpNtK0an", "-2Oj-Qfks6", "vrUEweqH-qi", "3xHEkG9x1Ff", "y2m7LMIYV8", "nips_2022_QRKmc0dRP75", "USWN_okhorXn", "48EMTfdxkFn", "CVnvpNtK0an", "CVnvpNtK0an", "X5qdsAAacNE", "X5qdsAAacNE", "ucMAUxUaK2d", "GG1KR1m9ylv", "GG1KR1m9ylv", "nips_2022_QRKmc0dRP75", "nips_2022_QRKmc0dRP75", "nips_2022_QRKmc0dRP75", "nips_2022_QRKmc0dRP75" ]

[ "mKk8J---6Jf", "c2-dqqIphpy", "XEyIwtjEig", "xun9GD2NB0y", "gX9iLKo-J7Z", "G6nyYipbZTV", "l1t-ZRcetn7", "u82gicOm7QX", "7bD4LCabMeP", "r2luKeGmC_I", "w6AN2XOsET", "RnQQwiuAMhY", "mHGXalAwqaA", "q4kA6Bk_3wH", "atbG9TkI4MRU", "MO4lZd71BE", "BLr5UzOaPZr", "fwPnWdGy-L", "qNh5ckeQ8UJ" ]

[ "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you for your detailed response. The additional results on real-world data look indeed very promising. I would like to encourage you to extend the limitations and conclusion section regarding scaling to real-world data with reference to the new results.\n\nOverall my concerns have been well addressed. I am keeping my rating of strongly recommending this paper to be accepted.", " I appreciate the fact that the mode is computationally efficient and has a comparable number of parameters to ResNet50, but you cannot make claims about perfromance advantages over prior work unless the same backbone is used in evaluation (in particular, given how narrow the margin is). This is even more important for the results in the main paper, where prior works use clearly inferior backbones (e.g. 6-layer CNNs). This remains a major issue, making evaluating the advantages of the proposed approach over prior work very challenging. ", " Thanks to the authors for providing detailed answers. The additional experiments on KIITI really helped to see the algorithm works in a real-world scenario, which resolved my main concern. I hope there will be enough space to add those results to the main draft, which is important to the overall story. \n\nMy other questions have been clarified and I don't have further questions. Overall I will keep my rating and recommend an accept. ", " We thank the reviewer for taking time to read our response. \n\n> I thank the authors for their detailed response, which addressed most of my concerns.\n\nWe are happy to have addressed most of the concerns. We would be glad if the reviewer could raise their score to reflect this.\n\nWe shall reply to other questions in the above response to our global comment.\n", " We thank the reviewer for the response. \n\n> Please report the results of your method with exactly the same backbone. \n\nDue to lack of time we are not able to do more additional experiments. However, we have already reported performance with different backbones and segmentation networks (Sup. Mat. - Table 1a, and expanded version below) showing our method is robust to work with many off-the-shelf segmentation networks.\n\nImportantly, we would like to draw attention to the fact that our model with a transformer architecture (SWIN-tiny) and ResNet-50 backbones are close in the parameter count and performance. \n\nAdditionally, we are computationally more efficient than both SAVi and Bao et al. Our model requires a single GPU for 2 days (peak VRAM of 18Gb, 23Gb for KITTI), whereas SAVi requires 8 GPUs for 12 or 30 hours and Bao uses 4 GPUs for 3 days ([link](https://github.com/zpbao/Discovery_Obj_Move/issues/3)). This is because our method does not need computationally expensive custom architectures, and works well with only a segmentation network.\n\nWe’ll update the tables with the additional requested experiments when they are ready. \n\n> can it be added to any learning-based method that predicts soft masks (egg, Bao et al)?\n\nPlease note we improve over Bao et al. even without the mask warping loss. We included it as a simple way to deal with noisy flow estimates on real data. The warping loss, like our proposed method for flow coherence loss, can be applied to any learning-based method that predicts masks (incl. Bao et al., SAVi etc). We shall expand our table 3(c) carrying out these experiments for the final version, to include additional methods.\n", " I thank the authors for reporting these encouraging results. However, the question of fairness of the evaluation remain open here as well. All the methods in Bao et al. used a ResNet50 backbone. Please report the results of your method with exactly the same backbone. \n\nAs to the warping loss, is it unique to the proposed approach, or can it be added to any learning-based method that predicts soft masks (egg, Bao et al)? If it can, then the corresponding results should be added as well.", " I thank the authors for their detailed response, which addressed most of my concerns. However, the fairness of comparison to the state-of-the-art remains a major issue. It is encouraging to see that the proposed approach is fairly robust to the backbone architecture, but the prior works which the authors claim to outperform use much more shallow backbones (6-layer CNN) than those reported above. For a fair comparison, exactly the same backbones need to be used in the state-of-the-art comparison table.\n\nThe same goes for the new comparison to Bao et al. All the methods reported in that work are evaluated with a ResNet50 backbone. The authors need to use an equivalent variant of their model for comparison. ", " Thank you for the detailed responses addressing most concerns raised in reviews. \n\nThe results on KITTI are particularly interesting and helpful to understand the performance of proposed method on real world data. The use dataset specific hand-crafted priors in ego-motion conv questions the generality of the method. The warp-loss is an interesting addition that integrates a general prior regarding videos to the loss. Overall, this is a great addition to the paper. \n\nThe concern on ground truth \"optical flow masks\" was similar to the concerns of another reviewer. In many synthetic datasets, optical flow segments the objects present quite well - in fact they can be comparable to the actual segmentation ground-truth. However, the KITTI results (where dataset contains camera motion) and especially the improvements with the \"warp-loss\" component clarify this. \n\nThe explanations relevant to the loss function / regularization is clarifies the concerns.\n\nOverall I feel the paper is fit for acceptance. ", " We thank the reviewer for taking time to review our work. We would like to address some misunderstandings (especially the static camera assumption) and answer further questions/requests.\n\n> The authors don't discuss prior work on learning image-based, unsupervised object segmentation from motion. In particular, DyStaB of Yang et al., CVPR'21 which operates in a single object regime, and very recent Discovering Objects that Can Move of Bao et al., CVPR'22 which can segment multiple instances. The novelty of the proposed approach compared to these methods is in the loss formulation, but conceptually they are very close.\n\nThere is indeed a vast literature on unsupervised segmentation, so we have focussed specifically on _multi-object_ decomposition from motion (e.g. SAVi) for a direct comparison to our work. As DyStaB performs foreground-background segmentation, it is not directly comparable to us. However, we will add a section to related work discussing motion-based single/salient object detection explaining the differences. \n\nAlthough the concurrent work “Discovering Objects that Can Move”, Bao et al. (CVPR 2022), was published after the submission deadline, for completeness, we have run additional experiments following their setting to compare to their approach. We discuss this in detail in a global response to all reviewers, including quantitative comparisons on real-world data. We show that we outperform [Bao22] as well as previous work, and we will include these experiments in the final version of our paper.\n\n> A major limitation that is not discussed in the paper is that the method relies on the static camera assumption. In fact, segmenting moving objects in the optical flow field with a static camera is trivial. Binary segmentation can be obtained by simple thresholding, but separating instances can also be done with a primitive approach, e.g. by fitting an affine motion model. \n> Going to the more general setting of a moving camera is much harder, however, and would require a very different approach.\n> Please evaluate your method on videos with a moving camera.\n\nWe ***do not***, in fact, assume that the camera is static. Instead, the model of each region’s motion (affine) accounts for the ***combined*** effect of camera motion _and_ object motion. The reviewer’s suggested baseline (segmentation by fitting an affine model) is a simplified version of one of our baselines, Choudhury et al. [5]. We achieve superior results (Table 2) and provide discussion and analysis as to why our proposed method is able to better handle multiple-object scenarios in Section A.2.\n\nTo further emphasize the fact that our approach does _not_ rely on a static camera assumption, we report results on MOVi-D and MOVi-E datasets below. These variants of the MOVi dataset have an explicitly moving camera. This does not cause our method to under-perform in any way; we show equally strong results while using the ***same*** settings as for all other experiments. \n\n| | | MOVi_D | | MOVi_E |\n|:----------------------- | --------:| ------:| --------:| ------:|\n| | FG-ARI | mIoU | FG-ARI | mIoU |\n| SAVi [24] (+Bbox sup.)* | <45 | | <55 | |\n| Our (Simplified Cov.) | 56.02 | 24.10 | 66.29 | 27.25 |\n\n(*- SAVi results from plot in [Singh22])\n\nAs mentioned before, we also include results of our method applied to the real-world driving dataset KITTI, which naturally has strong ego-motion. On this challenging setting, we also achieve state-of-the-art performance.\n\n> The objective is fairly complex and is not described in sufficient detail (both for the intuition behind the design choices and for the implementation details). \n\nWe will further detail our expanded explanation in the supplementary material to bring additional clarity to the readers. \nWhile the reviewer may perceive the model “fairly complex”, the math is directly derived from a small and simple set of assumptions (Section 3, Sec. A). We believe our method is quite simple in practice (Eq. 1). It only requires evaluating the loss on the output of the segmentation network and the flow. This is more straightforward than a pipeline using one method to obtain noisy labels and training a new network. \n\nAs an example, the proposal of Bao et al. [Bao22] centers around a way of including motion segmentation soft labels into a slot-attention network. This is an architecture-specific approach that relies on a different method to obtain soft labels. In contrast, our approach is simple enough that it can be applied to different architectures (Table 1(a) in Supp. Material) and even added to existing methods to improve their performance, as we show in our ablation experiments (Table 3(c)). \n", " > In fact, it took me a while to figure out if the model actually predicts optical flow (or some proxy for it), or if the flow is only used to compute the objective function. The latter seems to be the case, making the title misleading. \n\nWe believe the title is quite apt. “Predicting <...> patterns” rather than the motion itself (which would be “predicting optical flow”) — because we task the network to carve out regions where certain patterns might be present. We included “probable motion” as we define a probability distribution of optical flow patterns which the model seeks to satisfy (make more probable predictions). This gives “Predicting probable motion patterns”. We are willing to change the title if there is consensus between the reviewers that this would improve clarity.\n\n> Implementation details are provided in the supplementary, showing that the objective is fairly brittle and requires different hyper-parameters on different datasets.\n\nThis is not true. We show comparable results (within ~1.5%) with the _same_ hyperparameters for various datasets (Table 1(a), Supplementary Material). As part of our method, we also propose unsupervised approaches for the initial estimate of the covariance in a dataset-specific manner, that give slightly better performance, which we report in the main paper. However, the differences in performance are small and do not make or break the method.\n\n> On the same note, the complexity of the proposed objective seems unnecessary and the authors do not compare to any simpler baselines. \n\nWe have a comparison with the recent proposed method by Choudhury et al. [5], primarily due to its closeness to our approach and ability to be expanded to a multi-object setting. As their approach is similar but simpler in its formulation (non-probabilistic), that comparison should answer the reviewer’s concern. We touch on the similarity and the benefits of our more principled formulation in the section A.2 of the supplementary material.\n\n> For example, a state-of-the-art motion segmentation algorithm could be used to extract moving object segments first and these segments could them be used to supervise the masks directly. The benefit of such a baseline, besides simplicity, is that it would allow the method to generalize to videos with a moving camera, since motion segmentation methods are designed to handle the most general setting.\n> Please compare to a simpler baseline that computes motion segmentation with a sota method and uses it to supervise the masks.\n\nThe reviewer’s reference [Bao22] implements a more complex version of the suggested baseline, using masks to supervise a slot-attention model. As we have shown (global response), we outperform this approach. \n\n> The authors use a stronger backbone network compared to prior work (Mask2Former vs shallow CNNs used by most baselines), making all the experimental evaluations invalid. It is thus impossible to say if the proposed objective provides and real benefits compared to prior work.\n> Please compare to prior work using exactly the same backbone network.\n\nWe disagree with the reviewer on this statement. The appendix (Table A.1) contains a comparison of backbones using UNet, ResNet50 and Swin-tiny with similar results between all variants. \n\nAdditionally, many previous approaches have the motion model built into a custom network architecture (e.g. SAVi, SCALOR) and thus decoupling architecture and method is impossible. A benefit of our method is the ability to use an off-the-shelf segmentation network because the motion model is confined to the loss term. \n\nFurthemore, we also include experiments where our probabilistic approach is added to a previous method without any other changes (Table 3.c), improving its performance. \n\nTo further address this concern, we test in the table below two more backbones, obtaining comparable results even with ResNet18. We also include an experiment where we use the MaskFormer architecture (_mf_) as in our other baseline GWM [5] (Table 1) showing better performance still.\n\n| | | MOVi A | | MOVi C | | MovingClevr |\n|:-------------------- | ------:| ------:| ------:| ------:| ------:| -----------:|\n| | FG-ARI | mIoU | FG-ARI | mIoU | FG-ARI | mIoU |\n| m2f (swin-tiny) | 83.48 | 72.61 | 58.59 | 35.67 | 88.80 | 69.62 |\n| m2f (resnet50) | 83.44 | 68.06 | 60.32 | 34.80 | 90.40 | 67.07 |\n| m2f (***resnet18***)| 84.04 | 67.48 | 60.84 | 35.69 | 90.31 | 67.33 |\n| ***mf*** (swin-tiny)| 81.78 | 71.28 | 54.45 | 33.67 | 71.07 | 51.06 |\n\n> How is k chosen? \n\nFor direct comparison, $k$ is matched to the setting used in prior work [23, 24].\n", " We thank the reviewer for the encouragingly positive review and assessment of our contributions and presentation. We address the comments and questions below.\n\n> Another line of works exists that only focusses on unsupervised segmentation, with models that often make use of optical flow for training (and sometimes inference) and can be applied to more realistic data. The authors cite respective works, e.g. Mahendran et al. 2018, Yang et al. 2019, Choudhury et al. 2022. Empirical comparisons with these models would have been informative and would strengthen the paper, as these would allow to more directly compare the different approaches for optical flow based unsupervised segmentation.\n\nOur objective is to perform multi-object segmentation. Many unsupervised segmentation methods operate only in foreground/background scenarios, with extensions to the multi-object case unclear or non-trivial. We compare (Tab. 2) with the proposal of Choudhury et al. [5] (where the extension to multi-object is relatively straight-forward) and show better results. Based on your suggestion, we now also conducted experiments on real-word data (please see the global post above), where we achieve state-of-the-art performance on a real-world dataset.\n \n> Are the appearance-based models also trained on frames of the video variants of CLEVR and CLEVRTex? Or directly on CLEVR/CLEVRTex? In the latter case, an experiment testing whether the different training data influences the performance of appearance based models should be included.\n\nThe appearance-based models are trained on the original CLEVR/CLEVRTex using implementations/settings provided by Karazija et al. [23]. Below, we include a revised version of Table 3(c) with GWM trained on our video variant of the dataset. \n\n| | | ClevrTex | | OOD | | Camo |\n|:----------------------------- | ------:| --------:| ------:| -----:| ------:| -----:|\n| Model | FG-ARI | mIoU | FG-ARI | mIoU | FG-ARI | mIoU |\n| GNM [19] (ClevrTex) | 53.38 | 44.39 | 48.44 | 42.87 | 15.72 | 18.53 |\n| GNM [19] (MovingClevrTex) | 18.01 | 31.47 | 15.57 | 30.23 | 0.21 | 14.68 |\n| GNM+Our Loss (MovingClevrTex) | 63.84 | 55.26 | 59.01 | 48.65 | 51.00 | 47.63 |\n\nIn general, we observe that the method under-performs when trained on the video data, likely due to lack of scene diversity (to keep the dataset the same size, we trade-off the number of different scenes with video frames). We therefore already compared to a stronger baseline using the original (static) CLEVR/CLEVRTex training data. Nonetheless, augmenting the method with our loss, consistently improves performance. \n\n> Details about the dataset generation are not contained in the supplement, although promised in the main paper.\n\nThank you for pointing this out! We will update the supplementary with the missing section. In brief, we rely on the dataset generation code of Karazija et al. [23]. We augmented the code to (1) render multiple frames for each scene, (2) enable the built-in physics simulation of Blender (3) and sample initial velocity (normal and angular) for either one, two or all objects in the scene. The directions of the velocity are constrained to roughly aim at the scene center to maintain all objects in the frame and enable complex interactions such as collisions and occlusions. All other settings are the same as in [23]. The modified generation code is included in the original submission.\n\n> One limitation to add in my view would be the necessity of ground truth optical flow. The ablation study has shown a substantial performance drop when using optical flow predicted by SMURF, which probably makes it difficult to apply the method to natural videos where ground truth optical flow is not available.\n\nWe thank the reviewer for the suggestion. We shall include a mention of the limitation that our method currently does not directly model complex noise likely present in real-world scenarios and would benefit from direct handling of this aspect in the future. \nWe note, however, we also discuss our findings on real-world data in the global response to all reviewers (please see above). In these experiments, we follow the setting of [Bao22]., which uses KITTI data and RAFT as the flow estimator. To explicitly account for noisy flow areas in real-world data, we found it beneficial to include an additional loss term (dubbed _Warp Loss_), which adds more than 10 percentage points to the FG-ARI performance of our model. We describe this term in detail as part of our global response.\nThis is a simple way that the model could be made robust towards real-world flow estimators. \n", " We thank the reviewer for taking time to review our work and favorably assessing contributions, soundness and presentation. We would like to address some points in the weaknesses section and answer the questions raised.\n\n> Using ground-truth optical flow seems crucial for good performance (Table 3.a) - is this method scalable to real world data? Other methods using video supervision can operate on real-world data (e.g. [1]) \n>The authors note how similar models struggle in complex settings, but limit all their evaluations to synthetic datasets: how would this translate to real world settings? \n\nAs a similar concern has been raised by other reviewers, we have created a global response (please see [above](https://openreview.net/forum?id=_w2-1nXNjvv&noteId=atbG9TkI4MRU)) to discuss how our method translates to real-world settings. We conduct additional experiments on the KITTI dataset and show that our method still outperforms prior and concurrent work on this more complex, real-world setting. \n \n> Is the method really benefiting from the motion model or simply learning segmentation from the high quality ground-truth optical flow masks?\n\nWe are not entirely sure what the reviewer means by optical flow masks. The optical flow is not masked. Our network is trained to output segmentation masks. However, no form of annotations is used for training, only for evaluation. The loss is derived based on how well the predicted masks carve up the image into coherent optical flow regions, and _not_ computed against ground truth masks.\nThe motion model here is used explicitly to enable learning segmentation from the optical flow (HxW 2-channel image), rather than directly reconstructing the flow. It enables defining a prior that encodes a notion that the induced optical flow distribution comes from underlying objects. As we discussed in Section A.2, (Appendix), the probabilistic treatment of the motion model enables additional benefits in the multi-object paradigm that prior work lacks. As we show in our evaluation (Table 2), our method also compares favorably to methods that do not include motion models but rely on predicting optical flow directly (SAVi). ", " > Lack of clarity/simplicity in final loss function: can the authors construct a simpler version of the final loss between masks output from model and optical flow labels (closer to the actual implementation in code)? Many terms in the given equations are constants (or are they learnable params?)\n\nOur loss formulation is grounded in probabilistically modeling flow fields using a motion prior. The provided formulation of the loss is what is implemented in code (please see the provided code _code/src/dist.py:141_). Note that there is only a single term that is constant ($HW \\log 2 \\pi \\sigma^2$) and no learnable parameters. The constant term maintains a normalized probability distribution. All other terms depend on either the flow or the predicted masks. As we discuss in the supplementary (A.2 Further justification), these terms end up playing a role in for example biasing the model to use fewer masks to explain the objects. \n\n> Is comparing to other methods with the additional post-processing fair? The authors do include results without post-processing that are still above SOTA; those may be a better comparison.\n\nThanks. We included both results for this reason. Note that the post-processing in question is a simple deterministic hyper-parameter-free connected-components processing of the output masks that could be directly included in the model. The cost of this is negligible. As we state Section 3 (L175-182), the post-processing is included to address the shortcoming of the method where parts of the scene could be grouped in the same region for coincidentally having similar motion (e.g., due to free falling). As other methods could potentially benefit from such filtering as well, we also applied the same post-processing to other methods to verify the results. However as we show in Table 1, prior work does not benefit from this post-processing universally and in fact is hurt by it in some cases. \n\n> Line 114: more explanation for reasoning in ELBO for regularization\n\nOur loss is evaluated based on the sampled masks rather than the underlying (mask) distribution. The regularization term here aids in controlling the “shape’’ of the predicted mask distribution. While in deriving the loss we leave an option to adopt a better/complex mask distribution prior, in our experiments we simply use a uniform prior. We include the common $\\beta$ parameter from constraint optimisation [Higgins16] as that enables us to encourage the network to predict more solid masks by annealing this value, as discussed in the supplementary material (Sec. B, L80-84). \n\n> A direct formulation of the final loss function\n\nThe direct formulation of the final loss function would be rather lengthy and tedious as it would require manually performing many simple linear algebra manipulations that numeric processing libraries readily make available (e.g., finding the determinant of an inverse of a 3x3 matrix). Also implementing such a form would be wasteful as many terms can be computed jointly using efficient vectorised implementations. We describe in the supplementary material (Sec. A.1 “Affine motion likelihood”) the exact equations and steps how the loss is translated to code to make use of available BLAS libraries. \nWe will further update this section with additional explanation, the above discussions, and pseudo code showing how the provided equations can be combined to evaluate the loss. \n\n### References\n\n[Higgins16] - Higgins, Irina, et al. \"[Beta-vae: Learning basic visual concepts with a constrained variational framework.](https://openreview.net/forum?id=Sy2fzU9gl)\" ICLR‘16.", " We thank the reviewer for taking the time to read our work and positively assess its soundness, presentation and contributions. We would like to address the questions and concerns raised in the review.\n\n> One question is how well can the methods perform in real-world cases. \n\nThanks! As some of the other reviewers had a similar question, we have created a global response (please see [above](https://openreview.net/forum?id=_w2-1nXNjvv&noteId=atbG9TkI4MRU)) to address this. It turns out it does work: we have conducted additional experiments on _real-world_ data demonstrating that our method outperforms prior and concurrent work. \n\n> How did the prior distribution p0(m) initialize and how did different prior distributions affect the results?\n\nThe prior distribution $p_0(m)$ is a uniform categorical distribution, meaning $p_0(m) = 1/k$, where $k$ is the number of components. This distribution is parameter-free. \nDuring experimentation, we also considered a different mask prior distribution, a 2D Gaussian Mixture Model (with K components) by considering centroids and pixel coordinates as random variables to encode object compactness. However, this did not result in a discernible difference in our experiments. Instead, we found that restricting the entropy of the learned mask distribution, which in practice meant that the mask output was more “peaky”, had a larger effect on performance. This was achieved by controlling $\\beta$ parameter (Eq. 1) (See Supp. Mat. B, L80-85 for details).\n\n> It will be interesting to see what the authors’ thoughts on the potential to apply the proposed methods to the no-rigid motion are? What are the further requirements to achieve that?\n\nIt largely depends on the contents and the extent of the non-rigid motions. Our model assumes a rigid-motion prior but does not necessitate working on only rigid motions. Small amount of non-rigidity can be treated as noise, much like the imperfect affine approximation of the flow field, and could be handled as is. \nFor pronounced non-rigid motion (e.g., humans dancing or animals running), the motion could be explained at the level of object parts, thus a hierarchical segmentation scheme could be used to get around this and other problems common in this setting, such as self-occlusion and depth discontinuities, as we briefly mention in Sec. 4.5 (L274-275). \nWe will add this discussion to the future work section.\n\n> Line 111: Please elaborate on the assumption “We then assume that the flow depends only the regions”\n\nWe assume that optical flow within a region depends only on the region itself and the other regions have no influence. Intuitively, this is a reasonable assumption, as in large, the movement/flow of an object does not depend on the background or other objects thus enforcing this assumption encourages regions to correspond to objects. \n\n> Line 138: Please justify that “ We assume that regions are statistically independent ” is a reasonable assumption.\n\nThis follows the same reasoning as above. We assume that regions are statistically independent given their segmentations, that is the optical flow for the object depends only on the region. This in practice may confound two separate sources of motion for an object, e.g. camera egomotion and the objects’ inherent motion, however our model attempts to explain any such motion jointly for each object rather than disentangling possible sources of motions. Such a simplifying assumption has several benefits. Firstly, this helps induce a tractable probability distribution for an observed region. Secondly, this results in smaller regions being explained independently, which should align better with the affine motion prior assumption.\nWe will include these explanations in the paper.\n\n> Typos and small errors.\n\nThank you! We will address these in the revision. \n", " We thank all reviewers for their feedback and comments on the paper. For this rebuttal we have run additional experiments using real data as requested by reviewers which we collect here, and will refer to below in the individual responses. \nWe apply our method to the real-world scenario following the setting of the concurrent work by Bao et al. [Bao22]. Namely, we apply our method to the KITTI dataset using optical flow estimated by RAFT. Our findings are in the table below.\n\n| | KITTI (FG-ARI) |\n| ---------------------- | --------------:|\n| SA [32] | 13.8 |\n| S-IODINE [14] | 14.4 |\n| MONet [3] | 14.9 |\n| SCALOR [20] | 21.1 |\n| MCG [Arbeláez14] | 40.9 |\n| Bao et al. [Bao22] | 47.1 |\n| Ours (Simplified Cov.) | 46.1 |\n| Ours (Egomotion Cov.) | ***47.5*** |\n| Ours (+Warp loss) | 57.8 |\n\n_Ours (Simplified Cov.)_ refers to our method trained out-of-the-box on KITTI using the simplified hyper-parameters used in our previous experiments (Sec. B of Supplementary Material). It already achieves comparable performance to Bao et al.. _Ours (Egomotion Cov.)_ refers to our method applied with the covariance for the motion prior distribution ($\\Sigma$, Eq. 5) adjusted to account for strong egomotion characteristic of driving videos – we simply assume some positive scaling and shear in Y direction. This outperforms previous approaches and achieves state-of-the-art results. \nFinally, we conduct experiments with an additional loss term (_Warp Loss_) to further aid in dealing with the noise of the estimated flow. This term simply enforces consistency between adjacent frames by warping the predicted masks using optical flow, as follows:\n\n$L_{warp}(m_1, m_2, I_1, I_2, f_1, b_2) = w(I_2, f_1(I_1)) \\cdot d(m_2, f_1(m_1)) + w(I_1, b_1(I_2)) \\cdot d(m_1, b_2(m_2)),$\n\n$w(I_a, I_b) = |I_a - I_b| / \\sum_x (|I_a - I_b|)_x,$\n\n$d(m_a, m_b) = D_{KL}(m_a || m_b)/2 + D_{KL}(m_b || m_a)/2,$\n\nWhere $m_1,m_2$ are predicted k-way categorical mask probabilities, $I_1,I_2$ are frames, $f_1(\\cdot)$ indicates warping by forwards optical flow $f_1$ (or backward $b_2$). Regions where warping of RGB produces small errors will enforce matching of mask distributions.\nAlthough not necessary to surpass state-of-the-art performance, we can see that our method with this additional term (_Ours (+Warp loss)_) performs even better and shows how a noisy flow estimator can be integrated in our method. \n\nOverall, our method shows very strong performance in real world scenarios, improving the performance over previous and concurrent results.\n\n### References \n\n[Bao22] - Bao, Zhipeng, et al. \"[Discovering Objects that Can Move.](https://openaccess.thecvf.com/content/CVPR2022/papers/Bao_Discovering_Objects_That_Can_Move_CVPR_2022_paper.pdf)\", CVPR’22 (concurrent)\n\n[Arbeláez14] - Arbeláez, Pablo, et al. \"[Multiscale combinatorial grouping.](https://openaccess.thecvf.com/content_cvpr_2014/papers/Arbelaez_Multiscale_Combinatorial_Grouping_2014_CVPR_paper.pdf)\" CVPR’14.\n\n[Singh22] - Singh, Gautam et al. \"[Simple Unsupervised Object-Centric Learning for Complex and Naturalistic Videos.](https://arxiv.org/abs/2205.14065)\"\n", " The author presents a method for unsupervised object segmentation by using temporal motion patterns. The paper transforms the segmentation as a minimizing ELBO problem. Some practical tricks of Gumbel-softmax have been applied to make the ELBO differentiable. The evaluations on the physics-related simulation datasets were conducted and outperforms the other baselines. This paper converts a classic optimization problem into a differentiable learning problem, the overall idea is very interesting. The experiments have shown the proposed method has achieved the SOTA performance on simulated datasets.\n\nOne weakness is no real-world scenario experiments, it would be more convincing if some of the experiments were conducted on real-world videos. One question is how well can the methods perform in real-world cases. I’m not asking about adding more results in the rebuttal. It would be helpful if the authors can explain if the methods can apply to real-world cases and what are the potential limitations. For example, the KITTI dataset is one possible option, as it involves mainly rigid motions. But meanwhile, KITTI is a moving camera case, what are the possible concerns if the model is applied to a moving camera case. \n\nHow did the prior distribution p0(m) initialize and how did different prior distributions affect the results?\n\nIt will be interesting to see what the authors’ thoughts on the potential to apply the proposed methods to the no-rigid motion are? What are the further requirements to achieve that?\n\nSome other detailed comments:\n\nLine 111: Please elaborate on the assumption “We then assume that the flow depends only the regions”\n\nLine 138: Please justify that “ We assume that regions are statistically independent ” is a reasonable assumption.\n\nMatrix I first appeared in equation (5) but is explained in line 161.\n\nline 2 form -> from.\n\nLing 156, missing space after as.\n As the author stated, sometimes the motion doesn't provide enough information to segment the object. Maybe adding scene flow (3d flow with depth) can help to improve the performance. ", " The authors train a segmentation network that processes still images to produce object masks. Video based supervision is used. The masks predicted for a single image are converted to optical flow using a motion model proposed by the authors. Two different motion models are considered. Hand-crafted post-processing is used to improve final segmentation performance. \n\nThe key novelty is the proposed approach for matching object masks to an optical flow representation. The authors use a motion model (i.e. translation only / affine transform on each object region), introduce an efficient and differentiable implementation of matching, and evaluate the improvements over multiple datasets. Notable performance improvements are on out-of-domain datasets. Also, the method scores relatively better on the mIoU metric, denoting the multi-object capability. \n\nAblations highlight the significance of ground truth optical flow for training (low performance without it) as well as better motion model (translation only gives lower results). \n\nThe authors include code in supplementary, and promise to share all code, datasets publicly in future. ### Strengths\n1. A novel motion model based matching of object masks to optical flow\n2. The authors obtain considerable improvements over a range of datasets \n\n### Weaknesses\n1. Using ground-truth optical flow seems crucial for good performance (Table 3.a) - is this method scalable to real world data? Other methods using video supervision can operate on real-world data (e.g. [1]) \n2. Is the method really benefiting from the motion model or simply learning segmentation from the high quality ground-truth optical flow masks? \n3. The authors note how similar models struggle in complex settings, but limit all their evaluations to synthetic datasets: how would this translate to real world settings? \n4. Lack of clarity/simplicity in final loss function: can the authors construct a simpler version of the final loss between masks output from model and optical flow labels (closer to the actual implementation in code)? Many terms in the given equations are constants (or are they learnable params?) \n5. Is comparing to other methods with the additional post-processing fair? The authors do include results without post-processing that are still above SOTA; those may be a better comparison. \n\n[1] [Discovering Objects that Can Move](https://openaccess.thecvf.com/content/CVPR2022/papers/Bao_Discovering_Objects_That_Can_Move_CVPR_2022_paper.pdf) 1. Line 114: more explanation for reasoning in ELBO for regularization\n2. A direct formulation of the final loss function Yes, limitations discussed well. ", " The authors approach unsupervised instance segmentation of images by exploiting motion\npatterns in videos during training. Given an RGB input frame, a neural network is trained\nto predict a segmentation that allows to approximate the optical flow field of that frame\nwell when using a simple, parametric motion pattern for each segment (e.g., affine\nmotion). Since the segmentation is predicted based on the RGB frame only, the network\nis trained to predict segments that *potentially* move and can be used to segment images\nafter training. On recent, synthetic multi-object datasets the proposed model is\nshown to outperform recent state-of-the-art object-centric models in almost all cases. Unsupervised segmentation is an active area of research. The general approach of\ndefining objects as regions with a simple motion pattern when they move is not new; the\nrespective related work is cited. The particular instantiation of the\napproach in this work however is novel and shown to clearly improve over previous models in\nalmost all cases. A particular strength of the paper is the thorough comparison with\nprevious models. The authors tested a large range of models on the datasets using\nmultiple seeds, going beyond most related papers in the field.\n\nOn the other hand, the authors only compare to object-centric models that not only aim\nat learning to segment images or videos but also to learn a useful representation of\nthose objects. Another line of works exists that only focusses on unsupervised\nsegmentation, with models that often make use of optical flow for training (and\nsometimes inference) and can be applied to more realistic data. The authors\ncite respective works, e.g. Mahendran et al. 2018, Yang et al. 2019, Choudhury et al. 2022.\nEmpirical comparisons with these models would have been informative and would strengthen\nthe paper, as these would allow to more directly compare the different approaches for\noptical flow based unsupervised segmentation. - Are the appearance-based models also trained on frames of the video variants of\n CLEVR and CLEVRTex? Or directly on CLEVR/CLEVRTex? In the latter case, an experiment\n testing whether the different training data influences the performance of appearance\n based models should be included.\n\n- Details about the dataset generation are not contained in the supplement,\n although promised in the main paper.\n ## Limitations\nThe authors discuss limitations of their method adequately in a separate section. One\nlimitation to add in my view would be the necessity of ground truth optical flow. The\nablation study has shown a substantial performance drop when using optical flow\npredicted by SMURF, which probably makes it difficult to apply the method to natural\nvideos where ground truth optical flow is not available.\n", " The authors propose to learn unsupervised instance segmentation by grouping regions that tend to produce consistent optical flow. In particular, a network takes an image as input and predicts a distribution over k categories (segments) for every pixel. To compute the loss It also takes ground truth optical flow as input and a geometry-based, probabilistic objective then encourages the optical flow in each resulting region to conform to an affine motion model. The assumption is that each rigid object has a distinct affine motion pattern and thus the regions will correspond to object instances that move in that frame (not that the model itself only sees static frames, and learns the appearance of groups of pixels that tend to move together in the data). Crucially, this approach assumes that the camera in all videos is static, which the authors never explicitly mention. In the experiments on a few toy, synthetic datasets the proposed approach outperforms or performs on par with prior work, especially when evaluated on static images. Strengths:\n\nThe intuition behind the approach is fairly straightforward and sound (grouping pixels in the optical flow field based on flow direction and magnitude does result in segmenting rigidly moving instances, it is the classic approach for motion segmentation). \n\nThe actual formulation of using affine motion model consistency to supervise a grouping method is novel to the best of my knowledge.\n\nThe paper is well written with almost no typos or grammatical mistakes.\n\nThe approach seems to work well in toy videos with a static camera.\n\nA minimal ablation study is provided.\n\n\nWeaknesses:\n\nThe authors don't discuss prior work on learning image-based, unsupervised object segmentation from motion. In particular, DyStaB of Yang et al., CVPR'21 which operates in a single object regime, and very recent Discovering Objects that Can Move of Bao et al., CVPR'22 which can segment multiple instances. The novelty of the proposed approach compared to these methods is in the loss formulation, but conceptually they are very close.\n\nA major limitation that is not discussed in the paper is that the method relies on the static camera assumption. In fact, segmenting moving objects in the optical flow field with a static camera is trivial. Binary segmentation can be obtained by simple thresholding, but separating instances can also be done with a primitive approach, e.g. by fitting an affine motion model. Going to the more general setting of a moving camera is much harder, however, and would require a very different approach. \n\nThe objective is fairly complex and is not described in sufficient detail (both for the intuition behind the design choices and for the implementation details). In fact, it took me a while to figure out if the model actually predicts optical flow (or some proxy for it), or if the flow is only used to compute the objective function. The latter seems to be the case, making the title misleading. Implementation details are provided in the supplementary, showing that the objective is fairly brittle and requires different hyper-parameters on different datasets.\n\nOn the same note, the complexity of the proposed objective seems unnecessary and the authors do not compare to any simpler baselines. For example, a state-of-the-art motion segmentation algorithm could be used to extract moving object segments first and these segments could them be used to supervise the masks directly. The benefit of such a baseline, besides simplicity, is that it would allow the method to generalize to videos with a moving camera, since motion segmentation methods are designed to handle the most general setting.\n\nThe authors use a stronger backbone network compared to prior work (Mask2Former vs shallow CNNs used by most baselines), making all the experimental evaluations invalid. It is thus impossible to say if the proposed objective provides and real benefits compared to prior work.\n Please evaluate your method on videos with a moving camera.\n\nPlease compare to a simpler baseline that computes motion segmentation with a sota method and uses it to supervise the masks.\n\nPlease compare to prior work using exactly the same backbone network.\n\nHow is k chosen? How robust is your approach to the choice of k? The authors completely ignored the main limitation of their work - it's reliance on static camera." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 7, 8, 3 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 4, 5 ]

[ "w6AN2XOsET", "gX9iLKo-J7Z", "q4kA6Bk_3wH", "l1t-ZRcetn7", "G6nyYipbZTV", "atbG9TkI4MRU", "r2luKeGmC_I", "mHGXalAwqaA", "qNh5ckeQ8UJ", "qNh5ckeQ8UJ", "fwPnWdGy-L", "BLr5UzOaPZr", "BLr5UzOaPZr", "MO4lZd71BE", "nips_2022__w2-1nXNjvv", "nips_2022__w2-1nXNjvv", "nips_2022__w2-1nXNjvv", "nips_2022__w2-1nXNjvv", "nips_2022__w2-1nXNjvv" ]

[ "evE5eTX0-u1", "wQBZQCszvGc", "nLJ0XztbFkS", "ey2y9HKZGLt", "zrIcrnsYFuv", "uzxPaoo_1W", "GCbCxqyW-kB", "MicqF2OinCS", "jrHfQSnQbxe", "eUteb_cZV1f", "jyJ_ES_smDU", "E4ELTfU6ZYN", "DLfQ19cnLm0", "0Sfo9MplANP", "UC6yCqOq0OU", "vJHXoD7KF3B", "G6mZH01bCnE", "QaKaUVYvaCe" ]

[ "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " We sincerely thank the reviewers and AC for their contributions.\n\nThe reviewers asked many thoughtful questions, which inspired us a lot. Their meticulous review also helped us to better present our work.\n\nAfter discussion, most of the reviewer's concerns were resolved (2/4 reviewers raised their rating). We always welcome more questions, even after the discussion session has ended.\n\nThis paper proposes a simple, novel and effective framework to help deep learning models learn more. It is significantly different from existing methods, such as adversarial training, negative correlation learning and other methods, and has certain advantages in some scenarios.\nWe are looking forward to more excellent works based on this framework.", " Glad to receive your response. \n\nQ1. Thanks again for pointing out Q1 and increaseing the score. \n\nQ2. We would like to remind, as you also agree, that what we propose is a novel way to overcome shortcuts to learn more features. Our experiments show that it can handle different types of shortcuts.\nWe cannot validate all shortcuts, but experiments on CMNIST, ImageNet, CelebA, BAR, etc. datasets have covered a considerable number of cases.\nBecause the rebuttal time is limited, we cannot test the datasets you listed one by one, we further tested on ImageNet-9 and the results have been added in the appendix. We believe that among these several datasets, it is the most representative and challenging one.\n\nQ3. Thank you for your suggestion. We describe it in the appendix, and we will describe it in more detail if necessary.", " I thank the authors for their detailed response, and apologize for the delay. Some of my concerns have been satisfied, and I have updated the score appropriately.", " Thank you for the answers to my questions and additional results!\n\nQ1. The authors addressed a technical flaw of the paper -- invalid comparison to prior works in Table 1, and updated the results, thus, I increased my score from 3 to 4. With the proper comparison, there is now a quite significant gap in performance compared to the prior method ReBias.\n\nQ2. I believe that current empirical evaluation is not sufficient for the paper to be published at NeurIPS, and I strongly encourage the authors to add experiments on a wider range of benchmarks for better understanding of the method: ImageNet-9 [2], Dominoes (MNIST-CIFAR, MNIST-FashionMNIST, MNIST-MNIST) [3, 4], Waterbirds, CelebA [hair color, gender] [5]. (please see my original review for references).\n\nQ3.\n> We tested different combinations of lambdas and selected the one that performed better...\n\nHyper-parameter tuning strategy can influence the results quite a bit, in particular, whether one chooses the hyper-parameters based on average performance or performance on bias-conflicting split, so please clarify this in the next revision.\n\n\nI have read the other reviews and the responses, and while the paper is proposing an interesting approach, the empirical evaluation is limited and the clarity of the paper needs to be significantly improved, so I believe it is not ready for publication in the current form.\n", " Dear reviewer BFAY:\n\nWe sincerely thank you for the review and comments, which has helped us improve our paper. We are especially happy to receive your second round of responses, which gives us the opportunity to provide a better response. We have provided corresponding responses and results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest, Authors of Paper 627", " Dear reviewer T7g9:\n\nWe sincerely thank you for the review and comments. You have given many creative and constructive ideas about our work before. And we have provided corresponding responses and results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest, Authors of Paper 627", " Dear reviewer ius4 :\n\nWe sincerely thank you for the review and comments. You have given us a lot of professional and detailed advice before. And we have provided corresponding responses and results, which we believe have covered your concerns. We hope to further discuss with you whether or not your concerns have been addressed. Please let us know if you still have any unclear parts of our work.\n\nBest,\nAuthors of Paper 627", " **MSE**\n\nHere is the reference to the work which uses MSE loss for imbalanced classification.\n\nKato S, Hotta K. MSE Loss with Outlying Label for Imbalanced Classification[J]. arXiv preprint arXiv:2107.02393, 2021.\n\nThe example is used to illustrate that between predictions with the same cross-entropy loss, there are still differences that MSE can find.\nWe believe that if a prediction has a higher response to a class other than the correct class, it means that it is more likely to be wrong on other test samples. \nHere are some experimental results on CMNIST using cross-entropy and MSE loss. \n\n\n| Ratio (%) | CE | MSE |\n| --------- | ----- | ----- |\n| 0.5 | 65.45 | 66.64 |\n| 1.0 | 80.98 | 82.04 |\n| 2.0 | 85.21 | 84.93 |\n| 5.0 | 88.72 | 88.65 |\n\nUsing MSE is just a more intuitive option for us. The present results show no apparent difference in our method using CE and MSE. We will try to use CE as the loss on other datasets. If CE works better, we will make changes. Nevertheless, we would like to remind that this is not what we mainly want to share. We hope to provide a framework that suppresses shortcuts to learn more features. \nWe believe that more suitable loss selection and training methods are waiting for us to discover under this framework. For example, reviewer BFAY suggested perceptual loss as a loss that measures the difference between the reconstruction and the original image.\nWe think the proposed framework can work on more tasks. The design of loss will also vary. What we want to share the most is the idea of temporarily disabling shortcuts by modifying images and the design idea of roadblock loss.\n\n\n**Adversarial**\n\nWe used *Fast Gradient Sign untargeted Adversarial Attack*, and the epsilon is 0.3 for l2 in the former experiment. \n\nWe further experimented with different epsilons and also tried linf. \nBesides, we added the testing result on adversarial samples. It can be seen that adversarial training has helped the model to obtain corresponding adversarial robustness. \n\nThe table below was obtained on CMNIST (5pct).\n\n| epsilon | 1.00E-03 | 5.00E-03 | 1.00E-02 | 5.00E-02 | 1.00E-01 | 5.00E-01 |\n| -------- | -------- | -------- | -------- | -------- | -------- | -------- |\n| l2-acc | 68.45 | 66.13 | 71.03 | 73.37 | 71.59 | 76.69 |\n| l2-adv | 68.44 | 66.06 | 70.97 | 73.61 | 70.97 | 73.19 |\n| linf-acc | 69.47 | 73.66 | 77.26 | 67.7 | 51.58 | 11.35 |\n| linf-adv | 69.44 | 73.14 | 74 | 52.08 | 35.85 | 11.35 |\n\nWe provide some visualizations now (please refer to the new version of Appendix, Figure 8 & 9). We observed no appreciable behavior of modifying color or shape.\n\nWe also conduct experiments on *Projeccted Gradient Descent*, but it seems difficult to obtain effective adversarial examples using MLPs. So we tried using ResNet-18 as the backbone.\nepsilon=0.03, k=4, alpha=0.03/4. The accuracy is 92.91 on CMNIST (5pct) and 88.54 on adversarial examples. (vanilla can achieve 93.34).", " I thank the authors for a comprehensive response and revision of the manuscript. I still have a few lingering concerns, which I list below. \n\n1. The response is missing the reference to the work which uses MSE loss for imbalanced classification. The example given by the authors is also not entirely clear to me. I am not sure why predictions having a lower entropy should be penalized more. Further, it is not even clear to me if models which exhibit shortcut learning actually have predictions following the pattern of logits in the example. Finally, it would be nice if the authors could share some concrete empirical results on the difference between the CE and MSE loss, since that would address the concerns. \n2. I appreciate the comparisons with adversarial training provided by the authors, but I would also be interested in knowing the details of the adversarial training approach considered by the authors, in particular the number of attack steps and the maximum norm of the adversarial perturbation. A well tuned adversary should be able to change the colour of the image on CMNIST while keeping the shape to be the same, so it is somewhat surprising to me that this does not lead to a better result. \nI am inclined to change my score if the above concerns are addressed more concretely.", " Thank you for acknowledging the importance of our research question and methodological novelty. Below we will respond to the shortcomings you raised.\n\n\n**Originality**\n\nThank you for pointing this out. We think shortcut learning[1] is a good review, so we did not talk much about papers mentioned in shortcut learning. We have added a related discussion in the new version. We will also conduct further research.\n\n**Quality**\n\n**Q1** It was a severe carelessness. Thank you so much for pointing it out. For Table 1, we used the same three-layer MLP structure now, and we have updated Table 1. We also ran the methods listed in Table 1 and got close results. We did not get higher results and therefore used the results from the paper. We illustrated it in the table caption now.\n\n**Q2** We cannot add too many experiments due to time constraints. We conduct experiments on ImageNet, please refer to general response Q4; visualizations are in Appendix. We will experiment further on some interesting datasets. We believe that existing experiments have been able to demonstrate the effectiveness of our approach. \n\n**Q3** We tested different combinations of lambdas and selected the one that performed better, which is briefly described in the text. For other hyperparameters, we did not tune too much but adopted empirical settings. Both CMNIST and CelebA have validation sets with similar distributions to the training sets. BAR does not have a validation set, so we choose the results that perform better on the training set.\n\n**Q4** Alternate training means that models are alternately updated after each epoch. This process does not introduce hyperparameters that need to be tuned. Descriptions related to these issues have been added to the new manuscript.\n\n\n**Clarity**\n\nThank you for your patient suggestion. We have made changes in the new version. Datasets description, alternately training, unclear paragraphs, details in Table, and Figure captions are added.\n\n**Q5** We discussed how the final predictions are made in the sum-up (lines 134-142). The experimental results shown in the Tables are the results of EM. The selection is based on the performance of BM and EM at training time (training set or validation set).\n\nShortcuts are not necessarily wrong. In fact, the success of deep learning is largely due to the ability to find the most efficient features. So we prefer shortcuts to failures or pitfalls. If there's anything bad about shortcuts, that would be the reduction of the opportunity to learn more effective features. We want to provide a way to learn more effective features that are not necessarily better than shortcuts. Maybe the actual task can provide some priors to help us choose. Therefore, it is unreasonable and unnecessary to exclude shortcuts directly. We hope to clarify this with Figure 1. This is also the meaning of 'temporary'.\nRegarding computational complexity, our method also uses two classification models and may have similar results compared to some previous methods, so we did not compare them. Due to time constraints, there is no relevant content in this reply. We will consider discussing it later.\n\n**Q6** Please refer to general response Q3. \n\n**Significance**'\n\nThank you for your positive assessment of the importance and novelty of our research. Also, thank you very much for your detailed and pertinent suggestions. We will try to describe them as best we can.\n\n[1] Geirhos, R., Jacobsen, JH., Michaelis, C. et al. Shortcut learning in deep neural networks. Nat Mach Intell 2, 665–673 (2020). https://doi.org/10.1038/s42256-020-00257-z\n", " Thank you for acknowledging the importance of our research, protocols and experiments, which mean a lot to us. We will respond to your questions individually, hoping to clear some of your concerns. \n\nBelow we respond to each of your points. Some of them are discussed in the updated manuscript now. If you think there is anything else that is more important to be put into the main text, please feel free to suggest it.\n\n\n**Major1-1 Why does AE not learn to produce (untargeted) adversarial noise?**\n\nBeacuse the goal and the corresponding loss function different. Please refer to general response Q3 for more discussion. \n\n**Major1-2 Why does AE not learn to remove actual class information?**\n\nWhat information the AE removes is determined by what information the BM has learned. If BM has learned the actual class information, it is also removed. At this point, our method selects BM as the final model.\nUnlike LFF, we do not share the idea that simple is bad. Therefore, we only temporarily disable shortcuts. Our approach provides a way to learn other potentially effective features. As for how to choose them, it should be determined by the situation. We suggest some sum-up strategies in lines 134-142. For the debiasing task, when the ratio is low enough, it is difficult to judge who is the target and who is the bias. In methods such as LFF, it is assumed that what is learned first is bias, and the method breaks down when the target attribute becomes an easily learned attribute. Therefore, we propose to decide based on the performance during training. Because in the training set, the prediction accuracy of the target feature must be higher than the bias accuracy.\n\n**Major1-3 More complicated shortcut structures might exist.**\nThe proposed approach can continuously accumulate new EMs. However, in our experiments, the samples generated by the new AEs that keep both BM and EM at a loss often do not retain enough information. The debiasing task usually assumes only two, while in the conventional task, not only one feature is learned at a time. We do not observe the occurrence of complex shortcuts. We construct a three-attribute dataset to achieve this scenario, and with the second AE and EM, our approach can achieve the suppression of the first two attributes.\n\n**Major1-4 Dependent on the design of the AE model, only rather specific types of shortcuts might be addressed with the used AE model. Why ImageNet was not selected as a dataset.**\n\nWe believe that the proposed framework can handle various shortcuts without priors, which is a significant contribution. If BM can extract features to complete classification, AE can disable the features to confuse BM. We are also trying other generative models to get better results.\nPlease refer to general response Q4 for discussion about ImageNet. \n\n**Major1-5 To improve intuition about how AE works, please also provide AE modified samples for the BAR and CelebA and also provide saliencies for CMNIST and BAR.**\n\nWe have made adjustments in the updated manuscript, thanks for your suggestion. \n\n**Major1-6 How cherry-picked are samples in Fig 3 and 5.** \n\nFigure 3 shows randomly selected samples for each category. Figure 5 is randomly selected from samples classified correctly by both models. Well-chosen saliency maps may mislead our perceptions, and I had similar concerns when I read the article myself. We put more saliency maps in Appendix, and our code will be open-sourced. Hope these reduce some of your worries. \n\n**Major2** \n\nWe have indicated in the checklist and appendix that we will make the code public, so please do not worry about that. \n\n**Medium**\n\nShortcuts are not necessarily a bad feature, which seems misleading. So we want to convey this point through sum-up.\n\nOur method does introduce some invariance, which is why it can disable shortcuts. We do not know much about data augmentation methods and look forward to having a more in-depth discussion with you.\n", " Thank you for the compliment on our paper. It is a great encouragement for us. \n\n**Q1**\n\nIn the updated manuscript, we present visualizations across datasets, including reconstructions and saliency maps. Please refer to Figure3, Figure5. Related discussions are in lines 181-191, 202-211. These Figures are randomly selected. More visualization results are in the appendix (Figures 11-15).\n\n**Q2 & L1**\n\nThe requirements of our method for AE are actually not as high as those of other generative models. Because it only needs to make some changes based on the input without generating high-quality images from a simple input (noise or encoding). For regular datasets, the reconstruction results of the autoencoder are sufficient for classification with little impact. We also conducted experiments on ImageNet, and the results are as follows. Figures and some brief descriptions are included in Appendix A.7. Also, in Appendix A.3, you can see that we have constructed a scene with insufficient AE capability to conduct experiments, giving some interesting phenomena and analysis.\n\n**L2**\nDebiasing is not the core content, so we only discuss the basic debiasing tasks in this paper. We will further investigate the related work, and if necessary, we will discuss it in the appendix.\n", " Thanks for your thoughtful review and constructive comments. I will respond to the weaknesses (**W**) and questions (**Q**) you mentioned.\n\n**W1**\n\nThank you for pointing this out. We have discussed the literature you listed in the updated manuscript. \n\n**W2 & Q2**\n\nOur approach may be somewhat similar in form to adversarial training. However, there are clear differences in purpose and design. The intention of adversarial examples is to make predictions wrong, and untargeted attacks need to avoid correct predictions. However, the samples we construct through AE are intended to make predictions confusing, which means correct predictions and other possible categories are treated equally. We tested adversarial training on CMNIST, and the results are as follows. Related discussions are in lines 279-286 of the new version. \n| Ratio (%) | Vanilla | Adversarial(l2) |\n| --------- | ------- | --------------- |\n| 0.5 | 74.90 | 72.78 |\n| 1 | 65.77 | 64.14 |\n| 2 | 50.13 | 45.31 |\n| 5 | 33.07 | 30.47 |\n\n**W3 & Q3**\n\nMSE is closer to a distance metric than just classification loss. If only classification accuracy is considered, MSE may focus on unnecessary parts, but we believe that MSE is more in line with the need to suppress shortcuts. For example. the label is (1,0,0), there are 2 predictions, (0.8,0.1,0.1), (0.8,0.2,0). MSE think the former is better, while CE think they are the same. If we only aim at classification accuracy, the two should be the same. But we argue that the latter has higher confidence in an error class, which is more likely to lead to errors in tasks where shortcuts exist. This is not the first to use MSE loss with special considerations; for example, [1] discusses the application of MSE loss to imbalanced classification tasks.\n\nMSE is more prone to getting stuck in a local optimum, but in our task scenario, methods using CE have also gotten stuck in a local optimum. And our method keeps the model looking for new possibilities. Even if it falls into a local optimum, it is still likely to obtain a better solution under the overall framework of our method. We tried CE, and the results are not better.\n\n**Q1**\n\nThanks for your very enlightening question. \nPerceptual Loss may also apply here. We did not do too complicated a design on the loss function. We think such a framework would make much sense for the community and we cannot wait to share this and be able to highlight it. In addition, we are concerned that some losses, such as Perceptual Loss, may have a more explicit feature preference orientation, which requires more thought and experimentation to verify.\n", " We thank the reviewers for their thoughtful and constructive review of our manuscript. We were encouraged to hear that the reviewers found the shortcut problem we discussed to be important (Reviewers T7g9, ius4) and that they view our methodology as novel (Reviewer ius4, T7g9) and effective (Reviewer BFAY, dvxL). In response to feedback, we provide a general response to points raised by multiple reviewers, and an new version of manuscript is uploaded. We will also respond to questions raised by each reviewer individually.\n\n\n**Q1: What exactly did the AE learn?**\n\nAll reviewers are keen to note that the AE is at the core of our approach. Everyone asked some questions about AE. For example, the behaviour of AE on complex samples (Reviewers dvxL, T7g9, ius4)? \nIntuitively, what AE learns is an elimination method for the knowledge used by BM. In the updated manuscript, we present visualizations across datasets, including reconstructions and saliency maps. Please refer to Figure3, Figure5. Related discussions are in lines 181-191, 202-211. These Figures are randomly selected. More visualization results are in the appendix (Figures 11-15).\n\n\n**Q2: Why use MSE loss for classification?**\n\nMSE is closer to a distance metric than just classification loss. If only classification accuracy is considered, MSE may focus on unnecessary parts, but we believe that MSE is more in line with the need to suppress shortcuts. For example. the label is (1,0,0), there are 2 predictions, (0.8,0.1,0.1), (0.8,0.2,0). MSE think the former is better, while CE think they are the same. If we only aim at classification accuracy, the two should be the same. But we argue that the latter has higher confidence in an error class, which is more likely to lead to errors in tasks where shortcuts exist. This is not the first to use MSE loss with special considerations; for example, [1] discussed the application of MSE loss to imbalanced classification tasks.\nMSE is more prone to getting stuck in a local optimum, but in our task scenario, methods using CE have also gotten stuck in a local optimum. And our method keeps the model looking for new possibilities. Even if it falls into a local optimum, it is still likely to obtain a better solution under the overall framework of our method. We tried CE, and the results are not better. \n\n\n**Q3: Difference with adversarial training?**\n\nOur approach may be somewhat similar in form to adversarial training. However, there are clear differences in purpose and design. The intention of adversarial examples is to make predictions wrong, and untargeted attacks need to avoid correct predictions. However, the samples we construct through AE are intended to make predictions confusing, which means correct predictions and other possible categories are treated equally. We tested adversarial training on CMNIST, and the results are as follows. Related discussions are in lines 279-286 of the new version. We use *Fast Gradient Sign untargeted Adversarial Attack*, and the epsilon is 0.3.\n| Ratio (%) | Vanilla | Adversarial(l2) |\n| --------- | ------- | --------------- |\n| 0.5 | 74.90 | 72.78 |\n| 1 | 65.77 | 64.14 |\n| 2 | 50.13 | 45.31 |\n| 5 | 33.07 | 30.47 |\n\nWe also test different experimental setups and present some visualizations.\nPlease refer to Appendix (A.4) for more. \n\n**Q4:Why ImageNet was not selected as a dataset?**\n\nImageNet does not have multi-label or recognized bias, which makes further analysis difficult. So we didn't try the ImageNet experiment before. We tested our method with 10 classes of ImageNet, and the results are as follows. Figures and some brief descriptions are included in Appendix A.7.\n| Method | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Avg. |\n| ------- | ---- | ---- | ----- | ---- | ---- | ----- | ---- | ---- | ---- | ----- | ---- |\n| Vanilla | 92.0 | 88.0 | 92.0 | 84.0 | 96.0 | 100.0 | 98.0 | 90.0 | 92.0 | 94.0 | 92.6 |\n| Ours | 92.0 | 92.0 | 100.0 | 94.0 | 98.0 | 98.0 | 94.0 | 96.0 | 96.0 | 100.0 | 96.0 |\n\n\n**Q5: Reproducibility and Writing?**\n\nWe note that the reproducibility of our method also raises some concerns. \nWe have indicated in the checklist and appendix that we will make the code public, so please do not worry about that. \nWe apologize if our writing caused some difficulties. We have clarified ambiguities raised in review comments in the updated manuscript and will further polish our writing.\n\n[1] Kato S, Hotta K. MSE Loss with Outlying Label for Imbalanced Classification[J]. arXiv preprint arXiv:2107.02393, 2021.", " The paper tackles the problem of neural networks learning ‘simple’ features which cannot generalize well. It proposes to alleviate this problem of shortcut learning by generating synthetic data (“roadblocks”) in a manner which confuses the network while being close (in $l_2$ norm) to the original training data. A new model is trained on such examples, and it is hypothesized that this new model learns more robust features. The paper empirically shows that such models are more robust when there are spurious correlations in the data. The paper also presents visualizations of learnt features, as well as of the generated roadblocks, indicating that these do contribute to learning more robust features. Strengths - \n1. The empirical results on the debiasing task are promising. \n2. The method does not need any priors about the dataset in order to work.\n\nWeaknesses - \n1. The work misses several key references. Shortcut learning is very closely related to the problem of simplicity bias in neural networks [1], which is not cited in the work.\n2. The method is also very similar to training with adversarial examples [2]. This line of work is neither cited nor compared against. On the mentioned datasets, the generated images indeed look very similar to $l_2$ or $l_\\inf$ constrained adversarial attacks.\n3. The paper proposes using the MSE loss for classification, which is not standard.\n4. The writing of the paper can be improved significantly. \n\n\n[1] - Shah, Harshay, et al. \"The pitfalls of simplicity bias in neural networks.\" Advances in Neural Information Processing Systems 33 (2020): 9573-9585.\n[2] - Ilyas, Andrew, et al. \"Adversarial examples are not bugs, they are features.\" Advances in neural information processing systems 32 (2019).\n 1. How important is the distance metric for imposing loss between the generated images and the real images? Can a perceptual loss be used for the same?\n2. How does the method compare against simple adversarial training?\n3. Why was the MSE loss used for classification? Can cross-entropy give better results? Some of the limitations are listed in the weaknesses above. A more thorough empirical evaluation on other OOD tasks would also be appreciated. \n", " A method for OOD generalization is proposed. To prevent a model (Explorer Model) from learning \"shortcut features\" (simple features which do not work in OOD setting~spurious correlations), an autoencoder is trained, which tries to fool a pretrained model (Blocked Model) as an additional loss. The explorer model is then trained on the reconstructed image, from which some of the shortcut features were hopefully removed by AE to fool the Blocked model. Strengths:\n- Promising framework and approach, which does not require any external knowledge but relies on the interaction between autoencoder and blocked model.\n- Interpretability: can visualize reconstructed images to gain insight (e.g. Figure 3 of CMNIST)\n- Indirectly applicable to debiasing (by removing shortcut features)\n\nWeaknesses:\n- Relies on autoencoder reconstruction, which may be blurry and lower the prediction quality. - Can we see some samples of CelebA reconstructed by the autoencoder?\n- Can you discuss the relationship/tradeoffs with using a better autoencoder/pretrained autoencoder, which may limit the applicability of this method to harder datasets? Relies on autoencoder reconstruction, which may be blurry and lower the prediction quality.\n\nThis method seems to implicitly perform some debiasing, which should hopefully have a positive impact in terms of making better predictions. However, this should be more extensively tested on a wide variety of tasks to see if the usual fairness/bias metrics are consistently improved.", " The authors propose an approach to address the problem of shortcut vulnerability of deep vision models in image classification tasks. For a trained, shortcut exploiting model (BM) the authors propose to train a model (AE) that learns to modify training samples in a minimal way while yielding a maximum entropy prediction for the BM model. Using these manipulated samples, an explorer model is trained (EM) in a supervised manner to predict the original ground-truth labels. The intuition behind the approach is that AE learns to manipulate input samples specifically to remove the shortcut information in the image in order to enforce the explorer model to learn new, actual class information and is hence less shortcut vulnerable. \nEmpirical evidence is provided for the CMNIST, CelebA and BAR datasets indicating the improved classification generalization. Further, the authors provide qualitative evaluation in form of an inspection of the manipulated images, as well as saliency evaluations comparing BM and EM which suggest that the AE model in fact removed the shortcut information and that the EM model attends to more meaningful image areas than BM. In a nutshell, the work address a major, central problem of current ML The proposed solution to the problem is original and some interesting empirical results are provided. Still, I think some limitations / questions should be addressed more explicitly (see below). I would like to increase my rating in case stated limitations, questions (see below here under weaknesses) get addressed sufficiently.\n\nStrengths\n------------\nThe work addresses the problem of shortcut vulnerability of ML models in a supervised learning setup. This is of immense significans for the entire ML community. As far as I can tell, the authors propose a novel, original approach to tackle this challenge in the effort to traina more shortcut robust model. The authors present their central idea in a clear, easy to access manner and present some quantitative evidence that supports the central claims of the paper (Tab 1, 2). Also of value are the provided qualiatitve evaluations indicating that the modification model (AE) works as intended on the investigated dataset CMNIST (Fig. 3) and a saliency comparison for BM and EM (Fig 5) on the BAR dataset, indicating that EM attends to more meaningful image areas than BM.\n\nWeaknesses\n----------------\nMajor 1\n\nIt is not clear to me what the AE actually learns and in which cases it actually learns to remove shortcut information. I think the provided intuition how AE should work is sound and the provided results support this intuition, however question about how AE actually works and how well it generalizes to other cases remain unclear and should be addressed:\n* Why does AE not learn to produce (untargeted) adversarial noise? This would have the same effect as removing the shortcut, i.e., induce minimal change in the image and yield uniform classification. Please address in the text.\n* Why does AE not learn to remove actual class information? This is especially relevant in case of low correlations (ratio) between the shortcut and the actual target class in the training dataset. In those cases, AE would probably learn to also remove the actual class information. Please discuss this point.\n* More complicated shortcut structures might exist (shortcuts of shortcuts of shortcuts of ...). For this, see also [1] which should also be cited in intro / related work. This point seems partially addressed in L126-L133 but could be made more clear.\n* Dependent on the design of the AE model, only rather specific types of shortcuts might be addressed with the used AE model. Also see [1] for more shortcut examples. For example, it is not clear that AE would be able to address the texture bias on ImageNet. Please also address why ImageNet was not selected as a dataset.\n* To improve intuition about how AE works, please also provided AE modified samples for the BAR and CelebA dataset (similar to Fig 3 for CMNIST) and also provide saliencies for CMNIST and BAR (similar to Fig 5). Either Fig 3, 5 could be extended or additional images can be shown in the supplementary material.\n* How cherry-picked are samples in Fig 3 and 5. Information in the text is missing.\n\n[1] \"DiagViB-6: A Diagnostic Benchmark Suite for Vision Models in the Presence of Shortcut and Generalization Opportunities\", ICCV 2021\n\nMajor 2\n\nCode should be made available to enable reproducibility. I could not find a code publishing statement in the paper.\n\n\nMedium\n\n* The role of the sum-up combination is not clear. Is this used somewhere in the experiments or is this merely a proposal for an open-set-recognition task? If of no practical relevance for this work it could be left out entirely.\n* It should be noted somewhere that this training proceedure, similar to all data augmentation approaches, induces certain invariances in the EM model which might lead to unintended behavior on outliers.\n \n\n See weaknesses above. See weaknesses above.", " The paper proposed a learning approach for robustness to shortcut learning: after training a base model (BM) on the biased dataset, the auxiliary autoencoder (AE) is trained to modify train images such that their reconstruction is close to the original input but the trained model is outputting a uniform distribution over classes. Then another \"exploration\" model (EM) is trained on the modified inputs to predict the correct class. Thus, the intuition for the approach is that AE should remove the shortcuts from the inputs that BM learned, and EM will learn more diverse features. The approach was evaluated on ColorMNIST, CelebA and BAR benchmarks, and the authors provided additional analysis and visualizations of the features. The paper is addressing an important problem of learning diverse features and training models robust to shortcuts, and the proposed approach shows promising results on CelebA and BAR, however, the clarity and presentation can be significantly improved, and the paper is missing implementation and method details. The results on CMNIST are not directly comparable to prior work due to a different model architecture. Also, experiments on large scale datasets would be needed to demonstrate the practicality of the proposed method.\n\n\n### Originality\nThe paper is missing citations of the relevant literature on shortcut learning, simplicity bias, group robustness, and spurious correlations, e.g.:\n\nSagawa et al. Distributionally Robust Neural Networks for Group Shifts\n\nLiu et al. Just Train Twice: Improving Group Robustness without Training Group Information\n\nShah et al. The Pitfalls of Simplicity Bias in Neural Networks\n\nXiao et al. Noise or Signal: The Role of Image Backgrounds in Object Recognition\n\nTeney et al. Evading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions With Superior OOD Generalization\n\nNagarajan et al. Understanding the Failure Modes of Out-of-Distribution Generalization\n\nDagaev et al. A Too-Good-to-be-True Prior to Reduce Shortcut Reliance\n\nClark et al. Don't Take the Easy Way Out: Ensemble Based Methods for Avoiding Known Dataset Biases\n\nLee et al. Diversify and Disambiguate: Learning From Underspecified Data\n\nand others. To the best of my knowledge, the proposed approach is novel. However, I encourage authors to explicitly discuss the connection of their work with Just Train Twice [Liu et al], Dagaev et al (see above) and LfF as all of these prior works are based on using 2 models where the second model is correcting the biases of the first one similarly to the proposed approach (while it additionally uses an AE to modify the inputs).\n \n\n### Quality\n1. ColorMNIST experiments: In the Appendix A.1 it is mentioned that ColorMNIST dataset is setup as in Lee et al [1]. It is also mentioned that ResNet-18 is used in all experiments. I noticed that the numbers for the Vanilla, EnD, ReBias, LFF, and LDD in Table 1 in this paper are taken from the Table 2 in Lee et al [1] (they match those numbers exactly). However, right below Table 2 in [1] it is mentioned that an MLP architecture is used in the experiments, while this paper uses ResNet-18 so the comparison in Table 1 is not valid.\n(In general, I would also recommend that the authors explicitly say that which papers they took the numbers from for the prior methods in case they haven't re-run the methods.)\n\n2. While the Roadblocks approach works well on CelebA [Heavy Makeup, Gender] and BAR, it would be very helpful to see the performance on a large scale problem, e.g. ImageNet-9 [2]. It would also be interesting to see the results on a broader range of benchmarks in shortcut learning / spurious correlations, e.g. Dominoes (MNIST-CIFAR, MNIST-FashionMNIST, MNIST-MNIST) [3, 4], Waterbirds, CelebA [hair color, gender] [5]. These benchmarks vary in the strength of the spurious correlation / bias in train data and the complexity of the shortcut feature.\n\n3. How are hyper-parameters chosen for the models (lambdas loss coefficients, and also weight decays, learning rates, hyper-parameters of alternate training, etc)? Do authors use in-distribution validation set or bias-conflicting validation? This can have a high impact on the model's performance.\n\n4. I would encourage the authors to provide the reconstructed images like in Figure 3 for other datasets besides CMNIST.\n\n\n### Clarity\nClarity of the paper can be significantly improved. I strongly recommend the authors to add a brief datasets description to the main paper (e.g. the problem description, the nature of the bias / shortcut, the percentage of bias conflicting examples in train, etc). These details are not included in the paper, and some details become unclear without the context e.g. what \"Ratio %\" refers to in the Table 1.\n\nIt is mentioned that AE and EM are trained alternately, however, the details of this training are not described (i.e. are models alternately updated after each step or epoch?).\n\nI strongly encourage the author to add the high-level details on the prior works to which Roadblocks method is compared to either in the Experiments section or in the Related work. In particular, it will be helpful to know how prior works compare to Roadblock method in terms of computational complexity, memory, etc.\n\nSome paragraphs are unclear (e.g. lines 134-139, 172-176, 288-301) are not clearly written, lack details and context.\n\nI also strongly encourage authors to add more details in Table and Figure captions in the next revision of the paper (e.g. Figure 6 doesn't have titles for subplots to indicate which dataset they correspond to).\n\nIt is not clear how the final predictions are made with the proposed model: is only EM model used? It is not clearly explained in the paper.\n\nLine 47: \"shortcuts are disabled temporarily, not forever\", what does this mean? My understanding is that EM is trained on modified images outputted by AE so it is not clear what \"temporarily, not forever\" refers to.\n\nEquation (3): why are you using MSE loss and not cross-entropy loss for classification?\n\n\n### Significance\nWhile the paper is addressing an important problem and achieves promising results on CelebA and BAR, more details and experiments are needed for publication.\n\n**References**\n\n[1] Lee et al. Learning debiased representation via disentangled feature augmentation.\n\n[2] Xiao et al. Noise or Signal: The Role of Image Backgrounds in Object Recognition\n\n[3] Shah et al. The Pitfalls of Simplicity Bias in Neural Networks\n\n[4] Pagliardini et al. Agree to Disagree: Diversity through Disagreement for Better Transferability\n\n[5] Sagawa et al. Distributionally Robust Neural Networks for Group Shifts\n I have listed by questions and concerns above in the \"Strengths And Weaknesses\". Summary:\n\n1. Please provide the results for the ColorMNIST experiments with the MLP model (currently Roadblocks is using ResNet-18 while prior works are using MLP).\n\n2. It would be helpful to see results on other benchmarks, especially a larger scale problem like ImageNet-9, as well as Dominoes (MNIST-CIFAR, MNIST-FashionMNIST, MNIST-MNIST), Waterbirds, CelebA [hair color, gender].\n\n3. How are hyper-parameters chosen for the models (loss coefficients, weight decays, learning rates, hyper-parameters of alternate training, etc)? Is the validation split in-distribution or OOD (bias-conflicting)?\n\n4. Please provide more details on the alternate training of the models.\n\n5. It is not clear how the final predictions are made with the proposed model: is only EM model used?\n\n6. Equation (3): why are you using MSE loss and not cross-entropy loss for classification? Yes" ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 5, 4 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4 ]

[ "0Sfo9MplANP", "ey2y9HKZGLt", "zrIcrnsYFuv", "GCbCxqyW-kB", "MicqF2OinCS", "jyJ_ES_smDU", "eUteb_cZV1f", "jrHfQSnQbxe", "DLfQ19cnLm0", "QaKaUVYvaCe", "G6mZH01bCnE", "vJHXoD7KF3B", "UC6yCqOq0OU", "nips_2022_QjurhjyTAb", "nips_2022_QjurhjyTAb", "nips_2022_QjurhjyTAb", "nips_2022_QjurhjyTAb", "nips_2022_QjurhjyTAb" ]

[ "x6DFYSe9pxg", "yTYLR1x5nIb", "6LRcylo0FZZ", "10Ft_siXU8v", "CVSAo1u_KX1", "eGc9EWdE7uV", "SR3SG16CTTx", "EwrLZnnp6K", "nMmeMgybSwY", "2SLN6IS0I9B", "Qcpd-I-38K3", "s7BO_Pz5E08", "G0JoAMPW6Um", "8q21Epv-p2D", "B_sjXTHkp6_" ]

[ "official_reviewer", "author", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks the authors for your detailed response. The authors' explanation t on the \"real case\" makes good sense to me, but from the perspective of evaluating and demonstrating the proposed method, the \"real case\" may not provide strong evidence/confidence. Overall I feel that the method is promising and meanwhile there is room to improve the paper.", " \nThanks a lot for the response, we really appreciate your engagement with our work as we know this can be a very time consuming task!\n\n*Novelty*: We are very glad you agree! And we also agree with you that a larger part of the related work should include this area of research - we have currently updated the manuscript to include this in order to highlight our intentions given current space constraints, but with the extra camera-ready page we can fully explore this. If you have any additional suggestions on work to include it would be gratefully received!\n\n*Uncertainty*: Our apologies for the confusion - the added feature examples on that axis are the ones given to SMC in order to estimate the densities, **not** the ones given to the ensemble models when training in the first place, and so is not a relevant axis for the uncertainty estimation benchmark and does not effect performance. The only reason we included them in Fig 5 and not separately was due to, as above, space constraints - we can, and intend to, expand and introduce this properly in the camera-ready version.\n\nIf this has alleviated your concerns we kindly request you consider raising your recommendation, but if you have any further concerns, please do let us know!\n\nAll the best,\n\nThe Authors", " I thank the authors for their effort in editing to the manuscript.\n\n1. Novelty\nI agree that unsupervised + instance-wise weighting is a new combination. However a more thorough literature review on instance-wise weighting is needed. Again, I am sure each new method will differ from existing methods to some degree, but the author should properly refer to previous studies so that readers can better position the study and the problem being investigated.\n\n2. Uncertainty based weighting\nCould the author explain why increase sample size does not increase uncertainty performance in Figure 5? I found this very counter intuitive.\n\n", " Dear Reviewer 6vwo,\n\nOnce again, thank you for your thoughtful review. While we have this current period of discussion please do let us know if our response has addressed your concerns - we are keen to keep engaging with you to address any additional questions or comments.\n\nBest wishes,\n\nThe Authors", " Dear Reviewer gNf4,\n\nOnce again, thank you for your thoughtful review. While we have this current period of discussion please do let us know if our response has addressed your concerns - we are keen to keep engaging with you to address any additional questions or comments.\n\nBest wishes,\n\nThe Authors", " **Rebuttal Revision**\n\nDear Reviewers, thank you all for your thoughtful reviews and comments. We very much appreciate the general consensus that the problem we are working on and our proposed method is well-motivated and interesting. \n\nWe have provided individual responses to each of your reviews in the comments but we would also like to highlight that we have now uploaded a new version of the paper based on your feedback.\n\nAll changes in the text have been highlighted in blue for clarity and includes:\n\n- Notation and clarifications\n- Additional related work \n- Details on computational complexity\n- Added baselines in the MNIST example\n\nThanks again for your work, and if you have further questions please let us know!\n", " Thank you very much for your helpful feedback and comments. We aim to address all of the individual points in your review here but please also see the revised manuscript for changes.\n\n*”In this paper, the solid theoretical analysis (e.g., theorems) is missing…”*\n\n**Response**:\n\nWe would like to respectfully disagree with the premise that the manuscript should contain more theorems in order to be appropriate for a venue like NeurIPS. A very large proportion of the accepted papers at these top conferences do not contain such aspects as they focus on algorithmic advances, applications, or empirical studies - all of which advance our knowledge of the machine learning field effectively.\n\nWe are also not sure what theorems there are in our case that would provide some significant insight into the method. We aim to focus on a new problem that has been underappreciated by the research community thus far, and have proposed a novel solution to this. We have demonstrated experimentally that this method works well in the settings we are interested in, settings that existing methods fail significantly, and that they can be applied easily to a wide range of settings. We believe this would be of great use to the machine learning community in and of itself and that NeurIPS would be an excellent venue where many people might be interested in the work.\n\nIf you have any suggestions on what theory we could add in order to better understand the method or draw particular insight that we have not been able to demonstrate with our experiments then please do let us know as we are keen to build the understanding surrounding this method.\n\n*”The part about the time complexity analysis is suggested to be added.”*\n\n**Response**:\n\nThank you for the suggestion on including details on computational complexity. We have added a section in the appendix of the paper for the moment, but with the additional page provided in the camera ready version we can add it to the main paper. We also give a summary here:\n\nFor the training time, we essentially inherit the properties of a variational autoencoder, although the calculation of the regularisation terms requires calculating pairwise-distances between points, an operation that is $\\mathcal{O}(n\\log{}n)$ with $n$ the mini-batch size, something which should be taken into account. This is very manageable, especially as there is no need for this to be repeated or updated and the applications we see this being useful for are not time pressured.\n\nInference is fast, taking only a single pass through a network followed by calls to\nlow dimensional densities. The initial pass scales only linearly with input dimension, and the calls to the densities depend on the exact method of estimation, but realistically will be fast given their lower dimensionality. Again though, we consider most applications for this to not require a particularly fast inference time anyway.\n\n\n*”Some figures and tables (e.g., Figure 1, Table 1, Algorithm 1) are not mentioned in the main body…”*\n\n**Response**:\n\nThank you for pointing this out, we have made sure that references to all figures/tables/algorithms now appear in the main text, and not just footnotes as some were.\n\n*”The authors are suggested to make more clarifications for some descriptions or functions…”*\n\n**Response**:\n\nThank you for pointing this out, we will clarify these points in the paper, especially on line 212 where we now make the point that this is how we shall denote this object. We have made a small adjustment now - but with the additional space in the camera ready version we can really take the space to emphasise this.\n", " *”Could the author clarity \"augmentation of the individual models\" at line 46?”*\n\n**Response**:\n\nFor this, we simply mean that we do not alter the given models in any way - for example, we wouldn’t take models as pre-trained starting points and then refine them on more data.\n\n*”What is the added computation complexity of SMC?”*\n\n**Response**:\n\nIn terms of details on computational complexity, we have now added a section in the appendix of the paper for the moment, but with the additional page provided in the camera ready version we can add it to the main paper. We also give a summary here:\n\nFor the training time, we essentially inherit the properties of a variational autoencoder, although the calculation of the regularisation terms requires calculating pairwise-distances between points, an operation that is $\\mathcal{O}(n\\log{}n)$ with $n$ the mini-batch size, something which should be taken into account. This is very manageable, especially as there is no need for this to be repeated or updated and the applications we see this being useful for are not time pressured.\n\nInference is fast, taking only a single pass through a network followed by calls to\nlow dimensional densities. The initial pass scales only linearly with input dimension, and the calls to the densities depend on the exact method of estimation, but realistically will be fast given their lower dimensionality. Again though, we consider most applications for this to not require a particularly fast inference time anyway.\n\n*\"Figure components should be explained in the figure legend.\"*\n\n**Response**:\n\nThank you for pointing this out, we have now updated the legends to reflect this", " Thank you very much for your helpful feedback and comments. We aim to address all of the individual points in your review here but please also see the revised manuscript for changes.\n\n*Novelty*\n\n**Response**:\n\nWe would like to strongly contend the suggestion that our work is not novel.\n\nIn Huang et al. (2009), they point to the work of Verikas et al. (1999) which describes a method for weighted averaging with data dependent weights.\n\nTheir method works by subdividing the space into $k$ regions, and then finding the optimal weights *in that region* - thus some different examples will have different weights used but we can’t consider it truly instance-wise, only region-wise. \n\nMore importantly however, this method is *not* unsupervised - in order to calculate the weights in each region they state very clearly on page 435 that “we use a validation set to evaluate the performance” - and so this method cannot work in the settings that we describe, and so it cannot be that our work is doing the same thing.\n\nThat being said, we appreciate you pointing out this work and will add a discussion of it to the paper as the inclusion of data-dependent weights outside of the unsupervised setting should provide some useful background.\n\n*References*:\n\nHuang, F., Guoqing X., and Ruliang X., (2009). Research on ensemble learning. International Conference on Artificial Intelligence and Computational Intelligence . Vol. 3. IEEE.\n\nVerikas, A., Lipnickas, A., Malmqvist, K., Bacauskiene, M., & Gelzinis, A., (1999). Soft combination of neural classifiers: A comparative study. Pattern recognition letters, 20(4), 429-444.\n\n*On benchmarks and baselines*\n\n**Response**:\n \nWe have tried hard to design all of the experiments in the penultimate section of the paper to answer specific questions about the method and to allow a reader to better understand both the strengths and weaknesses of the method - presenting results not just on drug response but also MNIST and regression problems. Given the limited space we thought it better to focus on this rather than a repeated demonstration that SMC is the only method that works in the settings described, albeit using different base datasets.\n\nIt ultimately comes down to the fact that we do not know of any other unsupervised methods that make instance-wise predictions and thus we don’t believe there are any methods for which it makes sense to compare performance across a wide range of benchmarks. Simply put, if methods are not instance-wise then they will perform poorly on the benchmarks we use (which will be adaptations of existing datasets where the training domains of the individual models will be disjoint).\n\nWe hope you find this position compelling, although please let us know if you still have concerns. In the meantime however we have also added some more baselines to the MNIST experiments - including as we describe next, your suggestion for an uncertainty based weighting.\n\n*Uncertainty based weighting*\n\n**Response**:\n\nThank you for this suggestion, as we think it will be very helpful to demonstrate some of the finer points of our model. We have now included results for this in the MNIST example that can now be seen in Fig 5. As you can see, it performs quite poorly - this should not be particularly surprising though since neural networks are notoriously bad at calibrating their uncertainty in the first place (Guo et al. 2017). We should also note that they are specifically capturing *aleatoric* uncertainty (i.e. the inherent noise in the data), which unlike *epistemic* uncertainty will not tell us about whether the network has seen anything like the example in its training data and thus whether it may or may not be a useful model for making a prediction over this specific example. \n\nSupposing the models given to us were Bayesian models, we should be able to get further with this approach, but this is obviously significantly limiting, as we expect it less likely for groups to publish full posteriors over parameters, and is not something we have seen happen in the real world to a large extent. It’s worth noting as well that at scale, variational methods for Bayesian inference over neural network weights have been shown to result in poorly calibrated posterior predictive distributions as well given the approximations made in the posterior, so even there we may expect over-confidence (Ovardia et al. 2019).\n\n*References*:\n\nGuo, C., Pleiss, G., Sun, Y. and Weinberger, K.Q., (2017). On calibration of modern neural networks. International conference on machine learning (pp. 1321-1330). PMLR.\n\nOvadia, Y., Fertig, E., Ren, J., Nado, Z., Sculley, D., Nowozin, S., Dillon, J., Lakshminarayanan, B. and Snoek, J., (2019). Can you trust your model's uncertainty? evaluating predictive uncertainty under dataset shift. Advances in neural information processing systems, 32.", " Thank you very much for your helpful feedback and comments. We aim to address all of the individual points in your review here but please also see the revised manuscript for changes.\n\n*Real case study details and \"What is the number of features of the dataset used in the “real case study” in Section 4.3?\"*\n\n**Response**:\n\nWith respect to your questions on the real case study, yes the testing set was simulated as mentioned, but we should emphasise that the problem was a very real example that is currently being attempted to be solved in the pharmacological community. The point being here that the whole unsupervised ensemble learning is in fact a valid practical agenda and not just something we have fun with in made up settings.\n\nThe setting was five dimensional, as we described in Appendix A - which we agree is not particularly high dimensional and so yes does not fully allow us to explore the advantages of the method in that respect. However we believe that we managed to demonstrate that aspect well in the MNIST example, with the Vancomycin example now reflecting a real problem and that there are gains to be had even without the dimensionality reduction.\n\n*”What is the minimal requirement on the number of test samples?\"*\n\n**Response**:\n\nWe do not think it is quite as simple as to just need a minimum number of test examples, as we are also expecting some information from the ensemble models’ training domains and so if that is in the form of feature examples they can also be used effectively to reduce the number of test examples needed. Actually describing what the minimum number is is still an open question, and with fewer examples it will be harder for the model to learn a good representation and could be prone to overfitting quite easily. That being said, with the added regularisation and the intention to use very low dimensional latent spaces, this should alleviate some of the issues, and combined with reducing the capacity of the encoder/decoder networks should make it practical in a reasonably wide range of scenarios. \n\nIn terms of the test sets used in the paper, for MNIST we used the standard test set of 10,000 images, while the Vancomycin examples were validated on 6000 patients.\n\n*”Could you elaborate on D_Y…\"*\n\n**Response**:\n\nD_Y is an important part of the regularisation and plays a large role in our representation step as it is what allows the representation to reason about models based on their agreement on inputs. It is essentially simply a measure over the disagreement between the different predictive distributions between the ensemble methods - as such its calculation will vary between tasks but in the case of classification we can use a simple normalised KL divergence between the predictive categorical distributions for example. The multiplication is simply there as this is used as a weighting over the pairs, up-weighting ones that have similar predictions.\n\n*”In terms of related work…\"*\n\n**Response**:\n\nTo the best of our knowledge the existing instance-wise and dynamic ensembles require training data in order to work, making them inappropriate for the settings we are interested in. \n\nBased on reviewer feedback however, we think it appropriate now to include a number of alternative methods in the MNIST example for clarity - even though, as can be seen in Fig 5 now, they perform very badly in the environment since they are not designed for this setting.\n\n*Minor notation*\n\n**Response**:\n\nThank you for pointing this out, we have amended the notation in the manuscript.\n", " Thank you very much for your helpful feedback and comments. We aim to address all of the individual points in your review here but please also see the revised manuscript for changes.\n\n*\"A minor weakness wrt related work...\"*\n\n**Response**:\n\nThank you very much for the suggested additional related work - we discuss the topic of unsupervised learning based on ensemble member agreement briefly in the manuscript (lines 99-102) but we will now include these additional references as they are certainly very relevant and bring more depth to the discussion.\n\n\n*\"Which baseline methods have been tested for the MNIST use case?\"*\n\n**Response**:\n\nThe MNIST example is specifically designed to highlight that there are scenarios where global ensembles will fail significantly. Because of this we did not originally include the scores of other baseline methods as they didn’t seem to be a useful comparison, but based on reviewer feedback we have decided to include results on a few of the baselines, including majority voting and an uncertainty weighted ensemble. As we see though, they do quite badly since they produce global ensembles that are not appropriate for the task or have poorly calibrated and inappropriate uncertainty estimates.\n\n*\"Did you test the approach for more challenging image / natural language datasets?\"*\n\n**Response**:\nWe haven’t completed extensive testing on larger image and natural language datasets, although have confirmed that SMC does work in these settings.\n\nThe problem being that benchmarks for our task do not really exist - and so we would be simply repeating what we do with MNIST and taking an existing benchmark and processing it in a way that moved it into our setting, allowing us to control the level of shifts etc. in the data that each model in the ensemble was trained on, and engineering an example that SMC does well on. Thus, as long as autoencoders and neural classifiers can be applied to a benchmark, SMC should be able to output reasonable performance - which brings us to the second issue that we don’t believe that there are any appropriate instance-wise unsupervised emsembling methods to truly compare against.\n\nAs such, we didn’t think that simply including scores of only SMC on a variety of datasets would be the most useful thing to include in the experiments section or actually give readers much information about how well our method works, and rather use the limited space to explore the properties of the method.\n", " The paper proposes synthetic model combination, an unsupervised ensemble learning approach to make instance-wise predictions by assuming access to the feature distributions the available models have perceived. Instance-wise, here, refers to choosing the weights of individual models for each test instance. The central application for such an approach is trained models on private (e.g. highly sensitive) data, where model performance is sufficiently good on the original data. The authors propose to learn a latent space on available unlabeled test data (sampled from the original data distributions), which in addition to a reconstruction loss also takes into account agreements and disagreements of the available models. The approach is evaluated for a toy example to underpin the need for the approach, MNIST and Vancomycin Precision Dosing. The results are able to show that instance-wise predictions using the learned latent space are performing well if the assumptions are met.\n Strengths: The paper is well-writen and thoroghly introduces/motivates the topic and problem setting. The problem is further concisely distinguished from related fields, such as transfer learning. The taken approach is well motivated too. The empirical evaluation is rather thorough and the results are sufficiently discussed, such that the available claims can be supported. While the general problem of unsupervised ensemble learning is known, the approach is sufficiently novel and original.\n\nWeaknesses: A minor weakness wrt related work is missing coverage of existing unsupervised learning approaches which already incorporate agreement and disagreement based ensemble construction. Examples are [1,2]. It would also be interesting to see the performance of more challenging image or text datasets, but the current evaluation already supports central claims.\n\n[1] Platanios, E.A., Dubey, A. and Mitchell, T., 2016, June. Estimating accuracy from unlabeled data: A bayesian approach. In International Conference on Machine Learning (pp. 1416-1425). PMLR.\n[2] Platanios, E.A., Blum, A. and Mitchell, T.M., 2014, July. Estimating Accuracy from Unlabeled Data. In UAI (Vol. 14, p. 10). * Which baseline methods have been tested for the MNIST use case?\n\n* Did you test the approach for more challenging image / natural language datasets? The paper discusses limitations of the approach, such as varying model performances. The approach therefore works best if there are individual expert models for their respective domain. If a model varies in performance in its domain and cannot dominate other models, there might be problems. \n\nAs mentioned before, it remains unclear if the dimensionality reduction step also works sufficiently well for more complex problems.", " This paper studies the problem of unsupervised ensemble learning in the problem setting where a set of trained models and limited unlabelled test instances are given, but no access to the data used for training the models is available. The aim of the ensemble learning is to obtain a set of optimal weights of the models specific to each given test/new instance, to form an ensemble for predicting the label of the instance.\n\nA few demonstrating experiments, including one which is based on a real world medical problem, are presented to show the advantages of the proposed method and its limitations.\n Strength:\n1. The paper addresses a practical problem in ensemble learning.\n2. The research question is very well motivated and formulated.\n3. The overall design of the method is reasonable and sound.\n4. The experiment illustration has provided some strong evidence of the effectiveness of the proposed method.\n5. The paper is well written.\n\nWeakness:\n1. The experimental demonstration, although carefully designed, with each example intended for a justifiable purpose, overall the evaluation is not strong. In particular, I have some concerns about “real case study”:\n\na. the data used for the “real case study” is simulated patient data, not real patient data, which makes people wonder whether the proposed method would perform effectively in real world cases or not. \n\nb. the distributions of the predicted concentration by different models seem to have similar shapes/coverage, so I wonder if this is a good case study for demonstrating the expected advantage of the proposed method.\n\nc. this case does not seem to be a high-dimensional case, hence the evidence provided by this case does not demonstrate the expected strength of the proposed method for dealing with high-dimensional data.\n\n2. It is not clear as a minimal, how many unlabelled test instances are needed for learning the low-dimensional representations. For the experiment datasets, I cannot find information on the size of the test dataset either. A high requirement on test instances needed may limit the practical use of the proposed method.\n\nMinor: In formula (5), w_i(x) should be w(x)_i, to be consistent with the notation used in Section 3 (outline of the three main steps)\n 1. What is the minimal requirement on the number of test samples? \n2. What is the number of features of the dataset used in the “real case study” in Section 4.3?\n3. Could you elaborate on D_Y in (3) a bit more, e.g. its role, calculation and justification on the multiplication used?\n4. In terms of related work, I’d like to confirm - do all existing instance-wise or dynamic ensemble learning methods require model training data? Are there any methods which work in the same or similar setting of the proposed method? If yes, why the evaluation does not include a comparison study involving those methods?\n\n Yes.", " This paper proposed an approach named Synthetic Model Combination (SMC) that make weighted ensemble predictions based on local manifold context. In addition, the authors proposed a representation learning procedure to obtain the specified weights for SMC. The author provided examples and benchmarks on synthetic and real world datasets at the end. Strengths:\n\n-This work raises an important question that the ensemble process should be localized due to the partial information received during the training process of the contributing models.\n\n-Description of the problem is mostly clear and the article is well structured.\n\nWeaknesses:\n\n-Not novel. \nThe main contribution proposed in this article is a weighted ensemble on individual samples based on local context. This idea has been explored in previous studies (Huang 2009, Weighted Average with Data Dependent weights). The proposed autoencoder is new but seems to only be a way of obtaining weights. Authors need to state the added advantages of using an VAE. If it is the best way to obtain weights the author need to compare autoencoder with other methods to justify this approach.\n\n-Results not significant/lack of benchmarks:\nThe only benchmark is on a drug response estimation with incremental improvements. To demonstrate a general performance improvements, experiments on existing larger dataset like cifar10, imagenet, and other NLP datasets is needed.\n\n-Lack of comparison with existing methods:\nSimilar to the previous point. The author should systematically compare the SMC with existing ensemble learning approaches across multiple benchmarks.\n\n-The overall writing quality is not great. There are many non-idiomatic sentences with long clauses that hinders readability.\n\n-While I appreciate the illustration with well-colored diagrams, it can be a little distracting at times. Figure components should be explained in the figure legend. (e.g. dots in Figure 3.)\n\nRef:\nHuang, Faliang, Guoqing Xie, and Ruliang Xiao. \"Research on ensemble learning.\" *2009 International Conference on Artificial Intelligence and Computational Intelligence*\n. Vol. 3. IEEE, 2009. -It would be interesting to see how encoding simple uncertainty measures like variance or entropy as weights compares with weights calculated from VAE. Have the author performed similar experiments as a control?\n\n-Could the author clarity \"augmentation of the individual models\" at line 46?\n\n-What is the added computation complexity of SMC? NA", " This paper proposed a new ensemble method – Synthetic Model Combination (SMC) operating on the instance-wise level in the setting of unsupervised ensemble learning. The authors also introduced a novel unsupervised representation learning method. The experimental results on MNIST and Vancomycin Precision Dosing datasets validate the effectiveness of the proposed methods. Strengths: \n1. This paper is well-written. \n2. The problem this paper focuses on is important, and the method is interesting. \n\n\nWeaknesses:\n1. In this paper, the solid theoretical analysis (e.g., theorems) is missing. I think it is a necessary part, especially for a top machine learning conference like NeurIPS.\n2. Instance-wise level methods are expected to perform better than the methods learning the fixed weights for every instance, but at the cost of higher time complexity. The part about the time complexity analysis is suggested to be added. \n 1. Some figures and tables (e.g., Figure 1, Table 1, Algorithm 1) are not mentioned in the main body. The authors are suggested to link all the figures and tables to the main body. \n2. The authors are suggested to make more clarifications for some descriptions or functions. For example, you introduced p_{j}^{\\chi}(x) in line 212. More details about it are suggested to be added. \n Yes." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 6, 4, 5 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 3 ]

[ "2SLN6IS0I9B", "6LRcylo0FZZ", "nMmeMgybSwY", "B_sjXTHkp6_", "8q21Epv-p2D", "nips_2022_RgWjps_LdkJ", "B_sjXTHkp6_", "nMmeMgybSwY", "8q21Epv-p2D", "G0JoAMPW6Um", "s7BO_Pz5E08", "nips_2022_RgWjps_LdkJ", "nips_2022_RgWjps_LdkJ", "nips_2022_RgWjps_LdkJ", "nips_2022_RgWjps_LdkJ" ]

[ "D8pbxXp2bx", "x4f5UpbwVOP", "NqewAhhhQCM", "vmgMJ2Kv4A", "OriT8efpZTb", "tU66dVVuOp", "JWAh5rlcnV-" ]

[ "official_reviewer", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Hi,\n\nThe provided response answer my questions. Thanks!", " Thanks for your valuable comments. Appreciation for the approval and constructive suggestions.\n\nQ1: Thanks for this. We agree that it is important for object discovery to reduce human effort by automatically generating object labels. We attempt to evaluate the quality of discovered objects in Table 1. Both the supervised baseline and our localization network utilized the architecture of Faster R-CNN. “ClusterNet” here represents our method to generate object labels. Using our generated object labels as supervision, the Faster R-CNN can achieve 43.2 AP (the model is trained from scratch). Using 1137k human box annotations, the Faster R-CNN can achieve 54.4 AP. Especially when the prediction of motion information is more accurate, we will get better results (51.8 AP). We believe our method is very practical in some scenes with limited annotation. 43.2 AP vs. 33.8 AP when using 127k annotations. Also, in Table 2, the model architecture is the same, both utilized ClusterNet. The difference is the annotation setting (our generated object labels vs. human manual annotations).\n\nQ2: Your suggestion is inspiring to us. To be honest, we have tried to obtain 2D object labels from optical flow before; it requires motion decouple. Since optical flow represents the 2D projection of 3D motion (Ego motion and Object motion), the object motion obtained in this way (optical flow minus ego-motion projection) would be noisy. It could achieve 32.6 AP (initialized from 2D optical flow) compared with 43.2 AP (Now initialized from 3D scene flow). Another reason we use 3D scene flow now is that 2D optical flow usually needs a pre-trained model, but we can get 3D scene flow using non-learning methods. But your suggestion is enlightening; we haven’t tried to combine the two together. We believe a better combination would help initialize robust object labels.\n\nQ3: Thanks for this. We agree that static object discovery is crucial in joint iterative training. We appreciate your suggestions and will add another section (Static Object Discovery) in Sec 3.3 to introduce the 2D training strategy as well as our design for static objects. The outline is as follows: \n1. Discover static objects by appearance; this part will introduce the training strategy of the 2D localization network. It leveraged the generalization ability of the network to find more potential static objects.\n2. Discover static objects by temporal cues; this part will introduce how to use tracking to find static objects. The objects that have been found in some frames will be expanded to other frames. \n\n", " Thanks for your valuable comments. Appreciation for the approval and constructive suggestions.\n\nQ1: Fig. 1 only shows the high-level data flow. It will be better understood to watch with Table 6. The overall process can be divided into two steps: (1) 3D instance initialization and (2) joint iterative optimization. \n(1) 3D instance Initialization: This step represents iteration 0 in Table 6. It trained ClusterNet with the initial 3D pseudo labels, which utilize motion cues (3D scene flow learned from unsupervised method) to select moving HDBSCAN’s 3D proposals. Details can refer to L133-L150.\n(2) Joint iterative optimization: This step represents iterations 1-4 in Table 6. It iteratively trained our 2D localization network and our 3D ClusterNet by utilizing complementary informations of the two modalities. Take iteration 1 for example; the 3D proposals output by ClusterNet can be projected to 2D pseudo labels, we then trained the 2D localization network with these 2D pseudo labels. This is the 2D step in Sec 3.3. Next, the 2D proposals output by the 2D localization network can be used to refine 3D pseudo labels (using the 2D-3D cues and temporal cues), we subsequently train our ClusterNet with the refined 3D pseudo labels. This is the 3aD step in Sec 3.3. An iteration ends after a 2D step and a 3D step. The joint iterative optimization is consisted of several iterations. During inference, the localization network output 2D object bounding boxes on still-image and the ClusterNet output 3D instance segmentation on point clouds.\n\nQ2: Our network is initialized from scratch without any pre-trained weights. We add a column in Table 1 to specify how the network weights are initialized.\n| annotation setting | #images | #bboxes | network weights initialized from | AP$^{50}$ | AP$^{50}_{S}$ | AP$^{50}_{M}$ | AP$^{50}_{L}$ | AR$^{50}$ | AR$^{50}_{S}$ | AR$^{50}_{M}$ | AR$^{50}_{L}$ | \n| ---- | ---- | ---- | ---- |---- | ---- |---- | ---- |---- | ---- |---- | ---- |\n| fully manual annotation | 158k | 1137k |ImageNet |54.4 |20.5 |72.4 |90.9 |62.8 |35.5 |80.8 |94.0 |\n| fully manual annotation | 158k | 1137k |scratch |52.5 |23.5 |67.6 |86.3 |62.3 |34.9 |80.0 |93.3 |\n| 10% manual annotation | 15k | 127k |ImageNet |33.8 |5.5 |45.3 |74.9 |36.1 |9.7 |48.6 |76.7 |\n| 10% manual annotation | 15k | 127k |scratch |31.6 |5.7 |42.5 |72.2 |35.9 |8.6 |47.7 |75.3 |\n| ClusterNet (w/ gt sceneflow) | 158k | 0 |scratch |51.8 |21.3 |70.2 |89.5 |60.8 |30.2 |81.2 |94.8 |\n| ClusterNet | 158k | 0 |scratch |43.2 |18.4 |56.5|81.8 |55.4 |26.7 |71.9 |93.1 |\n\nQ3: We borrow the idea of center voting from VoteNet. The main differences are as follows: \n(1) Our network architecture is different. VoteNet uses a point-based backbone(PointNet) for feature extraction while our ClusterNet utilize a voxel-based backbone(Single-stride Transformer). Details can refer to L26-L38 in Appendix A. While VoteNet needs to downsample the whole scene into a fixed number of points, our method can handle more general scenes(no limit on the number of points). This advantage is suitable for our unsupervised object label generation since we need to assign each point an instance id.\n(2) The purposes of voting are different. VoteNet uses the voting module to aggregate features for later 3D object detection while we use voting for the direct 3D instance segmentation.\n\n", " Thanks for your valuable comments. Appreciation for the approval and constructive suggestions.\n\nQ1: We want to add some details to make the description more clear. Here “n” represents the number of instance segments in one frame of point cloud. 1) “n” can be different in each frame; it is not a fixed number. 2) the trained ClusterNet could output arbitrary number of clusters based on the predicted center offset of each point during inference. We use the Connected Component (CC) algorithm for instance grouping. Specifically, we move each point to its corresponding center according to the predicted offset and then group different centers within a distance threshold. Details can be found in Appendix A L35-L38. 3) for initial pseudo label generation, “n” is determined by motion cues. Referring to L139-L150, we select the movable (By Eq.5) segments from HDBSCAN’s cluster results as the initial instance segments.\n\nQ2: Thanks to the rapid development of autonomous driving technology and consumer electronics hardwares, it is more and more convenient to collect synchronized images and point cloud sequences nowadays. Well-synchronized camera-LiDAR systems are widespread in autonomous driving (L4), ADAS applications (L2), and consumer electronics (iPhone and iPad Pro). In the meantime, more and more datasets with well-synchronized camera-LiDAR sequences are generously provided by autonomous driving companies (e.g., Waymo, nuScenes, Argoverse), which make our research topic possible.\n\nQ3: We want to provide some details to make the description more clear. For a fair comparison between our generated labels and the fully supervised baseline, we use the same object detector(Faster R-CNN) and training techniques. We used the code implementation and training recipes provided by Detectron2(https://github.com/facebookresearch/detectron2).\n\nQ4: We would like to thank the reviewer for their kind suggestion. In order to be fully unsupervised, our model did not use any pre-training weights. In Table1, our result 43.2 AP is a Faster R-CNN trained from scratch with pseudo labels generated by our method. For the supervised baseline 54.4 AP, it is trained from ImageNet pre-training. We would make this more clear in Table 1 in the future revision by specifying the pre-training weights in use. We also added two experiments for the fully supervised supervised baseline trained from scratch. \n| annotation setting | #images | #bboxes | network weights initialized from | AP$^{50}$ | AP$^{50}_{S}$ | AP$^{50}_{M}$ | AP$^{50}_{L}$ | AR$^{50}$ | AR$^{50}_{S}$ | AR$^{50}_{M}$ | AR$^{50}_{L}$ | \n| ---- | ---- | ---- | ---- |---- | ---- |---- | ---- |---- | ---- |---- | ---- |\n| fully manual annotation | 158k | 1137k |ImageNet |54.4 |20.5 |72.4 |90.9 |62.8 |35.5 |80.8 |94.0 |\n| fully manual annotation | 158k | 1137k |scratch |52.5 |23.5 |67.6 |86.3 |62.3 |34.9 |80.0 |93.3 |\n| 10% manual annotation | 15k | 127k |ImageNet |33.8 |5.5 |45.3 |74.9 |36.1 |9.7 |48.6 |76.7 |\n| 10% manual annotation | 15k | 127k |scratch |31.6 |5.7 |42.5 |72.2 |35.9 |8.6 |47.7 |75.3 |\n| ClusterNet (w/ gt sceneflow) | 158k | 0 |scratch |51.8 |21.3 |70.2 |89.5 |60.8 |30.2 |81.2 |94.8 |\n| ClusterNet | 158k | 0 |scratch |43.2 |18.4 |56.5|81.8 |55.4 |26.7 |71.9 |93.1 |\n\nWeakness: Since unsupervised 2D object detection without any pre-training is a challenging task, only a few previous works have explored this field. In Appendix B Table 1, we tried to compare with more methods to verify the effectiveness of our method. The significant gain comes from combining 2D and 3D information (also temporal information). Our unsupervised method showed a significant improvement compared with those 2D methods. Recently, the authors of FreeSolo (CVPR2022) released their code, and we added the experiment results of their method for comparison. Results have already been updated in Table 1 in the revised manuscript. FreeSolo could only achieve a 1.0 AP score when using their approach to generate pseudo masks and retraining the Faster R-CNN. The reason for the low AP score is that such attention-based methods are just semantic-level discrimination. A row of cars in the scene often generates a large mask, which can not distinguish specific instances. Therefore, they can perform well in datasets with a primary object, but their method can not be to directly applied in complex driving scenes.\n\n| annotation setting | #images | #bboxes | network weights initialized from | AP$^{50}$ | AP$^{50}_{S}$ | AP$^{50}_{M}$ | AP$^{50}_{L}$ | AR$^{50}$ | AR$^{50}_{S}$ | AR$^{50}_{M}$ | AR$^{50}_{L}$ | \n| ---- | ---- | ---- | ---- |---- | ---- |---- | ---- |---- | ---- |---- | ---- |\n| FreeSolo | 158k | 0 |ImageNet |1.0 |0.2 |1.0|1.9 |2.2 |0.0 |0.1 |12.7 |\n\n", " The paper tackles the problem of object discovery. They propose the 4d unsupervised object discovery from 4D data - 3D point clouds and 2D RGB images with temporal information together with a new model, ClusterNet that is jointly iterative and optimized with a 2D localization network. Finally, results are reported on the Waymo Open Dataset. The paper tackles an important problem. It proposes the task of object discovery from 3D point clouds together with 2D images along with the temporal information which can be of interest for the community. I find the joint optimization to be interesting.\n\nMy main concern related to this paper is the comparison with state of the art which I find to be quite limited. I would have wished to see more comparisons with other methods for 2D unsupervised object detection. Since the comparison is quite limited, it is hard to estimate the gain brought by the proposed approach. So, the only estimate that remains is the comparison with the supervised case. However, for this setup I feel like there are little details about the used architecture. 1. How is \"n\" chosen for the number of instances?\n\n2. How hard is to collect data with cloud points?\n\n3. Can you give more details about the fully supervised baseline? Does it use a previously published method?\n\n4. In the implementation details (lines 218-232) it is stated that for example for 2D localization network, Faster R-CNN is utilized. Does this mean that you also initialize some weights with a pre-trained Faster R-CNN model or that you rely on the architecture? This aspect needs to be clearly stated. The authors discuss some of the limitations and some potential societal impact problems.\n", " The paper solves the problem of unsupervised object discovery by utilizing the 4D information (cloud point, and time), they designed an iterative refinement frameworks which do the 2D information refinement and 4D information refinement one-by-one (usually 4~5 iters). \n\nThe results achieves the best result under the new setting. A few ablations about the importance of cues, training strategies, etc are provided to help us to better understand the task and the methods. Pro:\n\n- Interesting and sound setting to explore the 4d unsupervised object discovery.\n- The writing is easy to follow from intuition, to method, and finally experimental parts.\n\n\nCon:\n- Figure 1 is not clear about the dataflow. I am totally missed.\n- One detail I am curious is that whether your network is initialized from scratch, or from another pretrained network. That counts about whether you can name it as 'unsupervised'.\n- The contribution claim of clusternet, can the author highlight the difference of it with VoteNet? Listed as above. Yes.", " In this paper, the authors have proposed a novel task named *4D Unsupervised Object Discovery*, aiming at discovery the objects from 4D sequential data (3D point clouds + 2D RGB images), without any human annotation.\n\nFor this purpose, they proposed a method called *ClusterNet* to automatically discovery the objects in 2D images (bounding boxes) and the objects in 3D point clouds (point-wise segments), which can be jointly optimized on the 4D sequential data by taking the temporal information into account. \n\nThe generated labels are evaluated in 2D object detection and 3D instance segmentation, showing on par results with supervised methods and superior performances compared to other object discovery methods. Furthermore, the 2D object boxes can be converted to 2D object segments by projecting the 3D instance segments to 2D images, which allows for joint segmentation on 4D data. Strengths:\n\n* This paper proposes a novel task and a novel method with clear presentations, and thorough ablation studies supporting the validation of each component of the proposed method.\n\n* While existing object discovery works mainly focus at extracting discriminative information from pure 2D or 3D data, this work chooses to combine the best of both modes by leveraging the 4D sequential data, and to consider the temporal information as well as the multi-modality constraints. This removes the dependence of a strong self-supervised learning models, and compensate the weaknesses of each side.\n\n* The superior experimental results shows that the advantages of object discovery on 4D data compared to pure 2D or 3D.\n\nWeaknesses:\n\n* No experimental result was given to demonstrate the quality of discovered objects by training existing models with the generated labels instead of the human annotations.\n\n 1. Since one important objective of object discovery is to reduce human effort by automatically generating object labels, retraining existing models with the generated object labels should be added to show the true efficiency of the proposed object discovery method. The performance gap between models trained with generated labels and human labels can serve as a key indicator for the final application in real world. \n\n2. As this method works on 4D data, the authors propose to initial object labels on 3D, then project to 2D and iteratively optimize them, I am wondering is it possible to initial object labels on both 2D and 3D by clustering moving objects with optical flows and scene flows. This is not necessary, but we might get better initial labels by looking at both modes.\n\n3. The current version of Sec 3.3 is a bit too abstractive, with many details hiding in several parts of the paper.\nFor example, it is not trivial to train the 2D localization network to discover static objects with initial proposals projected from 3D point clouds, a summarization of the training strategy (L276-290) could be added in Sec 3.3 to help the readers understand quickly how this was done. Yes, the limitations are discussed in the last section of the paper." ]

[ -1, -1, -1, -1, 5, 6, 6 ]

[ -1, -1, -1, -1, 3, 4, 4 ]

[ "vmgMJ2Kv4A", "JWAh5rlcnV-", "tU66dVVuOp", "OriT8efpZTb", "nips_2022_eQfuHqEsUj", "nips_2022_eQfuHqEsUj", "nips_2022_eQfuHqEsUj" ]

[ "cgv2699_0B", "XMiM1ap0zxz", "iVwxX7w-0JY", "o2dxZsuceGn", "dRjDHGyEDw_", "L2krzNkrFR", "zcdj85SVNql", "xhjGETmP95y", "4DOeKoHwQOf", "3yBC9hcgzJ2", "s9GblvLaZCj" ]

[ "author", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks for your suggestions. We will add this part to our manuscript and elaborate more. Yes, noise is an important reason for using median, and the mean vary per change in the shift. For example, inaccurate predictions in distant areas may constitute noise in the mean representations. When the depth values of all pixels are averaged, the relatively large depth errors in distant regions will dominate the mean representation and negatively influence the depth representations of all pixel locations. In contrast, median is less affected by these outliers.", " The authors addressed the concerns brought up in my previous review.\n\nQ2: It would be nice for the authors to add this snippet to the paper and elaborate more. In other words, the authors referred to prior works to justify their choice in using median, but they lack the reason why it works. Is it because of noise? Does the mean vary per change in the shift? Also, the relationship between this answer and Table A in the appendix is unclear. Please clarify in the paper; also, consider more information on this part, for it is a critical aspect of the proposed framework.\n\nAll-in-all, excellent work!", " thanks", " Thanks for the constructive comments. We will carefully check and improve the organization of our paper and provide analysis in the experiments.\n\n**Q1: Lack of depth in analysis for the many ablations conducted.**\n\n\nOur supplementary material contains more experiment results and analysis to validate the generalization and effectiveness of our contributions. Specifically, \nin Table A, we combine our design with another SOTA zero-shot learning method Leres[33], and the result shows that our design can still effectively improve the performance by up to 20\\%.\nIn Table B, we use two more evaluation metrics to evaluate the quality of depth boundaries on iBims-1 dataset.\nWe also conduct cross-domain experiments on two new synthesized datasets in Table C. We totally use 8 datasets to validate the generalization capability.\n\nAdditionally,\n1) We design a new model variant that combines our design based on the spatial domain and the depth domain, which further improves the optimal performance. (Please see our response to Q1 from Reviewer v9VC)\n2) We also conducted experiments to validate the generalization of our design under the standard fully supervised setting. (Please see our response to Q2 from Reviewer v9VC)\n3) We discuss a new strategy to obtain hierarchical normalization contexts, and please refer to our response to Q1 from Reviewer uzns.\n\n\n\n**Q2: Why the median in (1)? More elaboration on the insights could be worthwhile.**\n\nPrevious work by Midas[22] aims to explicitly remove the shift changes between different datasets by subtracting the median. Here we adopt the same basic normalization operators for fair comparisons and ablation studies. It can also be replaced with other operations, such as mean in Leres[33]. Our design can also be combined with Leres to effectively improve performance by 20\\%, as is shown in Table A of our supplementary material.\n\n**Q3: lack of demonstrating the final reconstruction results (just depth images depicted).**\n\nIn Fig. A of our supplementary material, we provide the visualization of the reconstructed point clouds. We also provide demo videos that synthesize multi-view images with our depth estimation models.\n", " **Q1: ... dividing the depth representation irregularly? ...consider additional semantic information...?**\n\nAs we aim to design a generic depth normalization algorithm, here we choose to define the hierarchical normalization based on regular patterns, e.g., grids, without using extra information, such that the optimization of each location is always based on multi-scale contexts. \n\nIt is a good idea to incorporate additional semantic knowledge into our design. In fact, our design provides a useful way to explicitly utilize semantic knowledge for improving predictions. For example, if we define a normalization context that covers stuff and objects based on panoptic segmentation, it emphasizes the spatial relations between different instances and stuff. On the other hand, if the normalization context is defined based on the instance masks, we can emphasize the fine-grained depth difference in object appearance, such as the structures of vehicles.\nIn an application that synthesizes multi-view images of faces based on the depth prediction of portrait images, we find utilizing portrait segmentation to define the local normalization context helps the prediction of faces quantitatively and qualitatively. \n\nHere, we discuss a simple but effective variant that randomly samples pixels to define the hierarchical normalization contexts. Specifically, for HDN in the spatial domain, we randomly sample 128 regions from the image as the contexts. The lower bound of cropping size is 1/8 of the raw size, with aspect ratio restricted in [3/4, 4/3]. For HDN in the depth domain (HDN-D), we randomly define 32 depth ranges based on the ground-truth depth range, and locations being covered by a sampled range constitute a normalization context. The lower bound of the sampled range is set as 1/8 of the ground truth depth range in the image. \nThe experiment over 5 benchmarks shows that the performance of HDNs in the depth domain and the spatial domain drops by 5% and 3%, respectively, on average, but still outperforms the baseline by 15\\% and 6\\%, respectively. Therefore, dividing the depth representation irregularly without extra knowledge also works, but is less effective than our initial design. Thanks for the valuable comments, and we will update these new findings and discussions in our latest manuscript.\n\n**Q2: Fig. 2 is hard to follow.**\n\nFig.2 is used to illustrate the idea of our proposed hierarchical normalization.\nThe left plot indicates a distribution of representations that may not necessarily be depth representations. (Thanks for the comments, and we should have shifted it a bit to indicate that it is not a normalized distribution.)\nIn the middle, we group different representations hierarchically, as indicated by the colors, and they are normalized individually. In the depth prediction task, each dot corresponds to the depth value of a pixel location. Different colors can correspond to different normalization contexts in HDN. For example, a color means an image sub-region in HDN-Spatial. We will improve the figure illustration.\n\n**Q3: if we only used a single dataset ... which does not suffer from depth scale or shift problem**\n\nPlease refer to our response to Q2 from Reviewer v9VC, where we provide experiments to validate the effectiveness of our design under the fully supervised setting that predicts metric depth. Our design is still very effective in this setting.\n\n**Q4: other loss functions may be used, for instance, AbsRel. It would be better if the other loss functions are compared.**\n\nLeres[33] is the SOTA method that also designs a scale-and-shift invariant loss.\nSection B.1 and Table A in our supplementary material show that our design can be nicely combined with it, which improves the performance by up to 20\\%.\n\nPrevious works[33][22] have discussed and concluded that the scale-and-shift changes between datasets can not be solved by AbsRel loss, with which the training can not converge. For example, if the gt value is small, e.g. gt=0.1, pred=1.0, the loss will be (1-0.1)/0.1=9.0, and using AbsRel as the loss can be very unstable.\n\n\n**Q5: Computation complex**\n\nAs our design is only operated on the predicted masks for computing loss, and the losses based on multi-scale contexts can be computed in parallel, the additional computation cost is negligible. For example, the number of training iterations per second is 2.37 iter/s for the SSI baseline and 2.29 iter/s for HDN-DR, with a batch size of 16 on 4 GPUs. \n\n**Q6:... which datasets are used for each evaluation of Table 2...**\n\nThanks for the advice. As different datasets are used in each work, we only indicate the total number of training images. We will add their detailed dataset information for clarification.\n\n**Q7:... Other backbone models**\n\nOur design is model-agnostic and can be used with any backbones. As DPT is the SOTA backbone, specifically designed for depth estimation tasks, we employ it to compare our best results with SOTAs.\n\n", " **Q1: It is not very clear if the improvement really comes from the proposed hierarchical depth loss**\n\nA: In Table 1 and Table A of our supplementary material, we make fair comparisons with the SOTA works, Midas[22] and Leres[33], where they correspond to the instance-level normalization methods. In the experiments, the datasets and training configurations are exactly the same, and the only difference is loss functions.\nThe results show that our loss outperforms Midas by an average of 22\\% on five benchmarks and outperforms Leres by an average of 20\\%. Notice that we also adopt the same basic normalization operations (see Eq.1 and Eq.A) for fair comparisons, such that all performance improvement comes from hierarchical normalization.\n\n\n\n**Q2: The formulation in equation (1) seems to be different from the original one in the SSI [22] paper. SSI solves for an optimal scale and shift between pred and gt depth, while equation (1) is normalizing using simple global stats such as median and mean. Why?**\n\nMidas[22] discusses two strategies to design scale-and-shift invariant losses. One option is to align the predicted depth maps with the ground-truth depth maps based on least squares. The other strategy is to explicitly shift and scale both the predicted maps and the ground-truth maps based on the median operations. Their experiments have shown that the second option produces much better performance. Therefore, we choose the second form of SSI. Another SOTA work by Leres[33] adopts a similar strategy but replaces the median operation with mean and std for normalization. Our method can also be combined with Leres to improve the performance by up to 20\\%, and the results are shown in Table A of our supplementary material.\n", " **Q1: Table 1 does not show the ablation when combining the different domains.**\n\nWe explore three strategies to combine the design of different domains.\n1) The first method is to directly combine the normalization contexts U (in Eq.3) generated by HDN-Depth (HDN-DR) and HDN-Spatial (HDN-S), respectively. We find that such a naive combination always produces results between the performance of two respective methods on each benchmark. The possible reason is that the hierarchical normalization contexts generated by two domains have some overlapped information, such as the global contexts. When they are averaged, these contexts are put with more weights during average, which can not further boost the performance.\n2) The second strategy is to take a weighted sum of the final losses (in Eq.3) generated by HDN-DR and HDN-S. By selecting multiple groups of hyper-parameters, the overall optimal result can improve HDN-DR and HDN-S across five benchmarks by an average of 0.2\\% and 10.1\\%, respectively. However, we find that it does not always produce superior performance on every benchmark. \nFor example, on DIODE dataset, the results of HDN-DR, HDN-S, and combination are 24.9, 36.4, and 25.3, respectively. \nThis indicates that some specific benchmarks may benefit more from the hierarchical normalization in some particular domains. Therefore assigning all weights to the loss of HDN-Depth generates the optimal performance in this benchmark.\n3) As the hierarchical normalizations on both domains contain overlapped information, such as global contexts, the third strategy is to only select unique information for fusion. Here we simply take the local normalization contexts (the lowest two levels) from spatial domain and fuse them with the hierarchical contexts in depth domain (HDN-DR). We find that this strategy can always produce better or comparable results across all benchmarks, which improves HDN-DR and HDN-S across five benchmarks by an average of 3.7\\% and 13.3\\%, respectively. \n\nWe will update the detailed results into our latest manuscript. We believe there exist better strategies to combine the idea of hierarchical normalization in two domains, which will be our future works. \n\n\n\n**Q2: Have the authors tested the loss on fully supervised monocular/stereo depth models?**\n\nWe conducted experiments under the standard fully supervised setting, where the goal is to predict the metric depth based on the training set of each benchmark. Specifically, we validate our design on the popular NYU V2 （*only using 795 training images in Eigen split*） dataset by adding our proposed HDN loss as an auxiliary loss to a standard L1 regression loss. The result is shown below.\n| Loss | NYUv2| \n|:--------:|:------------:|\n| L1 | 14.7 | \n|L1+SSI | 14.6 | \n|L1+HDN | **13.3**(-9.5\\%) | \n\n\nOur proposed loss can still effectively improve the performance, while the SSI baseline can hardly boost the performance, which shows the generalization capability of our methods in monocular depth estimation tasks. \nWe will update a more detailed comparison and analysis in our latest manuscript.\n\n\n**Q3: it is important to show the generalization of different models and datasets.**\n\n\nOur supplementary material contains more experiment results and analysis to validate the generalization and effectiveness of our contributions. Specifically, \nin Table A, we combine our design with another SOTA zero-shot learning method Leres[33], and the result shows that our design can still effectively improve the performance, by up to 20\\%.\nIn Table B, we use two more evaluation metrics to evaluate the quality of depth boundaries on iBims-1 dataset.\nWe also conduct cross-domain experiments on two new synthesized datasets in Table C. We totally use 8 datasets to validate the generalization capability.\n\nAdditionally,\n1) We design a new model variant that combines our design based on the spatial domain and the depth domain, which further improves the optimal performance. (see Q1).\n2) We also conducted experiments to validate the generalization of our design under the standard fully supervised setting (see Q2).\n3) We discuss a new strategy to obtain hierarchical normalization contexts, and please refer to our response to Q1 from Reviewer uzns.\n\n\n\n\n**Q4: will the proposed loss make the training significantly slower?**\n\nAs our design is only operated on the predicted masks for computing loss, and the losses based on multi-scale contexts can be computed in parallel, the additional computation cost is negligible. For example, the number of training iterations per second is 2.37 iter/s for the SSI baseline and 2.29 iter/s for HDN-DR, with the batch size of 16 on 4 GPUs. \n\n\n", " This paper proposes a normalization method for monocular-based depth estimation before computing the regression loss. It is based on scale-and-shift invariant loss. Instead of computing the median and doing the normalization globally, it split the depth map into multiple size patches and compute scale-and-shift invariant loss for each patch. They propose two strategies to generate the patches consisting of spatial domain splitting and depth domain splitting. In the zero-shot setting, the results show the model with the proposed normalization can outperform all baselines. 1. This paper is well written. It is easy to read.\n2. The proposed idea is clean and simple. We can easily apply it to other depth estimation models.\n3. The improvement on the zero-shot monocular depth estimation task is significant. \n\nWeakness:\n1. Table 1 does not show the ablation when combining the different domains. It is unclear if combing all of them can get the best performance.\n2. The proposed method can be applied to all monocular-based models. Have the authors tested the loss on fully supervised monocular/stereo depth models? This paper only presents the results in a zero-shot setting.\n3. The proposed method is very simple, so the contribution might be limited. To improve the contribution, it is important to show the generalization of different models and datasets. 1. Because it will compute multiscale scale-and-shift invariant loss, will the proposed loss make the training significantly slower? None", " This paper presents a novel normalization technique for learning monocular depth estimation networks with various sources of datasets that may have different depth scales. Unlike the previous approach that learns with the image-level normalization, which often disregards the fine-grained depth difference, this paper presents a multi-scale depth normalization that hierarchically normalizes the depth representations based on both spatial information and depth distributions. Experimental results have shown the superiority of this method even though the technique is relatively simple. + The idea of using multi-scale normalization, inspired by conventional normalization methods such as AlexNet, SIFT, and HOG, is very simple, but effective.\n+ Dividing the normalization candidates as spatial and depth axis is interesting and makes sense.\n+ The state-of-the-art performance is attained. - Using a hierarchical normalization has been already used in many other fields, as the authors also described, and applying this for monocular depth estimation is the first attempt in our knowledge, so it would be fine. However, due to its simplicity, I think more through experiments should be conducted. For instance, why not dividing the depth representation irregularly? or is there any way to consider additional semantic information, e.g., object boundaries, and divide the depth representation with respect to this semantic information? Without this kinds of through experiments, it would be hard to say this regular hierarchical representation is optimal. \n- Fig. 2 is hard to follow. In the left, what the authors tries to say? Maybe different colors are coming from the different spatial location? It would be better if it is clarified.\n- It would be interesting if we only used a single dataset for learning monocular depth estimation networks which does not suffer from depth scale or shift problem, e.g., KITTI itself. Maybe performance is degraded with this additional local normalization layers? \n- To overcome depth scale and shift problem, other loss functions may be used, for instance, AbsRel. It would be better if the other loss functions are compared. \n- Computation complex may be evaluated as well.\n\nMinor comments:\n- It would be great if the authors clarify which datasets are used for each evaluation of Table 2. \n- Other backbone models such as Monodepth2 can also be used? In many applications, the CNN-based models are still popularly used, so this experiment would be very interesting.\n\nOverall I like such a simple idea, but more through evaluations would be required to argue this is optimal. I really want to see the rebuttal. The authors well mentioned the limitations of this paper.", " The authors introduce a novel strategy for monocular depth estimation that focuses on both global structure and fine-grained details. Their implementation is effective at preserving fine-grained details via the spatial and depth domains using Hierarchical Normalization. Ultimately, performing well in terms of accuracy, even against state-of Art benchmarks from before our work was published. An interesting solution to a renowned problem in monocular depth estimation.\n\nClearly motivated by the shortcomings of existing SOTA.\n\nThe presentation is nice, for the most part; the language is okay but should be further improved if accepted for publication.\n\nWeaknesses:\nSeems the authors ran out of space, with many means to improve figures and tables to increase the data-to-ink ratio.\n\nFigure 3-4 : why not share x and y axes labels and make graphs easier to see in less space.\n\nAdd future work to the Limitations section.\n\nBe consistent with style: different tables use different schemes (some use arrows, others use colors).\n\nAvoid orphans (single words taking up entire lines, like line 205).\n\nLack of depth in analysis for the many ablations conducted. Why the median in (1)? More elaboration on the insights could be worthwhile. A lack of limitations in the ability to be extended to MVS; lack of demonstrating the final reconstruction results (just depth images depicted).", " The paper studies zero-shot monocular depth estimation. One way to improve zero-shot performance is to train on a combination of datasets. The problem with this strategy is that different datasets has different scales and shifts. One way to address this issue is to train with a scale and translation invariant loss (SSI [22]). This paper argues that the SSI loss is normalized over an entire image. A more effective way is to normalize over a small local window or a certain depth range. This paper thus propose a hierarchical depth normalization training loss, which helps their model to achieve state-of-the-art performance in zero-shot depth estimation on five major benchmarks. Strength:\n+ This paper proposes a simple yet very effective version of the scale-shift-invariant loss for training depth estimation network. This loss proves to help in improving zero-shot depth estimation (Table 1). I like this idea.\n\nWeakness:\n- It is not very clear if the improvement really comes from the proposed hierarchical depth loss (Table 2). The \"Ours\" model differs from SOTAs in the training data, the number of training samples, and the network architecture. The conclusion would be more solid if only one thing is changed at a time. For example it is unclear if it is fair to claim that \"our method outperforms previous methods by a large margin on multiple benchmarks with fewer training data than recent state-of-the-art methods, such as Leres [33] and Midas [22].\", because it could be a result of using higher quality training data.\n\n 1. The formulation in equation (1) seems to be different from the original one in the SSI [22] paper. SSI solves for an optimal scale and shift between pred and gt depth, while equation (1) is normalizing using simple global stats such as median and mean. Why? The authors have adequately addressed the limitations and potential negative societal impact of their work." ]

[ -1, -1, -1, -1, -1, -1, -1, 5, 5, 6, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, 4, 4, 3, 5 ]

[ "XMiM1ap0zxz", "o2dxZsuceGn", "dRjDHGyEDw_", "3yBC9hcgzJ2", "4DOeKoHwQOf", "s9GblvLaZCj", "xhjGETmP95y", "nips_2022_BNqRpzwyOFU", "nips_2022_BNqRpzwyOFU", "nips_2022_BNqRpzwyOFU", "nips_2022_BNqRpzwyOFU" ]

[ "98umemuh2wM", "_ANhalNCWc", "MyDJaCq92f2", "IQTwNdpcJUE", "HBJ2TFX5dN-", "I1IsdUnd4Xg", "_XuqSAFXfCk", "YQTbYn6xCO7", "HxXBOkYRBRs", "lImxYnZcwM8", "SkgyUAJdz5L" ]

[ "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thank you very much for your answers and clarifications. I updated my review and raised the score.\n\n", " I thank the authors for addressing my concerns. I upgraded my score to 7.", " We cordially thank you for your helpful feedback and hope to address the limitations you mentioned in the following:\n\n> Where did you show that the non-Gaussianity is not increasing?\n\nWe have updated Section 4 to make this more prominent (see Proposition 2 and surrounding paragraphs). G does not change because the employed coupling layer is linear (see Lemma 1 in Appendix B). However, the fact that G is constant was an understatement: The proof of Proposition 2 allows a broader class of couplings that achieve exactly the covariance given in Eq. (10), but also decrease G. In other words: *While our theory only shows how S can be brought to zero, it leaves room for the involved coupling layers to reduce G*.\nShowing a convergence rate for G is beyond the scope of this work, however.\n\n> Could similar results be derived for other flow architectures?\n\nThank you for pointing this out. Indeed, our result holds for arbitrary coupling flows (i.e. architectures that split incoming vectors in halves and leave one half unchanged) equipped with ActNorm (for r and u to be present). This is the case for NICE (Dinh et al. 2014), RealNVP (Dinh et al. 2016), and GLOW (Kingma & Dhariwal, 2018); Flow++ (Ho et al. 2019); nonlinear-squared flow (Ziegler & Rush 2019); linear, quadratic (Müller et al. 2019), cubic (Durkan et al. 2019a), and rational quadratic splines (Durkan et al. 2019b); neural autoregressive flows (Huang et al. 2020), and unconstrained monotonic neural networks (Wehenkel & Louppe, 2019). *For all these architectures, our theory guarantees the demonstrated convergence of the non-Standardness*. Note that none of our theorems or proofs have to be altered to be applied here.\n\nThe updated version of our paper reflects this insight and we propose to rename the paper to “Whitening Convergence Rate of Coupling Flows”.\n\n> On the right plot of Figure 2, it looks like that deviations are almost exclusively present in two quadrants, which might hint towards a systematic deviation. How do the authors explain this phenomenon?\n\nWe attribute this phenomenon to the training dynamics (batch size 2048 is almost two orders of magnitude less than the number of parameters to be learnt ((D/2)^2 + D=154,448). We observed that increasing the batch size or reducing the learning rate makes the deviations vanish to arbitrarily small values.\n", " We cordially thank you for your helpful feedback and hope to address the limitations you mentioned in the following:\n\n> Q1: How large is the influence of having [$r$ and $u$]? Can it be at least empirically shown that the same convergence is achieved? Can it be at least empirically shown that the same convergence is achieved? \n\nPractically, $r$ and $u$ have been observed to be helpful. They were introduced in Glow as ActNorm as a replacement for an invertible BatchNorm (Kingma & Dhariwal, NeurIPS 2018). We have updated the paper to make this more clear.\n\nTechnically, the single-layer bounds still hold, as we estimate the effect of r and u on the passive dimensions to be zero. The multi-layer bounds require the use of r and u for the Assumption 2 to persist (i.e. tr Sigma = D). Empirically, the same convergence behavior is achieved.\n\n> Q2: Would you agree that [...] one could learn the mean, [...] diagonal (or even the full covariance) of the Gaussian base distribution?\n\nThe mean and diagonal of the Gaussian base distribution are already implicitly learnt via ActNorm (see Q1). Regarding the off-diagonal entries of the covariance, one would need to parametrize the covariance in a clever way such that (i) it remains positive definite, and (ii) we can easily compute its determinant. While the issue (i) can be addressed in various ways, we are not aware of parameterizations that also satisfy (ii), in addition to (i).\n\nOur work implies that it is not even necessary to modify the base distribution, as we show that the non-Standardness can be reduced using just a few layers.\n\n> Q2 (continued): If \"non-Standardness\" decreases, \"non-Gaussianity\" could still remain a problem, no?\n\nWe have made Proposition 2 and the text around it more precise to make the relation to non-Gaussianity more clear: We guaranteed that G never increases by the coupling which minimizes non-Standardness S. This is, in fact, an understatement: The proof of Proposition 2 allows a broader class of couplings that achieve exactly the covariance given in Eq. (10), but also decrease G. In other words: *While our theory only shows how S can be brought to zero, it leaves room for the involved coupling layers to reduce G*. We give the details for this more general result in the updated text surrounding Proposition 2.\nShowing a convergence rate for G is beyond the scope of this work, however.\n\nThis also brings to light that our theory does not only hold for affine coupling blocks (i.e. Glow/RealNVP). Indeed, our results also apply to all other coupling architectures that can represent linear functions. This is the case for all coupling architectures aware to us, i.e. NICE (Dinh et al. 2014), RealNVP (Dinh et al. 2016), and GLOW (Kingma & Dhariwal, 2018); Flow++ (Ho et al. 2019); nonlinear-squared flow (Ziegler & Rush 2019); linear, quadratic (Müller et al. 2019), cubic (Durkan et al. 2019a), and rational quadratic splines (Durkan et al. 2019b); neural autoregressive flows (Huang et al. 2020), and unconstrained monotonic neural networks (Wehenkel & Louppe, 2019). *For all these architectures, our theory guarantees the demonstrated convergence of the non-Standardness*. Note that none of our theorems or proofs have to be altered to be applied here. The updated version of our paper reflects this insight and we propose to rename the paper to “Whitening Convergence Rate of Coupling Flows”. We thank reviewer X9Dq for inspiring this generalization.\n\n> Q3: What are the assumptions on the functions s(⋅) and t(⋅)?\n\nIn general, we would expect that s and t need to be able to represent complicated functions to learn arbitrary distributions p(x).\nHowever, our theory only requires that s can represent a constant value, and t a linear function in p to reduce the non-Standardness as presented. In regards to non-Gaussianity, more flexible functions will be needed, as linear couplings cannot change it (see Q2). The exact condition will depend on the coupling architecture used.\n\nMany thanks for the other detailed comments. We have already included some of your suggestions and will work on the remainder for the final version of this paper. Regarding the log-scaling of the network depth, few layers are sufficient to fit the non-Standardness, so we focus the figure on the first layers. We still show the later layers in the plot to show that the architecture is well-equipped to learn the dataset.\n", " We cordially thank you for your helpful feedback and hope to address the limitations you mentioned in the following:\n\n> the actual minimization procedure may not decrease the non-standardness at all, since there may be a tradeoff between these terms. Therefore, studying one of these terms alone seems unrealistic, and I don't know how it should relate to practical methods.\n\nIt is true that the actual minimization of the joint loss L = G + S may result in a different coupling than the one proposed in our paper. However, the layer we propose can always be achieved and we show that it causes a fast convergence of the non-Standardness.\n\nRegarding non-Gaussianity: The coupling that we propose in Proposition 2 was built to reduce non-Standardness, but it has freedom to also reduce non-Gaussianity. We adapted the explanation in the paper to make this more precise: Proposition 2 merely guaranteed that G never increases by the coupling which minimizes non-Standardness S. This was, in fact, an understatement: The proof allows a broader class of couplings that achieve exactly the covariance given in Eq. (10), but also decrease G. In other words: *While our theory only shows how S can be brought to zero, it leaves room for the involved coupling layers to reduce G*. We give the details in the updated text around Proposition 2. Showing a convergence rate for G is beyond the scope of this work, however.\n\nWe hope that this also clarifies the limitations of our work, mentioned in the last section.\n\nIn terms of practical implications, our main takeaway is that we don’t need to worry about reducing the non-Standardness, as already few layers suffice to reduce it by large.\n\nThe clarification about non-Gaussianity also brings to light that our theory does not only hold for affine coupling blocks (i.e. Glow/RealNVP). Our results also apply to all other coupling architectures that can represent linear functions. This is the case for all coupling architectures aware to us, i.e. NICE (Dinh et al. 2014), RealNVP (Dinh et al. 2016), and GLOW (Kingma & Dhariwal, 2018); Flow++ (Ho et al. 2019); nonlinear-squared flow (Ziegler & Rush 2019); linear, quadratic (Müller et al. 2019), cubic (Durkan et al. 2019a), and rational quadratic splines (Durkan et al. 2019b); neural autoregressive flows (Huang et al. 2020), and unconstrained monotonic neural networks (Wehenkel & Louppe, 2019). *For all these architectures, our theory guarantees the demonstrated convergence of the non-Standardness*. Note that none of our theorems or proofs have to be altered to be applied here. The updated version of our paper reflects this insight and we propose to rename the paper to “Whitening Convergence Rate of Coupling Flows”. We thank reviewer X9Dq for inspiring this generalization.\n\n> Can be we guaranteed that the reduction is close to 50% for real data, or can we estimate somehow the expected reduction from a dataset?\n\nThe ‘close to 50%’-heuristic is backed by our theory in the limit where S is close to zero (depending on the dimension, we obtain between 50%-55% reduction). For all other cases, one can evaluate the precise bound on; we conjecture that the tight bound computed for the initial data will also hold for several layers.\n\n> Are you able to write your bounds as high probability bounds rather than bounds on the expected decrease?\n\nThis is a relevant point, thank you for pointing it out. We strongly suspect a concentration result to hold, as we are dealing with high dimensional random (rotation) matrices. This is backed by our experiments, where increasing dimensions quickly made the variance of the involved expectations vanish (see e.g. the small Interquartile Range in Figure 3). Showing such a concentration result is technically challenging and therefore beyond the scope of this work.\n\n> What proof techniques used might be more broadly interesting and applicable?\n\nWe identify two new main ideas: (i) reduce the loss by a single layer and draw conclusions for a deep flow; (ii) split the KL divergence into constituents via a Pythagorean theorem.\n\n", " If any questions arose since your review, we are happy to address them.\n\nPlease note that we clarified two points in the paper: (i) We give more details on the non-Gaussianity. (ii) We show that our results apply not only to affine coupling flows, but to all coupling architectures known to us. See the general comment \"More details on non-Gaussianity and generalization to all coupling architectures\" for more details.", " We cordially thank all reviewers for their helpful feedback. We have updated the paper in two ways:\n\n1) We give more details on the consequences of our results for non-Gaussianity G. Proposition 2 already guaranteed that G never increases by the coupling which minimizes non-Standardness S. This was, in fact, an understatement: The proof of Proposition 2 allows a broader class of couplings that achieve exactly the covariance given in Eq. (10), but also decrease G. In other words: *While our theory only shows how S can be brought to zero, it leaves room for the involved coupling layers to reduce G.* We give the details in the updated text around Proposition 2. Showing a convergence rate for G is beyond the scope of this work, however.\n\n2) This clarification also brings to light that our theory does not only hold for affine coupling blocks (i.e. Glow/RealNVP). Our results also apply to all other coupling architectures that can represent linear functions. This is the case for all coupling architectures aware to us: \nNICE (Dinh et al. 2014), RealNVP (Dinh et al. 2016), and GLOW (Kingma & Dhariwal, 2018); Flow++ (Ho et al. 2019); nonlinear-squared flow (Ziegler & Rush 2019); linear, quadratic (Müller et al. 2019), cubic (Durkan et al. 2019a), and rational quadratic splines (Durkan et al. 2019b); neural autoregressive flows (Huang et al. 2020), and unconstrained monotonic neural networks (Wehenkel & Louppe, 2019).\n*For all these architectures, our theory guarantees the demonstrated convergence of the non-Standardness.* Note that none of our theorems or proofs have to be altered to be applied here. The updated version of our paper reflects this insight and we propose to rename the paper to “Whitening Convergence Rate of Coupling Flows”.\nWe thank reviewer X9Dq for inspiring this generalization.\n\nThe supplementary material is now included in the main pdf for better readability.", " This paper provides new theoretical insights on the affine coupling in normalizing flows.\nThe contributions of the paper are clearly presented within 4 points at the end of the introduction section. The paper is well written. \n\nThe contributions are theoretical contributions that allow to better understand the underlying mechanism of the affine coupling in normalizing flows.\n\nIt is worth noting that many theoretical results in normalizing flows were derived for the optimal transport. This paper investigates affine coupling by providing novel insights. This includes providing a novel point of view of the affine coupling layers as whitening transformation, and convergence analysis with explicit convergence rate and deep network guarantee. We find this work very interesting. We do not have any question. yes", " This paper studies normalizing flows, which is an approach for generative modeling relying on minimizing the KL divergence between a data distribution fed through a pushforward map implemented with neural networks and the standard Gaussian distribution. To generate samples, one can sample from the standard Gaussian and then invert this network. The paper studies a particular variant of normalizing flows called affine coupling flows, which use RealNVP layers. The main theoretical result analyzes a decomposed KL divergence into a non-Gaussian part and a nonstandardness part. Theorem 1 shows that the nonstandardness can decrease after the application of an affine coupling block, and the result is made interpretable in Theorem 2. Theorem 3 then shows that for deeper networks the nonstandardness can decrease at an exponential rate. Experiments confirm the upper bound and show the exponential decrease with respect to deep networks. Strengths\n- There is not existing theory studying the optimization properties of RealNVP layers. This paper tackles an important open question evaluating theoretically the effectiveness of these layers.\n- The paper is generally well-written.\n- The decomposition of the KL divergence into parts seems to be a useful tool for the analysis of these layers.\n\nWeaknesses\n- The result stands alone and is not close to a complete result. What I mean by this is that the non-Gaussianity term and the non-standardness results are optimized together when the RealNVP layers are implemented. This means that, in theory, the actual minimization procedure may not decrease the non-standardness at all, since there may be a tradeoff between these terms. Therefore, studying one of these terms alone seems unrealistic, and I don't know how it should relate to practical methods.\n- While the exponential decrease is interesting and seems to hold in practice, I don't see how this theoretical result could be useful in guiding methodology. The authors suggest a heuristic for the reduction of the nonstandardness but this only seems to be motivated by the experiments and not the theory. Can be we guaranteed that the reduction is close to 50% for real data, or can we estimate somehow the expected reduction from a dataset?\n- The tight upper bound takes exponential time to compute and is hard to interpret, while the looser bounds appear to be quite loose according to the plots.\n\nUpdate: \nI still have reservations about the interaction of the non-Gaussianity term with the non-standardness term. However, the author's answers alleviate at least some of my concern, and so I will raise my score. - Are you able to write your bounds as high probability bounds rather than bounds on the expected decrease? \n- What proof techniques used might be more broadly interesting and applicable? The limitations of the analysis do not appear to be discussed in the text, contrary to the fact that the authors mention that they are discussed in Section 6.", " A **normalizing flow** (NF) is a generative model that transforms a complex distribution using a chain of invertible transformations into a simple distribution. Furthermore, a NF models the exact likelihood using the change of variables formula and can be trained via the maximum likelihood principle.\n\nMany different transformations have been considered in the past. One of those is the so-called affine coupling layer. **This paper is about** a theoretical analysis of the whitening convergence rate of affine coupling flows. To do so, the authors show that the KL divergence used for training can be split into two parts handling \"non-Gaussianity\" and \"non-Standardness\". The authors then provide bounds on the \"non-Standardness\" and argue that each affine coupling layer (followed by a rotation (for reasons)) typically reduces the \"non-Standardness\" by approx. 50%. **Strengths:**\nThe paper is well written and mostly easy to follow. The authors begin by arguing that maximum likelihood estimation is equivalent to minimizing the KL divergence and decompose this KL divergence into two parts handling \"non-Gaussianity\" and \"non-Standardness\". Then, they derive bounds for the \"non-Standardness\" part for a single affine coupling layer as well as for a concatenation of such. Although I did not check every detail of the proofs, the derivation appears to be sound.\n\n**Weaknesses:**\n- The use of $r$ and $u$ in Equation (4) appear to be non-standard within the literature. It is unclear if the results still hold if this *architecture change* is not present. (See also Question 1 below.)\n- If the loss can be seen as \"non-Gaussianity\" plus \"non-Standardness\", the main challenge seems to be the \"non-Gaussianity\", not \"non-Standardness\". However, the paper is only concerned with bounding \"non-Standardness\". The more important part seems to be ignored. Hence, the usefulness of the bounds is questionable. (See also Question 2 below.)\n\n**Minor comments/questions:**\n- The pdf should be built without boxes around links\n- Why is the $x$-axis scaled non-linearly in Figure 1?\n- Please rephrase lines 89-91.\n- The actual (negative log-)likelihood objective could be stated in Section 3 along with a case of a flow that consists of multiple transformations/layers for completeness.\n- Please avoid starting a sentence with variables/symbols (e.g., lines 91 & 106).\n- lines 96, 127, etc.: (1) might be mistaken as a reference to an equation, hence use (i).\n- lines 99, 115: RealNVP does not mention any rotation. A rotation layer is used in Glow [6], however, the rotation is learned and not fixed. Nevertheless, I think Glow should be mentioned there.\n- line 103: The passive part is not transformed!\n- Equation (4): Please introduce $p_0$ and $a_0$, e.g., within the sentence above.\n- Lines 116-118 should be mentioned earlier.\n- Cite or provide a link for FrEIA.\n- line 181: The comma should be after Thm. 2.\n- line 291: \"We iterate adding such\"\n- line 302: additive\n- [4,5] are ICLR papers.\n- Why are arXiv identifiers provided, i.e., in [3,8,...]?\n\n**After the author feedback:**\nI have read the author feedback and the other reviews. Especially reviewer X9Dq shared my concern that only the non-Standardness part of the loss is considered whereas the non-Gaussianity part seems to be the real challenge. However, the authors provided clarifications, actually to both points I raised in **Weaknesses** above, which is why is raise my score to 7. **Q1:** To me, the use of $r$ and $u$ in Equation (4) appear to be non-standard within the literature and I assume they are learned as parameters during training. If those are not used (i.e. the standard affine coupling is being used) I assume the bounds do no longer hold. How large is the influence of having those? Can it be at least empirically shown that the same convergence is achieved? \n\n**Q2:** Would you agree that instead of learning 2D additional parameters per layer ($r,d$), one could learn the mean and a diagonal (or even the full covariance) of the Gaussian base distribution. Such a distribution is still easy to handle but would change the setting: the flow would just have to handle the (more challenging) part of \"non-Gaussianity\". Moreover, the analysis presented only considers bounds on the \"non-Standardness\" part of the loss, however, the \"non-Gaussianity\" part seems to be the real challenge. If \"non-Standardness\" decreases, \"non-Gaussianity\" could still remain a problem, no?\n\n**Q3:** What are the assumptions on the functions $s(\\cdot)$ and $t(\\cdot)$? Line 105 states they can be arbitrary but I would assume that their expressiveness largely influences the amount of layers/blocks needed.\n The authors flagged that they discussed the negative societal impact of their work in line 410, however, I do not see such a discussion except the comment in lines 410-412.\n", " In the article, the authors analyze the convergence of affine coupling flows. So far, it has only been shown that this type of normalizing flows converges weakly to an arbitrary target distribution. However, from this result it cannot be concluded that it converges in maximum likelihood.\n\nThe authors obtain a stronger convergence guarantee by decomposing the KL-divergence into a part measuring the non-Gaussianity, i.e. the KL between the flow density and a Gaussian with mean and variance as the data, and the non-Standardness, i.e. the KL-divergence of the just mentioned Gaussian distribution and a Standard Normal distribution. They prove bounds of the non-Standardness for single and multiple affine coupling layers and thereby prove convergence while quantifying the convergence rate. The authors validate the bound and the convergence rate empirically on EMNIST as well as a toy dataset. **Strengths**\n\nAffine Coupling Flows are very popular, being used in countless scientific research projects as well as applications. Hence, getting a better understanding of whether and how they converge is a very important problem. The authors give an intuitive decomposition of the training objective, and I appreciate its visualization in Figure 1. They very thoroughly analyze the non-Standardness, provide and prove several bounds, thereby proving and quantifying convergence. The proofs in the appendix are very detailed and I tried to verify them. To the best of my knowledge, they seem correct but I am not an expert regarding the convergence of machine learning algorithms, so I might have missed something.\n\nI like the short paragraph before the conclusion section very much since the authors provide an intuitive heuristic derived from their results, i.e. that the non-Standardness is reduced by about 50% with every affine coupling layer added to a flow model. This will be very useful for practitioners.\n\n**Weaknesses**\n\nThe main weakness of the paper is that it only considers bounds for the non-Standardness. They only show empirically for EMNIST that the non-Gaussianity decreases similarly; however, this might be highly dependent on the nature of the target distribution, a fact not being reflected in the paper. The authors claim on lines 146-147 that it does not increase but it is not clear to me where this is shown. It might be buried somewhere in the appendix, but this result should be placed more prominently in the main paper.\n\nThe paper focuses on affine coupling flows. However, it would also be interesting to briefly discuss whether the bounds could be extended to other flow architectures.\n\nSince the authors computed the non-Standardness to verify their bound, I was wondering whether the non-Standardness could not be reduced by just whitening the data through a linear transformation before training a flow. In this case, only the non-Gaussianity needs to be minimized. I suppose that this is impractical for large high-dimensional datasets; however, the authors could try this on a smaller toy dataset.\n\n**Conclusion**\n\nI think this is a strong paper and I lean towards accepting it and, hence, I score this paper with a 6. If the authors can clarify some of the criticism I mentioned, I am willing to increase my score.\n\n**Edit**\n\nGiven that the authors addressed my concerns and even showed that their theorems extend to all coupling flows I will upgrade my score to 7. * Where did you show that the non-Gaussianity is not increasing?\n* Could similar results be derived for other flow architectures?\n* On the right plot of Figure 2, it looks like that deviations are almost exclusively present in two quadrants, which might hint towards a systematic deviation. How do the authors explain this phenomenon? The main limitation is that the authors only proved and verified the convergence rate of the non-Standardness, but not the non-Gaussianity." ]

[ -1, -1, -1, -1, -1, -1, -1, 7, 6, 7, 7 ]

[ -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 3 ]

[ "IQTwNdpcJUE", "MyDJaCq92f2", "SkgyUAJdz5L", "lImxYnZcwM8", "HxXBOkYRBRs", "YQTbYn6xCO7", "nips_2022_TN4UpY_Qzo", "nips_2022_TN4UpY_Qzo", "nips_2022_TN4UpY_Qzo", "nips_2022_TN4UpY_Qzo", "nips_2022_TN4UpY_Qzo" ]

[ "kMb14T_2bo3", "bn2Mqazl2a", "rEhznd9Q7Kb", "mi65h3Uu7OL", "ImrwxFMDsG", "g_ru2EyLv2", "I5I8QUQ3UZ", "eEvU4YFw7k", "O8ssLygdECe", "kcJCCPtCW1U", "sa--Du3gzTB", "AvsDpF2jR-k", "02nadlsOd5g", "JIDiriK_7l7", "LwXTdj7ToEY", "8aEznvc_ozd", "lLwAdAoH1Ph", "rRQ00r1SpUO", "fdUA2hJmOHu", "rbtIWurtrn", "F1AsW4wF82", "SLceQUnFwAS", "4-gqI1QIDZz", "zlVUOsd-fZ", "j6cJY-KvHiH", "40mwN1tRK7", "EK_fvoWwaiH", "ScNtecbcONF", "pGYGI3H1HhB", "JKzoCZfWy1Y" ]

[ "author", "author", "author", "author", "official_reviewer", "author", "official_reviewer", "official_reviewer", "author", "author", "official_reviewer", "official_reviewer", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "author", "official_reviewer", "official_reviewer", "official_reviewer", "official_reviewer" ]

[ " Thanks again for your kind comments. We will carefully consider your suggestions to further revise our paper.", " Thanks a lot for your kind reminder. We will further carefully consider Eq.(1) and add more explanations in the revised version.", " Thanks very much for your careful and insightful review! We also think these discussions with you are very valuable. We promise to add our discussion and the complete experiments you mentioned in the revised version.", " (2) The \"class-dependent\" label noise in the single-label cases can be modeled by a $C \\times C$ transition matrix, bridging the transition from clean single label to noisy single label, while in this paper, the \"class-dependent\" label noise for class label $Y_j$ can be modeled by a $2 \\times 2$ transition matrix, bridging the transition from clean label $Y^j$ to noisy label $\\bar{Y}^{j}$.\n\nWe will clearly state the definition and the differences in the revised version.\n\n\n\n> **Q9:** it would be better if the authors use MS-COCO data under PMD label noise.\n\n**A9:** Following your good suggestion, we introduce PMD label noise [6], into the MS-COCO datasets. Comparison for classification performance can be seen in Table 1-5. The results verify the effectiveness of our approach in a very realistic scene. \n\n\n\n| mAP(%)/ OF1(%) / CF1(%) | PMD-Type-I | PMD-Type-II | PMD-Type-III |\n| ----------------------- | ----------------------------- | ------------------------- | ------------------------- |\n| Standard | 61.04/44.68/39.45 | 64.79/61.47/54.57 | **64.29**/59.37/52.45 |\n| Reweight-T max | 60.49/57.84/49.68 | **64.97**/62.37/56.73 | 64.25/59.84/53.24 |\n| Reweight-T 97% | 59.41/52.27/50.45 | 63.31/52.73/52.09 | 62.39/52.60/51.90 |\n| Reweight-DualT max | 60.51/61.30/60.22 | 62.55/58.64/59.10 | 62.27/58.37/57.96 |\n| Reweight-DualT 97% | 53.60/32.18/33.27 | 59.86/33.89/38.22 | 58.35/34.56/38.06 |\n| Reweight-Ours | **61.84**/**63.96**/**60.93** | 64.78/**65.14**/**61.05** | 64.19/**63.27**/**60.20** |\n\nTable 1-5: Comparison with PMD label noise on MS-COCO dataset (%). \n\n\n\n> **Q10:** Under (0,0) setup, why is the proposed method worse than 'standard', and much worse than AGCN on mAP and OF1 metrics.\n\n**A10:** (1) Theoretically, when the noise transition matrices are accurately estimated under (0,0) setup, which will be identity matrices, the Reweight method will degenerate into the form of the Standard method [9]. While when the estimation of transition matrices has an error, it will make the empirical risk biased to the ideal expected risk with clean data. Hence, the estimation error of transition matrices is the main reason why the Reweight method with estimated matrices, including our proposed method is worse than the Standard method. \n\n(2) As shown in Table 1-6, the unbiased Reweight-Ours(tau=0.0) is still a little worse than the Standard method on mAP and OF1 scores. It may be because we use the loss on validation set, rather than the mAP scores on validation set to select the model after warmup standard training in Reweight methods[2], since we found the loss on validation set is more sutibale to select model for importance reweighting under label noise cases.\n\n(3) To reduce the negative effect of estimation error, we suggest to use another risk-consistent algorithm, T-reversion [1], which jointly tunes the transition matrices and classifier with Reweight technique. As shown in Table 1-6, Reversion-Ours(tau=0.5) method can achieve a similar performance compared with the unbiased Reweight-Ours(tau=0.0).\n\n(4) The main reason of the gap between the performances of the proposed method and AGCN is the well-designed network of AGCN. Appendix L has shown the risk-consistent methods can also help AGCN perform better under label noise, and here we also test Reweight-AGCN-Ours under (0,0) setup. As shown in Table 1-6, Reweight-AGCN-Ours seems be more robust to the estimation error, the mAP of AGCN-R-Ours(tau=0.5) is just about 0.05 lower than AGCN under (0,0) setup. \n\n\n\n| | Standard | Reweight-Ours(tau=0.0) | Reweight-Ours(tau=0.5) | Reversion-Ours(tau=0.5) | AGCN | AGCN-R-Ours(tau=0.0) | AGCN-R-Ours(tau=0.5) |\n| ------------------ | :------: | :--------------------: | :--------------------: | :---------------------: | :---: | :------------------: | -------------------- |\n| mAP (%) | 73.14 | 72.98 | 72.74 | 72.99 | 74.61 | 74.47 | 74.54 |\n| OF1 (%) | 72.62 | 72.19 | 71.78 | 72.08 | 73.15 | 73.21 | 72.71 |\n| CF1 (%) | 68.65 | 68.33 | 69.41 | 69.11 | 69.74 | 69.37 | 70.41 |\n| Estimation Error | / | 0.00 | 13.94 | 11.20 | / | 0.00 | 11.43 |\n\nTable 1-6: Comparison with different methods on MS-COCO dataset under (0, 0) setup (%).", " Thanks for the detailed explanation about possible label noise with multi-labels. I agree that hardly confused class pairs usually account for the majority of all label pairs, but also this is not all the case.\n\nModeling realistic label noise in a multi-label setup is very challenging. But, I give your study a high value in that your assumption/approach is a possible way as early work on this topic.\n\nWhile reading your paper, I had some time to think about what kind of label noise should be considered in the multi-label setup. This was a valuable time to discuss with you and will be of great help to ready my future research. \n\nI appreciate the authors' active rebuttal and they provided ample opinion about my concerns. My concerns are not completely resolved but this is attributed to a very complex definition of label noise in a multi-label setup. Therefore, I agree with most of the opinions of the authors and, decide to increase my score to '5'.\n\nBest,", " Thanks a lot for your feedback. We further address your mentioned concerns as follows.\n\n> **Q7:** There could be large-scale data including many confusing class labels. Therefore, I don't think the situation will differ a lot compared to the single-label recognition task if we assume the same labeling budget.\n\n**A7:** **I agree with you that there are many confusing class pairs on the typical large-scale datasets with a large number of classes. While we claim those hardly confused class pairs usually account for the majority of all label pairs for the following reasons:**\n\n(1) Among a large number of classes in the typical large-scale multi-label datasets, e.g. MS-COCO and OpenImages datasets, most label pairs belong to significantly different superclasses, and therefore, these label pairs are hardly confused. For example, in MS-COCO datasets, there are 80 classes, which belong to 10 hardly confused superclasses (outdoor, food, indoor, appliance, sports, person, animal, vehicle, furniture, accessory, electronic, kitchen). In OpenImages dataset, there are 19,957 classes, and also have significantly different superclasses, such as Toy, Budilding, Medical equipment, Clothing, Insect and so on (a part of these superclasses can be seen in [17]). \n\n(2) Consistent with the above discussion, the research works about real-world label noise [15,16] show that noisy labels usually flips to some similar class labels in the real-world scene. For example, In CIFAR-100N, which is a re-annotated version of the CIFAR-100 with real-world human annotations, most classes are more likely to be mislabeled into less than four fine classes[15]. In ANIMAL-10N, the label noise mainly happens between five pairs of confusing animals [16]. \n\nHence, on the typical multi-label datasets like MS-COCO and OpenImages datasets, the hardly confused label pairs account for the majority.\n\n**In addition, we claim that noisy multi-label learning has various real-world scenes, and some of them can not be seen as the label flips like single-label recognition tasks:**\n\n(a) Due to the labeler's confusion, when labeling the music emotion, the annotator may label happy music with \"happy\" and \"existing\", which will lead to partial multi-labels.\n\n(b) Due to the complex label correlations, when labeling fashion attributes, people may miss some fabric classes if \"Mickey\" style label appears, which will lead to missing multi-labels.\n\n(c) For saving labeling costs, people manually verified machine-populated labels, which will lead to missing multi-labels, and the large OpenImages dataset is built in this way.\n\n(d) For saving labeling costs, annotators may roughly assign each instance a set of candidate labels, which will lead to partial multi-labels.\n\nIn the real-world noisy multi-label learning, it even may be the mixture of the label flips like single-label recognition tasks and the above several scenes. Faced with various complicated real-world multi-label label noise, it is very hard to be always suitable. Our approach works when the label noise of one class label is only dependent on the label correlations with a few classes, and nearly independent on the label correlations with most classes. We think this condition can be nearly satisfied in many real-world scenes, because generally speaking, the multi-label label noises for class j are usually dependent on confusing features for itself, and the majority of classes will not share the same confusing features, which is also verified by the experiments in Table 1-2 and Table 1-5 in the typical datasets.\n\n**Besides, thanks for your insightful comments. We will add the discussion about our label noise assumption in the appendices.**\n\n> **Q8:** I recommend the authors clearly state the definition (and the differences) of 'class-dependent' in the setup of the paper so that it will not make ambiguity for readers.\n\n**A8:** Thanks a lot for your good suggestion. \n\nIn this paper, the \"class-dependent\" label noise for class label $Y_j$ means that the flip probabilities are dependent on class label $Y^j=0$ or $Y^j=1$. The differences between this definition and the \"class-dependent\" label noise in the single-label cases are as follows:\n\n (1) The \"class-dependent\" label noise in the single-label cases represent the flip probability from class $i$ to class $j$ ($i$ and $j$ are two different classes), while in this paper, the \"class-dependent\" label noise for class label $Y_j$ is only dependent on $Y^j=0$ or $Y^j=1$, which is independent on another class $Y^i$ , i.e. $P\\left(\\bar{Y}^{j}| Y^{j}, Y^{i}\\right) = P\\left(\\bar{Y}^{j}| Y^{j} \\right)$.\n\n[14] Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations. ICLR 2022.\n\n[15] SELFIE: Refurbishing Unclean Samples for Robust Deep Learning. ICML 2019.\n\n[16] https://storage.googleapis.com/openimages/2018_04/bbox_labels_600_hierarchy_visualizer/circle.html", " Thank you very much for your feedback. They address my concerns. ", " Thanks for your great efforts.\n\nA kind reminder is that Eq.(1) should be further considered and revised, since the equality may not hold in most cases.\n\nI decide to increase my rating. It is an interesting work although there still exist some problems with the manuscript.", " Thank you very much for your kind comments. As for your question, we think the sample selection for class label j is mainly biased on the easy-to-discriminative features for itself, and due to the complex label correlations, Eq.(1) will not hold when the instances of class labels i and j share the major discriminative features. The sample bias is the main factor that contributes to the error for our estimator. Thanks again for your efforts in reviewing this paper. ", " Following your good suggestions, we have added ablation studies about label correlation and the sample selection threshold, and updated them in the revised version. Is there something unclear in our response and revision? We would like to further explain it.", " Thanks for authors' feedback. The responses deal with most of my concerns. I agree that this is generally an interesting work.\n\nDue to the complex label correlations, does the equality still hold in Eq.(1)?\n\n", " I appreciate your detailed response to my concerns. This is my opinion on each part:\n\n*Class-independent label noise*: I understand what it means to use 'class-independent' in this paper, i.e., label 0 and 1 for each class. But, I am not sure if this is class-dependent because the definition of 'class' does not stand for '0' and '1'. It is more appropriate to say 'asymmetric label flipping' in which the flip probability depends on '1' and '0'. I think that the context of using 'class-dependent' should be the same with single-label setups. Although the authors provided an example, where most of the class labels are hardly confused by each other in multi-label learning, there could be large-scale data including many confusing class labels. For example, data with a large number of classes like OpenImages data with 19,957 classes, and data with many confusing attributes in Fashion data like DeepFashion with 1,000 attributes class. Therefore, I don't think the situation will differ a lot compared to the single-label recognition task if we assume the same labeling budget. I recommend the authors clearly state the definition (and the differences) of 'class-dependent' in the setup of the paper so that it will not make ambiguity for readers.\n\n*Results with PMD*: In addition, the authors additionally perform experiments with PMD label noise in more realistic cases. I agree that this is useful to see the effectiveness of the method. But, it would be better if the authors use MS-COCO data; each instance of VOC only contains less than 2 positive labels on average, which is more like a single-label classification.\n\n**Results with (0,0) setup*: In Table 1-3, except CF1, the proposed method is worse than 'standard', and much worse than AGCN. Could you please discuss the reason (which is a negative/weakness of the proposed methods to use in practice)?\n", " Thank you for reviewing this paper. There are less than three days left until the end of the author-reviewer discussion. We hope you can give some feedback on our response so that we can further explain it if something is unclear.", " Thank you for reviewing this paper. There are less than three days left until the end of the author-reviewer discussion. We hope you can give some feedback on our response so that we can further explain it if something is unclear.", " Thanks a lot for your efforts in reviewing this paper. We tried our best to address your mentioned concerns. Are there unclear explanations? We could further clarify them.", " Thanks a lot for your efforts in reviewing this paper. We tried our best to address your mentioned concerns. Are there unclear explanations? We could further clarify them.", " Thanks a lot for your efforts in reviewing this paper. We tried our best to address your mentioned concerns. Are there unclear explanations? We could further clarify them.", " Thanks a lot for your efforts in reviewing this paper. We tried our best to address your mentioned concerns. Are there unclear explanations? We could further clarify them.", " We further represent the estimation error between the estimated transition matrices and $P(\\bar{Y}^j|Y^j)$ to illustrate the effectiveness of our estimator. As shown in Table 1-4, the proposed estimation method leads to the smallest or second smallest estimator errors across various cases. \n\n| Estimation Error | Pair-wise 10% | Pair-wise 15% | Pair-wise 20% | PMD-Type-I | PMD-Type-II | PMD-Type-III |\n| ------------------- | :---------------: | :---------------: | :---------------: | :---------------: | :---------------: | :---------------: |\n| T-estimator max | 1.99$\\pm$0.02 | 2.97$\\pm$0.01 | 3.95$\\pm$0.01 | 8.70$\\pm$0.13 | 5.66$\\pm$0.02 | 6.13$\\pm$0.02 |\n| T-estimator 97% | 5.22$\\pm$0.02 | 5.53$\\pm$0.10 | 5.08$\\pm$0.09 | `3.45`$\\pm$`0.13` | 4.01$\\pm$0.16 | `4.02`$\\pm$`0.03` |\n| DualT-estimator max | **1.06$\\pm$0.03** | **1.36$\\pm$0.09** | `1.62`$\\pm$`0.06` | 4.31$\\pm$0.42 | `3.52`$\\pm$`0.07` | 4.33$\\pm$0.04 |\n| DualT-estimator 97% | 14.49$\\pm$0.02 | 14.13$\\pm$0.05 | 13.47$\\pm$0.04 | 9.35$\\pm$0.01 | 10.78$\\pm$0.01 | 10.72$\\pm$0.01 |\n| Our estimator | `1.82`$\\pm$`0.05` | `2.19`$\\pm$`0.03` | **1.55$\\pm$0.04** | **1.29$\\pm$0.07** | **1.71$\\pm$0.16** | **1.96$\\pm$0.20** |\n\nTable 1-4: Comparison with the estimation error between the estimated transition matrix and $P(\\bar{Y}^j|Y^j)$.\n\n", " \n> **Q5:** The mAP score is low on MS-COCO dataset.\n\n**A5:** The results of some methods under (0, 0) setup on MS-COCO dataset are shown in Table 1-3. CSRA and AGCN use the default hyperparameters. In order to complete repeated experiments of different methods under various cases with our limited computing resources, for MS-COCO datasets, we adopted images with 224 x 224 resolution, and use Adam optimizer with 5e-5 leaning rate and 128 batch size for 30 epochs, which will converge faster, and may have a drop of best mAP score compared with the optimal setting. In addition, a littile difference is that we use 10% of the training set as the validation set to perform model selection, while some results in the related work are obtained using all training dataset for learning. And according to the previous work [11], the ResNet-101 using ImageNet pretraining and 224x224 resolution achieves 75.2% mAP, which is about 2.1% higher than our Standard baseline with ResNet-50. We think this will not affect the effectiveness of the results.\n\n\n| | Standard | GCE | CDR | CSRA | AGCN | **Reweight-T max** | Reweight-T 97% | Reweight-DualT max | Reweight-DualT 97% | **Reweight-Ours** |\n| ------- | :------: | :---: | :---: | :---: | :-------: | :----------------: | :------------: | :----------------: | ------------------ | ----------------- |\n| mAP (%) | 73.14 | 73.37 | 73.16 | 73.85 | **74.61** | 72.99 | 71.27 | 71.59 | 67.97 | 72.74 |\n| OF1 (%) | 72.62 | 72.89 | 72.65 | 72.71 | **73.15** | 72.44 | 60.44 | 69.82 | 42.9 | 71.78 |\n| CF1 (%) | 68.65 | 68.37 | 68.17 | 69.18 | **69.74** | 68.28 | 58.36 | 68.73 | 44.93 | 69.41 |\n\nTable 1-3: Comparison on MS-COCO dataset under (0, 0) setup (%).\n\n\n\n> **Q6:** The paper writing should be improved, particularly the theoretical section.\n\n**A6:** Thank you for your suggestion. We have modified the presentation and uploaded the revised version, and especially we detailed the proof of Theorem 3 in Appendix E. We highly appreciate your insightful comments. \n\n[11] Learning Spatial Regularization with Image-level Supervisions for Multi-label Image Classification. CVPR 2017.\n\n[12] Multi-label image recognition with graph convolutional networks. CVPR 2019.\n\n[13] How does disagreement help generalization against label corruption? ICML 2019.\n\n[14] Detecting Corrupted Labels Without Training a Model to Predict. ICML 2022.", " | mAP(%)/ OF1(%) / CF1(%) | Pair-wise 10% | Pair-wise 15% | Pair-wise 20% |\n| ----------------------- | ------------------------------------------------ | -------------------------------------------------------- | -------------------------------------------------------- |\n| Standard | **85.32$\\pm$0.09**/80.71$\\pm$0.17/77.88$\\pm$0.13 | 83.19$\\pm$0.05/78.69$\\pm$0.13/75.34$\\pm$0.26 | 82.06$\\pm$0.34/77.12$\\pm$0.34/73.10$\\pm$0.82 |\n| Reweight-T max | 84.67$\\pm$0.24/80.48$\\pm$0.34/77.73$\\pm$0.39 | 82.75$\\pm$0.20/77.75$\\pm$0.09/75.43$\\pm$0.17 | 81.54$\\pm$0.06/76.68$\\pm$0.16/74.36$\\pm$0.13 |\n| Reweight-T 97% | 84.54$\\pm$0.12/78.79$\\pm$0.10/77.67$\\pm$0.29 | 83.08$\\pm$0.34/76.00$\\pm$0.32/75.95$\\pm$0.33 | 81.17$\\pm$0.82/73.01$\\pm$0.84/73.92$\\pm$1.02 |\n| Reweight-DualT max | 84.92$\\pm$0.15/**80.96$\\pm$0.36**/78.49$\\pm$0.39 | **83.42$\\pm$0.14**/78.89$\\pm$0.22/76.64$\\pm$0.18 | 82.29$\\pm$0.05/78.87$\\pm$0.19/75.57$\\pm$0.88 |\n| Reweight-DualT 97% | 83.87$\\pm$0.24/70.59$\\pm$0.19/73.90$\\pm$0.14 | 77.97$\\pm$0.17/59.64$\\pm$0.37/65.79$\\pm$0.10 | 75.50$\\pm$0.11/57.40$\\pm$0.18/60.23$\\pm$0.18 |\n| Reweight-Ours | 84.75$\\pm$0.08/80.87$\\pm$0.24/**78.84$\\pm$0.24** | 83.34$\\pm$0.11/**79.54$\\pm$0.02**/**77.56$\\pm$0.06** | **82.50$\\pm$0.03**/**79.70$\\pm$0.04**/**77.49$\\pm$0.09** |\n\nTable 1-1: Comparison with pair-wise label noise.\n\n\n> **Q3：**The evaluation is unrealistic.\n\n**A3:** To further verify our approach in more realistic cases, we introduce one instance-dependent label noise, PMD label noise [6], into the VOC2007 datasets. For PMD label noise, data near the decision boundary are harder to distinguish and more likely to be mislabeled, which is much realistic. Comparison for classification performance in this case can be seen in Table 1-2. The results show our approach can also achieve better performance.\n\n| mAP(%)/ OF1(%) / CF1(%) | PMD-Type-I | PMD-Type-II | PMD-Type-III |\n| ----------------------- | ---------------------------------------------------- | ---------------------------------------------------- | ------------------------------------------------ |\n| Standard | 78.03$\\pm$0.42/57.55$\\pm$2.64/51.95$\\pm$2.43 | **82.98$\\pm$0.36**/77.07$\\pm$0.10/74.07$\\pm$0.60 | **82.09$\\pm$0.69**/75.93$\\pm$0.38/72.65$\\pm$0.79 |\n| Reweight-T max | 77.74$\\pm$0.69/63.58$\\pm$3.06/58.70$\\pm$0.95 | 82.60$\\pm$0.30/77.42$\\pm$0.57/74.34$\\pm$0.57 | 81.92$\\pm$0.59/76.33$\\pm$0.92/73.15$\\pm$0.77 |\n| Reweight-T 97% | 78.04$\\pm$0.73/72.00$\\pm$1.04/**72.34$\\pm$0.41** | 82.32$\\pm$0.59/77.07$\\pm$0.47/75.83$\\pm$0.21 | 81.88$\\pm$0.54/76.63$\\pm$0.32/**75.27$\\pm$0.34** |\n| Reweight-DualT max | 78.20$\\pm$0.77/69.30$\\pm$3.85/65.35$\\pm$2.36 | 82.79$\\pm$0.27/77.81$\\pm$0.57/74.90$\\pm$0.65 | 81.71$\\pm$1.04/76.77$\\pm$0.78/73.86$\\pm$0.67 |\n| Reweight-DualT 97% | 75.46$\\pm$0.62/60.17$\\pm$1.18/62.28$\\pm$1.36 | 80.02$\\pm$0.22/67.20$\\pm$0.32/71.22$\\pm$1.00 | 80.39$\\pm$0.28/70.03$\\pm$2.10/71.50$\\pm$1.02 |\n| Reweight-Ours | **78.52$\\pm$0.65**/**73.16$\\pm$2.55**/72.17$\\pm$1.64 | 82.50$\\pm$0.29/**78.02$\\pm$0.37**/**76.22$\\pm$0.45** | 81.85$\\pm$0.41/**77.26$\\pm$0.63**/74.98$\\pm$0.62 |\n\nTable 1-2: Comparison with PMD label noise (%). The definition of Type-I, Type-II, and Type-III can be found in the original paper [6].\n\n\n\n> **Q4:** There is no detailed mention of how to resolve the class-imbalance problem.\n\n**A4:** The class-imbalance problem we refer to is the positive-negative class imbalance, which makes it difficult for the networks to accurately estimate the noisy posterior probability, and most of transition matrix estimation methods heavily depend on the accurate fitting of the noisy posterior probability. Since our estimator utilizes label correlations to perform transition matrix estimation, which does not need to accurately estimate the noisy posterior probability, it naturally avoids this problem in the transition matrix estimation.\n\n\n\n[6] Learning with Feature-Dependent Label Noise : A Progressive Approach. ICLR 2021.\n\n[7] CCMN: A General Framework for Learning with Class-Conditional Multi-Label Noise. TPAMI 2022.\n\n[8] Multi-Label Learning with Missing Labels. ICPR 2014.\n\n[9] Partial Multi-Label Learning. AAAI 2018.\n\n[10] Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels. NeurIPS 2018.\n", " Thank you very much for your comments on this paper. We address your concerns as follows.\n\n> **Q1:** The reasons for the assumption of instance-independent noise.\n\n**A1:** (1) In the single-label case, given only noisy examples, the instance-dependent transition matrix $T_{ik}(X=x)=P(\\bar{Y}=k|Y=i,X=x)$ is non-identifiable without any additional assumption[1], which also holds in the multi-label scenario. For example, $P(\\bar{Y}^j=k|X=x)=\\sum_{i=0}^1 T^j_{ik}P(Y^j=i|X=x)$ and $P(\\bar{Y}^j=k|X=x)=\\sum_{i=0}^1 T^{\\prime j}_{ik} P^{\\prime}(Y^j=i|X=x)$ are both valid, when \n\n$T_{ik}^{\\prime j}(X=x)=T^j_{ik}(X=x) P(Y^j=i | X=x) / P^{\\prime}(\\bar{Y}^j=i | X=x)$. \n\n\n(2)The existing estimation methods [2-4] for instance-dependent transition matrices are hard to be applied in the multi-label case since these methods need to accurately approximate the noisy posterior probability of certain instances, which is very difficult in multi-label learning due to the positive-negative class imbalance. Besides, PTD [2], the most famous instance-dependent matrix estimation algorithm, needs much more anchor points in the multi-label case than in the single-label case, making it not applicable, because it needs to decompose instances into much more parts with multiple objects in one instance, and estimate transition matrices for each class label.\n\n\n\n(3) Class-dependent transition matrices can not only be used in statistically consistent algorithms but also can be used to estimate the overall noise rate for noise detection methods [13,14]. We believe an accurate estimation method for class-dependent transition matrices in multi-label cases can promote the research of noise detection methods for noisy multi-label learning.\n\n\n\n> **Q2:** The noise injection protocol is more like \"class-independent\" label noise, and it is not realistic.\n\n**A2:** (1) In the single-label case, the \"class-independent\" label noise means each label is flipped independently with a constant probability $\\rho$, and the \"class-dependent\" label noise for class label $Y$ means the flip probabilities $\\rho_y$ are the same for all training labels when $Y=y$ [4]. Correspondingly, in this paper, the \"class-dependent\" label noise for class label $Y_j$ means that the flip probabilities are dependent on $Y^j=0$ or $Y^j=1$. The definition of this noise model is consistent with \"Class-Conditional Multi-Label Noise\" in [7], and this type of noise injection protocol is also adapted in previous works [7,8] about noisy multi-label learning.\n\n\n(2) As stated in the paper, the noise injection protocol we used can simulate various situations, including multi-label learning with missing labels [8], partial multi-label learning [9], and class-conditional multi-label noise [7].\n\n\n(3) We think that although the label noise model is independent on label correlations, this class-dependent model and the proposed estimation method are very useful in most realistic multi-label cases, because, unlike the single-label recognition task, most of the class labels are hardly confused by each other in multi-label learning, such as \"bird\" vs \"car\", \"person\" vs \"clock\", \"bear\" vs\"apple\", and \"blue\" vs \"football\". These labels have correlations, i.e. $P\\left(Y^{i}=0 | Y^{j}=0\\right) \\neq P\\left(Y^{i}=0 | Y^{j}=1\\right)$, but their label noise will be nearly independent on their clean label correlations in the real scene, i.e. $P\\left(\\bar{Y}^{j}| Y^{j}, Y^{i}\\right) = P\\left(\\bar{Y}^{j}| Y^{j} \\right), P\\left(\\bar{Y}^{i}| Y^{j}, Y^{i}\\right) = P\\left(\\bar{Y}^{i}| Y^{i} \\right)$, and these labels massively exist in MS-COCO and OpenImages datasets. With such labels, the equation in Line 192 still holds and our approach also works well. Besides, in the implementation of our estimator, we perform the R times estimation for each transition matrix, and get the final estimation by Eq.(7). If the label noise of two labels is not independent on their correlations, they maybe can not get a meaningful probability estimation and will be discarded, or our approach will not choose the solution as the final estimation by Eq.(7), since it does not similar to other solutions. To further verify this statement, we introduce pair-wise label noise [10], which mistakes a class label with another label with a certain probability, into the VOC2007 datasets. Comparison for classification performance can be seen in Table 1-1. Note that as class labels in VOC2007 dataset are unbalanced, in order to prevent class change, we only test with pair-wise label noise less than 20%.\n\n[1] Are Anchor Points Really Indispensable in Label-Noise Learning? NeurIPS 2019.\n\n[2] Parts-dependent Label Noise: Towards Instance-dependent Label Noise. NeurIPS 2020.\n\n[3] A Second-Order Approach to Learning With Instance-Dependent Label Noise, CVPR 2021.\n\n[4] Learning with Bounded Instance- and Label-dependent Label Noise. ICML 2020.\n\n[5] Making deep neural networks robust to label noise: A loss correction approach. CVPR 2017.", " > **Q3:** Lack of ablation study about the sample selection threshold $\\tau$.\n\n**A3:** (1)The sample selection we adopted is to estimate this clean probability of samples by modeling sample loss values with a GMM model [5,6] using the Expectation-Maximization algorithm. If the clean sample can be distinguished according to loss values, and its estimated probability is accurate, the best threshold will be about 0.5. Hence, $\\tau=0.5$ is a typical value in related works [5,6], and we follow this practice in our experiments.\n\n(2) Using the classification performance on noisy validation set as the criterion for model selection is a typical and empirically useful practice [7-10] in label-noise learning, even in the cases with instance-dependent label noise [9,10]. In this paper, we use mAP score on the noisy validation set as the criterion for model selection. Table 2-1 shows the ablation study about $\\tau$, which represents $\\tau=0.5$ is a good choice both according to mAP scores on the noisy validation set and according to mAP scores on the clean test dataset.\n\n| mAP (validation/test) | (0,0.2) | （0.2,0） | （0.1,0.1) | （0.017,0.2) | Average |\n| --------------------------------------------------- | :-----------------------------------: | --------------------------------- | ------------------------------------- | --------------------------------- | ------------------- |\n| $\\tau=0.4$ | 71.49$\\pm$1.01/84.09$\\pm$0.62 | 48.37$\\pm$0.55/83.83$\\pm$0.23 | 44.02$\\pm$0.82/83.69$\\pm$0.68 | **56.45$\\pm$1.97**/84.30$\\pm$0.32 | 55.08/83.98 |\n| $\\tau=0.5$ | **72.50$\\pm$0.68**/**84.77$\\pm$0.40** | 48.06$\\pm$0.58/**83.92$\\pm$0.16** | **44.30$\\pm$1.54**/**84.01$\\pm$0.46** | 56.16$\\pm$1.90/84.36$\\pm$0.59 | **55.26**/**84.27** |\n| $\\tau=0.6$ | 71.44$\\pm$1.00/84.18$\\pm$0.65 | **48.38$\\pm$0.57**/83.84$\\pm$0.29 | 44.00$\\pm$0.86/83.70$\\pm$0.66 | 56.37$\\pm$1.90/**84.37$\\pm$0.29** | 55.05/84.01 |\n\nTable 3-2: Ablation study about the sample selection threshold $\\tau$ on VOC2007 datasets.\n\n\n\n\n\n> **Q4:** Can the proposed method deal with the server imbalance issue?\n\n**A4:** For most of the estimation methods of the transition matrix, they need to accurately estimate the noisy posterior probability. The server positive-negative class imbalance, making it difficult for the networks to accurately estimate the noisy posterior probability. Since our estimator utilizes label correlations to perform transition matrix estimation, which does not need to accurately estimate the noisy posterior probability, it naturally avoids this problem in the transition matrix estimation.\n\n\n\n> **Q5:** Can authors report other common performance metrics used in multiple-label learning are the ranking-based metrics, like P@K, R@K, NDCG@k?\n\n**A5:** Thank you for your advice. However, P@K, R@K, and NDCG@k are the metrics used for retrieval task, and our work is about multi-label classification learning. The evaluation metrics we reported are widely in related works [11,12,13], including the mean average precision (mAP), overall F1-measure (OF1) and per-class F1-measure (CF1) . Actually, the mAP metric is a ranking-based metric [14,15], which only depends on the order of prediction confidence for labels.\n\n\n\n> **Q6:** What is $n_a$ in computing?\n\n**A6:** $n_a$ is the cardinality of original multi-label dataset, which refers to the average number of labels appearing in one instance, and we have defined it when introducing datasets in Section 4.\n\n[5] Unsupervised Label Noise Modeling and Loss Correction. ICML 2019.\n\n[6] DivideMix: Learning with Noisy Labels as Semi-supervised Learning. ICLR 2020. \n\n[7] Robustness of Accuracy Metric and its Inspirations in Learning with Noisy Labels. AAAI 2021.\n\n[8] Are Anchor Points Really Indispensable in Label-Noise Learning? NeurIPS 2019.\n\n[9] Parts-dependent Label Noise: Towards Instance-dependent Label Noise. NeurIPS 2020.\n\n[10] A Second-Order Approach to Learning With Instance-Dependent Label Noise, CVPR 2021.\n\n[11] Multi-label image recognition with graph convolutional networks. CVPR 2019.\n\n[12] Attention-driven dynamic graph convolutional network for multi-label image recognition. ECCV 2020.\n\n[13] Asymmetric loss for multi-label classification. ICCV 2021.\n\n[14] A Review on Multi-Label Learning Algorithms. TKDE 2014.\n\n[15] The PASCAL Visual Object Classes Challenge 2007 (VOC2007).", " Thank you very much for your comments on this paper. We address your concerns as follows.\n\n> **Q1:** The concern around the mixed performance of the proposed method on estimation of the transition matrices and classification. In which circumstance the proposed method can be applied and perform better?\n\n**A1:** (1) Theoretically, a statistically consistent algorithm with accurate transition matrices can guarantee to vanish the differences between the classifiers learned from noisy data and the optimal ones from clean data by increasing the size of noisy examples [1,2]. When the size of noisy data is infinite, these consistent algorithms can guarantee to obtain the optimal classifier. While, in the real-world datasets, the size of noisy data is finite, and therefore, a statistically consistent algorithm with more accurate transition matrices will obtain a classifier close to the optimal one with a higher probability. That is to say, when transition matrices become more accurate, the learned classifier becomes more likely to be better, but does not always become better. It is the main reason for the mixed performance of the proposed method on the estimation of the transition matrices and classification. Besides, the probability that a statistically consistent algorithm with accurate transition matrices obtains a classifier close to the optimal one, will become higher by increasing the size of noisy data. Hence, if our method can achieve a more accurate estimation, a statistically consistent algorithm with our estimator will be more likely to be better in various cases, and its advantage will become more significant when the size of noisy data is large.\n\n(2) Our experimental results accord with the above discussion. As seen in Section 4.2, on all datasets, among those consistent methods, Rewight algorithm with our estimator (named \"Reweight-Ours\") obtains the most best or second-best results on the three metrics, which is due to the smaller error of our estimation. On MS-COCO dataset, which is much larger than VOC2007 and VOC2012 datasets, Rewight algorithm with our estimator achieves a more significant and stable advantage among the consistent methods.\n\n(3) As shown in Section 4, when compared with those methods without considering noise labels across the datasets, our method can perform much better on the OF1 and CF1 metrics, which shows the model learned by our method can approximate the true class posterior well. Besides, our method can also help some methods without considering noise labels, e.g. CSRA and AGCN, perform much better in noisy multi-label learning, which has been shown in Appendix L.\n\n(4) Noise transition matrices can not only be used in statistically consistent algorithms, but also can be used to estimate noise rate for noise detection methods [3,4]. We believe an accurate estimation method for transition matrices in multi-label cases can promote the research of noise detection methods for noisy multi-label learning.\n\n\n\n> **Q2:** Ablation studies showing how the proposed model benefits from label correlation \n\n**A2:** Thank you for your suggestion. According to the results in Appendix B, we divide all labels (except class label 50) on MS-COCO dataset into two categories: one is very likely to have a correlation with class label 50 (the label belonging to this category is termed as \"label A\") and the other is less likely to have a correlation with class label 50 (the label belonging to this category is termed as \"label B\") . Table 3-1 shows the mean estimation error of transition matrices for class label 50 by using the correlations of label 50 and label A (or B) in various cases. The results represent the estimation error will be smaller using the correlations with label A, which means stronger label correlations can lead to better estimation in our approach.\n\n| Estimation Error | (0,0.2) | (0.2,0) | （0.1,0.1) | （0.017,0.2) | Average |\n| -------------------------- | :-----------------: | :-----------------: | :-----------------: | :-----------------: | :-------: |\n| using label 50 and label A | **0.025$\\pm$0.024** | **0.090$\\pm$0.049** | **0.106$\\pm$0.051** | **0.099$\\pm$0.040** | **0.080** |\n| using label 50 and label B | 0.057$\\pm$0.062 | 0.139$\\pm$0.111 | 0.198$\\pm$0.123 | 0.172$\\pm$0.104 | 0.269 |\n\nTable 3-1: Mean estimation error of transition matrices for class label 50 on MS-COCO dataset using the correlations with different labels.\n\n[1] Are Anchor Points Really Indispensable in Label-Noise Learning? NeurIPS 2019.\n\n[2] Classification with noisy labels by importance reweighting. TPAMI 2016.\n\n[3] How does disagreement help generalization against label corruption? ICML 2019.\n\n[4] Detecting Corrupted Labels Without Training a Model to Predict. ICML 2022.\n", " Thank you very much for your comments on this paper. We address your concerns as follows.\n\n> **Q1:** The unbiased assumption is unreasonable.\n\n**A1:** We agree with you that this assumption will not strictly hold due to the complex label correlations, and this is the main error our approach leads to. But as we stated in Section 3.2, we claim that this bias for estimating $P(\\bar{Y}^{i} \\mid Y^{j})$ will not too large, since some simplest samples for each label can be easily selected without being affected by the presence or absence of other labels. And In Section 4.1, our empirical results justify this by showing a little gap between the estimation error of our estimator with the biased sample selection and an unbiased one.\n\n\n\n> **Q2:** The estimated label co-occurrence may be imprecise due to the insufficient labels used for frequency counting\n\n**A2:** We found this phenomenon in the experiments, and reported it as the limitations in Appendix G. Although this estimation error of frequency counting will converge to zero exponentially fast [1], when the number of one label appearing is too small, e.g. less than 50, the estimation of its transition matrix is still difficult to be accurate. We think it may be better to estimate the transition matrix using Dual-T estimator for this class label.\n\n\n\n> **Q3:** There are many typos.\n\n**A3：**Thank you for your concern. We have fixed the typos and uploaded the revised version.\n\n\n\n> **Q4:** The references are not cited properly. In experiments, the citations for multi-label with missing labels and partial multi-label are missed.\n\n**A4:** Thank you for your suggestion. We have added some references about multi-label with missing labels [2,3] and partial multi-label learning [4,5] in the revised version.\n\n\n\n> **Q5:** How to determine the threshold $\\tau$, especially without the clean validation set?\n\n**A5:** (1)The sample selection we adopted is to estimate this clean probability of samples by modeling sample loss values with a GMM model [6,7] using the Expectation-Maximization algorithm. If the clean sample can be distinguished according to loss values, and its estimated probability is accurate, the best threshold will be about 0.5. Hence, $\\tau=0.5$ is a typical value in related works [6,7], and we follow this practice in our experiments.\n\n(2) Using the classification performance on noisy validation set as the criterion for model selection is a typical and empirically useful practice [8-11] in label-noise learning, even in the cases with instance-dependent label noise [10,11]. In this paper, we use mAP score on noisy validation set as the criterion for model selection. Table 2-1 shows the ablation study about $\\tau$, which represents $\\tau=0.5$ is a good choice both according to mAP scores on the noisy validation set and according to mAP scores on the clean test dataset.\n\n| mAP (validation/ test) | (0,0.2) | （0.2,0） | （0.1,0.1) | （0.017,0.2) | Average |\n| --------------------------------------------------- | :-----------------------------------: | --------------------------------- | ------------------------------------- | --------------------------------- | ------------------- |\n| $\\tau=0.4$ | 71.49$\\pm$1.01/84.09$\\pm$0.62 | 48.37$\\pm$0.55/83.83$\\pm$0.23 | 44.02$\\pm$0.82/83.69$\\pm$0.68 | **56.45$\\pm$1.97**/84.30$\\pm$0.32 | 55.08/83.98 |\n| $\\tau=0.5$ | **72.50$\\pm$0.68**/**84.77$\\pm$0.40** | 48.06$\\pm$0.58/**83.92$\\pm$0.16** | **44.30$\\pm$1.54**/**84.01$\\pm$0.46** | 56.16$\\pm$1.90/84.36$\\pm$0.59 | **55.26**/**84.27** |\n| $\\tau=0.6$ | 71.44$\\pm$1.00/84.18$\\pm$0.65 | **48.38$\\pm$0.57**/83.84$\\pm$0.29 | 44.00$\\pm$0.86/83.70$\\pm$0.66 | 56.37$\\pm$1.90/**84.37$\\pm$0.29** | 55.05/84.01 |\n\nTable 2-1: Ablation study about the sample selection threshold $\\tau$ on VOC2007 datasets.\n\n\n\n\n\n[1] Concentration inequalities - A nonasymptotic theory of independence. Concentration Inequalities, 2013.\n\n[2] Multi-Label Learning with Missing Labels. ICPR 2014.\n\n[3] Multi-label Learning with Missing Labels Using Mixed Dependency Graphs. IJCV 2018.\n\n[4] Partial Multi-Label Learning. AAAI 2018.\n\n[5] Partial Multi-Label Learning With Noisy Label Identification. TPAMI 2022.\n\n[6] Unsupervised Label Noise Modeling and Loss Correction. ICML 2019.\n\n[7] DivideMix: Learning with Noisy Labels as Semi-supervised Learning. ICLR 2020. \n\n[8] Robustness of Accuracy Metric and its Inspirations in Learning with Noisy Labels. AAAI 2021.\n\n[9] Are Anchor Points Really Indispensable in Label-Noise Learning? NeurIPS 2019.\n\n[10] Parts-dependent Label Noise: Towards Instance-dependent Label Noise. NeurIPS 2020.\n\n[11] A Second-Order Approach to Learning With Instance-Dependent Label Noise, CVPR 2021.", " Thank you very much for your kind comments on this paper. We address your concerns as follows.\n\n> **Q1:** Some formulas like in line 192 are recommended to be written in more simplified way.\n\n**A1:** Thank you for your suggestion. The noisy multi-label case scenario is different from the noisy multi-class case, and each class label $Y^j$ has corresponding noise labels $\\bar{Y}^j$ and transition matrices $T^j$, which may make our formulas less clear.\n\n> **Q2:** The experimental results are recommended to be presented in different forms but not just tables.\n\n**A2:** Following your kind suggestion, we have added some charts to show more experimental results in the appendices, and we have updated the revised version. \n\n> **Q3:** Can the authors clarify the originality of the proof of Theorem 1-4?\n\n**A3:** The proof of Theorem 1 and 4 is established directly based on the basic properties of probability and matrix, where we prove them by transforming the probability problem into the decomposition problem of a matrix. The proof of Theorem 2 and 3 is based on some Kruskal’s identiability results from [1-4]. Liu et al.[3] first built identifiability of the noise transition matrix based on the Kruskal’s identifiability results in the noisy multi-class learning. Inspired by them, we use the same Kruskal’s identiability results to prove that If $\\bar{Y}^i$ and $\\bar{Y}^k$are independent given ${Y}^j$, $T^j$ is identifiable, and if not, it is unidentifiable.\n\n> **Q4:** Some dots should be replaced by \\cd, e.g. the dots in line 190 and line 204.\n\n**A4:** Thanks very much for your correction. We have fixed them in the revised version, and we highly appreciate your careful comments. \n\n\n[1] Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear algebra and its applications, 1977.\n\n[2] On the uniqueness of multilinear decomposition of n-way arrays. Journal of Chemometrics: A Journal of the Chemometrics Society. 2000.\n\n[3] Identifiability of label noise transition matrix. arXiv, 2022.\n\n[4] The analysis of three-way arrays by constrained PARAFAC methods. DSWO Press, Leiden University, 1993.", " This paper deals with how to estimate the 'noise transition matrix' under a multi-label setup. Like a single-label setup, the authors attempted to make an idea without using 'anchor points' for matrix estimation. They leverage the 'sample selection' method (ie., GMM) for extra clean supervision and provide a detailed mathematical derivation for the matrix estimation. The experimental section includes VOC and MS-COCO datasets; they injected a synthetic label noise with two factors, controlling the flip ratio of '1'->'0' and '0'->'1'. Under the proposed synthetic noise, the method works well and outperforms other simple extensions of similar works (but developed under the single-label setup).\n ### Strengths\n1. This paper is the first approach to estimating the noisy transition matrix for handling noisy labels with multi-labels. \n2. Leveraging mismatched label correlation is useful.\n3. The method shows higher performance than other simple baselines.\n\n### Weaknesses\nI agree that estimating the noise transition matrix helps make a statistically consistent classifier. However, I felt some major weaknesses of this paper, as below:\n1. **Assumption of Instance-independent Noise.** As the authors said, many previous studies make the same assumption for matrix estimations. But, there have been numerous recent studies to overcome this in the same direction [1-3]. I agree that dealing with 'instance-dependent' label noise in a multi-label setup is very difficult to address. At least, the author should mention what is more challenging in this setup compared to the single-label case. And, why making this assumption is reasonable with a more specific reason. Just saying 'the vast majority of current algorithms mainly focus' is not enough as a research paper.\n2. **Noise Injection Protocol.** According to the paper, the authors assume the class-dependent label noise and aim to estimate an accurate noise transition matrix under this assumption. However, the noise injection protocol in Line 217 looks like 'class-independent label noise. Specifically, the $\\rho just means the probability of '0' (or '1') being flipped to '1' (or '0') without any consideration of class pairs like <i, j>; only class j associates with the flipping and no connection between classes. Therefore, this is not very realistic and not class-dependent label noise. Did I get it wrong?\n3. **Unrealistic Evaluation.** Related to the second weakness, the author should have included at least one realistic real noisy data. There are benchmark data with noisy multi-label instances, called OpenImages database. The author can find other better datasets if possible. Without realistic evaluation, I am not convinced of the robust results in the paper since the injection protocol is very unrealistic.\n4. **Class Imbalance Problem & Low mAP.** Unlike single-label classification, the biggest difference in multi-label setup is 'class imbalance'. The authors also mentioned that this problem is very severe in Lines 44 & 102. However, there is no detailed mention of how to resolve this issue with the proposed idea throughout the paper. Next, when I am looking at the results on MS-COCO, the mAP value is too low compared with other multi-label papers using the same ResNet-50 pre-trained models. As an example, [4] shows ResNet-50 with GAP head achieves around 80mAP on MS COCO dataset (refer to Figure 6). However, in this paper, the mAP was less than 70 with Standard at the easiest noise setup (0.0, 0.2); this is a 20% missing label scenario. There are 20% missing labels but I think 20% of missing labels do not make 10mAP drops. Could you report the performance of your method and others under (0, 0) setup? This is a very good reference to check whether your implementation is correct and whether your method is still comparable with a zero-noise setup.\n\n**[1]** Approximating instance-dependent noise via instance-confidence embedding, arXiv 2021\n\n**[2]** A Second-Order Approach to Learning With Instance-Dependent Label Noise, CVPR 2021\n\n**[3]** An Information Fusion Approach to Learning with Instance-Dependent Label Noise, ICLR 2022\n\n**[4]** ML-Decoder: Scalable and Versatile Classification Head, arXiv 2021\n Please see the weakness section above. Please see the weakness section above. In addition, the paper writing should be improved, particularly the theoretical section. Too many results are omitted and borrowed from [16, 24, 25, 31].", " The paper proposes a new estimator to estimate the transition matrix in noisy multi-label learning. The main idea of the estimator is to utilize the clean label co-occurrence as a constraint to help the estimation of the transition matrix. Specifically, authors derive a two-stage method to estimate then transition probabilities. At the first stage, the paper utilizes an existing technique to select clean labels for estimating the label occurrence. Although the estimated label occurrence is biased due to the selection bias, authors claims that the selection biased cannot lead to large estimation error. At the section stage, the paper obtains the label co-occurrence with frequency counting and use the mismatch of label correlation to estimate the transition matrix. Strength\n\n1. The motivation of the proposed method is reasonable. The information of label co-occurrence is useful for the transition matrix estimation.\n\n2. The paper reports extensive experiments to validate the effectiveness of the proposed method.\n\n3. The paper conducts comprehensive analyses for noisy multi-label learning.\n \n\nWeakness\n\n1. In section 3.2, authors claim that the label co-occurrence estimated by using selected clean labels is unbiased. This is based on the assumption that “given Y^j”, the features about class j is biased, while the features about another class i is unbiased. The assumption is unreasonable, since the features are biased with respect to class i and class j co-occur in an image.\n\n2. Authors select a small number of clean labels for estimating the label co-occurrence. However, the estimated label co-occurrence may be imprecise due to the insufficient labels used for frequency counting, especially for positive labels.\n\n3. There are many typos, such as page 4 line 168 Ys; Algorithm 1 line 4 Dt; page 2 line 48 “while “bird” and “sky” are always co-occurrence”.\n\n4. The references are not cited properly. In experiments, the citations for multi-label with missing labels and partial multi-label are missed.\n How to determine the threshold \\tau, especially without the clean validation set? None", " \nThis paper presents a way of estimating the noise transition matrix for noisy multi-label learning, which makes use of label correlations through a bilinear decomposition based on frequency counting. It first theoretically studies the identifiable problem of estimating the noise transition matrix under the multilevel setting, which then leads to the development of the bilinear decomposition-based method for estimating the noise transition matrix. Experiments results derived from several image datasets show that the proposed method can better estimate the transition matrix. Strengths\n\nLabel-nosing learning is an important and challenging problem not just in multi-class classification and also in the multi-label setting. This paper presents a bilinear decomposition-based approach based a simple frequency counting with a clearly described algorithm. \n\nThe proposed estimation method is well motivated with a set of theorems that study the identifiable problem in the multi-label learning setting, which seems to be thorough with proper proof in the Appendix. The proof is also easy to follow. \n\nOverall, the paper is written well, and most of the notations were clear and well-organized to guide the readers through the text. \n\n\nWeaknesses\n\nMy major concern is around the performance of the proposed estimation method. In terms of estimation of the transition matrices, it outperforms the competitors in most of the settings, which is good. However, when coming to the classification performance, the proposed method is not a clear winner, particularly compared with those without considering noise labels across the datasets. For instance, for varying levels of noise, it is hard to conclude the behaviour of the proposed method. \n\nAblation studies showing how the proposed model benefit from label correlation and deal with imbalance issue are missing. For example, there is a running parameter $\\tau$ used in Stage 1 to select the sample set $\\mathcal{D}^j_t$, which I believe will have an impact on the performance of the proposed method. 1. Label correlation plays an important role in the proposed estimation. Even though assumption 2 is validated in the appendix. Could the authors empirically show this role with some examples from the experiments? For example, labels can be strongly correlated and or weakly correlated. Is it possible to study the association between the strength of label correlation and the model performance? \n2. The server imbalance issue is indeed a challenging problem in multi-label learning, which I agree with the authors. I am wondering if the proposed method can deal with this issue? If so, how?\n3. Other common performance metrics used in multiple-label learning are the ranking-based metrics, like P@K, R@K, NDCG@k, etc. Could the authors consider one of the metrics, say NDCG@K? \n4. How will the threshold $\\tau$ affect the model performance?\n5. Given the mixed performance of the proposed method, Is there any consistent takeaway message here? I.e., In which circumstance the proposed method can be applied and perform better?\n6. What is $n_a$ in computing $\\rho{-}$ in line 222? The authors have addressed the limitations and border impact in the appendix. ", " This paper discusses the estimation problem of the transition matrices in the noisy multi-label setting. They study the identifiability problem of the class-dependent transition matrix in noisy multi-label learning and propose a new estimator by exploiting label correlations without both anchor points and accurate fitting of noisy class posterior inspired by the identifiability results. Experimentally, the effectiveness of the proposed method is also illustrated. **Strenghths:** \n1. They utilize the mismatch of label correlations to identify the transition matrix without both anchor points and accurate fitting of noisy class posterior in noisy multi-label learning.\n2. The method is effective to the issue with both theoretical analyses and empirical results support this method.\n3. Clear writing and structure.\n\n**Weaknesses:** \n1. Some formulas like in line 192 are recommended to be written in more simplified way.\n2. The experimental results are recommended to be presented in different forms but not just tables. 1. Can the authors clarify the originality of the proof of Theorem 1-4? \n2. Some dots should be replaced by $\\cd$, e.g. the dots in line 190 and line 204. They address it adequately in Appendix." ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 7, 4, 6 ]

[ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, 5, 3, 1 ]

[ "I5I8QUQ3UZ", "eEvU4YFw7k", "ImrwxFMDsG", "AvsDpF2jR-k", "g_ru2EyLv2", "AvsDpF2jR-k", "40mwN1tRK7", "O8ssLygdECe", "sa--Du3gzTB", "pGYGI3H1HhB", "j6cJY-KvHiH", "rbtIWurtrn", "pGYGI3H1HhB", "EK_fvoWwaiH", "JKzoCZfWy1Y", "pGYGI3H1HhB", "ScNtecbcONF", "EK_fvoWwaiH", "F1AsW4wF82", "F1AsW4wF82", "SLceQUnFwAS", "EK_fvoWwaiH", "zlVUOsd-fZ", "pGYGI3H1HhB", "ScNtecbcONF", "JKzoCZfWy1Y", "nips_2022_GwXrGy_vc8m", "nips_2022_GwXrGy_vc8m", "nips_2022_GwXrGy_vc8m", "nips_2022_GwXrGy_vc8m" ]