What Variables Affect Out-of-Distribution Generalization in Pretrained Models?

Authors: md  yousuf harun
kyungbok  lee
jhair  gallardo
giri  krishnan
christopher  kanan
yousuf  harun
Venue: NeurIPS_cc_2024_Conference
Published: 2024-04-24 19:05:48

Abstract: Embeddings produced by pre-trained deep neural networks (DNNs) are widely used; however, their efficacy for downstream tasks can vary widely. We study the factors influencing transferability and out-of-distribution (OOD) generalization of pre-trained DNN embeddings through the lens of the tunnel effect hypothesis, which is closely related to intermediate neural collapse. This hypothesis suggests that deeper DNN layers compress representations and hinder OOD generalization. Contrary to earlier work, our experiments show this is not a universal phenomenon. We comprehensively investigate the impact of DNN architecture, training data, image resolution, and augmentations on transferability. We identify that training with high-resolution datasets containing many classes greatly reduces representation compression and improves transferability. Our results emphasize the danger of generalizing findings from toy datasets to broader contexts.

Main paper: 
 introduction: 
 Understanding deep neural network (DNN) representations has been a central focus of the deep learning community. It is generally accepted that a DNN's initial layers learn transferable universal features, with deeper layers being task-specific [1] [2] [3] [4] [5] [6] [7] [8] . At NeurIPS-2023, [9] challenged this view with evidence for the tunnel effect hypothesis:The Tunnel Effect Hypothesis: An overparameterized N -layer DNN forms two distinct groups:1. The extractor consists of the first K layers, creating linearly separable representations. 2. The tunnel comprises the remaining N -K layers, compressing representations and hindering OOD generalization.To test the tunnel effect hypothesis, they trained models on an in-distribution (ID) dataset and compared linear probes trained and evaluated on either ID or OOD datasets for embeddings produced by each DNN layer. They showed that ID accuracy increased monotonically, whereas OOD accuracy rapidly decreased after the extractor (Fig. 1 ). The likely cause of the tunnel effect is intermediate neural collapse [10] . Both [10] and [9] showed that collapsed/tunnel layers could be static without needing learning. If these results are universal, they suggest universal visual features learned in early layers and using embeddings from the penultimate layers of pre-trained DNNs, need to be rethought. However, both [9] and [10] limited their experiments to datasets with low-resolution images and relatively few categories (CIFAR-10, MNIST). Given the widespread use of embeddings from pre-trained DNNs for downstream OOD tasks, we aim to assess the universality of the tunnel effect and the variables that influence its strength † .If the tunnel effect is stronger in models trained on toy datasets like CIFAR-10 but diminishes for largescale datasets, this may explain why many algorithms evaluated only on toy datasets are ineffective on larger datasets such as ImageNet. This disparity has persisted across problem settings, including open set classification [11] , active learning [12] , OOD detection [13] , uncertainty quantification [14] , dataset distillation [15] , and continual learning [16] [17] [18] .Our paper makes the following contributions:1. We define metrics to measure the strength of the tunnel effect and use a SHAP-based analysis to assess each variable's impact, e.g., image resolution, number of semantic classes, and DNN architecture. Using 64 pre-trained ID backbones and 8,604 linear probes, we identify conditions that exacerbate, reduce, and eliminate the tunnel effect. 2. Using our metrics, we find that widely used ImageNet-1K pre-trained CNN and ViT backbones do not exhibit tunnels, except for ResNet-50. 3. In contrast to [9] , we find that the tunnel strongly impacts forgetting in continual learning. This suggests the generality of many continual learning systems depends on tunnel strength, which is heavily influenced by architectural and training dataset choices. 4. We establish a link between impaired OOD generalization and the characteristics of widely used toy datasets, with both resolution and a small number of classes exacerbating the tunnel effect. 5. We propose a revised tunnel effect hypothesis, in which the tunnel's strength is influenced by training data diversity.2 Related Work Strong evidence for the tunnel effect was given in [9] , but their experiments are limited. First, they only study MLPs and CNNs, whereas ViT models are now widely used. Second, their experiments only use 32 × 32 images, and we hypothesize that higher resolution images could mitigate the tunnel effect by promoting learning hierarchical representations. Third, they do not control for the impact of data augmentation, where data augmentation is known to improve OOD generalization [19] [20] [21] [22] [23] [24] . Lastly, they define tunnel as starting at the layer where a linear probe on the ID dataset achieves at least 95% of the final ID accuracy, ignoring OOD generalization. This is problematic since OOD generalization is central to their tunnel effect definition. Here, we measure tunnel effect strength using OOD performance.Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?Answer: [Yes] Justification: Our claims in our introduction and abstract are directly supported by our Main Experiments. We also provided supporting experiments, which were not mentioned in the introduction or abstract.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 
learning embeddings that generalize: 
 Pretrained DNNs are widely used to produce embeddings for downstream tasks, e.g., DNNs trained on ImageNet generalize effectively to many computer vision tasks [25] [26] [27] . Several studies [28] [29] [30] [31] observe that ImageNet ID accuracy is highly predictive of OOD accuracy, while others [22, [32] [33] [34] find that observation does not always hold. Another example is CLIP [35] , which has better OOD generalization due to larger and more diverse training data [36] . We disentangle the role of data quantity versus the level of semantic variability.Many works suggest that representations learned in earlier layers are more universal across image datasets whereas later layers are more task-specific [1] [2] [3] [4] [5] [6] [7] [8] 32] . This observation has guided the development of many transfer and continual learning methods. We revisit this phenomenon by studying the impact of DNN architecture on OOD generalization.Number of Samples. We conducted 64 experiments using ImageNet-100 to assess the impact of the number of samples on the tunnel effect. We varied the number of training data per class from 100, 200, 500, and 700 while keeping the number of classes fixed at 100.Resolution. Since [9] only studied 32 × 32 image datasets, the impact of image resolution on the tunnel effect is unknown. We hypothesized that higher resolutions would result in more hierarchical features, resulting in reducing the tunnel effect. To test this, we trained models on ImageNet-100 with 32 × 32, 64 × 64, 128 × 128, and 224 × 224 images, while keeping the number of parameters for each architecture constant. We conduct 48 experiments per resolution (192 total).DNN Architecture Variables. We study the tunnel effect in eight DNN architectures drawn from three families: VGG [53] , ResNet [54] , and ViT [55] . We study the role of the size of the k × k stem, which is the size of the first CNN filter or the ViT's patch size. Because over-parameterization is central to the tunnel effect hypothesis, we measure the over-parameterization level [56] , γ = P /N , where P is the number of DNN parameters and N is the number of ID training samples. We conducted 416 experiments to assess the impact of architecture type, depth, over-parameterization level, stem style, and spatial reduction.We ensure that each DNN architecture uses the same number of parameters across image resolutions.To do this for the VGG family, we created VGGm, which replaces the two fully connected layers before the output layer with a ResNet-style global average pooling layer. Since the original VGG is designed for high-resolution images (224 × 224), it includes the max-pool in all 5 stages to progressively reduce the spatial dimension, s of the features (s × s × c) across VGG layers. To capture this, we introduce a variable named spatial reduction by which a stem layer (first layer) reduces the spatial dimension of input images. Spatial reduction, ϕ is defined as the ratio of the output spatial dimension s out to the input spatial dimension s in , i.e., ϕ = s out /s in . For instance, spatial reduction at a layer that reduces the spatial dimension from 32 × 32 into 16 × 16 becomes 0.5, whereas a DNN that did no spatial reduction would have ϕ = 1. We also created another variant, VGGm †, to study the impact of spatial reduction on the tunnel effect. The difference between VGGm (ϕ = 0.5) and VGGm † (ϕ = 1) is that VGGm includes max-pool in all 5 stages whereas VGGm † omits max-pool in the first 2 stages for 32 × 32 input resolution. Compared to VGGm, VGGm † achieved higher ID accuracy on ImageNet-100 (see Table 11 ). For ResNet, we use the original ResNet architecture [54] .To keep model size constant across resolutions for ViT models, we use a fixed patch size of 8 × 8, with the number of patches being larger for higher-resolution images. Following [57] , we used 2D sin-cos position embeddings to encode spatial information.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [Yes] Justification: We discuss the limitations of our work in Sec. 5, where we point out that we only study vision datasets and primarily supervised learning approaches.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
datasets: 
 ID Datasets. In our main experiments, we train DNNs on 3 ID datasets: For each of the 64 DNNs trained on an ID dataset in our main results, we compute our OOD generalization metrics on each OOD dataset, resulting in 512 values per metric. These values are derived from 8,604 linear probes (ID and OOD). We study the impact of each variable on OOD generalization in isolation using paired Wilcoxon signed-rank tests at α = 0.05, where pairs are constructed to control for the impact of other variables, and we use Cliff's Delta to measure effect sizes [68] , which is appropriate for ratio data. For Cliff's Delta (δ), we follow the standard practice of defining a negligible effect for |δ| < 0.147, small effect for 0.147 ≤ |δ| < 0.33, medium effect for 0.33 ≤ |δ| < 0.474, and large effect for |δ| ≥ 0.474.To jointly analyze and rank the contribution of each variable, we use SHAP † , which determines the contribution of each input variable to its output [69, 70] . Following [71] , we train Gradient Boosting Regression models to predict three output targets: a) % OOD performance retained, b) Pearson correlation, and c) ID/OOD alignment, from 8 input variables: 1) resolution, 2) augmentation, 3) ID class count, 4) spatial reduction, 5) stem, 6) CNN vs. ViT, 7) over-parametrization level, and 8) depth. We then obtain SHAP values for each variable, where using Gradient Boosting Regression facilitates controlling for variable interaction effects [71] . Because SHAP magnitude does not indicate the direction of a variable's impact, for each of the 3 models, we fit a linear regression model between each variable and its corresponding SHAP values to obtain its slope. Positive slopes indicate the variable improves the metric. We call this SHAP Slope. Details are given in Appendix A.9.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper. • The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). • The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) • The assumptions made should be given (e.g., Normally distributed errors). • It should be clear whether the error bar is the standard deviation or the standard error of the mean. • It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified. • For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates). • If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text. 
main experiments: 
 In [9] , all architectures were trained with CIFAR-10 or CIFAR-100, and all experiments were conducted with 32 × 32 images. Instead, most of our experiments use ImageNet-100 as the ID dataset, where image resolution is varied. We also include experiments on CIFAR datasets. In our main experiments, for each of our 64 DNNs, we produced 8 OOD linear probe curves and 1 ID linear probe curve (576 total), which required computing 8604 linear probes. From this, we obtain 512 values for each of our 3 metrics under various conditions.Results for our SHAP Slope analysis computed across all 512 OOD experiments are summarized in Fig. 2 , which shows the impact of each variable on the % OOD performance retained and ID/OOD alignment. The SHAP Slope figure for Pearson Correlation is given in Appendix C since it has nearly identical trends to % OOD performance retained. The R 2 for % OOD performance retained, ID/OOD alignment predictions, and Pearson Correlation are 0.62, 0.44, and 0.73, respectively. Each variable's positive/negative impact is consistent across all 3 of our SHAP analyses. Our main findings are given below, with additional findings in Appendix C.Our metrics reveal that increasing the ID class count, higher resolutions, and using augmentations improve OOD generalization. For % OOD performance retained and Pearson Correlation, increasing the number of ID classes had the greatest impact, whereas, for ID/OOD alignment, increasing resolution did. This is likely because ID/OOD alignment curves are not normalized using the best OOD accuracy, resulting in resolution's role being obscured for the other two metrics. Across metrics, using augmentations had the second greatest positive impact. These results indicate that increasing between-class diversity (more classes), greater within-class diversity (augmentations), and higher image resolutions improve OOD generalization.While [9] argued that the primary source of the tunnel effect is over-parameterization, our results indicate it plays a minor role compared to other factors. Our results indicate that using a larger stem and excessive DNN depth somewhat impair generalization. For all metrics, the choice of ViT or CNN had the least impact on OOD generalization, consistent with the hypothesis that much of the reported benefits of ViTs for image classification are due to training with larger datasets, stronger augmentation policies, and other tricks [72] .Using the average % OOD performance retained across the 8 OOD datasets to analyze all 64 of our DNNs, 4 had negligible (non-existent) tunnels, 8 had weak tunnels, 13 had medium tunnels, and 39 had strong tunnels. We use intervals of [100%, 95%] for negligible, [90%, 95%) for weak, [80%, 90%) for medium, and [0%, 80%) for strong tunnel. This demonstrates that the tunnel effect is not universal and depends on variables. Next, we dive into the factors that influence tunnel effect strength.In Fig. 3 , example linear probe plots illustrate that augmentations play a major role in reducing the tunnel effect. To further analyze the impact of augmentation on OOD generalization, we compared all of our experiments in which augmentation was used or omitted with all other variables controlled using paired Wilcoxon Signed-Rank tests (256 paired experiments, 512 total). For % OOD performance retained, augmentations significantly decreased the tunnel effect with 64.26% retained without augmentations and 78.41% with (p < 0.001), which had a medium effect size (|δ| = 0.370). For Pearson correlation, augmentations also had a significant effect where ρ increased from 0.77 to 0.86 (p < 0.001), with a medium effect size (|δ| = 0.374). For ID/OOD alignment, augmentations increased alignment from 0.15 to 0.25 (p < 0.001), with a medium effect size (|δ| = 0.357).Illustrative examples showing how increasing resolution improves OOD generalization are given in Fig. 1 given in Table 12 . The findings are consistent with our SHAP analysis: training on higher-resolution images improves OOD generalization, whereas low-resolution datasets increase tunnel effect strength. Additional results are given in the Appendix C.13.A t-SNE analysis for various layers from VGGm-11 models trained on 32 × 32 and 224 × 224 images is given in Fig. 4 . The low-resolution model exhibits much greater intermediate neural collapse [10] and representation compression than the high-resolution model. This is likely why many OOD detection algorithms that work well for CIFAR fail for higher-resolution datasets [11] . These results highlight the dangers of extrapolating findings from low-resolution datasets to all of deep learning. Stem. Our SHAP results indicate that increasing stem size hurts OOD generalization. To further study this, we conducted a paired test over 64 paired experiments between ResNet-18, which uses a 7 × 7 stem, and VGGm-17, which uses a 3 × 3 stem. Increasing the stem from 3 to 7 significantly decreased the % OOD performance retained from 76.74% to 66.66% (p < 0.001), with a small effect size (|δ| = 0.306). However, for Pearson correlation, there was no significant difference (p = 0.145). For ID/OOD alignment, increasing the stem significantly reduced the score from 0.27 to 0.21 (p < 0.001), with a small effect size (|δ| = 0.226). Fig. 12 provides box plots of % OOD performance retained and ID/OOD alignment for the three stem values.Depth. Our SHAP analysis revealed that increasing depth impairs OOD generalization. As shown in Fig. 10 , increasing depth impairs OOD performance retention for each architecture family. To study this further, we compared VGGm-11 and VGGm-17 using 48 paired experiments (96 total). Increasing depth significantly decreased % OOD performance retained from 89.19% to 69.41% (p < 0.001), with a large effect size (|δ| = 0.539). Likewise, Pearson correlation significantly decreased from 0.94 to 0.80 (p < 0.001), with a large effect size (|δ| = 0.497). ID/OOD alignment also significantly decreased from 0.28 to 0.25 (p < 0.001) with a small effect size (|δ| = 0.161).Over-parameterization Level. Our SHAP analysis showed that over-parameterization level negatively impacts OOD generalization. Fig. 11 shows how increasing the over-parameterization level decreases % OOD performance retained. We conducted paired tests between VGGm- 6 , increasing the number of classes greatly reduces the tunnel effect (Figs. 6a and 6b ). To examine the role of the dataset size, we vary the number of samples per class from 100, 200, 500, and 700 while keeping the class count constant at 100, which has a relatively small impact on the tunnel effect (Figs. 6c and 6d ).We also studied OOD generalization for eight widely used ImageNet-1K pre-trained CNN and ViT backbones trained with either supervised learning (SL) or self-supervised learning (SSL). We studied 9 , the tunnel effect is absent in most models and is weakly present in both SL and SSL ResNet-50.Additional results are given in Appendix C.11. Appendix A.6 includes implementation details.Catastrophic forgetting is a central focus in continual learning [17, 77] . Many methods assume forgetting occurs mostly in later layers with earlier layers serving as universal features [16, 78, 79] . The original tunnel effect paper challenged this [9] . They trained VGG-19 on two tasks sequentially, where the first task included half of the CIFAR-10 classes and the second task included the other half. After training on each task, the tunnel and extractor were saved. They found no forgetting when tunnels were swapped, indicating no learning occurred in the tunnel for task 2, and they found reduced forgetting when fine-tuning the extractor alone. These findings are worth assessing beyond CIFAR-10. We ask: What is the role of the tunnel in mitigating forgetting?We replicated their general approach by training ResNet-18 on ImageNet-100, where the first task had the first 50 classes and the second had the rest. After learning each task t, we saved the extractor E t , tunnel T t , and the classification head. We conducted this experiment with 32 × 32 and 224 × 224 images. Using the tunnel definition from [9] , tunnels T 1 and T 2 correspond to layers 14-17 for 32 × 32 images and 15-17 for 224 × 224 images. See Appendix A.7 for additional details.Results are given in Table 2 . Unlike the findings in [9] , when we swapped tunnels T 1 and T 2 , accuracy was greatly reduced for both resolutions, indicating that essential learning happened within the tunnel.Next, we replicated their fine-tuning experiments. If fine-tuning E 2 alone reduces forgetting more than fine-tuning E 2 with T 1 , it suggests the tunnel has a detrimental impact on mitigating forgetting. We found that fine-tuning E 2 alone improved task 1 accuracy less than fine-tuning E 2 + T 1 , indicating T 1 helps reduce forgetting. Our findings, which contradict [9] , suggest the "tunnel" plays an essential role in mitigating catastrophic forgetting, consistent with prior work [5] .  
discussion & conclusions: 
 We conducted extensive experiments to investigate the generality of the tunnel effect in a wide range of transfer settings. Our study indicates that the best way to mitigate the tunnel effect, and thereby increase OOD generalization, is to increase diversity in the ID training dataset, especially by increasing the number of semantic classes, using augmentations, and higher-resolution images; hence, we revise the tunnel effect hypothesis as follows:The Tunnel Effect Hypothesis: An overparameterized N -layer DNN forms two distinct groups:1. The extractor consists of the first K layers, creating linearly separable representations.2. The tunnel comprises the remaining N -K layers, compressing representations and hindering OOD generalization. K is proportional to the diversity of training inputs, where if diversity is sufficiently high, N = K.Earlier works on the tunnel effect [9] and intermediate neural collapse [10] exclusively used 32 × 32 images for ID training. We found that while DNNs trained on CIFAR always exhibited the tunnel effect, the tunnel effect was greatly reduced for ImageNet-100 at higher resolutions. This discrepancy helps explain why methods validated on CIFAR and similar datasets may not generalize in many scenarios [11] [12] [13] [14] [15] [16] [17] [18] . We urge the community to use high-resolution datasets with 100 or more categories to improve the generality of findings, especially for studies related to representation learning, neural collapse, and OOD detection/generalization.Limitations & Future Work. While our work validates the existence of tunnels, future research should focus on developing theoretical frameworks to help explain the tunnel effect. We rigorously studied OOD generalization on vision datasets with supervised learning. Future work could study non-vision, multi-modal [80] , and biased datasets [81, 82] , where the tunnel effect has not yet been studied. While we studied pre-trained SSL backbones, we could not do our SHAP analysis without having more SSL backbones. Valuable insights for SSL could be obtained by conducting carefully controlled paired experiments, as done in our main experiments. This would require probing at least four different SSL algorithms for each variable analyzed, where training each SSL DNN would require over 10× more time than our supervised DNNs. Additionally, SSL methods employ more advanced augmentation policies than ours, where we used random-resized crops and horizontal flips. Replicating our SHAP analysis with multiple augmentation policies could reveal whether the OOD generalization capabilities of SSL algorithms are due to their augmentation policies versus their objective functions. Lastly, identifying regularizers or other techniques that mitigate tunnel formation should be sought for continual learning methods that start from scratch using small initial sets. This could greatly improve forward transfer, leading to more efficient continual learning methods [83] [84] [85] [86] . 
experiments compute resources: 
 Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?Answer: [Yes]Justification: We specified compute resources in Appendix A.10, where we provided the total time in aggregate for running all experiments (48 days) and our hardware, which is one machine with four NVIDIA A5000 GPUs shared among lab members. Since we trained over 64 DNN backbones and almost 10,000 linear probes, it is not feasible to provide this information for each backbone and linear probe.Guidelines:• The answer NA means that the paper does not include experiments.• The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage. • The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute. • The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper). 
code of ethics: 
 Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines? 
 
 Appendix: In experiments with CNNs, at each layer l, for each sample, we extract features of dimension H l × W l × C l , where H l , W l , and C l denote the height, width and channel dimensions respectively. Next, following [37] , we apply 2 × 2 adaptive average pooling on each spatial tensor (H l × W l ). After average pooling, features of dimension 2 × 2 × C l are flattened and converted into a vector of dimension 4C l . Finally, a linear probe is trained on the flattened vectors. In experiments with ViTs, following [87] , we apply global average-pooling (GAP) to aggregate image tokens excluding the class token and train a linear probe on top of GAP tokens.VGGm ID Training: For training VGGm-11/17 on ImageNet-100, we employ the AdamW optimizer with an LR of 6 × 10 -3 and a WD of 5 × 10 -2 for batch size 512. The model is trained for 100 epochs using the Cosine Annealing LR scheduler with a linear warmup of 5 epochs. We use label smoothing of 0.1 with cross-entropy loss. For CIFAR-10 and CIFAR-100 datasets, we use an LR of 0.01 for batch size 512. We train VGGm-11 for 100 and 70 epochs in experiments without augmentations and with augmentations respectively. Whereas VGGm-17 is trained for 100 epochs in both settings without augmentations and with augmentations.Varying Number of Classes and Sample Size: VGGm-11 uses LR of 8 × 10 -3 and WD of 5 × 10 -2 .VGGm-17 uses WD of 1 × 10 -2 instead of 5 × 10 -2 . For both with and without augmentation, We train VGGm-11 for 100 epochs and VGGm-17 for 200 epochs.VGGm Linear Probing: We use the AdamW optimizer with a flat LR of 1 × 10 -3 and a WD of 0 for batch size 128. The linear probes are trained for 30 epochs. We use label smoothing of 0.1 with the cross-entropy loss.ResNet ID Training: For training ResNet-18/34, we employ the AdamW optimizer with an LR of 0.01 and a WD of 0.05 for batch size 512. The model is trained using the Cosine Annealing LR scheduler with a linear warmup of 5 epochs. We use label smoothing of 0.1 with cross-entropy loss. We use 100 epochs to train ResNet-18 in experiments without augmentation. In experiments with augmentations, we train ResNet-18 for 80 epochs using random resized crop and random horizontal flip augmentations. The ResNet-34 models are trained for 100 epochs in experiments with and without augmentations.ResNet Linear Probing: In the linear probing experiment, we use the AdamW optimizer with an LR of 1 × 10 -3 and a WD of 0 for batch size 128. The linear probes are trained for 30 epochs. We use label smoothing of 0.1 with cross-entropy loss.For ViT training, we follow the codebase of DeiT [88] and A-ViT [89] . We also use timm library [90] .ViT ID Training: For training ViT-Tiny/ViT-Tiny+, we employ the AdamW optimizer with an LR of 8 × 10 -4 and a WD of 0.05 for batch size 96. We use the Cosine Annealing LR scheduler with a linear warm-up (5 epochs). We also use label smoothing of 0.1 with cross-entropy loss. We train the ViT-Tiny for 100 and 40 epochs in experiments without augmentations and with augmentations respectively. Whereas the ViT-Tiny+ is trained for 100 and 60 epochs in experiments without augmentations and with augmentations respectively. In the experiments with augmentations, we use random resized crop and random horizontal flip. Following [57, 87] , we omit class token and instead use GAP token by global average-pooling image tokens for classification head.ViT Linear Probing: We use the AdamW optimizer with LR of 0.01 and WD of 1 × 10 -4 for batch size 512. The linear probes are trained for 30 epochs. We use label smoothing of 0.1 with cross-entropy loss. Pre-trained Model Linear Probing. We attach a linear probe layer to each block of ViT models and each Conv2d layer of CNN models. In the ConvNeXt block, which has three layers, only the 7x7 layer uses Conv2d. Therefore, using the Conv2d layer results in one layer per ConvNeXt block for linear probing. We use the AdamW optimizer with a WD of 0 and a batch size of 512. Linear probes are trained for 30 epochs using cross-entropy loss with label smoothing of 0.1. For all ViT models and ResNet-50 Supervised model, the LR is 5 × 10 We describe the implementation details of continual learning experiments that are presented in Sec. 4.3. We adapt the experimental design from [9] for this study. We use the same linear probing approach and definition of the tunnel to identify tunnels in ResNet-18 models during continual learning experiments. We train the model on two subsequent tasks and each task contains non-overlapping 50 ImageNet classes.Continual Learning. We employ the AdamW optimizer with LR of 0.01 and WD of 0.05 for batch size 512. The model is trained for 50 epochs using the Cosine Annealing LR scheduler with a linear warmup of 5 epochs (for the first task). We use label smoothing of 0.1 with cross-entropy loss.Tunnel Layers. For 32 × 32 resolution, tunnels T 1 and T 2 correspond to ResNet layer 14-17. For 224 × 224 resolution, tunnels T 1 and T 2 correspond to ResNet layer 15-17.Finetune. In this experiment, we use the AdamW optimizer with LR of 0.01 and WD of 5e-2 for batch size 512. The number of epochs is 50. We use label smoothing of 0.1 with cross-entropy loss.A Step LR scheduler is used. In particular, we reduce LR by a factor of 0.1 at predefined milestones, which are set to occur at the 20th and 40th epochs.In all experiments, we use image augmentations namely random resized crop, random horizontal flip, mixup [91] , and cutmix [92] . For mixup and cutmix augmentations, we use participation probability of 0.6 and 0.4 respectively. We set coefficient β = 1.0 for cutmix and coefficient α = 0.1 for mixup.We adapt image pre-processing steps from [89] for various image resolutions. We use the same number of network parameters, hyperparameters, and identical settings for all image resolutions. For a fair comparison, we choose hyperparameters to maximize the performance of all compared methods or models.Accuracy. For accuracy in all experiments including ID training and ID or OOD linear probing, we use the best top-1 accuracy (%).Pearson Correlation. We compute the Pearson correlation ρ between ID accuracy and OOD accuracy using the following equation,ρ = ∑ n i=1 (x i -x)(y i -y) √ ∑ n i=1 (x i -x) 2 ∑ n i=1 (y i -y) 2.(EQUATIONIn this formula, x i represents the ID accuracy at the i-th layer, and y i represents the OOD accuracy at the i-th layer. x and y are the average of ID and OOD accuracy over layers, respectively. The index i spans from the first layer (1) to the penultimate layer (n) of models since ID and OOD accuracy are computed at each layer. ρ ∈ [-1, 1], where ρ = 1 indicates a perfect positive linear relationship, and ρ = -1 indicates a perfect negative linear relationship.Wilcoxon Signed-Rank Test. To measure the significance of the difference between the two groups, we performed a Wilcoxon signed-rank test between the two groups. We compared % OOD performance retained, Pearson correlation, and ID/OOD alignment metrics between each pair. We used the wilcoxon function from the spicy.stats python library.Cliff's Delta. The effect size (Cliff's Delta) quantifies the statistical difference between the two sets. A bigger effect size denotes a bigger difference and the order is negligible < small < medium < large. We computed Cliff's Delta for % OOD performance retained, Pearson correlation, and ID/OOD alignment metrics to measure the effect size between the two groups. We used the cliffs_delta function from the cliffs_delta python library (https://github.com/neilernst/cliffsDelta).Reasons for Multiple Metrics. The Pearson correlation metric gauges the correlation between ID and OOD accuracy, indicating tunnel behavior (low correlation), but doesn't quantify the tunnel effect's magnitude. The % OOD performance retained metric assesses the tunnel effect's magnitude and identifies tunnel layers but solely compares OOD performance between the highest and penultimate layers, neglecting ID accuracy. The ID/OOD alignment metric addresses this by considering both ID and OOD accuracy. To ensure robustness, we employ all metrics to comprehensively capture ID and OOD performance and their relation to the tunnel effect.We describe the implementation details of SHAP slope analyses that are presented in Sec. 4.1.1. For SHAP analysis, categorical variables (e.g., CNN vs ViT) are treated as one-hot vectors, while noncategorical values are transformed into ordinal numbers. We calculate SHAP values on a Gradient Boosting Regression model, which is trained on our set of 512 experiments to predict a metric from the manipulated input variables already described in the main section of this work. We use the Huber loss to train the Gradient Boosting Regression model.While SHAP values themselves can give us insights into the impact of each variable, their interpretation from commonly used plots like SHAP mean absolute bar plot (Fig. 7a ) or SHAP Beeswarm plot (Fig. 7b ) is limited. We want to show both the impact and the relationship direction of each variable with the predicted metric. To do this, for each variable, we fit a linear model on the obtained SHAP values and the normalized ordinal values of the variable. An example can be seen in Fig. 7c . In this way, the value of the slope tells us the impact of the variable on the predicted metric, while the sign of the slope tells us the direction. For each metric, we L 1 normalize the slope values. A positive slope means that increasing the variable's value increases the predicted metric, while a negative slope means that increasing the variable's value decreases the value of the predicted metric. A bigger value in any direction indicates that the predicted metric is more sensitive to the corresponding variable.We coined the plot containing the slopes for each variable as the "SHAP Slope" plot.We trained a total of 64 backbones and 10,652 linear probes to finalize our manuscript. We ran all experiments using four NVIDIA A5000 GPUs, including training backbones and linear probes. The aggregated compute time is ∼1,161 (wall clock) hours (48 days).All datasets are widely used and publicly available. We provide a link to the license if it exists. Despite their widespread use, we were unable to identify the license for CIFAR-10, CIFAR-100, ImageNet-1K, CUB-200, Aircrafts-100, Flowers-102, and STL-10 datasets.We used 11 datasets in total in our paper and they are ImageNet-1K, ImageNet-100, ImageNet-R, CIFAR- We calculate the Pearson correlation metric over all 512 experiments, using the formula described in Sec. A.8. Fig. 8 shows the SHAP Slope plot for the Pearson correlation metric. The gradient-boosting regression model got a R 2 of 0.73 when predicting this metric. The variables follow a similar trend as seen in Sec. 4.1.1 for % OOD performance retained metric, where ID class count, augmentation, spatial reduction, and resolution have a positive impact on Pearson correlation. Again, ID class count stands out as the most influential variable for Pearson correlation, suggesting that input diversity enhances OOD generalization. In contrast, depth, over-parameterization level, stem, and CNN vs We conduct 224 experiments on ImageNet-100, exploring various model architectures, and resolutions (32 × 32 and 224 × 224), with and without augmentations, and evaluate them on 8 different OOD datasets mentioned in Sec. 3.3. Additionally, to examine resolution in a more fine-grained manner, we conduct 96 experiments with resolutions of 64 × 64 and 128 × 128 using VGGm-17, ResNet-18, and ViT-T+, also on ImageNet-100 and the same 8 OOD datasets. We conduct 96 more experiments on ImageNet-100, varying class numbers while keeping image numbers constant, and vice versa. To compare the effect of the ID dataset, we perform 64 experiments on CIFAR-10 and CIFAR-100 as ID datasets with their native resolution (32 × 32), exploring VGGm-11 and VGGm-17 models, with and without augmentations, and evaluate them on all OOD datasets. We do the same for VGGm †-11 and VGGm †-17 on CIFAR-100, resulting in another 32 experiments. This totals 512 OOD experiments.In this section, we summarize results in terms of OOD accuracy and three metrics e.g., % OOD performance retained, Pearson correlation, and ID/OOD alignment. This helps analyze the strength of the tunnel effect and OOD generalization in various transfer settings. The following subsections present results in terms of different metrics and discuss the findings.In Table 4 , we compare OOD accuracy among models trained on the ImageNet-100 ID dataset with varied resolutions. The insights derived from three metrics regarding the influence of variables on the tunnel effect are consistent with observations of OOD accuracy. Models exhibiting weaker or negligible tunnel effects tend to attain higher OOD accuracy compared to those with stronger tunnel effects.In Table 5 , we compare % OOD performance retained among models trained on the ImageNet-100 ID dataset with varied resolutions. Models exhibiting weaker or no tunnel effect tend to achieve higher % OOD performance retained compared to those displaying a stronger tunnel effect. In Table 6 , we compare the Pearson correlation among models trained on the ImageNet-100 ID dataset with varied resolutions. We observe that the Pearson correlation adeptly captures the tunnel effect across different models and settings.In Table 7 , we compare ID/OOD Alignment among models trained on the ImageNet-100 ID dataset with varied resolutions. More performant models obtain higher ID/OOD alignment scores across various experiments compared to less performant models. The impact of different variables and interventions on the ID/OOD alignment is shown in Fig. 19 and Fig. 20 .In this section, we analyze how DNN architecture impacts % OOD performance retained across transfer settings. To investigate this, We create a boxplot (Fig. 9 ) that shows % OOD performance retained of each model trained on ImageNet-100 ID dataset with resolutions 32 × 32 and 224 × 224. We find that DNN architecture greatly impacts the OOD generalization. Among CNNs, VGGm-11 shows superior performance. In terms of CNN vs. ViT, ViTs perform better than CNNs when augmentations are used. Augmentations benefit both CNNs and ViTs, but ViTs seem to benefit more from augmentations.In this section, we analyze how DNN depth impacts the tunnel effect. Fig. 10 shows that smaller models have higher % OOD performance retained than larger (deeper) models. Therefore, the depth of DNN has an adverse impact on OOD generalization and the tunnel effect. In this section, we investigate the relationship between overparameterization level and % OOD performance retained. We use experimental results from models trained on ImageNet-100 ID dataset with resolutions 32 × 32 and 224 × 224 for this analysis. To do this, we compute average % OOD performance retained across overparameterization levels and create a boxplot using this data. Fig. 11 shows that % OOD performance retained decreases as over-parameterization level increases. Therefore, overparameterization level has an adverse impact on OOD generalization.This section analyzes how the stem affects tunnel formation. We use experimental results of models trained on ImageNet-100 ID dataset with resolutions 32 × 32 and 224 × 224. For CNNs, the stem represents kernel size (3 × 3 and 7 × 7) at the stem layer whereas, for ViTs, it is patch size (8 × 8). Fig. 12 reveals that increasing stem hurts % OOD performance retained. In particular, when comparing CNNs (VGGm's 3 × 3 and ResNet's 7 × 7), increasing stem from 3 to 7 decreases average % OOD performance retention. However, ViTs (8 × 8) perform better than CNNs. On the other hand, stem significantly impacts ID/OOD alignment. Across all compared models, increasing stem shows a significant negative impact on ID/OOD alignment.In this section, we study how augmentation affects the tunnel effect. We used all 512 experiments to assess the impact of augmentation. 256 experiments used augmentations and another 256 experiments did not use any augmentation. In experiments with augmentation, we used random resized crop and random horizontal flip. Fig. 13 exhibits that increasing augmentation greatly improves % OOD performance retained. This section explores the relationship between the ID class count and the tunnel effect. We use experimental results from the VGGm-11 models trained with ImageNet-100, CIFAR-10, and CIFAR-100 using 32 × 32 resolution and image augmentations. Fig. 14 displays how the number of ID classes affects the tunnel effect and OOD performance. We see that more ID classes reduce the strength of the tunnel effect and enhance OOD generalization.For the statistical analysis, we consider 16 paired experiments (32 total) comparing CIFAR-10 and CIFAR-100 datasets (ID). The compared models are VGGm-11, VGGm-17, VGGm †-11, and VGGm †-17. Increasing the number of CIFAR classes from 10 to 100 increased % OOD performance retained from 35.81% to 73.42% (p < 0.001), with a large effect size (|δ| = 0.758). Similarly, the Pearson correlation was improved from 0.54 to 0.88 (p < 0.001), with a large effect size (|δ| = 0.742). And, ID/OOD alignment reached 0.22 from 0.12 (p = 0.013), with a large effect size (|δ| = 0.531).Fig. 15 shows OOD performance for various dataset configurations with varied classes and samples per class. Increasing class counts significantly impacts OOD performance, whereas, increasing the number of training samples has less impact.In Fig. 16 and Fig. 14 , we observe that the tunnel effect is present in various ID datasets e.g., ImageNet-100, CIFAR-10, and CIFAR-100. Therefore, the tunnel effect is not a characteristic of a particular ID dataset such as CIFAR-10. With the prevalence of large pre-trained models, many research and applications are driven by these models. They show impressive transferability, especially those trained with SSL methods. Our goal is to explain this phenomenon using the tunnel effect hypothesis. Although the tunnel effect is hypothesized to be present in all over-parameterized DNNs, in [9] , only supervised DNNs were studied. Using pre-trained models, we study both SSL and SL models. For SSL pre-trained models, we study the following:• ResNet-50 pre-trained with SwAV [73] ,• ViT-B pre-trained with DINO V1 [75] ,• ViT-B pre-trained with MAE [50] ,• ViT-B pre-trained with MUGS [74] , and • ConvNeXt-B V2 pre-trained with FCMAE [76] .For SL pre-trained models, we study ResNet-50 [54] , ConvNext-B V1 [72] , and ViT-B [55] which are pre-trained with SL loss and data labels. We carry out 72 experiments in total of which 27 are for 3 SL models and 45 are for 5 SSL models. All SL and SSL models are pre-trained and fine-tuned (SSL only) on ImageNet-1K dataset. In total, we trained 1980 linear probes for ID and OOD datasets. Appendix A. 6 gives additional details and model configurations.Due to limited computational resources, we could not pre-train our own SSL models to do a rigorous paired analysis. SSL training is approximately 16× more expensive than SL, considering multiplicative factors, e.g., ∼ 8× more epochs and ∼ 2× more forward passes. Thus, we could only evaluate publicly available pre-trained models released by their creators. We find that SHAP analysis appears to be less informative due to the small sample size and because most of the pre-trained models do not exhibit the tunnel effect, resulting in less variability. Therefore, we focus on OOD linear probe analysis.In Fig. 17 and Table 9 , we observe that the tunnel is not present in most cases except for the ResNet-50 models. As shown in Table 8 , the SSL method, MUGS achieves the highest average OOD accuracy among all methods. In terms of DNN architecture, ViT-B exhibits better OOD performance than ResNet-50. Interestingly, among CNNs, ConvNeXt-B, which adapts design choices from Swin- transformer [95] , shows better OOD performance than ResNet-50. They also rival ViTs. This corroborates our argument that DNN architecture matters for OOD performance.The comparison between SSL and SL models is not straightforward as there are multiple factors involved, e.g., pretext tasks, training epochs, augmentations, and so on. Except for MAE, other SSL methods exhibit strong OOD performance compared to SL counterparts (Table 8 ). Previous works [52, 96] also found that MAE performs poorly in linear evaluation. When we compared SL vs. SSL models in the same family, in terms of average OOD accuracy, SSL (71.42%) outperforms SL (68.83%). As illustrated in Fig. 18 , SSL models perform better than SL models in terms of % OOD performance retained. We report the ID accuracy of these models in Table 10 . Given that SSL methods employ more augmentations than their SL counterparts (see Table 3 ), the performance improvements of SSL methods over SL ones are likely, in part, due to stronger augmentations, which is also argued in prior studies [97, 98] . While complimenting earlier works, our work confirms that large pre-trained models do not form tunnels, adding valuable perspectives to current knowledge. We also examine the impact of different variables and interventions on the ID performance, OOD performance, and ID/OOD alignment by analyzing the actual accuracy (no normalization). We show these results in Fig. 19 and Fig. 20 . We observe that the actual accuracy trends are consistent with our previous findings where variables that improve (degrade) OOD generalization also show higher (lower) ID/OOD alignment.Here we present additional resolution results. The image resolution shows a significant impact on the tunnel effect and OOD transferability. As shown in Fig. 19a , higher resolution images achieve higher performance in terms of ID accuracy, OOD accuracy, and ID/OOD alignment. ViT. Fig. 23 and Fig. 24 show the results for ViT-T+ models trained on ImageNet-100 with varied image resolutions in experiments with and without augmentations. When augmentation is omitted, low-resolution inputs show a weaker tunnel effect than high-resolution inputs. However, both lowand high-resolution inputs significantly mitigate the tunnel effect when augmentations are used.Rank Analysis. We examine the numerical rank of the representations evaluated on the ID dataset, following prior work [9] . In Fig. 25 , we observe that a model trained on high-resolution images maintains a higher rank than a model trained on low-resolution images, corroborating our previous findings (Sec. 4.1.3). The representations rank for resolution 32 × 32 plummets after the extractor, exhibiting the neural collapse phenomenon [10] whereas resolution 224 × 224 retains a much higher rank in the corresponding layers. The degradation in OOD accuracy and ID representation rank is more pronounced for low-resolution images than for high-resolution images. As a result, a model trained on low-resolution images exhibits a stronger tunnel effect than one trained on high-resolution images. In this section, we report additional statistical results for different variables and interventions. Table 12 includes average results with confidence interval. Also, there is no overlap between CIFAR-10 and CIFAR-100 so using one as ID and the other as OOD retains OOD challenges. It is evident that OOD evaluations in all our experiments are substantially robust due to dissimilar classes and significant distribution shifts between ID and OOD datasets.NeurIPS Paper ChecklistJustification: The research described in this paper adheres to the NeurIPS Code of Ethics. It does not involve human subjects, all datasets are public and widely used, and our work does not have the potential for harmful societal consequences.Guidelines:• The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 


Decision: This paper provides a thorough investigation of a recently observed phenomenon in deep learning called the "tunnel effect." The hypothesis states that initial layers create linearly-separable representations, while subsequent layers (referred to as the "tunnel") compress these representations with minimal impact on overall performance. This paper verifies the existence of the tunnel effect and demonstrates that it can be mitigated with richer data. Additionally, the authors verify that representations created by compression layers can negatively impact out-of-distribution (OOD) generalization performance. These claims are supported across multiple architectures, datasets, and other learning settings (including self-supervised learning). Compared to the original paper that discovered this phenomenon, this submission offers a much broader empirical analysis.

The majority of reviewers find the paper borderline, with the exception of reviewer gM3N, who rates the paper as "accept." Concerns raised by reviewers with borderline ratings include a lack of theoretical support and unsurprising conclusions. In contrast, reviewer gM3N, who provided the most thorough review of this submission, believes the paper makes an important contribution with potential implications for understanding and improving OOD generalization ability, as it challenges existing assumptions about the universality of the tunnel effect hypothesis.

The overall rating for the paper is borderline accept. After reading all the reviews and responses, I tend to agree with reviewer gM3N. Not every paper needs a theoretical contribution, especially when it is thorough from an empirical standpoint, and I think the authors have done a reasonable job in their empirical investigation. I also believe that verifying the existence of the tunnel effect while also showing that it is not a universal effect, and doing so across different learning settings (as done in the paper), is a non-trivial contribution. I therefore recommend acceptance.

Reviews: review: paper_summary: paper_summary: This paper studies the factors influencing out-of-distribution (OOD) generalization of pre-trained DNN embeddings through the lens of the tunnel effect hypothesis, which suggests deeper DNN layers compress representations and hinder OOD performance.
strength_weakness: strength_weakness: - The technical contribution is limited. The experiments on OOD generalization discussed in the paper are rather trivial and do not yield sufficiently insightful conclusions.

- The paper is poorly written. As an evaluation-focused study, it fails to effectively organize the relationship between the arguments and experiments, making it rather disorganized.

- The paper does not provide significant theoretical contributions, focusing primarily on empirical results without delving into the underlying theoretical frameworks or offering new theoretical insights.
questions: questions: please refer to the weakness.
limitations: limitations: yes
paper_summary: paper_summary: This paper studies how well self-supervised models transfer after self-supervised pretraining.  Using linear probe experiments on top of frozen encoders, and by varying the depth in the model being fed to the linear probe, they study the effect of network depth on ID performance and OOD (transfer learning) performance.  They find that the previously studied "tunnel effect hypothesis" can be diminished by increasing the diversity of pretraining data (which they demonstrate using data augmentation).
strength_weakness: strength_weakness: Scope:  The results of the paper seem fairly narrowly scoped.  I am not sure how these findings can really inform pretraining in ways that aren't already well understood (e.g. "use more diverse data" is already a fairly well established paradigm).  Thus it seems like the impact of this paper is fairly limited.

Experimental evaluation seems somewhat limited:  While the authors do run a large number of individual training runs, it is not clear to me that they performed a particularly wide experimental study.
questions: questions: How can we interpret these results in the context of other methods like SSL, where the learning goals seem to be more directly targeting removal of any tunnel effects?
limitations: limitations: Yes.
paper_summary: paper_summary: This paper investigates the "tunnel effect" in NNs introduced in a NeurIPS 2023 paper. According to the “tunnel effect” the deeper layers compress representations, limiting OOD generalization. The authors challenge the prior assumption that the tunnel effect is universal. They imply that it's heavily influenced by training data diversity.
They analyze a large number of NNs on various datasets with varying resolutions and introduce three metrics to quantify the tunnel effect's strength. Using a SHAP-based approach, they disentangle the impact of augmentation, number of classes, sample size, resolution, and the architecture.
Their experiments suggest that increasing the diversity of the training data (more classes, augmentations, and higher image resolutions) mitigates the tunnel effect and improves OOD generalization. Depth and overparameterization have the opposite effect. 
Based on these findings, they propose a revised tunnel effect hypothesis where its strength is inversely proportional to training data diversity.
strength_weakness: strength_weakness: Although the paper is a very solid work, the main worry that I have is about the confounding variables in the experiments and the revised hypothesis, which might limit the significance of the contribution:
* For example, Figure 1 claims that the increased resolution mitigates the tunnel effect. But intuitively, if you increase the resolution of the image, you also increase the resolution of the activation maps in the bottleneck layers. Still this doesn’t tell us anything about the architectures per se. Yes, the tunnel effect can be “sidestepped” if you increase the resolution, but then you run into the same issues if you increase the depth.
* OOD accuracy is measured on a number of datasets (NINCO [61], ImageNet-R [62], CIFAR-100 [60], CIFAR-10 [59], Oxford 102 Flowers [63], CUB- 173 200 [64], Aircrafts [65], Oxford-IIIT Pets [66], and STL-10 [67]). However, I wonder what such experiments tell us about the “kind” of OOD that we are testing for. For example, if one tests for compositional or systematic OOD generalization, it becomes very clear what the learnings are, and which particular flaws the models have. I feel that on these benchmarks it is hard to make the similar conclusions.
* Certain findings I find limited in the sense that they are already known, e.g. “Our metrics reveal that increasing the ID class count, higher resolutions, and using augmentations improve OOD generalization”.
* In these figures/results, typically normalized accuracy or performance retained are discussed. However, in ML it is also important to understand the actual accuracy, and these are not easy to find in the paper. Ideally for each figure/results discussion, the reader would be pointed to a table (in the appendix) that contains absolute numbers on the datasets. For example, it is claimed that "overparametrization negatively impacts OOD generalization .. since increasing overparametrization decreases OOD performance **retained**".
However I feel that without the absolute numbers this claim cannot be made. E.g. if both the IID and OOD performance improved by increasing overparametrization, but the IID performance improved more than OOD performance, one cannot claim that OOD performance decreased, quite contrary.
* L281: “Depth. Our SHAP analysis revealed that increasing depth impairs OOD generalization.” - Depending on how you increase depth (e.g. if you have pooling layers), to me this is an obvious consequence of additional compression that you may have in that case.
* The paper claims that their continual learning results contradict [9] and suggest the “tunnel” plays an essential role in mitigating catastrophic forgetting. However, they only replicate the experiment with ResNet-18 on ImageNet-100. To strengthen this claim, the authors could expand the continual learning analysis to include different architectures and datasets.
questions: questions: 1. This citation has the wrong year and NeurIPS number: “Wojciech Masarczyk, Mateusz Ostaszewski, Ehsan Imani, Razvan Pascanu, Piotr Miło ́s, and Tomasz Trzcinski. The tunnel effect: Building data representations in deep neural networks. Advances in Neural Information Processing Systems, 36, 2024.”.
Please cross-check other references too.
2. SHAP papers should be cited the first time it is mentioned in the text.
3. Could you clarify a bit further the reasoning / logic behind the “Metric 3: ID/OOD Alignment”? I find it a bit hard to wrap my head around it in its current form. Specifically why you choose to have a product of the two values and the respective “baseline” values that are subtracted.
4. What do you mean by “more hierarchical features” in L136? Isn’t the tunnel effect reduced because the size of the activation maps is increased, so the bottleneck is decreased?
5. L275: Perhaps a more appropriate wording here would be "7x7 kernel size" instead of "7x7 stem"?
limitations: limitations: The limitations and societal impacts have been addressed.
paper_summary: paper_summary: The paper sets out to evaluate empirically the generality (referred to as "universality") of the "tunnel hypothesis", the idea that compression at later layers may hinder OOD performance.
strength_weakness: strength_weakness: How empirical evaluations may provide any conclusive answer to the question of generality of a hypothesis is unclear to me. 

The use of linear probing cannot be taken as the yardstick for this study. The validity of any result is further compromised by the choice of SHAP in the place of a sound knowledge extraction method for the evaluation of the results. SHAP is known to produce unreliable results.
questions: questions: What does it mean to "disentangle samples and classes"?

What is "diversity of inputs"?
limitations: limitations: Please define linear probe and probe accuracy and how it is used in the paper.  

It is very unclear how swapping tunnels might help you answer the question of mitigating forgetting.

Comments: title: Response to the authors
comment: Thanks for your responses. Unfortunately, the paper's technical and theoretical contributions are insufficient, so I will maintain my original score, which is below the acceptance threshold.
Dear Reviewer,

Thank you for your thorough review and valuable feedback. Your insights have been instrumental in enhancing our work. We truly appreciate the time and effort you dedicated to this review.
Dear Reviewer,

We sincerely thank you for your constructive feedback and for reconsidering the score.

Regarding the concern about scope, we would like to emphasize that our work introduces new perspectives on the tunnel effect, providing researchers and practitioners with insights to _systematically_ design interventions that prevent tunnel formation and enhance OOD transferability or downstream tasks. We firmly believe that our work offers a meaningful contribution to the field and has the potential to inspire future research.

If you have any further concerns or comments, we would be more than happy to address them.
I have read the rebuttal from the authors.  I think their response reduces my concerns slightly and will therefore raise my score correspondingly.
I thank the authors for their additional comments and clarifications.

I will maintain my score and I still think this is a solid paper.

I have also read the reviews of other reviewers and find it somewhat disappointing that they have not yet engaged in a discussion with the authors.
Dear Reviewer WrHJ,

Thank you for dedicating your time to reviewing our work. Your feedback has been instrumental in enhancing our research, and we are pleased to hear that you find our work very interesting. We have made every effort to address your remaining concerns.

We understand your schedule may be busy, but we would greatly appreciate it if you could review our responses to ensure we have fully addressed your points. If you have any further questions or suggestions, please do not hesitate to share them. We are committed to addressing any additional points you may have.

Thank you once again for your valuable contribution to our research.
Dear Reviewer gXLk,

Thank you for dedicating your time to reviewing our work. Your feedback has been instrumental in enhancing our research.

We understand you may have a busy schedule, but we would greatly appreciate it if you could review our responses to ensure we have fully addressed your concerns. If you have any further questions or suggestions, please do not hesitate to share them. We are committed to addressing any additional points you may have.

Thank you once again for your valuable contribution to our research.
Dear Reviewer gM3N,

Thank you for dedicating your time to reviewing our work. Your feedback has been instrumental in enhancing our research.

We understand you may have a busy schedule, but we would greatly appreciate it if you could review our responses to ensure we have fully addressed your concerns. If you have any further questions or suggestions, please do not hesitate to share them. We are committed to addressing any additional points you may have.

Thank you once again for your valuable contribution to our research.
Dear Reviewer tyj4,

We sincerely appreciate your time in reviewing our work. Your feedback has been invaluable in improving our research.

We understand you may have a busy schedule, but we would greatly appreciate it if you could review our responses to ensure we have fully addressed your concerns.  If you have any further questions or suggestions, please feel free to share them. We are committed to addressing any additional points you may have.

Thank you again for your valuable contribution to our research.