Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper proposes a new method called Deep Combinatorial Aggregation (DCA) which is a family of approaches for ensembling deep neural network models, often with weight-sharing. DCA trains multiple different versions of each neural network "component" (with different initializations), then samples from all possible combinations of the components at test-time to generate an empirical distribution of predictions. Among the "components" considered by the paper are layers, trunks (i.e., residual blocks), and complete models. The paper shows that the uncertainty estimates generated by DCA are comparable, or better than, existing methods such as MC-Dropout across CIFAR-10 and SVHN datasets, for in-domain, distribution shift, and out-of-distribution settings. The authors measure uncertainty via negative log-likelihood (NLL), Brier score, and ECE. Furthermore, the paper also proposes a method called deep combinatorial weight averaging (DCWA) for merging the models from a DCA ensemble into a single model.
strengths_and_weaknesses: ## Strengths

**S1. DCA generalizes the notion of using stochastic networks for predictive uncertainty estimates** \
Assuming my understanding to be correct (see Q1), DCA generalizes MC-Dropout to other stochastic model components, including layers, trunks, and even entire models. Furthermore, like dropout, DCA proposes a method (DWCA) to merge the individual models into a single model. This perspective is helpful in understanding ways to leverage model stochasticity for empirical uncertainty quantification.

**S2. Experiments show strength of DCA** \
The reasonably comprehensive set of experiments show that DCA outperforms (or at least matches) the performance of existing methods such as MC-Dropout and deep ensemble.

## Weaknesses

**W1. Unclear justification for consistency enforcing loss (CEL)** \
While the experimental evidence suggests that CEL is helpful, I struggle to understand why such an approach should be beneficial. It seems to go against the intuition that to get good uncertainty estimates, one should train diverse and independent models, instead of explicitly encouraging their predictions to be similar (which also breaks independence).

**W2. Lacking clarity in OOD experiments** \
How are the ROC curves in Figure 3 generated? Namely, how are you using the models trained on multi-class classification to perform outlier detection (binary classification)? Some more description is warranted.

**W3. Missing downstream tasks** \
While the results on uncertainty estimates are impressive, I would hope to see a discussion of how much the gain in uncertainty estimation performance affects downstream tasks (e.g., active learning or Bayesian optimization).

**W4. Missing discussion of scalability** \
How does the DCA approach scale to larger datasets or other data modalities? Would similar approaches work on, e.g., transformer models in NLP tasks?
questions: **Q1. Would it be appropriate to consider DCA to be generalization of MC-Dropout?** \
Specifically, it seems to me that neuronwise DCA is essentially MC-Dropout. Is my understanding correct?

**Q2. How is modelwise DCA different from deep ensemble?** \
The paper writes:
> Note that modelwise DCA is similar to deep ensemble, except that its model copies are trained with distinct data within each training epoch, ...

Does "its" refer to modelwise DCA or deep ensemble? In either case, I don't fully understand what you mean by "model copies are trained with distinct data within each training epoch."

**Q3. Why do the in-domain results not include layerwise DCA models?**
limitations: My main concern about DCA's limitations is how it scales to larger datasets/models and other data modalities. The authors do not seem to discuss this limitation.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper proposes an effective ensembling technique for deep neural networks. The key idea is sharing the intermediate representation spaces among ensemble components. If we interpret deep neural networks as a chain of non-linear transformations mapping one representation space into another, this paper attempts to ensemble such intermediate mappings (DCA; Deep Combinatorial Aggregation). Furthermore, the authors suggest a weight averaging strategy compressing the proposed combinatorial ensemble to reduce the inference cost (DCWA; Deep Combinatorial Weight Averaging).

* * *
POST-REBUTTAL EDIT: Thank you for your time on the rebuttal. One remaining concern is the lack of large-scale experiments. Nevertheless, I believe the presented results (i.e., outperforming deep ensembles for in-domain, common corruptions, and out-of-distribution settings) are sufficient to verify the proposed method can benefit the community. Accordingly, I raised my score to 6.
strengths_and_weaknesses: It is noteworthy that the proposed method explicitly verifies the benefits of ensembling intermediate mappings of deep neural networks. Although some of the existing Bayesian Neural Networks (BNNs) also can be interpreted in this way, further analysis of granularity provided in the paper makes distinct contributions.

I especially like the variety of experiments provided in the paper, including in-domain classification performance, robustness on common corruptions, and predictive uncertainty on out-of-distribution examples. Such experimental results clarify the benefits of the proposed ensembling method.

Nevertheless, there isn’t enough experimental evidence to fully accept the superiority of the proposed DCA and DCWA methods. Experiments for PreResNet-20 on CIFAR-10 and SVHN, provided in the paper, are limited in terms of scalability and generality. It is necessary to secure diversity in datasets and network structures.
questions: 
- How are the weights initialized for DCA and DCWA? In the case of DCWA, ensemble components should have nearly identical weight values to be averaged, and the same should probably go for the initial weights.
- In Table 3, why does CEL improve Modelwise DCA? It seems counter-intuitive; CEL reduces the predictive diversity, which can worsen the ensemble performance (as stated in lines 188-194). Perhaps CEL improves the performance of each individual ensemble member while decreasing the diversity among ensemble members. To check this, why don't we measure the classification performance of each individual?
- I also suggest clarifying that the improvement of Consistency Enforcing Loss (CEL) is distinct from regularization effects due to the smoothed label; the objective of CEL, defined in Equation 4, can be interpreted as Knowledge Distillation or Label Smoothing [Yuan et al., 2021]. I believe that further comparison with "NLL + Label Smoothing" will enhance the arguments in lines 160-178 and 295-302.
- Experimental evidence on large-scale datasets (e.g., ResNet-50 on ImageNet-1k) will be strong support for the paper, but I know that there are computational constraints to do so. One compromise is to start DCA (or DCWA) training from the pre-trained checkpoint (e.g., provided by torchvision); SWA [Izamilov et al., 2018] and SWA-Gaussian [Maddox et al., 2019] also provided ImageNet results in this way.

1. Yuan et al., Revisiting Knowledge Distillation via Label Smoothing Regularization, 2021.
2. Izmailov et al., Averaging Weights Leads to Wider Optima and Better Generalization, 2018.
3. Maddox et al., A Simple Baseline for Bayesian Uncertainty in Deep Learning, 2019. 
limitations: This paper described the limitations of the work in Section 6; “Similar to deep ensemble, DCA requires multiple times the computational butdge to perform the joint training, compared to the standard baseline”.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: * **(1)** The authors introduce the deep combinatorial aggregation method, which could produce exponential ensemble model proposals by combining different parts of two neural networks.
* **(2)** A weight averaging strategy called DCWA is proposed to produce a new average model.
* **(3)** A consistency enforcing loss function for DCA is proposed to promote the similarity of different ensemble proposals.


strengths_and_weaknesses: * **(Strengths 1)** The key motivation of this paper is similar and clear. 
* **(Strengths 2)** The paper is well-organized and easy to follow.
* **(Strengths 3)** The potential limitations of the method have been well illustrated in the paper.

**However, I still have the following concerns and confusions:**
* **(Concerns 1)** Compared to other ensemble methods such as MCDropout [5] and SWA, the efficiency and complexity of this training method may increase significantly. Meanwhile, MCDropout[5] and other related works also could provide a variety of models without any additional computation cost. Compared with them, the method seems to have no advantages. 
* **(Concerns 2)** Since only one model proposal is trained per iteration, I am concerned that the model is hard to converge when the number of ensemble proposals is large. Meanwhile, when the number of model proposals is large, the training time may increase significantly.
* **(Concerns 3)** As elaborated in Section 2.2, the model parameters are not decomposable in general. Therefore, a coarser multilayer trick is employed. However, this trick will reduce the number of model proposals. 
* **(Concerns 4)** To help the DCA parameter training, predictive consistency is employed. However, as illustrated in Section 4, it has the risk of reducing the diversity of the model predictions.
questions: **However, I still have the following concerns and confusions:**
* **(Concerns 1)** Compared to other ensemble methods such as MCDropout [5] and SWA, the efficiency and complexity of this training method may increase significantly. Meanwhile, MCDropout[5] and other related works also could provide a variety of models without any additional computation cost. Compared with them, the method seems to have no advantages. 
* **(Concerns 2)** Since only one model proposal is trained per iteration, I am concerned that the model is hard to converge when the number of ensemble proposals is large. Meanwhile, when the number of model proposals is large, the training time may increase significantly.
* **(Concerns 3)** As elaborated in Section 2.2, the model parameters are not decomposable in general. Therefore, a coarser multilayer trick is employed. However, this trick will reduce the number of model proposals. 
* **(Concerns 4)** To help the DCA parameter training, predictive consistency is employed. However, as illustrated in Section 4, it has the risk of reducing the diversity of the model predictions.
limitations: This paper studies ensemble learning, a classic machine learning algorithm with almost no potential negative social impact.
review_title: null

Meta-review: metareview: The work proposes an ensembling technique for improved uncertainty and OOD predictive performance. The idea is to use multiple permutations of a certain component (e.g., layers, residual blocks) for both training and testing. Like efficient ensembles such as BatchEnsemble, most parameters are shared across ensemble members and a component is used multiple times depending on its selection for a given permutation in the combinatorial space. Overall, this results in an ensemble over a wider variety of networks, with a higher diversity than if one used completely independent networks for each ensemble member. There are further variants for efficiency such as "Deep combinatorial weight averaging".

The idea is conceptually simple and only requires the addition of a training objective to enforce consistency. The experiments are also quite thorough.

I agree with two of the three reviewers, disagreeing with Reviewer tdmd. One of the main concerns is that while the method outperforms baselines like MC Dropout, there's a lack of a theoretical explanation. I believe this can be helpful but is not a necessity, particularly when theory for efficient ensembles of neural networks is quite a difficult setting to study formally without sweeping assumptions. Other concerns like efficiency/complexity compared to more efficient methods like MC Dropout, SWA, and BatchEnsemble; and training time and convergence difficulties are adequately addressed in the rebuttal.

In related work, I would recommend discussing recent works that have also examined improving the diversity of ensembles for improved uncertainty/robustness, particularly those that have proposed a diversity penalty. To name a few: [1], [2], [3].

[1] A Diversity-Penalizing Ensemble Training Method for Deep Learning. Wentao Zhang, Jiawei Jiang, Yingxia Shao, Bin Cui https://arxiv.org/abs/2112.13316

[2] Hyperparameter Ensembles for Robustness and Uncertainty Quantification. Florian Wenzel, Jasper Snoek, Dustin Tran, Rodolphe Jenatton https://arxiv.org/abs/2006.13570

[3] Learning under Model Misspecification: Applications to Variational and Ensemble methods. Andres R. Masegosa https://arxiv.org/abs/1912.08335
confidence: Certain
Decision: Accept