Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper contributes an empirical analysis of deep ensembles. In particular, it seeks to understand whether an ensemble provides a distinct benefit over a single, larger model. The experiments on standard vision benchmarks cover both in-distribution and out-of-distribution performance.
strengths_and_weaknesses: This paper makes a strong claim: "deep ensembles [...] do not provide benefits distinct from what could be achieved by a standard [larger] neural network." Section 4.4 provides some empirical evidence for this, but its comparing ensembles of ResNet18 to a single WideResNet-18-4 (a related but different architecture), so I'm not convinced this is sufficient. The other evidence is in the form of out-of-distribution detection / robustness experiments, where it's found ensembles have no consistent benefits over single models. However, it's already well-known that ensembles (like most neural networks) lack the necessary distance-awareness property necessary for principled uncertainty estimation (see eg https://arxiv.org/abs/2006.10108). In summary, (1) for iD experiments, this paper appears to be comparing apples and oranges, and it's not clear why the same architecture wasn't used (with different hyperparameters) to increase model capacity; and (2) for OOD, it's already known ensembles aren't to be trusted away from their training data. Therefore, I think this work would benefit from a reframing that emphases instead the paragraph on Line 68: "this paper does not disagree per se with prior claims about the benefits of ensembles," which is seemingly in conflict with the first quoted line above.

I didn't see much discussion of overfitting, which seems very relevant to the benefits (or lack thereof) of ensembles. Another common way to think about ensembles is as an approximate Monte Carlo estimate of the posterior over model parameters. I would have liked to see this interpretation of ensembles discussed, since it implies an orthogonal benefit over single models, namely accounting for the uncertainty of the network parameters. On the other hand, increasing the size of a single model would in general be expected to lead to increased overfitting, without additional regularization. It might be nice to discuss some Bayesian Ensembling work, such as "Approximately Bayesian Ensembling"

Overall, I think this work has many qualities (well-written, detailed experiments, considers an important question), but I think it suffers from two important downsides. First, I don't think the claims regarding ensembles in iD settings are supported by the experiments. Second, the remarks about deep ensembles in OOD settings (e.g., "We therefore suggest caution when using ensembles to differentiate sources of
uncertainty in downstream applications") are already well-established by prior work. Finally, the scope of the experiments is somewhat limited to a small number of vision datasets, and I would have liked to see the (quite broad) claims further supported by experiments on other modalities. In summary, it would be very interesting if the main claims of this paper are true, but to show that would require a significantly expanded S4.4. 


questions: * In S4.4, how do you control overfitting / underfitting and hyperparameter tuning?
* In S5.2, it's not clear why ECE was not used. Can you offer a more detailed explanation?
limitations: I think the work would benefit from some more discussion of limitations, e.g. limited modalities considered.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper considers whether deep ensembles offer distinct benefits beyond individual models in uncertainty quantification (UQ) and out-of-distribution(OOD) detection. To study this problem, this paper empirically tests two hypotheses: 1)ensemble diversity is responsible for improved UQ; 2) ensemble diversity is responsible for improved (OOD detection) robustness. According to the empirical results, deep ensembles do not provide additional benefits to UQ and OOD detection as a single model with similar capacity.
strengths_and_weaknesses: ## Strength
- This paper proposes novel methods to verify whether ensemble diversity can bring additional benefits. Specifically, in testing the first hypothesis, this paper computes $E[var\mid E[U]]$ in terms of $E[U(f(x))]$. This demonstrates that the InD and OOD uncertainties estimated by deep ensembles are basically determined by the uncertainties of single models.
- This paper conducts comprehensive experiments, including homogeneous, heterogeneous, and implicit ensemble. 
- This paper is significant in that it empirically demonstrates that previous commonly accepted understandings of deep ensemble benefits might not be totally correct.
- This paper explicitly discusses how its findings are connected to previous papers.

## Weakness
- Though this paper focuses on UQ and OOD detection, it is also good to report the accuracies of both ensemble methods and single models to ensure a fair comparison. For instance, in line 226, it will be good to report also the accuracies of ensemble and single model.

questions: - In line 160, it is written that *ensemble uncertainty = ensemble diversity + average single model uncertainty* is a common metric. Can some references be provided?
- From my understanding, $\mathbb{f}=[f_1, \ldots, f_M]$. If this understanding is correct, can you provide the definition of $p(y=i \mid \mathbb{f(x)})$?
- In line 216, it is written that "the performance gains from ensembling are somehow fundamentally different than the performance gains from increasing a single model's capacity." It is not clear what that fundamental difference is.
limitations: This paper does not explicitly discuss its limitations.
review_title: null

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: The authors show with extensive empirical experiments that the power of ensemble models (in terms of effective OOD robustness and uncertainty quantification) can be replicated by a single larger model as well, therewith arguing the common belief that ensemble models are ways to achieve better performance as opposed to single models. 
strengths_and_weaknesses: Originality:
This work does not propose a new idea, but challenges an existing belief. Which is original and brings a fresh view.

Quality:
The paper is of high quality. Many experiment, also in different settings, have been performed rigorously. 

Clarity:
The paper is written clearly.

Significance:
It is important work that challenges a common belief about ensemble models. Even though, in practice, the use of ensembles might still remain popular, the learning points of this paper are useful for the community. 


Minor point: 
Eq. 2: I assume the superscript (i) refers to the class index in the C-dimensional vector. It was, however, not defined.
questions: Given the option to parallelize an ensemble of models during training, an ensemble might in some cases still be preferred, as also mentioned by the authors. Having a guideline in terms of how large a single model should be, would thus be very helpful. So can the authors give an indication how to know how large/complex a single model should be to match performance of an ensemble model? Did the authors now choose, for example, the same number of total trainable parameters for the single model as compared to the cumulative number of parameters of the ensemble?

Large models have the tendency to overfit on the training set, causing compromised test set performance. An ensemble of smaller models may have the advantage that the final result may be better, since either of the models that are part of the ensemble did not overfit that heavily. Is this a view the authors agree on? It might be an interesting addition to the discussion section of the paper. 

limitations: Yes, this has been tackled.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper analyzes the causes of advantages of deep ensemble methods. Specifically, they show that:
1) Ensemble diversity does not contribute to an ensemble’s ability to detect OOD data. Improvements to UQ on OOD datasets are not due to changes in ensemble diversity.
2) OOD performance of deep ensembles are determined by their in-distribution (InD) performance and thus they do not provide an additional  "effective robustness".
strengths_and_weaknesses: Strengths:
- There is a strong contribution to understanding the deep ensembles. The paper shows that ensemble diversity is not responsible for the robustness and the robustness of the model with the OOD data is explainable by the performance increase in InD data. The Paper also shows improvements to UQ on OOD datasets are not due to changes in ensemble diversity.
- The paper is written well and it is easy to follow.

Weakness:

-"Discussion: When should we use deep ensembles?" Either this is not a very good title or the question itself is not well answered in the discussion. Something else is discussed under this title.

questions: Can you explain what this "little benefit" is?
4.4."We conclude that, with regards to UQ and performance improvements, ensemble diversity offers little benefit over what can be obtained with single models."
limitations: - It is positive that they point the following limitation of the paper out and include in the paper that they have not done such experiments:
"We emphasize that our analysis only focuses on ensembles of neural networks, and does not necessarily apply to ensembling techniques in general (e.g. as applied to random forests or gradient boosted decision trees)."
review_title: null

Meta-review: metareview: This paper challenges a widely held view in deep learning: that deep ensembles are always superior to single models when it comes to uncertainty quantification and robustness. The authors convincingly show that a single big model may do equally well, and that much of the benefit of ensembles over single models of the same size seems to derive more from their improved accuracy than from their diversity. The reviewers thoroughly investigated the authors' claims and engaged in discussion. All reviewers are convinced that the main claim of the paper is mostly correct, and that it is a very interesting finding. I therefore strongly recommend accepting this paper.
confidence: Certain
Decision: Accept