Discovering Environments with XRM

W1. If I understand correctly, the method seems to rely on the fact that misclassified examples are such because they do not contain a "spurious correlation" that a model would learn by default. The twin training serves to reinforce the tendency of one of the trained models to capture this spurious correlation. If this is indeed the case, then the overall methods seems to depend on the (common) heuristic that models learn spurious correlations by default (a.k.a. shortcut learning). I think this is the same heuristic that is used in the existing methods criticised in Section 3. Critically, this heuristic relies on the fact that we know that the chosen architecture/training set lead to learnin undesirable spurious correlations by default. What if one applies the method to a situation where a perfectly-fine, "robust" model is learned by default? I'm guessing that the method would then be detrimental.

I'm not suggesting that we should be able to do better without additional knowledge (in fact [1] seems to show it's not possible) but the authors here do claim to do so, hence the need to point out this possible limitation (see also W5).

If my understanding of the method is correct, the method is also very similar to the following.

• Works in the debiasing literature (e.g. LfF) that train a pair of models that respectively rely/do not rely on spurious features. These works are discussed in Sect. 3, and I do understand that they rely to some extent to the tuning of model capacity to ensure that it captures the spurious feature, but I am not convinced that the proposed parallel training (which seem to be the essential difference) leads to the discovery of something fundamentally different.
• Works in the "model diversity" literature that train a pair of models that differ in their predictions [5,6]. These also proceed to train models in parallel, in a was that seems conceptually very similar to the step 1 proposed here (implementation details aside).

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W2. The proposed method only partitions the data into 2 "environments". I don't think this is really in line with the literature on DG (with which this work is supposed to connect) that are mostly based on invariance learning and need a large number of training environments (e.g. IRM). This work therefore seems much more related to the simpler setting of "debiasing" methods (e.g. LfF) that aim at removing the reliance of a model from one precise biased feature.

The methods used for the second phase are indeed simple baselines for debiasing, and not really DG methods. These are very strong baselines in these settings (and with the datasets considered), but I'm not sure this is what the reader would expect given all the mentions about DG.

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W3. Absence of a comprehensive review of related work. Some directly-related methods are correctly cited/discussed throughout the paper, but there are other connected areas that are not really discussed (examples below).

[1,2] discuss conditions under which environment discovery is possible. I think the theoretical statements in [1] are particularly important to discuss (I am not sure how the proposed method overcomes the impossibility stated in that paper; see also W5). [3] was an early method that also proposed to "unshuffle" data (a term used in this paper) by simply clustering the data. Looking at the visualizations of discovered "environments" in Fig. 3, one wonders if these could also be discovered with such as simple clustering baseline. [4] is another recent method that also seems to claim discovering partitions in the data (I suspect it has similar flaws to those discussed in the paper; it has appeared at ICCV 2023 after the ICLR deadline so it's totally fine to dismiss it though).

[1] ZIN When and How to Learn Invariance Without Environment Partition

[2] Provably Invariance Learning without Domain Information

[3] Unshuffling data for improved generalization

[4] Invariant Feature Regularization for Fair Face Recognition

[5] Agree to Disagree: Diversity through Disagreement for Better Transferability

[6] Diversify and Disambiguate: Learning From Underspecified Data

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W4: No discussion or empirical exploration of the limitations of the methods. No precise statement of the assumptions on which the method relies.

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Minor comments (no need to comment in the rebuttal; these do not affect my rating of the paper)

• W-minor 1. The writing style is unusual for a technical paper. There are many verbose statements, emotional words, exclamation marks, etc. This is actually a great writing style in other circumstances, but it does not maximize the clarity and efficiency of communication. This does not directly affect my rating of the paper, but it made the reading more tedious. I would suggest using a more concise style and neutral tone for the benefit of the readers.

• W-minor 2. The existing methods for environment discovery based on 2 phases is described twice in sections 1 and 3. It could be clearer to merge these. Section 3 is a mix of review/background material/motivation/related work. It's not bad at all in its contents, but it could be easier for the readers to stick with common sections like "related work", "background", etc.

• W-minor 3. Note that the initial premise stated in the very first sentence of the abstract is not really correct (although it does not really affect the rest of the paper): "Successful out-of-distribution generalization requires environment annotations (...) therefore (...) we must develop algorithms to automatically discover environments" Using multiple training environments/domains is only one approach to improve OOD generalization.

I have several concerns as follows:

1. The paper should provide a clear discussion on the identifiability challenges presented in [1], which demonstrate that learning invariance without domain partition can be generally impossible. It is crucial to address the need for imposing inductive bias, additional assumptions, conditions, or auxiliary information to ensure the effectiveness of the proposed method. A thorough exploration of these aspects would enhance the paper's theoretical foundation and its practical applicability.

2. According to [2, 3], spurious features are defined as any nodes in the causal graph other than the direct causes of the label. However, I have concerns about the evaluations conducted on datasets like waterbird, which explicitly contain only one dominating spurious feature. These datasets may not fully reflect the implications of the proposed methods on more realistic and high-dimensional datasets such as ImageNet variants. Moreover, the paper relies on the assumption that Empirical Risk Minimization (ERM) learns spurious features first, but it may not hold true for all types of spurious features as discussed in [2, 3]. It would be valuable to address these concerns and provide further insights into the generalizability of the method to diverse real-world datasets.

3. If a large number of spurious features are present, [1] demonstrates that there are necessary and sufficient conditions for learning invariance without explicit domain partitions, which can be quite restrictive. I have concerns about whether the proposed two-stage method can effectively address this problem given the limitations imposed by these conditions. It would be valuable for the authors to discuss how their method overcomes or accommodates these restrictions and whether it can achieve satisfactory results in scenarios with a significant number of spurious features.

4. Several studies [5, 6] have highlighted the challenges associated with learning invariance in the presence of many spurious features. In a recent paper, [4] discovered that when dealing with a large number of spurious features, each ERM model tends to learn a subset of these features. [4] further demonstrates that rather than exclusively focusing on learning invariant features, it is beneficial for OOD performance to diversify the learned spurious features (referred to as spurious feature diversification). Spurious feature diversification is shown to explain the effectiveness of empirically strong methods like SWAD and Model soup. It would be valuable to investigate whether the proposed method (XRM) can enhance spurious feature diversification and demonstrate effective performance on a broader range of real-world datasets, such as PACS, OfficeHome, DomainNet, or ImageNet variants.

Correct me if I was wrong. I would increase the score if (part of) my concerns were addressed.

[1] Yong Lin et.al., ZIN: When and how to learn invariance without domain partition.

[2] Martin Arjovsky et.al., Invariant Risk Minimization

[3] Jonas Peters, et.al.,. Causal inference using invariant prediction: identification and confidence intervals

[4] Yong Lin et.al., Spurious Feature Diversification Improves Out-of-distribution Generalization

[5] Ishaan Gulrajani et.al., In Search of Lost Domain Generalization

[6] Elan Rosenfeld et.al., The Risks of Invariant Risk Minimization

[7] Junbum Cha et.al., SWAD: Domain Generalization by Seeking Flat Minima

[8] Mitchell Wortsman et.al., Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time

1. The paper's claims may be slightly overstated. While the focus on subpopulation shift in distribution shift is indeed important, it might be more appropriate to avoid claiming to solve a long-standing problem in out-of-distribution generalization without further empirical studies on widely recognized DG benchmarks such as DomainBed and Wilds. These additional experiments could provide more convincing evidence of the proposed approach's effectiveness.
2. The paper lacks a comprehensive discussion of important related works concerning data splitting strategies for improved DG performance and subpopulation shift, such as references [1], [2], [3] and [4]. Notably, in [1], the authors have theoretically demonstrated the challenges of learning the invariant correlation between samples and labels in the absence of prior information. Including these relevant works would enhance the paper's literature review and contextualize the proposed approach.

Typo:

In the first sentence of the paragraph above section 4.2, it appears that the authors have inadvertently added a redundant "we.”

[1] ZIN: When and How to Learn Invariance Without Environment Partition? [2] Provably Invariant Learning without Domain Information. [3] Rethinking Invariant Graph Representation Learning without Environment Partitions. [4] Just Mix Once: Worst-group Generalization by Group Interpolation.