Paper: Learning to ignore: Single Source Domain Generalization via Oracle Regularization (ICLR-2024)

Reviewer comment (Experiments):
Lack of Comprehensive Ablation Study. The loss function of the task model, as presented in equation (2), comprises several loss terms, each containing multiple sub-components. Without a thorough ablation study, it's challenging to understand the contribution of each sub-component towards the overall DG performance or to verify that the combination proposed by the authors is indeed the most effective. Specific questions that arise from this include, but are not limited to:  
- What would the results be if the last two terms in equation (2) were removed, i.e., simply using the examples generated by the generator alongside the original examples in ERM training?  
- How does the oracle model alone perform on the DG task? Given that the oracle model is trained on a much larger dataset, it may already see images in varying styles. Is the DG performance improvement in PROF mainly due to domain leakage from the oracle model?  
- How crucial are D and P, and the Barlow Twins in equations (3) and (5)? What would the results look like if simple feature matching/logit matching/probability matching were used instead?  
- What would be the impact of using a different number of augmented views in equation (5)?  
- Could the authors provide more rationale behind the current generator's design? Is there a specific reason it must be designed this way? How would the results be affected if a different generator was used?  
These questions highlight the need for a more detailed ablation study to fully understand and validate the proposed method. Without such an analysis, it's reasonable to question the necessity of each component and specific design.

Author response:
# Ablation Study

> "What would the results be if the last two terms in equation (2) were removed, i.e., simply using the examples generated by the generator alongside the original examples in ERM training?"
- **Alignment is helpful in increasing both ID and OOD performance. We include a new experiment result to show this.** Using simply the cross-entropy loss, the OOD performance drops. In Digits, the average score is 68.10. This is significantly lower than both PROF(81.82) and our baseline MDAR(78.80) The effect of using the augment & alignment method was studied earlier in the sDG literature and the field of self-supervised learning(e.g., Supervised Contrastive Learning [1]). Empirically, we add an experimental result on the effect of alignment.
- Without Alignment, the OOD generalization score is: mnist_m: 73.06/ usps: 81.56/ svhn: 56.47/ syndigit: 62.35

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> "How does the oracle model alone perform on the DG task? ... Is the DG performance improvement in PROF mainly due to domain leakage from the oracle model?"
- **Information on the performance of oracles is included in Appendix D. On Oracles.** We utilized pretrained models which are expected to exist in many real-world cases. The oracle we used (i.e., RegNet-Y-16GF) is pretrained on the Instagram dataset.
- **We believe that domain leakage has not taken place.** If there were a domain leakage, the OOD results should be much higher than what we have presented. This can be inferred from the result in Table 3, where PROF outperformed conventional methods by a large gap.

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> "How crucial are D and P, and the Barlow Twins in equations (3) and (5)? What would the results look like if simple feature matching/logit matching/probability matching were used instead?"
- **The role of projection heads is a long, studied topic in the field of self-supervised learning.** To us, the role of the projection head was significant as the cost of directly aligning the feature outputs of H_o and H (two vectors of length 3024) is immensively expensive. We have also tested the method of relational knowledge distillation [2], but could not produce similar results as PROF. We have not used logit matching methods, as we did not aim to use the classification layer, as it is fitted to the original task.
- **Barlow Twins is very helpful in converging the alignment loss**, mainly because it works well on small batch sizes, hence fit for our cases such as PACS.

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> "What would be the impact of using a different number of augmented views in equation (5)?"
- **Raising the number of augmented views in the alignment optimization affects the generalizability of the task model.** With its optimum being 3~4. This was originally studied in the field of self-supervised learning, where increasing the number of augmented views significantly helps performance ( Please refer to Section 11. of Khosla et al. (2021) [1]), However, raising this number increases the cost, with very marginal gains in OOD generalizability after a certain point.

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> "Could the authors provide more rationale behind the current generator's design? Is there a specific reason it must be designed this way? How would the results be affected if a different generator was used?"
- **The generator design follows the work of Li et al. (2021).** As mentioned in the paper, the generator design follows the work of Li et al. (2021). The authors presented a progressive domain expansion method via augmentation. This method fits our case as we aim to mitigate issues derived by repetitive augmentation.

***
[1] Khosla et al. Supervised Contrastive Learning, 2021.
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[2] Park et al., Relational Knowledge Distillation, 2019.

Reviewer comment (Theory):
While the critique of sDG methods and the subsequent motivation for the proposed method is commendable, mere verbal analysis falls short of expectations. There appears to be a void in terms of rigorous theoretical groundwork. Specifically, the paper lacks a deep theoretical analysis, such as the provision of a generalization bound, that sheds light on the functioning and merits of PROF.

Author response:
**We provide an analysis from the causal perspective, using the insight of a previous work from a different domain.** The focus of our work lies in approaching the generalization problem from a causal perspective, focusing on the effect of data augmentation. Our work adopts the identification process of the causal model from the work of Kugelgen et al. (2021) [1] but provides a new perspective on the causal model with the inclusion of the domain variable D. This is elaborated in Section 3. A causal interpretation of data augmentation.

Reviewer comment (Writing):
In the abstract, it is mentioned “analyzing the data generating process“. But, I did not find any explicit explanations in the main paper.

Author response:
> "In the abstract, it is mentioned “analyzing the data generating process“. But, I did not find any explicit explanations in the main paper."  
- Regarding your note on the absence of explicit analysis on “the data generating process”, we ask you to refer to Section 3. “A causal interpretation of data augmentation” on page 3.

Reviewer comment (Evaluation):
The experimental results and the analysis mention that the proposed PROF regularizer only performs well under some large domain shift scenarios. Will this limit the application and the contribution of the proposed method?

Author response:
> "The experimental results and the analysis mention that the proposed PROF regularizer only performs well under some large domain shift scenarios. Will this limit the application and the contribution of the proposed method?"  
- **PROF can be used for both large/small distribution shifts, but intended for large shifts.** We believe that for small domain shifts (e.g., image corruption), data augmentation is sufficient. However, this approach would not work between large domain shifts. Intuitively, it is not easy to imagine augmenting a photo of a dog with a cartoon image of a dog. While recent progress in generative models may help this issue, such methods are costly, and hence not readily available for use.

Reviewer comment (Novelty):
What is the difference or the benefit of the proposed baseline MDAR, compared with other augment and align methods?

Author response:
> "What is the difference or the benefit of the proposed baseline MDAR, compared with other augment and align methods?"   
- **MDAR is a strong baseline. We use it for fair comparison against PROF.** We design MDAR as a fair baseline against PROF. MDAR works well on small batch sizes as it uses a non-contrastive alignment loss [2]. Hence compared to conventional methods, MDAR converges better than conventional alignment objectives (e.g., Supervised Contrastive Loss).

Reviewer comment (Experiments):
As the PROF aims to guide the task model to learn more domain-invariant knowledge from the oracle model, I think a study of different oracle models’ influence is necessary.

Author response:
> "I think a study of different oracle models’ influence is necessary."  
- **We have investigated different oracles.** We showed that for general cases,  a pretrained model trained on photo images (e.g., RegNet-Y-16GF) is effective for oracle regularization. Naturally, such a model may not work for digit classification tasks. The extensive analysis of oracles is reported in Appendix D. *On Oracles*.

Reviewer comment (Evaluation):
While measuring the mid-train fluctuations, are the results an average of multiple experiments or a single experiment? Is it statistically significant?

Author response:
> "While measuring the mid-train fluctuations, are the results an average of multiple experiments or a single experiment? Is it statistically significant?"  
- **Mid-train fluctuation is prevalent, and PROF repetitively stabilizes it.** The mid-train fluctuations are the results of individual experiments, but we observe that OOD fluctuation exists on every run. This matches the fluctuations reported in Arpit et al., (2022) [1]. We view this issue as a significant threat to the credibility of the model.

Reviewer comment (Writing):
It is currently very difficult to follow and understand what, precisely, is the problem being solved, why it is important, and what is the exact novel idea being contributed. Sections 2 & 3 introduce numerous concepts (causal graphs, augmentation, training dynamics, distillation, etc.) from previous work, but do not clearly explain why these observations should form the logical starting point of a system for single-source domain generalization.

Author response:
> "it’s very difficult to follow and understand what, precisely, is the problem being solved, why we should care, and what is the exact novel idea being contributed"

- **We answer the question: Is augmentation reliable for generalization?** To our understanding, the focus of the sDG task lies in designing effective data augmentation techniques to improve model robustness. However, existing works on sDG often overlook the discussion on the safety of using augmentation for robustness. Our work questions this very point, “Is augmentation reliable for generalization?”
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> "why these observations should form the logical starting point of a system for single source domain generalization"

- **We illuminate an overlooked uncertainty of data augmentation using causality.** To answer this question, we start from a causal perspective. The causal examination aims to understand the underlying mechanism of data augmentation. Using a causal model, we reveal that data augmentation in the sDG setting does not promise domain-invariance. While we adopt the results of Kugelgen et al. (2021) [1], we are different from their work in the sense that we add an additional variable into the model, the domain variable D. To the best of our knowledge, this is the first work to utilize causal models to reveal the uncertainty of augmentation-based sDG.

Reviewer comment (Novelty):
Figure 2 illustrates the system, which has a surprisingly large number of components – ensembling of generators, augmentation schemes, distillation from an oracle, an oracle regularizer, and the use of a multi-domain alignment loss – many of which are adapted from previous works. It is not clear why this specific combination of components is useful, which ones are new, and how these pieces work together.

Author response:
> "Figure 2 illustrates the system which has a surprisingly large number of components"

- **Our data augmentation module is intended to observe the long-term effect of data augmentation on generalizability.** As mentioned in the second line of Section 4.3., the aim of the complex data augmentation module is to allow repetitive augmentation. Unlike random data augmentation, our adversarial augmentation creates augmented views that are supposedly helpful for OOD robustness. Nonetheless, even in this case, the phenomenon of OOD fluctuation is present. As for now, PROF is the first method to significantly mitigate such issues. In a similar work of Arpit et al., (2022) [2], the authors used an ensemble of models to mitigate the fluctuation. Ours produces the stabilization effect with a single model.

Reviewer comment (Evaluation):
The results are mixed at best: for example, in Table 2, “Ours” is not better than metaCNN on any column (but is bolded in multiple places incorrectly). Table 3 results are quite variable, and Table 4 has no baseline comparisons.

Author response:
> "The results are mixed at best"
- **Generally, PROF stabilizes the phenomenon of OOD fluctuation, fulfilling its main objective.** We hope to underline that the focus of our method lies in mitigating the uncertainty of augmentation, revealed as the OOD fluctuation phenomenon. To be best of our knowledge, PROF is the only method that directly targets this problem. In this sense, PROF fulfills its objective in the stabilization of OOD performance.
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> "table 4 having no baseline comparisons"
- **The office-home dataset is not a conventional dataset for sDG. But Why?** The Office-Home dataset(Table 4) is not a conventional dataset in the field of sDG. As there are no reported baselines, we used our baseline (MDAR) for comparison. In terms of both OOD fluctuation and generalizability, PROF outperforms the baseline. We hence derive a question: If augmentation can mitigate the problem of distribution shifts, why is it not effective under large distribution shifts?

Reviewer comment (Evaluation):
Although the authors motivate the paper by claiming that PROF is better than augment-and-align as it reduces mid-training OOD fluctuations, they fail to explain the failure modes (e.g., training domain: Cartoon, Target Domain Sketch: 0.70 -> 3.91). More study is required to properly understand when the proposed method becomes unstable.

Author response:
> "they fail to explain the failure modes"
- **The failing cases do not weaken our logic.** As mentioned in Appendix D, we recognize that there are limitations in our method PROF. PROF relies on the idea of a generalized oracle model. From this perspective, our hypothesis on the failing cases is that the pretrained models that we approximate as oracles (e.g., RegNet-Y-16GF) are originally trained on real-photo images. We expect that if the oracle is also trained with cartoon or sketch images, it would show no defects in the reported failing cases.