Adversarially Robust Models may not Transfer Better: Sufficient Conditions for Domain Transferability from the View of Regularization
This work addresses the theoretical gap in understanding how adversarial robustness relates to domain generalization for machine learning researchers, offering a nuanced perspective that challenges common assumptions.
The paper tackles the relationship between adversarial robustness and domain generalization, showing through theoretical analysis and experiments that robustness is neither necessary nor sufficient for transferability, with regularization being a more fundamental factor, and provides counterexamples where robustness and generalization are negatively correlated.
Machine learning (ML) robustness and domain generalization are fundamentally correlated: they essentially concern data distribution shifts under adversarial and natural settings, respectively. On one hand, recent studies show that more robust (adversarially trained) models are more generalizable. On the other hand, there is a lack of theoretical understanding of their fundamental connections. In this paper, we explore the relationship between regularization and domain transferability considering different factors such as norm regularization and data augmentations (DA). We propose a general theoretical framework proving that factors involving the model function class regularization are sufficient conditions for relative domain transferability. Our analysis implies that ``robustness" is neither necessary nor sufficient for transferability; rather, regularization is a more fundamental perspective for understanding domain transferability. We then discuss popular DA protocols (including adversarial training) and show when they can be viewed as the function class regularization under certain conditions and therefore improve generalization. We conduct extensive experiments to verify our theoretical findings and show several counterexamples where robustness and generalization are negatively correlated on different datasets.