  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.
