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Deep models often fail to generalize well in test domains when the datadistribution differs from that in the training domain. Among numerousapproaches to address this Out-of-Distribution (OOD) generalization problem,there has been a growing surge of interest in exploiting Adversarial Training(AT) to improve OOD performance. Recent works have revealed that the robustmodel obtained by conducting sample-wise AT also retains transferability tobiased test domains. In this paper, we empirically show that sample-wise AT haslimited improvement on OOD performance. Specifically, we find that AT can onlymaintain performance at smaller scales of perturbation while Universal AT (UAT)is more robust to larger-scale perturbations. This provides us with clues thatadversarial perturbations with universal (low dimensional) structures canenhance the robustness against large data distribution shifts that are commonin OOD scenarios. Inspired by this, we propose two AT variants with low-rankstructures to train OOD-robust models. Extensive experiments on DomainBedbenchmark show that our proposed approaches outperform Empirical RiskMinimization (ERM) and sample-wise AT. Our code is available athttps://github.com/NOVAglow646/NIPS22-MAT-and-LDAT-for-OOD.

Improving Out-of-Distribution Generalization by Adversarial Training with Structured Priors