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We propose to study and promote the robustness of a model as per itsperformance through the interpolation of training data distributions.Specifically, (1) we augment the data by finding the worst-case Wassersteinbarycenter on the geodesic connecting subpopulation distributions of differentcategories. (2) We regularize the model for smoother performance on thecontinuous geodesic path connecting subpopulation distributions. (3)Additionally, we provide a theoretical guarantee of robustness improvement andinvestigate how the geodesic location and the sample size contribute,respectively. Experimental validations of the proposed strategy on\textit{four} datasets, including CIFAR-100 and ImageNet, establish theefficacy of our method, e.g., our method improves the baselines' certifiablerobustness on CIFAR10 up to $7.7\%$, with $16.8\%$ on empirical robustness onCIFAR-100. Our work provides a new perspective of model robustness through thelens of Wasserstein geodesic-based interpolation with a practical off-the-shelfstrategy that can be combined with existing robust training methods.

Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesics