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

翻译：我们提出通过训练数据分布的插值来研究和提升模型的鲁棒性。具体而言：(1) 我们通过寻找连接不同类别子群分布测地线上的最坏情况Wasserstein重心来实现数据增强；(2) 对模型进行正则化，使其在连接子群分布的连续测地线路径上保持更平滑的性能；(3) 此外，我们提供了鲁棒性提升的理论保证，并分别探究了测地线位置与样本量对鲁棒性的贡献。在包括CIFAR-100和ImageNet在内的四个数据集上的实验验证表明了我们方法的有效性——例如，该方法在CIFAR-10上将基线模型的可证明鲁棒性提升高达7.7%，在CIFAR-100上将经验鲁棒性提升达16.8%。我们的工作通过Wasserstein测地线插值的视角为模型鲁棒性提供了新见解，并提出了一种可即插即用的实用策略，能够与现有鲁棒训练方法相结合。