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能。具体而言：(1) 通过寻找连接不同类别子群分布测地线上的最坏情况Wasserstein重心进行数据增强；(2) 沿连接子群分布的连续测地线路径对模型进行正则化处理，以获取更平滑的性能表现；(3) 同时给出鲁棒性提升的理论保证，并分别探究测地线位置与样本规模对鲁棒性的贡献。在包含CIFAR-100和ImageNet在内的四个数据集上的实验验证表明，本方法具有显著有效性——例如，在CIFAR-10上将基线模型的可证明鲁棒性提升至$7.7\%$，在CIFAR-100上实证鲁棒性提升达$16.8\%$。我们的工作通过Wasserstein测地线插值视角为模型鲁棒性研究提供了新思路，并提供了一种可直接与现有鲁棒训练方法结合的实用现成策略。