Lu Wang, Xuanqing Liu, Jinfeng Yi, Yuan Jiang, Cho-Jui Hsieh
Metric learning is an important family of algorithms for classiﬁcation and similarity search, but the robustness of learned metrics against small adversarial perturbations is less studied. In this paper, we show that existing metric learning algorithms, which focus on boosting the clean accuracy, can result in metrics that are less robust than the Euclidean distance. To overcome this problem, we propose a novel metric learning algorithm to ﬁnd a Mahalanobis distance that is robust against adversarial perturbations, and the robustness of the resulting model is certiﬁable. Experimental results show that the proposed metric learning algorithm improves both certiﬁed robust errors and empirical robust errors (errors under adversarial attacks). Furthermore, unlike neural network defenses which usually encounter a trade-off between clean and robust errors, our method does not sacriﬁce clean errors compared with previous metric learning methods.