Towards Certified Robustness of Distance Metric Learning

• URL: http://arxiv.org/abs/2006.05945v2
• Date: Tue, 16 Aug 2022 15:16:12 GMT
• Title: Towards Certified Robustness of Distance Metric Learning
• Authors: Xiaochen Yang, Yiwen Guo, Mingzhi Dong, Jing-Hao Xue
• Abstract summary: We advocate imposing an adversarial margin in the input space so as to improve the generalization and robustness of metric learning algorithms. We show that the enlarged margin is beneficial to the generalization ability by using the theoretical technique of algorithmic robustness.
• Score: 53.96113074344632
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Metric learning aims to learn a distance metric such that semantically similar instances are pulled together while dissimilar instances are pushed away. Many existing methods consider maximizing or at least constraining a distance margin in the feature space that separates similar and dissimilar pairs of instances to guarantee their generalization ability. In this paper, we advocate imposing an adversarial margin in the input space so as to improve the generalization and robustness of metric learning algorithms. We first show that, the adversarial margin, defined as the distance between training instances and their closest adversarial examples in the input space, takes account of both the distance margin in the feature space and the correlation between the metric and triplet constraints. Next, to enhance robustness to instance perturbation, we propose to enlarge the adversarial margin through minimizing a derived novel loss function termed the perturbation loss. The proposed loss can be viewed as a data-dependent regularizer and easily plugged into any existing metric learning methods. Finally, we show that the enlarged margin is beneficial to the generalization ability by using the theoretical technique of algorithmic robustness. Experimental results on 16 datasets demonstrate the superiority of the proposed method over existing state-of-the-art methods in both discrimination accuracy and robustness against possible noise.

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