Reinforcing Adversarial Robustness using Model Confidence Induced by Adversarial Training

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Xi Wu, Uyeong Jang, Jiefeng Chen, Lingjiao Chen, Somesh Jha ;
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5334-5342, 2018.

Abstract

In this paper we study leveraging confidence information induced by adversarial training to reinforce adversarial robustness of a given adversarially trained model. A natural measure of confidence is $\|F(x)\|_\infty$ (i.e. how confident $F$ is about its prediction?). We start by analyzing an adversarial training formulation proposed by Madry et al.. We demonstrate that, under a variety of instantiations, an only somewhat good solution to their objective induces confidence to be a discriminator, which can distinguish between right and wrong model predictions in a neighborhood of a point sampled from the underlying distribution. Based on this, we propose Highly Confident Near Neighbor (HCNN) a framework that combines confidence information and nearest neighbor search, to reinforce adversarial robustness of a base model. We give algorithms in this framework and perform a detailed empirical study. We report encouraging experimental results that support our analysis, and also discuss problems we observed with existing adversarial training.

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