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In this paper we study leveraging confidence information induced byadversarial training to reinforce adversarial robustness of a givenadversarially trained model. A natural measure of confidence is $\|F({\bfx})\|_\infty$ (i.e. how confident $F$ is about its prediction?). We start byanalyzing an adversarial training formulation proposed by Madry et al.. Wedemonstrate that, under a variety of instantiations, an only somewhat goodsolution to their objective induces confidence to be a discriminator, which candistinguish between right and wrong model predictions in a neighborhood of apoint sampled from the underlying distribution. Based on this, we proposeHighly Confident Near Neighbor (${\tt HCNN}$), a framework that combinesconfidence information and nearest neighbor search, to reinforce adversarialrobustness of a base model. We give algorithms in this framework and perform adetailed empirical study. We report encouraging experimental results thatsupport our analysis, and also discuss problems we observed with existingadversarial training.

Reinforcing Adversarial Robustness using Model Confidence Induced by Adversarial Training