Switching One-Versus-the-Rest Loss to Increase Logit Margins for Adversarial Robustness

Sekitoshi Kanai, Shin'ya Yamaguchi, Masanori Yamada, Hiroshi Takahashi, Kentaro Ohno, Yasutoshi Ida

Keywords: Adversarial examples, Deep learning, Loss function, Adversarial training

TL;DR: We prove that one-versus-rest loss (OVR) increases logit margins two times greater than cross-entropy and propose switching between cross-entropy and OVR by the criterion of logit margins to improve adversarial robustness.

Abstract: Adversarial training is a promising method to improve the robustness against adversarial attacks. To enhance its performance, recent methods impose high weights on the cross-entropy loss for important data points near the decision boundary. However, these importance-aware methods are vulnerable to sophisticated attacks, e.g., Auto-Attack. In this paper, we experimentally investigate the cause of their vulnerability via margins between logits for the true label and the other labels because they should be large enough to prevent the largest logit from being flipped by the attacks. Our experiments reveal that the histogram of the logit margins of naive adversarial training has two peaks. Thus, the levels of difficulty in increasing logit margins are roughly divided into two: difficult samples (small logit margins) and easy samples (large logit margins). On the other hand, only one peak near zero appears in the histogram of importance-aware methods, i.e., they reduce the logit margins of easy samples. To increase logit margins of difficult samples without reducing those of easy samples, we propose switching one-versus-the-rest loss (SOVR), which switches from cross-entropy to one-versus-the-rest loss (OVR) for difficult samples. We derive trajectories of logit margins for a simple problem and prove that OVR increases logit margins two times larger than the weighted cross-entropy loss. Thus, SOVR increases logit margins of difficult samples, unlike existing methods. We experimentally show that SOVR achieves better robustness against Auto-Attack than importance-aware methods.

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