Rectifying Adversarial Sample with Low Entropy Prior for Test-Time Defense

Abstract

Existing defense methods fail to defend against unknown attacks and thus raise generalization issue of adversarial robustness. To remedy this problem, we attempt to delve into some underlying common characteristics among various attacks for generality. In this work, we reveal the commonly overlooked low entropy prior (LE) implied in various adversarial samples, and shed light on the universal robustness against unseen attacks in inference phase. LE prior is elaborated as two properties across various attacks as shown in Fig. 1 and Fig. 2: 1) low entropy misclassification for adversarial samples and 2) lower entropy prediction for higher attack intensity. This phenomenon stands in stark contrast to the naturally distributed samples. The LE prior can instruct existing test-time defense methods, thus we propose a two-stage REAL approach: Rectify Adversarial sample based on LE prior for test-time adversarial rectification. Specifically, to align adversarial samples more closely with clean samples, we propose to first rectify adversarial samples misclassified with low entropy by reverse maximizing prediction entropy, thereby eliminating their adversarial nature. To ensure the rectified samples can be correctly classified with low entropy, we carry out secondary rectification by forward minimizing prediction entropy, thus creating a Max-Min entropy optimization scheme. Further, based on the second property, we propose an attack-aware weighting mechanism to adaptively adjust the strengths of Max-Min entropy objectives. Experiments on several datasets show that REAL can greatly improve the performance of existing sample rectification models.