Singular Regularization with Information Bottleneck Improves Model's Adversarial Robustness

Adversarial examples are one of the most severe threats to deep learning models. Numerous works have been proposed to study and defend adversarial examples. However, these works lack analysis of adversarial information or perturbation, which cannot reveal the mystery of adversarial examples and lose proper interpretation. In this paper, we aim to fill this gap by studying adversarial information as unstructured noise, which does not have a clear pattern. Specifically, we provide some empirical studies with singular value decomposition, by decomposing images into several matrices, to analyze adversarial information for different attacks. Based on the analysis, we propose a new module to regularize adversarial information and combine information bottleneck theory, which is proposed to theoretically restrict intermediate representations. Therefore, our method is interpretable. Moreover, the fashion of our design is a novel principle that is general and unified. Equipped with our new module, we evaluate two popular model structures on two mainstream datasets with various adversarial attacks. The results indicate that the improvement in robust accuracy is significant. On the other hand, we prove that our method is efficient with only a few additional parameters and able to be explained under regional faithfulness analysis.