Abstract: The emergence of adversarial attacks poses a substantial threat to the large-scale deployment of deep neural networks(DNNs) in real-world scenarios,especially in security-related domains.Most of the current defense methods are based on heuristic assumptions and lack analysis of model robustness.How to improve the robustness of DNN and improve the interpretability and credibility of the robustness has become an essential part of the field of artificial intelligence security.This paper proposes to analyze the robustness of the model from the perspective of singular values.In the adversarial environment,the improvement of model robustness is accompanied by a smoother distribution of singular values.Further analysis shows that the smooth distribution of singular values means that the model has more diverse classification confidence sources and thus has higher adversarial robustness.Based on the analysis,an adversarial training algorithm based on singular value suppress(SVS) is proposed.Experiments show that the algorithm improves the robustness of the model and can achieve accuracy of 55.3% and 54.51% respectively on CIFAR-10 and SVHN when facing the powerful white-box attack PGD(Project Gradient Descent) method,exceeding the most representative adversarial training methods at present.

Key words: Deep learning, Adversarial defense, Adversarial training, Adversarial robustness, Singular value decomposition