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Recent research on the robustness of deep learning has shown that VisionTransformers (ViTs) surpass the Convolutional Neural Networks (CNNs) under someperturbations, e.g., natural corruption, adversarial attacks, etc. Some papersargue that the superior robustness of ViT comes from the segmentation of itsinput images; others say that the Multi-head Self-Attention (MSA) is the key topreserving the robustness. In this paper, we aim to introduce a principled andunified theoretical framework to investigate such an argument on ViT'srobustness. We first theoretically prove that, unlike Transformers in NaturalLanguage Processing, ViTs are Lipschitz continuous. Then we theoreticallyanalyze the adversarial robustness of ViTs from the perspective of the CauchyProblem, via which we can quantify how the robustness propagates throughlayers. We demonstrate that the first and last layers are the critical factorsto affect the robustness of ViTs. Furthermore, based on our theory, weempirically show that unlike the claims from existing research, MSA onlycontributes to the adversarial robustness of ViTs under weak adversarialattacks, e.g., FGSM, and surprisingly, MSA actually comprises the model'sadversarial robustness under stronger attacks, e.g., PGD attacks.

Understanding Adversarial Robustness of Vision Transformers via Cauchy Problem