Perturbation diversity certificates robust generalization

Whilst adversarial training has been proven to be one most effective defending method against adversarial attacks for deep neural networks, it suffers from over -fitting on training adversarial data and thus may not guarantee the robust generalization. This may result from the fact that the conventional adversarial training methods generate adversarial perturbations usually in a supervised way so that the resulting adversarial examples are highly biased towards the decision boundary, leading to an inhomogeneous data distribution. To mitigate this limitation, we propose to generate adversarial examples from a perturbation diversity perspective. Specifically, the generated perturbed samples are not only adversarial but also diverse so as to certify robust generalization and significant robustness improvement through a homogeneous data distribution. We provide theoretical and empirical analysis, establishing a foundation to support the proposed method. As a major contribution, we prove that promoting perturbations diversity can lead to a better robust generalization bound. To verify our methods' effectiveness, we conduct extensive experiments over different datasets (e.g., CIFAR10, CIFAR-100, SVHN) with different adversarial attacks (e.g., PGD, CW). Experimental results show that our method outperforms other state-of-the-art (e.g., PGD and Feature Scattering) in robust generalization performance.