Toward Adversarial Robustness via Semi-supervised Robust Training

Adversarial examples have been shown to be the severe threat to deep neural networks (DNNs). One of the most effective adversarial defense methods is adversarial training (AT) through minimizing the adversarial risk Radv, which encourages both the benign example x and its adversarially perturbed neighborhoods within the ℓp-ball to be predicted as the ground-truth label. In this work, we propose a novel defense method, the robust training (RT), by jointly minimizing two separated risks (Rstand and Rrob), which is with respect to the benign example and its neighborhoods respectively. The motivation is to explicitly and jointly enhance the accuracy and the adversarial robustness. We prove that Radv is upper-bounded by Rstand + Rrob, which implies that RT has similar effect as AT. Intuitively, minimizing the standard risk enforces the benign example to be correctly predicted, and the robust risk minimization encourages the predictions of the neighbor examples to be consistent with the prediction of the benign example. Besides, since Rrob is independent of the ground-truth label, RT is naturally extended to the semi-supervised mode (i.e., SRT), to further enhance the adversarial robustness. Moreover, we extend the ℓp-bounded neighborhood to a general case, which covers different types of perturbations, such as the pixel-wise (i.e., x + δ) or the spatial perturbation (i.e., AX + b). Extensive experiments on benchmark datasets not only verify the superiority of the proposed SRT method to state-of-the-art methods for defensing pixel-wise or spatial perturbations separately, but also demonstrate its robustness to both perturbations simultaneously. The code for reproducing main results is available at urlhttps://github.com/THUYimingLi/Semi-supervisedRobustTraining.