Papers › Toward Adversarial Robustness via Semi-supervised Robust Training
Toward Adversarial Robustness via Semi-supervised Robust Training
Yiming Li, Baoyuan Wu, Yan Feng, Yanbo Fan, Yong Jiang, Zhifeng Li, Shu-Tao Xia
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 R_(adv), 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 (R_(stand) and R_(rob)), 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 R_(adv) is upper-bounded by R_(stand) + R_(rob), 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 R_(rob) 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 \url{https://github.com/THUYimingLi/Semi-supervised_Robust_Training}.
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