Semi-supervised robust training with generalized perturbed neighborhood. (April 2022) - Li, Yiming; Wu, Baoyuan; Feng, Yan; Fan, Yanbo; Jiang, Yong; Li, Zhifeng; Xia, Shu-Tao
Highlights: We propose a robust training method by jointly minimizing standard risk and robust risk, which is naturally extended the semi-supervised mode. By generalizing the definition of the perturbed neighborhood to cover different types of perturbations, our method achieves the joint robustness to different perturbations, such as the pixel-wise and spatial perturbation. Experiments on benchmark datasets verify the superiority of the proposed SRT method to state-of-the-art adversarial training methods, as well as the robustness of SRT to pixel-wise and spatial perturbations simultaneously. Abstract: Adversarial examples have been shown to be a 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 a d v, which encourages both the benign example x and its adversarially perturbed neighborhoods within the ℓ p -ball to be predicted as the ground-truth label. In this paper, we propose a novel defense method, the robust training (RT), by jointly minimizing two separated risks ( i . e ., R s t a n d and R r o b ), which are 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 a d v is upper-bounded by R s t a n d + R r o b, which implies that RT has similar effect as AT. Intuitively, minimizing the standard risk enforces the benign example to be correctly predicted, while the robust risk minimization encourages the predictions of the neighbor examples to be consistent with the prediction of the benign example. Besides, since R r o b is independent of the ground-truth label, RT is naturally extended to the semi-supervised mode ( i . e ., SRT), to further enhance its effectiveness. Moreover, we extend the ℓ p -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 ., A x + b ). Extensive experiments on benchmark datasets not only verify the superiority of the proposed SRT to state-of-the-art methods for defending pixel-wise or spatial perturbations separately but also demonstrate its robustness to both perturbations simultaneously. Our work may shed the light on the understanding of universal model robustness and the potential of unlabeled samples. The code for reproducing main results is available at https://github.com/THUYimingLi/Semi-supervised_Robust_Training .