Toward Adversarial Robustness via Semi-supervised Robust Training

Abstract

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 ${\ell }_p$-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 ${\ell }_p$-bounded neighborhood to a general case, which covers different types of perturbations, such as the pixel-wise ($i.e.$, $x+\delta$) 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}.

arXiv comment19 pages

References in corpus (11)

• Wide Residual Networks
• Theoretically Principled Trade-off between Robustness and Accuracy
• Towards Deep Neural Network Architectures Robust to Adversarial Examples
• Fast is better than free: Revisiting adversarial training
• Exploring the Landscape of Spatial Robustness
• Towards the first adversarially robust neural network model on MNIST
• On Detecting Adversarial Perturbations
• Adversarial Robustness through Local Linearization
• Are Labels Required for Improving Adversarial Robustness?
• advertorch v0.1: An Adversarial Robustness Toolbox based on PyTorch
• First-order Adversarial Vulnerability of Neural Networks and Input Dimension

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