Subspace Adversarial Training

Single-step adversarial training (AT) has received wide attention as it proved to be both efficient and robust. However, a serious problem of catastrophic overfitting exists, i.e., the robust accuracy against projected gradient descent (PGD) attack suddenly drops to $0\%$ during the training. In this paper, we understand this problem from a novel perspective of optimization and firstly reveal the close link between the fast-growing gradient of each sample and overfitting, which can also be applied to understand the robust overfitting phenomenon in multi-step AT. To control the growth of the gradient during the training, we propose a new AT method, subspace adversarial training (Sub-AT), which constrains the AT in a carefully extracted subspace. It successfully resolves both two kinds of overfitting and hence significantly boosts the robustness. In subspace, we also allow single-step AT with larger steps and larger radius, which further improves the robustness performance. As a result, we achieve the state-of-the-art single-step AT performance: our pure single-step AT can reach over $\mathbf{51}\%$ robust accuracy against strong PGD-50 attack with radius $8/255$ on CIFAR-10, even surpassing the standard multi-step PGD-10 AT with huge computational advantages. The code is released$\footnote{\url{https://github.com/nblt/Sub-AT}}$.