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There has been a recent surge in single-step adversarial training as it showsrobustness and efficiency. However, a phenomenon referred to as ``catastrophicoverfitting" has been observed, which is prevalent in single-step defenses andmay frustrate attempts to use FGSM adversarial training. To address this issue,we propose a novel method, Stable and Efficient Adversarial Training (SEAT),which mitigates catastrophic overfitting by harnessing on local properties thatdistinguish a robust model from that of a catastrophic overfitted model. Theproposed SEAT has strong theoretical justifications, in that minimizing theSEAT loss can be shown to favour smooth empirical risk, thereby leading torobustness. Experimental results demonstrate that the proposed methodsuccessfully mitigates catastrophic overfitting, yielding superior performanceamongst efficient defenses. Our single-step method can reach 51% robustaccuracy for CIFAR-10 with $l_\infty$ perturbations of radius $8/255$ under astrong PGD-50 attack, matching the performance of a 10-step iterativeadversarial training at merely 3% computational cost.

Stable and Efficient Adversarial Training through Local Linearization