Our goal is to understand why the robustness drops after conducting adversarial training for too long. Although this phenomenon is commonly explained as overfitting, our analysis suggest that its primary cause is perturbation underfitting. We observe that after training for too long, FGSM-generated perturbations deteriorate into random noise. Intuitively, since no parameter updates are made to strengthen the perturbation generator, once this process collapses, it could be trapped in such local optima. Also, sophisticating this process could mostly avoid the robustness drop, which supports that this phenomenon is caused by underfitting instead of overfitting. In the light of our analyses, we propose APART, an adaptive adversarial training framework, which parameterizes perturbation generation and progressively strengthens them. Shielding perturbations from underfitting unleashes the potential of our framework. In our experiments, APART provides comparable or even better robustness than PGD-10, with only about 1/4 of its computational cost.
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