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Since adversarial examples appeared and showed the catastrophic degradationthey brought to DNN, many adversarial defense methods have been devised, amongwhich adversarial training is considered the most effective. However, a recentwork showed the inequality phenomena in $l_{\infty}$-adversarial training andrevealed that the $l_{\infty}$-adversarially trained model is vulnerable when afew important pixels are perturbed by i.i.d. noise or occluded. In this paper,we propose a simple yet effective method called Input Gradient Distillation(IGD) to release the inequality phenomena in $l_{\infty}$-adversarial training.Experiments show that while preserving the model's adversarial robustness,compared to PGDAT, IGD decreases the $l_{\infty}$-adversarially trained model'serror rate to inductive noise and inductive occlusion by up to 60\% and16.53\%, and to noisy images in Imagenet-C by up to 21.11\%. Moreover, weformally explain why the equality of the model's saliency map can improve suchrobustness.

Releasing Inequality Phenomena in $L_{\infty}$-Adversarial Training via Input Gradient Distillation