Title: Regularizing hard examples improves robustness. Abstract: Recent studies have validated that pruning hard-to-learn examples from training improves the generalization performance of neural networks (NNs). In this study, we investigate this intriguing phenomenon—the negative effect of hard examples on generalization—in adversarial training. Particularly, we theoretically demonstrate that the increase in the difficulty of hard examples in adversarial training is significantly greater than the increase in the difficulty of easy examples. Furthermore, we verify that hard examples are only fitted through memorization of the label in adversarial training and that the memorization of hard examples is attributed to the significant increase in the difficulty of hard examples. We find that the increased difficulty of hard examples brings about the functioning of hard examples as label corrupted data in adversarial training, thereby leading to the memorization of those hard examples and deterioration of the robustness performance. Based upon these observations, we propose a new approach, difficulty proportional label smoothing (DPLS), to mitigate the negative effect of hard examples, thereby improving the adversarial robustness of NNs. Notably, our experimental result indicates that our method can successfully leverage hard examples while circumventing the negative effect.