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Deep Neural Networks are vulnerable to adversarial attacks. Among many defense strategies, adversarial training with untargeted attacks is one of the most effective methods. Theoretically, adversarial perturbation in untargeted attacks can be added along arbitrary directions and the predicted labels of untargeted attacks should be unpredictable. However, we find that the naturally imbalanced inter-class semantic similarity makes those hard-class pairs become virtual targets of each other. This study investigates the impact of such closely-coupled classes on adversarial attacks and develops a self-paced reweighting strategy in adversarial training accordingly. Specifically, we propose to upweight hard-class pair losses in model optimization, which prompts learning discriminative features from hard classes. We further incorporate a term to quantify hard-class pair consistency in adversarial training, which greatly boosts model robustness. Extensive experiments show that the proposed adversarial training method achieves superior robustness performance over state-of-the-art defenses against a wide range of adversarial attacks. The code of the proposed SPAT is published at https://github.com/puerrrr/Self-Paced-Adversarial-Training.