Adversarial training integrates adversarial examples during model training to enhance robustness. However, its application in fixed dataset settings differs from real-world dynamics, where data accumulates incrementally. In this study, we investigate Adversarially Robust Class Incremental Learning (ARCIL), a method that combines adversarial robustness with incremental learning. We observe that combining incremental learning with naive adversarial training easily leads to a loss of robustness. We discover that this is attributed to the disappearance of the flatness of the loss function, a characteristic of adversarial training. To address this issue, we propose the Flatness Preserving Distillation (FPD) loss that leverages the output difference between adversarial and clean examples. Additionally, we introduce the Logit Adjustment Distillation (LAD) loss, which adapts the model's knowledge to perform well on new tasks. Experimental results demonstrate the superiority of our method over approaches that apply adversarial training to existing incremental learning methods, which provides a strong baseline for incremental learning on adversarial robustness in the future. Our method achieves AutoAttack accuracy that is 5.99\%p, 5.27\%p, and 3.90\%p higher on average than the baseline on split CIFAR-10, CIFAR-100, and Tiny ImageNet, respectively. The code will be made available.

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