Data-Driven Lipschitz Continuity: A Cost-Effective Approach to Improve Adversarial Robustness

As deep neural networks (DNNs) are increasingly deployed in sensitive applications, ensuring their security and robustness has become critical. A major threat to DNNs arises from adversarial attacks, where small input perturbations can lead to incorrect predictions. Recent advances in adversarial training improve robustness by incorporating additional examples from external datasets or generative models. However, these methods often incur high computational costs, limiting their practicality and hindering real-world deployment. In this paper, we propose a cost-efficient alternative based on Lipschitz continuity that achieves robustness comparable to models trained with extensive supplementary data. Unlike conventional adversarial training, our method requires only a single pass over the dataset without gradient estimation, making it highly efficient. Furthermore, our method can integrate seamlessly with existing adversarial training frameworks and enhances the robustness of models without requiring extra generative data. Experimental results show that our approach not only reduces computational overhead but also maintains or improves the defensive capabilities of robust neural networks. This work opens a promising direction for developing practical, scalable defenses against adversarial attacks.