Exploring the Adversarial Frontier: Quantifying Robustness via Adversarial Hypervolume

The escalating threat of adversarial attacks on deep learning models, particularly in security-critical fields, has highlighted the need for robust deep learning systems. Conventional evaluation methods of their robustness rely on adversarial accuracy, which measures the model performance under a specific perturbation intensity. However, this singular metric does not fully encapsulate the overall resilience of a model against varying degrees of perturbation. To address this issue, we propose a new metric termed as the adversarial hypervolume for assessing the robustness of deep learning models comprehensively over a range of perturbation intensities from a multi-objective optimization standpoint. This metric allows for an in-depth comparison of defense mechanisms and recognizes the trivial improvements in robustness brought by less potent defensive strategies. We adopt a novel training algorithm to enhance adversarial robustness uniformly across various perturbation intensities, instead of only optimizing adversarial accuracy. Our experiments validate the effectiveness of the adversarial hypervolume metric in robustness evaluation, demonstrating its ability to reveal subtle differences in robustness that adversarial accuracy overlooks.