Curvature Dynamic Black-box Attack: revisiting adversarial robustness via dynamic curvature estimation

Adversarial attack reveals the vulnerability of deep learning models. For about a decade, countless attack and defense methods have been proposed, leading to robustified classifiers and better understanding of models. Among these methods, curvature-based approaches have attracted attention because it is assumed that high curvature may give rise to rough decision boundary. However, the most commonly used \textit{curvature} is the curvature of loss function, scores or other parameters from within the model as opposed to decision boundary curvature, since the former can be relatively easily formed using second order derivative. In this paper, we propose a new query-efficient method, dynamic curvature estimation(DCE), to estimate the decision boundary curvature in a black-box setting. Our approach is based on CGBA, a black-box adversarial attack. By performing DCE on a wide range of classifiers, we discovered, statistically, a connection between decision boundary curvature and adversarial robustness. We also propose a new attack method, curvature dynamic black-box attack(CDBA) with improved performance using the dynamically estimated curvature.