Adversarial examples are known as carefully perturbed images fooling image classifiers. We propose a geometric framework to generate adversarial examples in one of the most challenging black-box settings where the adversary can only generate a small number of queries, each of them returning the top-$1$ label of the classifier. Our framework is based on the observation that the decision boundary of deep networks usually has a small mean curvature in the vicinity of data samples. We propose an effective iterative algorithm to generate query-efficient black-box perturbations with small $\ell_p$ norms for $p \ge 1$, which is confirmed via experimental evaluations on state-of-the-art natural image classifiers. Moreover, for $p=2$, we theoretically show that our algorithm actually converges to the minimal $\ell_2$-perturbation when the curvature of the decision boundary is bounded. We also obtain the optimal distribution of the queries over the iterations of the algorithm. Finally, experimental results confirm that our principled black-box attack algorithm performs better than state-of-the-art algorithms as it generates smaller perturbations with a reduced number of queries.

本文提出一种有效的黑盒攻击算法，用于生成三维深度神经网络的对抗样例，该算法利用网络决策边界以及小曲率特性来生成具有小l_p范数的有效迭代算法，该算法获得了比现有算法更好的结果。

GeoDA: 一个基于几何的黑盒对抗攻击框架