Deep networks have recently been shown to be vulnerable to universal
perturbations: there exist very small image-agnostic perturbations that cause
most natural images to be misclassified by such classifiers. In this paper, we
propose the first quantitative analysis of the robustness of classifiers to
universal perturbations, and draw a formal link between the robustness to
universal perturbations, and the geometry of the decision boundary.
Specifically, we establish theoretical bounds on the robustness of classifiers
under two decision boundary models (flat and curved models). We show in
particular that the robustness of deep networks to universal perturbations is
driven by a key property of their curvature: there exists shared directions
along which the decision boundary of deep networks is systematically positively
curved. Under such conditions, we prove the existence of small universal
perturbations. Our analysis further provides a novel geometric method for
computing universal perturbations, in addition to explaining their properties.

本文通过理论分析和几何方法，探究深度神经网络在面对普适性扰动时的稳健性，并揭示了决策边界几何形态（平坦或曲线）与稳健性之间的关系，证明了在正曲率方向上存在共享决策边界的情况下，存在极小的普适性扰动。