We present a theoretical study of the robustness of parameterized networks to random input perturbations. Specifically, we analyze local robustness at a given network input by quantifying the probability that a small additive random perturbation of the input leads to misclassification. For deep networks with rectified linear units, we derive lower bounds on local robustness in terms of the input dimensionality and the total number of network units.

翻译：本文对参数化网络在随机输入扰动下的鲁棒性进行了理论研究。具体而言，我们通过量化输入的小型加性随机扰动导致误分类的概率，分析了给定网络输入处的局部鲁棒性。针对具有整流线性单元的深度网络，我们基于输入维度和网络单元总数推导了局部鲁棒性的下界。