这篇论文提出了一种计算简单的方法，能告诉你神经网络对输入噪声的容忍上限，还画出了鲁棒性曲线，帮你量化模型稳定性。
该论文研究神经网络对输入值随机噪声扰动的鲁棒性。作者提出一种基于高概率的鲁棒性度量，给出均方误差的上界，且将网络视为黑箱计算。在多个真实数据集上的实验验证了方法的有效性。论文还引入鲁棒性曲线概念，用于分析数据内部和跨数据集的鲁棒性特征。
Robustness of neural networks to random noise perturbations of their inputs
We investigate the problem of the robustness of a trained neural network to the perturbation of its input values. More specifically, we examine the interplay between the accuracy of the network, as measured by the mean squared error, and robustness. Accordingly, we present a robustness measure, which, with high probability, suggests an upper bound on the mean squared error of the network, with respect to an input data set, for a given perturbation of the input values of the network. The measure we propose is both simple and efficient to compute, treating the neural network as a black box. We provide experimental results on several real-world data sets showing the efficacy of the proposed method. We also introduce the concept of robustness curves, which allows us to further analyse robustness within and between data sets.