Robustness of neural networks to random noise perturbations of their inputs
It offers a practical tool for practitioners to assess neural network robustness to input noise, but the approach is incremental.
This paper proposes a simple and efficient robustness measure for neural networks that provides an upper bound on the mean squared error under random input perturbations, validated on real-world datasets.
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.