Robustness of neural networks to random noise perturbations of their inputs

2026-06-30

AI Summary

This study investigates the relationship between the robustness of neural networks under random input perturbations and their prediction accuracy, measured by mean squared error (MSE). To address this, the work proposes an efficient, computable black-box robustness metric that, without requiring access to internal model architecture, provides a high-probability upper bound on the network’s MSE over an entire dataset under a given perturbation. The method innovatively introduces robustness curves, enabling systematic comparison and analysis of robustness across different datasets. Experimental evaluations on multiple real-world datasets demonstrate that the proposed approach accurately quantifies and effectively captures a model’s sensitivity to input noise, offering a practical tool for assessing robustness in diverse settings.

Abstract

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.

Problem

• robustness
• neural networks
• input perturbations
• mean squared error
• random noise

Innovation

• robustness measure
• input perturbation
• mean squared error
• black-box analysis
• robustness curves