# Robustness of neural networks to random noise perturbations of their inputs

arXiv: https://arxiv.org/abs/2606.31581 · HTML: https://mlsanity.com/paper/2606.31581/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 7 of 7)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [Limitations of the Lipschitz constant as a defense against adversarial examples](https://mlsanity.com/paper/1807.09705/) (2018)
- [A Closer Look at Classification Evaluation Metrics and a Critical Reflection of Common Evaluation Practice](https://mlsanity.com/paper/2404.16958/) (2024)
- [Assessing Robustness of Machine Learning Models using Covariate Perturbations](https://mlsanity.com/paper/2408.01300/) (2024)

## Abstract (arXiv)

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.