# Robustness of classifiers to uniform ℓp and Gaussian noise

arXiv: https://arxiv.org/abs/1802.07971 · HTML: https://mlsanity.com/paper/1802.07971/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2018.

## Built on by (most cited first, 1 of 1)

- [Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification](https://mlsanity.com/paper/2101.09306/) (2021)

## Abstract (arXiv)

We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the ℓp ball for p ∈ [1, ∞] and Gaussian noise with an arbitrary covariance matrix. We characterize this robustness to random noise in terms of the distance to the decision boundary of the classifier. This analysis applies to linear classifiers as well as classifiers with locally approximately flat decision boundaries, a condition which is satisfied by state-of-the-art deep neural networks. The predicted robustness is verified experimentally.