# Robustness of classifiers to uniform $\ell_p$ and Gaussian noise

1 MC2 - Modèles de calcul, Complexité, Combinatoire
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We study the robustness of classifiers to various kinds of random noise models. In particular, we consider noise drawn uniformly from the $\ell_p$ ball for $p \in [1, \infty]$ 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.
Document type :
Conference papers
Domain :

https://hal.archives-ouvertes.fr/hal-01715012
Contributor : Jean-Yves Franceschi <>
Submitted on : Thursday, February 22, 2018 - 11:22:18 AM
Last modification on : Tuesday, April 16, 2019 - 5:12:07 PM
Long-term archiving on : Wednesday, May 23, 2018 - 12:34:49 PM

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paper_robustness_lp_new.pdf
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### Identifiers

• HAL Id : hal-01715012, version 1
• ARXIV : 1802.07971

### Citation

Jean-Yves Franceschi, Alhussein Fawzi, Omar Fawzi. Robustness of classifiers to uniform $\ell_p$ and Gaussian noise. 21st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018, Apr 2018, Playa Blanca, Spain. ⟨hal-01715012⟩

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