Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks
Louis Béthune, Paul Novello, Guillaume Coiffier, Thibaut Boissin, Mathieu Serrurier, Quentin VINCENOT, Andres Troya-Galvis
Abstract
We propose a new method, dubbed One Class Signed Distance Function (OCSDF), to perform One Class Classification (OCC) by provably learning the Signed Distance Function (SDF) to the boundary of the support of any distribution. The distance to the support can be interpreted as a normality score, and its approximation using 1-Lipschitz neural networks provides robustness bounds against $l2$ adversarial attacks, an under-explored weakness of deep learning-based OCC algorithms. As a result, OCSDF comes with a new metric, certified AUROC, that can be computed at the same cost as any classical AUROC. We show that OCSDF is competitive against concurrent methods on tabular and image data while being way more robust to adversarial attacks, illustrating its theoretical properties. Finally, as exploratory research perspectives, we theoretically and empirically show how OCSDF connects OCC with image generation and implicit neural surface parametrization.
BibTeX
@inproceedings{icml2023_robustoneclasscl,
title = {Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks},
author = {Louis Béthune and Paul Novello and Guillaume Coiffier and Thibaut Boissin and Mathieu Serrurier and Quentin VINCENOT and Andres Troya-Galvis},
booktitle = {ICML 2023},
year = {2023}
}