Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks

Louis Béthune (1, 2) , Paul Novello (3) , Thibaut Boissin (3) , Guillaume Coiffier (4) , Mathieu Serrurier (1, 2) , Quentin Vincenot (5) , Andres Troya-Galvis (5)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 UT3 - Université Toulouse III - Paul Sabatier
3 IRT Saint Exupéry - Institut de Recherche Technologique
4 PIXEL - Structurer des formes géométriques
5 THALES [France]

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 underexplored 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. Our code is available at https://anonymous.4open. science/r/CSDFL.

Domains: Neural and Evolutionary Computing [cs.NE]; Computer Science [cs]

Louis Béthune, Paul Novello, Thibaut Boissin, Guillaume Coiffier, Mathieu Serrurier, et al.. Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks. 40th International Conference on Machine Learning, Jul 2023, Honolulu, Hawaii, United States. pp.2245-2271, ⟨10.5555/3618408.3618504⟩. ⟨hal-03977272v2⟩