Robust One-Class Classification with Signed Distance Function using 1-Lipschitz Neural Networks
Louis Bu00e9thune,u00a0Paul Novello,u00a0Guillaume Coiffier,u00a0Thibaut Boissin,u00a0Mathieu Serrurier,u00a0Quentin Vincenot,u00a0Andres Troya-Galvis
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.
