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We propose a new method, dubbed One Class Signed Distance Function (OCSDF),to perform One Class Classification (OCC) by provably learning the SignedDistance Function (SDF) to the boundary of the support of any distribution. Thedistance to the support can be interpreted as a normality score, and itsapproximation using 1-Lipschitz neural networks provides robustness boundsagainst l2 adversarial attacks, an under-explored weakness of deeplearning-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 andimage data while being way more robust to adversarial attacks, illustrating itstheoretical properties. Finally, as exploratory research perspectives, wetheoretically and empirically show how OCSDF connects OCC with image generationand implicit neural surface parametrization. Our code is available athttps://github.com/Algue-Rythme/OneClassMetricLearning

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