https://neckpinch.com/authors/leon-bungert/New arXiv papers by Leon Bungert, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2404.14402/arxiv:2404.14402Mon, 22 Apr 2024 00:00:00 GMTLeon Bungert, Tim Laux, Kerrek Stinson — We connect adversarial training for binary classification to a geometric evolution equation for the decision boundary. Relying on a perspective that recasts adversarial training as a regularization problem, we introduce a modified training scheme that constitutes a minimizing movements scheme for a nonlocal perimeter functional. We prove that the scheme is monotone and consistent as the adversarial budget vanishes and the perimeter localizes, and as a consequence we rigorously show that the scheme approximates a weighted mean curvature flow. This highlights that the efficacy of adversarial training may be due to locally minimizing the length of the decision boundary. In our analysis, we introduce a variety of tools for working with the subdifferential of a supremal-type nonlocal total variation and its regularity properties.Mean curvature flowAnisotropic & nonlocal flowsWeak & singular flows