Bungert, Leon and Laux, Tim and Stinson, Kerrek (2024) A mean curvature flow arising in adversarial training. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 192: 103625. ISSN 0021-7824, 1776-3371
Full text not available from this repository. (Request a copy)Abstract
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. (c) 2024 Published by Elsevier Masson SAS.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | IMPLICIT TIME DISCRETIZATION; ALGORITHM; Mean curvature flow; Adversarial training; Adversarial machine learning; Minimizing movements; Monotone and consistent schemes |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Tim Laux |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 04 Dec 2025 06:29 |
| Last Modified: | 04 Dec 2025 06:29 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64916 |
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