A mean curvature flow arising in adversarial training
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.
Cite
@article{arxiv.2404.14402,
title = {A mean curvature flow arising in adversarial training},
author = {Leon Bungert and Tim Laux and Kerrek Stinson},
journal= {arXiv preprint arXiv:2404.14402},
year = {2025}
}