A mean curvature flow arising in adversarial training

arXiv:2404.14402v1 Announce Type: cross
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 …

abstract adversarial adversarial training arxiv binary classification cs.lg decision equation evolution flow functional math.ap mean movements perspective prove regularization training type