A mean curvature flow arising in adversarial training
<|reference_start|>A mean curvature flow arising in adversarial training: 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.<|reference_end|>
@article{bungert2024a,
    title={A mean curvature flow arising in adversarial training},
    author={Leon Bungert, Tim Laux, Kerrek Stinson},
    journal={arXiv preprint arXiv:2404.14402},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.14402},
    primaryClass={math.AP cs.LG}
}