mlsanityData to 7 Oct 2026

A mean curvature flow arising in adversarial training

arXiv 2404.14402 ↗First posted 22 Apr 2024math.AP cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 15 of its 38 references that are in the map. First posted on arXiv 22 Apr 2024.

Builds on

15 of 38 references.

References · 15

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2013Intriguing properties of neural networkscited by 5,114
  4. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,510
  5. 2021Fast Minimum-norm Adversarial Attacks through Adaptive Norm Constraintscited by 50
  6. 2020Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Ratescited by 49
  7. 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
  8. 2022The Many Faces of Adversarial Riskcited by 28
  9. 2020Lipschitz regularity of graph Laplacians on random data cloudscited by 26
  10. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  11. 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
  12. 2022Gamma-convergence of a nonlocal perimeter arising in adversarial machine learningcited by 10
3 more
  1. 2021Uniform Convergence Rates for Lipschitz Learning on Graphscited by 9
  2. 2023It begins with a boundary: A geometric view on probabilistically robust learningcited by 3
  3. 2023On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computationcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 1.

4 papers.

  1. 2024Uniform Convergence of Adversarially Robust Classifierscited by 1
  2. 2025Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategiescited by 1
  3. 2025Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functionscited by 1
  4. 2026Duality for the Adversarial Total Variationcited by 0