mlsanityData to 14 Oct 2026

On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it

arXiv 2301.03662 ↗First posted 9 Jan 2023cs.LG math.AP math.OCcited by 4

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Abstract (arXiv)

We propose iterative algorithms to solve adversarial problems in a variety of supervised learning settings of interest. Our algorithms, which can be interpreted as suitable ascent-descent dynamics in Wasserstein spaces, take the form of a system of interacting particles. These interacting particle dynamics are shown to converge toward appropriate mean-field limit equations in certain large number of particles regimes. In turn, we prove that, under certain regularity assumptions, these mean-field equations converge, in the large time limit, toward approximate Nash equilibria of the original adversarial learning problems. We present results for nonconvex-nonconcave settings, as well as for nonconvex-concave ones. Numerical experiments illustrate our results.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 41 of its 60 references that are in the map. First posted on arXiv 9 Jan 2023.

Builds on

41 of 60 references.

References · 41

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
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  11. 2017Improving the Adversarial Robustness and Interpretability of Deep Neural Networks by Regularizing their Input Gradientscited by 236
  12. 2019You Only Propagate Once: Accelerating Adversarial Training via Maximal Principlecited by 183
29 more
  1. 2018Robustness via curvature regularization, and vice versacited by 175
  2. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 170
  3. 2019Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methodscited by 148
  4. 2020Near-Optimal Algorithms for Minimax Optimizationcited by 119
  5. 2019Lower Bounds on Adversarial Robustness from Optimal Transportcited by 53
  6. 2019Scaleable input gradient regularization for adversarial robustnesscited by 47
  7. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 46
  8. 2021Distributionally Robust Learningcited by 44
  9. 2015A Unified Gradient Regularization Family for Adversarial Examplescited by 43
  10. 2020On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regimecited by 39
  11. 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
  12. 2018Theoretical Analysis of Adversarial Learning: A Minimax Approachcited by 31
  13. 2020A mean-field analysis of two-player zero-sum gamescited by 28
  14. 2022The Many Faces of Adversarial Riskcited by 28
  15. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  16. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  17. 2014Continuum limit of total variation on point cloudscited by 24
  18. 2020Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspectivecited by 22
  19. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  20. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  21. 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
  22. 2020Adversarial Classification: Necessary conditions and geometric flowscited by 19
  23. 2022Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classificationcited by 15
  24. 2022An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Gamescited by 14
  25. 2019Label-similarity Curriculum Learningcited by 11
  26. 2022Gamma-convergence of a nonlocal perimeter arising in adversarial machine learningcited by 10
  27. 2021Minimax Optimization with Smooth Algorithmic Adversariescited by 8
  28. 2021On the regularized risk of distributionally robust learning over deep neural networkscited by 8
  29. 2018Adversarially Robust Training through Structured Gradient Regularizationcited by 5

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Cited by year

Citing papers per year: 2023: 1; 2024: 2; 2025: 1.

4 papers.

  1. 2023Strategic Distribution Shift of Interacting Agents via Coupled Gradient Flowscited by 5
  2. 2024Analysis of Kernel Mirror Prox for Measure Optimizationcited by 4
  3. 2024Mirror Descent-Ascent for mean-field min-max problemscited by 2
  4. 2025Gradient Flow Sampler-based Distributionally Robust Optimizationcited by 2