mlsanityData to 13 Oct 2026

Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transport

arXiv 2609.22240 ↗First posted 4 Sep 2026cs.LG math.PR math.STcited by 0

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Abstract (arXiv)

The purpose of this paper is to rigorously quantify the statistical and learning-theoretic properties of adversarial training models for classification. Equivalently, we establish the statistical properties of empirical optimal partial transport. Precisely, first we provide two types of central limit theorems (CLT): CLT centered at the expected empirical value, and CLT centered at the population one with smoothing. These results are based on the uniqueness of optimal potential for various equivalent optimal transport formulations, and the empirical process theory argument. For the binary setting, we indeed prove the uniqueness of optimal potential by leveraging the connection between optimal partial transport and the derived multi-marginal optimal transport formula. As byproducts, we also obtain the stability of a saddle point of the adversarial training model, and the sample complexity and concentration probability of the generalization error.

Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 44 of its 89 references that are in the map. First posted on arXiv 4 Sep 2026.

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References · 44

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,336
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,379
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  4. 2023Not what you've signed up for: Compromising Real-World LLM-Integrated Applications with Indirect Prompt Injectioncited by 1,417
  5. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 287
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  12. 2022A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologiescited by 44
32 more
  1. 2022The curse of overparametrization in adversarial training: Precise analysis of robust generalization for random features regressioncited by 41
  2. 2020Provable tradeoffs in adversarially robust classificationcited by 40
  3. 2019Adversarial Robustness May Be at Odds With Simplicitycited by 39
  4. 2020Randomization matters. How to defend against strong adversarial attackscited by 37
  5. 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
  6. 2020Adversarial Example Gamescited by 34
  7. 2025Adversarial Attacks on Robotic Vision Language Action Modelscited by 31
  8. 2022The Many Faces of Adversarial Riskcited by 28
  9. 2025Adversarial Reasoning at Jailbreaking Timecited by 28
  10. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  11. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  12. 2016Inference for Empirical Wasserstein Distances on Finite Spacescited by 21
  13. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  14. 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
  15. 2020Adversarial Classification: Necessary conditions and geometric flowscited by 19
  16. 2018Adversarial Attacks on Face Detectors using Neural Net based Constrained Optimizationcited by 18
  17. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  18. 2022Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classificationcited by 15
  19. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 13
  20. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  21. 2024Adversarial Training Can Provably Improve Robustness: Theoretical Analysis of Feature Learning Process Under Structured Datacited by 12
  22. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  23. 2021Adversarial robustness for latent models: Revisiting the robust-standard accuracies tradeoffcited by 8
  24. 2022Nash Equilibria and Pitfalls of Adversarial Training in Adversarial Robustness Gamescited by 8
  25. 2023Characterizing the Optimal 0-1 Loss for Multi-class Classification with a Test-time Attackercited by 6
  26. 2023The Adversarial Consistency of Surrogate Risks for Binary Classificationcited by 6
  27. 2024An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classificationcited by 5
  28. 2023Asymptotic confidence sets for random linear programscited by 3
  29. 2024A Notion of Uniqueness for the Adversarial Bayes Classifiercited by 3
  30. 2022Inference for Projection-Based Wasserstein Distances on Finite Spacescited by 1
  31. 2025Adversarial Surrogate Risk Bounds for Binary Classificationcited by 1
  32. 2025Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functionscited by 1

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