mlsanityData to 14 Oct 2026

On the existence of solutions to adversarial training in multiclass classification

arXiv 2305.00075 ↗First posted 28 Apr 2023cs.LG math.OC stat.MLcited by 9

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Abstract (arXiv)

We study three models of the problem of adversarial training in multiclass classification designed to construct robust classifiers against adversarial perturbations of data in the agnostic-classifier setting. We prove the existence of Borel measurable robust classifiers in each model and provide a unified perspective of the adversarial training problem, expanding the connections with optimal transport initiated by the authors in previous work and developing new connections between adversarial training in the multiclass setting and total variation regularization. As a corollary of our results, we prove the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting, a result that improves results in the literature of adversarial training, where robust classifiers were only known to exist within the enlarged universal σ-algebra of the feature space.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 22 of its 41 references that are in the map. First posted on arXiv 28 Apr 2023.

Builds on

22 of 41 references.

References · 22

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2017Wild Patterns: Ten Years After the Rise of Adversarial Machine Learningcited by 414
  3. 2020Precise Tradeoffs in Adversarial Training for Linear Regressioncited by 77
  4. 2019Lower Bounds on Adversarial Robustness from Optimal Transportcited by 53
  5. 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
  6. 2020Adversarial Example Gamescited by 34
  7. 2022The Many Faces of Adversarial Riskcited by 28
  8. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  9. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  10. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  11. 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
  12. 2020Adversarial Classification: Necessary conditions and geometric flowscited by 19
10 more
  1. 2022Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classificationcited by 15
  2. 2022Gamma-convergence of a nonlocal perimeter arising in adversarial machine learningcited by 10
  3. 2022Nash Equilibria and Pitfalls of Adversarial Training in Adversarial Robustness Gamescited by 8
  4. 2019Mumford-Shah functionals on graphs and their asymptoticscited by 6
  5. 2020From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data cloudscited by 6
  6. 2013A Method Based on Total Variation for Network Modularity Optimization using the MBO Schemecited by 4
  7. 2016A new analytical approach to consistency and overfitting in regularized empirical risk minimizationcited by 4
  8. 2018Stochastic Block Models are a Discrete Surface Tensioncited by 3
  9. 2022The Consistency of Adversarial Training for Binary Classificationcited by 3
  10. 2019Total variation based community detection using a nonlinear optimization approachcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 2; 2026: 2.

9 papers.

  1. 2023The Adversarial Consistency of Surrogate Risks for Binary Classificationcited by 6
  2. 2023It begins with a boundary: A geometric view on probabilistically robust learningcited by 3
  3. 2024Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifiercited by 2
  4. 2024Genetic Column Generation for Computing Lower Bounds for Adversarial Classificationcited by 1
  5. 2024Uniform Convergence of Adversarially Robust Classifierscited by 1
  6. 2025Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functionscited by 1
  7. 2025Unveiling the Role of Randomization in Multiclass Adversarial Classification: Insights from Graph Theorycited by 0
  8. 2026Duality for the Adversarial Total Variationcited by 0
  9. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0