mlsanityData to 7 Oct 2026

The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification

arXiv 2204.12676 ↗First posted 27 Apr 2022cs.LG math.AP math.OCcited by 21

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Abstract (arXiv)

We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in the paper and 2) a family of multimarginal optimal transport problems where the number of marginals is equal to the number of classes in the original classification problem. These new theoretical results reveal a rich geometric structure of adversarial learning problems in multiclass classification and extend recent results restricted to the binary classification setting. A direct computational implication of our results is that by solving either the barycenter problem and its dual, or the MOT problem and its dual, we can recover the optimal robust classification rule and the optimal adversarial strategy for the original adversarial problem. Examples with synthetic and real data illustrate our results.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 22 of its 50 references that are in the map. First posted on arXiv 27 Apr 2022.

Builds on

22 of 50 references.

References · 22

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  2. 2017StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translationcited by 1,036
  3. 2013Fast Computation of Wasserstein Barycenterscited by 216
  4. 2019A Wasserstein-type distance in the space of Gaussian Mixture Modelscited by 75
  5. 2019Lower Bounds on Adversarial Robustness from Optimal Transportcited by 52
  6. 2015Scalable Bayes via Barycenter in Wasserstein Spacecited by 44
  7. 2014Multi-marginal optimal transport: theory and applicationscited by 41
  8. 2019Adversarial Robustness May Be at Odds With Simplicitycited by 39
  9. 2019An Optimal Transport approach for the Schr"odinger bridge problem and convergence of Sinkhorn algorithmcited by 38
  10. 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
  11. 2020Adversarial Example Gamescited by 34
  12. 2019Multi-marginal Wasserstein GANcited by 32
10 more
  1. 2021Wasserstein barycenters are NP-hard to computecited by 28
  2. 2022The Many Faces of Adversarial Riskcited by 28
  3. 2019On the Complexity of Approximating Multimarginal Optimal Transportcited by 27
  4. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  5. 2020Wasserstein barycenters can be computed in polynomial time in fixed dimensioncited by 23
  6. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  7. 2020Adversarial Classification: Necessary conditions and geometric flowscited by 19
  8. 2021Unbalanced Multi-Marginal Optimal Transportcited by 11
  9. 2017Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithmcited by 9
  10. 2020Multimarginal Optimal Transport by Accelerated Alternating Minimizationcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 5; 2024: 8; 2025: 4; 2026: 2.

21 papers.

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  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. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  4. 2024Contrasting Multiple Representations with the Multi-Marginal Matching Gapcited by 8
  5. 2023Characterizing the Optimal 0-1 Loss for Multi-class Classification with a Test-time Attackercited by 6
  6. 2023The Adversarial Consistency of Surrogate Risks for Binary Classificationcited by 6
  7. 2024An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classificationcited by 5
  8. 2023On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce itcited by 4
  9. 2023On the Role of Randomization in Adversarially Robust Classificationcited by 4
  10. 2024A mean curvature flow arising in adversarial trainingcited by 4
  11. 2024A Notion of Uniqueness for the Adversarial Bayes Classifiercited by 3
  12. 2024Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifiercited by 2
9 more
  1. 2025Neural Estimation for Scaling Entropic Multimarginal Optimal Transportcited by 2
  2. 2024Asymptotic Behavior of Adversarial Training Estimator under ℓ_∞-Perturbationcited by 1
  3. 2024Genetic Column Generation for Computing Lower Bounds for Adversarial Classificationcited by 1
  4. 2024Uniform Convergence of Adversarially Robust Classifierscited by 1
  5. 2025Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategiescited 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