mlsanityData to 7 Oct 2026

A Unified Wasserstein Distributional Robustness Framework for Adversarial Training

arXiv 2202.13437 ↗First posted 27 Feb 2022cs.LG cs.CVcited by 36

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Abstract (arXiv)

It is well-known that deep neural networks (DNNs) are susceptible to adversarial attacks, exposing a severe fragility of deep learning systems. As the result, adversarial training (AT) method, by incorporating adversarial examples during training, represents a natural and effective approach to strengthen the robustness of a DNN-based classifier. However, most AT-based methods, notably PGD-AT and TRADES, typically seek a pointwise adversary that generates the worst-case adversarial example by independently perturbing each data sample, as a way to "probe" the vulnerability of the classifier. Arguably, there are unexplored benefits in considering such adversarial effects from an entire distribution. To this end, this paper presents a unified framework that connects Wasserstein distributional robustness with current state-of-the-art AT methods. We introduce a new Wasserstein cost function and a new series of risk functions, with which we show that standard AT methods are special cases of their counterparts in our framework. This connection leads to an intuitive relaxation and generalization of existing AT methods and facilitates the development of a new family of distributional robustness AT-based algorithms. Extensive experiments show that our distributional robustness AT algorithms robustify further their standard AT counterparts in various settings.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). Builds on 47 of its 80 references that are in the map. First posted on arXiv 27 Feb 2022.

Builds on

47 of 80 references.

References · 47

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  4. 2013Intriguing properties of neural networkscited by 5,114
  5. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  6. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,510
  7. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,442
  8. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  9. 2017Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learningcited by 918
  10. 2017Evasion Attacks against Machine Learning at Test Timecited by 686
  11. 2020RobustBench: a standardized adversarial robustness benchmarkcited by 659
  12. 2019Adversarial Training for Free!cited by 638
35 more
  1. 2020On Adaptive Attacks to Adversarial Example Defensescited by 547
  2. 2020Overfitting in adversarially robust deep learningcited by 504
  3. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
  4. 2019Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attackcited by 333
  5. 2020Attacks Which Do Not Kill Training Make Adversarial Learning Strongercited by 242
  6. 2019Improving Adversarial Robustness via Promoting Ensemble Diversitycited by 213
  7. 2020Bag of Tricks for Adversarial Trainingcited by 199
  8. 2020Geometry-aware Instance-reweighted Adversarial Trainingcited by 198
  9. 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 182
  10. 2016Statistics of Robust Optimization: A Generalized Empirical Likelihood Approachcited by 182
  11. 2019Adversarial Training and Robustness for Multiple Perturbationscited by 182
  12. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 169
  13. 2020Self-Adaptive Training: beyond Empirical Risk Minimizationcited by 126
  14. 2015Distributionally Robust Logistic Regressioncited by 124
  15. 2019Defense Against Adversarial Attacks Using Feature Scattering-based Adversarial Trainingcited by 95
  16. 2020Learnable Boundary Guided Adversarial Trainingcited by 93
  17. 2020Smooth Adversarial Trainingcited by 89
  18. 2020Adversarial Distributional Training for Robust Deep Learningcited by 79
  19. 2021Improving Adversarial Robustness via Channel-wise Activation Suppressingcited by 76
  20. 2015Distributional Smoothing with Virtual Adversarial Trainingcited by 61
  21. 2019Wasserstein Robust Reinforcement Learningcited by 50
  22. 2020Neural Topic Model via Optimal Transportcited by 50
  23. 2019Robustness to Adversarial Perturbations in Learning from Incomplete Datacited by 49
  24. 2019Accurate, reliable and fast robustness evaluationcited by 43
  25. 2019Distributionally Robust Reinforcement Learningcited by 40
  26. 2020Distributional Robustness and Regularization in Reinforcement Learningcited by 39
  27. 2018Wasserstein Distributionally Robust Stochastic Control: A Data-Driven Approachcited by 27
  28. 2019Wasserstein Smoothing: Certified Robustness against Wasserstein Adversarial Attackscited by 25
  29. 2017Semi-supervised Learning based on Distributionally Robust Optimizationcited by 12
  30. 2020Improving Adversarial Robustness by Enforcing Local and Global Compactnesscited by 11
  31. 2021Understanding and Achieving Efficient Robustness with Adversarial Supervised Contrastive Learningcited by 8
  32. 2019Perturbations are not Enough: Generating Adversarial Examples with Spatial Distortionscited by 5
  33. 2020Improving Ensemble Robustness by Collaboratively Promoting and Demoting Adversarial Robustnesscited by 4
  34. 2021On Label Shift in Domain Adaptation via Wasserstein Distancecited by 2
  35. 2020Learning to Attack with Fewer Pixels: A Probabilistic Post-hoc Framework for Refining Arbitrary Dense Adversarial Attackscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 12; 2024: 9; 2025: 6; 2026: 4.

36 papers.

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  1. 2024Erasing Undesirable Concepts in Diffusion Models with Adversarial Preservationcited by 48
  2. 2022Efficient and Effective Augmentation Strategy for Adversarial Trainingcited by 43
  3. 2025Fantastic Targets for Concept Erasure in Diffusion Models and Where To Find Themcited by 34
  4. 2023Transformed Distribution Matching for Missing Value Imputationcited by 31
  5. 2022Learning to Re-weight Examples with Optimal Transport for Imbalanced Classificationcited by 23
  6. 2023Vector Quantized Wasserstein Auto-Encodercited by 22
  7. 2024Text-Enhanced Data-free Approach for Federated Class-Incremental Learningcited by 16
  8. 2023Wasserstein distributional robustness of neural networkscited by 15
  9. 2022Adaptive Distribution Calibration for Few-Shot Learning with Hierarchical Optimal Transportcited by 14
  10. 2022Adversarial Examples in Random Neural Networks with General Activationscited by 13
  11. 2023Flow-based Distributionally Robust Optimizationcited by 13
  12. 2022Global-Local Regularization Via Distributional Robustnesscited by 11
24 more
  1. 2023Certified Robust Neural Networks: Generalization and Corruption Resistancecited by 11
  2. 2024LLM Reading Tea Leaves: Automatically Evaluating Topic Models with Large Language Modelscited by 11
  3. 2024Towards Fairness-Aware Adversarial Learningcited by 10
  4. 2024Neural Topic Modeling with Large Language Models in the Loopcited by 10
  5. 2023Optimal Transport Model Distributional Robustnesscited by 5
  6. 2024Optimal Transport for Structure Learning Under Missing Datacited by 5
  7. 2024Toward Robust Neural Reconstruction from Sparse Point Setscited by 5
  8. 2023Generating Adversarial Examples with Task Oriented Multi-Objective Optimizationcited by 2
  9. 2023Optimal Transport Regularized Divergences: Application to Adversarial Robustnesscited by 2
  10. 2023Upper and lower bounds for the Lipschitz constant of random neural networkscited by 2
  11. 2024Enhancing Adversarial Robustness via Uncertainty-Aware Distributional Adversarial Trainingcited by 2
  12. 2025FOCoOp: Enhancing Out-of-Distribution Robustness in Federated Prompt Learning for Vision-Language Modelscited by 2
  13. 2023Parameter Estimation in DAGs from Incomplete Data via Optimal Transportcited by 1
  14. 2025Wasserstein distributional adversarial training for deep neural networkscited by 1
  15. 2026Taming the Long Tail: Rebalancing Adversarial Training via Adaptive Perturbationcited by 1
  16. 2023Bridging Optimal Transport and Jacobian Regularization by Optimal Trajectory for Enhanced Adversarial Defensecited by 0
  17. 2023On robust overfitting: adversarial training induced distribution matterscited by 0
  18. 2024Distributionally and Adversarially Robust Logistic Regression via Intersecting Wasserstein Ballscited by 0
  19. 2025Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimizationcited by 0
  20. 2025Mitigating Semantic Collapse in Generative Personalization with Test-Time Embedding Adjustmentcited by 0
  21. 2025Learning to Forget with Information Divergence Reweighted Objectives for Noisy Labelscited by 0
  22. 2026Uncertainty-aware Causal Decision Making via Effect Bound Decompositioncited by 0
  23. 2026Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergencescited by 0
  24. 2026Confusion-Geometry Rebalancing for Long-Tailed Adversarial Trainingcited by 0