mlsanityData to 7 Oct 2026

Maximum Mean Discrepancy Test is Aware of Adversarial Attacks

arXiv 2010.11415 ↗First posted 22 Oct 2020cs.LG stat.MLcited by 44

Not on the map. Why?

Abstract (arXiv)

The maximum mean discrepancy (MMD) test could in principle detect any distributional discrepancy between two datasets. However, it has been shown that the MMD test is unaware of adversarial attacks -- the MMD test failed to detect the discrepancy between natural and adversarial data. Given this phenomenon, we raise a question: are natural and adversarial data really from different distributions? The answer is affirmative -- the previous use of the MMD test on the purpose missed three key factors, and accordingly, we propose three components. Firstly, the Gaussian kernel has limited representation power, and we replace it with an effective deep kernel. Secondly, the test power of the MMD test was neglected, and we maximize it following asymptotic statistics. Finally, adversarial data may be non-independent, and we overcome this issue with the wild bootstrap. By taking care of the three factors, we verify that the MMD test is aware of adversarial attacks, which lights up a novel road for adversarial data detection based on two-sample tests.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Oct 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 9; 2023: 3; 2024: 10; 2025: 11; 2026: 6.

44 papers.

Sort:

By area:

  1. 2021AugMax: Adversarial Composition of Random Augmentations for Robust Trainingcited by 89
  2. 2021Better Safe Than Sorry: Preventing Delusive Adversaries with Adversarial Trainingcited by 58
  3. 2021Probabilistic Margins for Instance Reweighting in Adversarial Trainingcited by 57
  4. 2021CausalAdv: Adversarial Robustness through the Lens of Causalitycited by 37
  5. 2022Bilateral Dependency Optimization: Defending Against Model-inversion Attackscited by 30
  6. 2023Detecting Adversarial Data by Probing Multiple Perturbations Using Expected Perturbation Scorecited by 20
  7. 2024Detecting Machine-Generated Texts by Multi-Population Aware Optimization for Maximum Mean Discrepancycited by 20
  8. 2023Defenses in Adversarial Machine Learning: A Surveycited by 14
  9. 2024A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Sciencecited by 14
  10. 2022Fast and Reliable Evaluation of Adversarial Robustness with Minimum-Margin Attackcited by 13
  11. 2022Towards Lightweight Black-Box Attacks against Deep Neural Networkscited by 13
  12. 2022CADet: Fully Self-Supervised Out-Of-Distribution Detection With Contrastive Learningcited by 11
32 more
  1. 2022Generalizing Adversarial Explanations with Grad-CAMcited by 9
  2. 2023The Representation Jensen-Shannon Divergencecited by 9
  3. 2026HATS: Hardness-Aware Trajectory Synthesis for GUI Agentscited by 9
  4. 2022Evaluating Aleatoric Uncertainty via Conditional Generative Modelscited by 8
  5. 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
  6. 2022Towards Adversarial Purification using Denoising AutoEncoderscited by 6
  7. 2024Improving Accuracy-robustness Trade-off via Pixel Reweighted Adversarial Trainingcited by 6
  8. 2025DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testingcited by 6
  9. 2024A Unified Data Representation Learning for Non-parametric Two-sample Testingcited by 5
  10. 2025One Stone, Two Birds: Enhancing Adversarial Defense Through the Lens of Distributional Discrepancycited by 3
  11. 2022Adversarial Attack and Defense for Non-Parametric Two-Sample Testscited by 2
  12. 2024Learning Representations for Independence Testingcited by 2
  13. 2025PAFT: Prompt-Agnostic Fine-Tuningcited by 2
  14. 2025Sample-Specific Noise Injection For Diffusion-Based Adversarial Purificationcited by 2
  15. 2024Binary Hypothesis Testing for Softmax Models and Leverage Score Modelscited by 1
  16. 2025Topological Signatures of Adversaries in Multimodal Alignmentscited by 1
  17. 2025Temporal Distribution Shift in Real-World Pharmaceutical Data: Implications for Uncertainty Quantification in QSAR Modelscited by 1
  18. 2025Anchor-based Maximum Discrepancy for Relative Similarity Testingcited by 1
  19. 2021Detecting Adversaries, yet Faltering to Noise? Leveraging Conditional Variational AutoEncoders for Adversary Detection in the Presence of Noisy Imagescited by 0
  20. 2022Btech thesis report on adversarial attack detection and purification of adverserially attacked imagescited by 0
  21. 2024Discerning the Chaos: Detecting Adversarial Perturbations while Disentangling Intentional from Unintentional Noisescited by 0
  22. 2024Certifiably Robust Model Evaluation in Federated Learning under Meta-Distributional Shiftscited by 0
  23. 2024Adversarial Purification by Consistency-aware Latent Space Optimization on Data Manifoldscited by 0
  24. 2025Boosting Statistic Learning with Synthetic Data from Pretrained Large Modelscited by 0
  25. 2025Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Datacited by 0
  26. 2025Are Two Datasets Close Enough With Statistical Significance? A Kernel Distributional Closeness Testing Approachcited by 0
  27. 2025CORE-ReID V2: Advancing the Domain Adaptation for Object Re-Identification with Optimized Training and Ensemble Fusioncited by 0
  28. 2026A Unified Perspective on Adversarial Membership Manipulation in Vision Modelscited by 0
  29. 2026LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetrycited by 0
  30. 2026A nonparametric two-sample test using a parametric integral probability metriccited by 0
  31. 2026USAD: Uncertainty-aware Statistical Adversarial Detectioncited by 0
  32. 2026ElasticBack: Stealthy Conditional Backdoor in LLM-Agent Skills via Coupled Trigger-Rule Optimizationcited by 0