mlsanityData to 7 Oct 2026

Adversarial Purification with the Manifold Hypothesis

arXiv 2210.14404 ↗First posted 26 Oct 2022cs.LG cs.CR cs.CVcited by 8

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Abstract (arXiv)

In this work, we formulate a novel framework for adversarial robustness using the manifold hypothesis. This framework provides sufficient conditions for defending against adversarial examples. We develop an adversarial purification method with this framework. Our method combines manifold learning with variational inference to provide adversarial robustness without the need for expensive adversarial training. Experimentally, our approach can provide adversarial robustness even if attackers are aware of the existence of the defense. In addition, our method can also serve as a test-time defense mechanism for variational autoencoders.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 37 of its 55 references that are in the map. First posted on arXiv 26 Oct 2022.

Builds on

37 of 55 references.

References · 37

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
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  10. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,510
  11. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,442
  12. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
25 more
  1. 2018Robustness May Be at Odds with Accuracycited by 873
  2. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  3. 2020Overfitting in adversarially robust deep learningcited by 504
  4. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 402
  5. 2018Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Modelscited by 362
  6. 2017MagNet: a Two-Pronged Defense against Adversarial Examplescited by 268
  7. 2017PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examplescited by 243
  8. 2021Fixing Data Augmentation to Improve Adversarial Robustnesscited by 201
  9. 2020Bag of Tricks for Adversarial Trainingcited by 199
  10. 2018Disentangling Adversarial Robustness and Generalizationcited by 171
  11. 2020Torchattacks: A PyTorch Repository for Adversarial Attackscited by 156
  12. 2021Adversarial purification with Score-based generative modelscited by 132
  13. 2020Maximum-Entropy Adversarial Data Augmentation for Improved Generalization and Robustnesscited by 121
  14. 2021Robust Learning Meets Generative Models: Can Proxy Distributions Improve Adversarial Robustness?cited by 113
  15. 2021Globally-Robust Neural Networkscited by 106
  16. 2020RayS: A Ray Searching Method for Hard-label Adversarial Attackcited by 94
  17. 2016Measuring Neural Net Robustness with Constraintscited by 90
  18. 2020Stochastic Security: Adversarial Defense Using Long-Run Dynamics of Energy-Based Modelscited by 58
  19. 2021Adversarial Attacks are Reversible with Natural Supervisioncited by 47
  20. 2020Dual Manifold Adversarial Robustness: Defense against Lp and non-Lp Adversarial Attackscited by 45
  21. 2021Online Adversarial Purification based on Self-Supervisioncited by 45
  22. 2019PuVAE: A Variational Autoencoder to Purify Adversarial Examplescited by 28
  23. 2021Fighting Gradients with Gradients: Dynamic Defenses against Adversarial Attackscited by 19
  24. 2019On-manifold Adversarial Data Augmentation Improves Uncertainty Calibrationcited by 18
  25. 2022Reverse Engineering of Imperceptible Adversarial Image Perturbationscited by 17

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 3; 2026: 1.

8 papers.

  1. 2024Text-Guided Attention is All You Need for Zero-Shot Robustness in Vision-Language Modelscited by 23
  2. 2023Probabilistic and Semantic Descriptions of Image Manifolds and Their Applicationscited by 3
  3. 2024Pre-trained Multiple Latent Variable Generative Models are good defenders against Adversarial Attackscited by 1
  4. 2025Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Datasetcited by 1
  5. 2025Rectifying Adversarial Sample with Low Entropy Prior for Test-Time Defensecited by 1
  6. 2025Adversarial Machine Learning Attacks on Financial Reporting via Maximum Violated Multi-Objective Attackcited by 1
  7. 2023Blending adversarial training and representation-conditional purification via aggregation improves adversarial robustnesscited by 0
  8. 2026Complementary Text-Guided Attention for Zero-Shot Adversarial Robustnesscited by 0