mlsanityData to 7 Oct 2026

A Manifold View of Adversarial Risk

arXiv 2203.13277 ↗First posted 24 Mar 2022cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

The adversarial risk of a machine learning model has been widely studied. Most previous works assume that the data lies in the whole ambient space. We propose to take a new angle and take the manifold assumption into consideration. Assuming data lies in a manifold, we investigate two new types of adversarial risk, the normal adversarial risk due to perturbation along normal direction, and the in-manifold adversarial risk due to perturbation within the manifold. We prove that the classic adversarial risk can be bounded from both sides using the normal and in-manifold adversarial risks. We also show with a surprisingly pessimistic case that the standard adversarial risk can be nonzero even when both normal and in-manifold risks are zero. We finalize the paper with empirical studies supporting our theoretical results. Our results suggest the possibility of improving the robustness of a classifier by only focusing on the normal adversarial risk.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 22 of its 38 references that are in the map. First posted on arXiv 24 Mar 2022.

Builds on

22 of 38 references.

References · 22

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  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. 2016Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translationcited by 1,471
  8. 2018Robustness May Be at Odds with Accuracycited by 873
  9. 2019Adversarial Training for Free!cited by 638
  10. 2020Overfitting in adversarially robust deep learningcited by 504
  11. 2019Unlabeled Data Improves Adversarial Robustnesscited by 415
  12. 2017Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuningcited by 288
10 more
  1. 2019Adversarial Examples Improve Image Recognitioncited by 283
  2. 2020Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examplescited by 275
  3. 2018Disentangling Adversarial Robustness and Generalizationcited by 171
  4. 2020Understanding and Mitigating the Tradeoff Between Robustness and Accuracycited by 148
  5. 2018Is Robustness the Cost of Accuracy? -- A Comprehensive Study on the Robustness of 18 Deep Image Classification Modelscited by 135
  6. 2019When NAS Meets Robustness: In Search of Robust Architectures against Adversarial Attackscited by 87
  7. 2018Adversarial vulnerability for any classifiercited by 78
  8. 2016A Boundary Tilting Persepective on the Phenomenon of Adversarial Examplescited by 70
  9. 2020Dual Manifold Adversarial Robustness: Defense against Lp and non-Lp Adversarial Attackscited by 45
  10. 2019On Robustness to Adversarial Examples and Polynomial Optimizationcited by 14

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Cited by year

Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 1.

4 papers.

  1. 2022Learning Probabilistic Topological Representations Using Discrete Morse Theorycited by 20
  2. 2023Enhancing Modality-Agnostic Representations via Meta-Learning for Brain Tumor Segmentationcited by 14
  3. 2025When Flatness Does (Not) Guarantee Adversarial Robustnesscited by 3
  4. 2024Adversarial Vulnerability as a Consequence of On-Manifold Inseparibilitycited by 0