mlsanityData to 7 Oct 2026

Adversarial vulnerability for any classifier

arXiv 1802.08686 ↗First posted 23 Feb 2018cs.LG cs.CR cs.CVcited by 78

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Abstract (arXiv)

Despite achieving impressive performance, state-of-the-art classifiers remain highly vulnerable to small, imperceptible, adversarial perturbations. This vulnerability has proven empirically to be very intricate to address. In this paper, we study the phenomenon of adversarial perturbations under the assumption that the data is generated with a smooth generative model. We derive fundamental upper bounds on the robustness to perturbations of any classification function, and prove the existence of adversarial perturbations that transfer well across different classifiers with small risk. Our analysis of the robustness also provides insights onto key properties of generative models, such as their smoothness and dimensionality of latent space. We conclude with numerical experimental results showing that our bounds provide informative baselines to the maximal achievable robustness on several datasets.

Key facts. Cited by 78 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Feb 2018.

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Citing papers per year: 2021: 20; 2022: 19; 2023: 9; 2024: 15; 2025: 8; 2026: 7.

78 papers.

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  1. 2021Trustworthy AI: From Principles to Practicescited by 206
  2. 2021Detecting Adversarial Examples from Sensitivity Inconsistency of Spatial-Transform Domaincited by 29
  3. 2022Gradient Methods Provably Converge to Non-Robust Networkscited by 27
  4. 2023The Double-Edged Sword of Implicit Bias: Generalization vs. Robustness in ReLU Networkscited by 23
  5. 2021Universal Adversarial Perturbations Through the Lens of Deep Steganography: Towards A Fourier Perspectivecited by 18
  6. 2021The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networkscited by 16
  7. 2021Towards Evaluating the Robustness of Deep Diagnostic Models by Adversarial Attackcited by 15
  8. 2022Adversarial Examples in Random Neural Networks with General Activationscited by 13
  9. 2021Building Reliable Explanations of Unreliable Neural Networks: Locally Smoothing Perspective of Model Interpretationcited by 12
  10. 2022On the Robustness of Bayesian Neural Networks to Adversarial Attackscited by 12
  11. 2021Benign Overfitting in Adversarially Robust Linear Classificationcited by 11
  12. 2022Adversarial robustness of sparse local Lipschitz predictorscited by 11
38 more
  1. 2023Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustnesscited by 11
  2. 2021Interpolated Joint Space Adversarial Training for Robust and Generalizable Defensescited by 10
  3. 2024Detecting Brittle Decisions for Free: Leveraging Margin Consistency in Deep Robust Classifierscited by 10
  4. 2023It Is All About Data: A Survey on the Effects of Data on Adversarial Robustnesscited by 9
  5. 2021On the regularized risk of distributionally robust learning over deep neural networkscited by 8
  6. 2023Adversarial Examples Exist in Two-Layer ReLU Networks for Low Dimensional Linear Subspacescited by 8
  7. 2024Scaling Laws for Black box Adversarial Attackscited by 8
  8. 2022Towards Effective and Robust Neural Trojan Defenses via Input Filteringcited by 7
  9. 2024On the Computability of Robust PAC Learningcited by 6
  10. 2021Bridging the Gap Between Adversarial Robustness and Optimization Biascited by 5
  11. 2022Adversarial attacks on neural networks through canonical Riemannian foliationscited by 5
  12. 2024Can Implicit Bias Imply Adversarial Robustness?cited by 5
  13. 2024Towards Adversarial Robustness via Debiased High-Confidence Logit Alignmentcited by 5
  14. 2025Shifting the Paradigm: A Diffeomorphism Between Time Series Data Manifolds for Achieving Shift-Invariancy in Deep Learningcited by 5
  15. 2021Improved Estimation of Concentration Under ℓp-Norm Distance Metrics Using Half Spacescited by 4
  16. 2021Robustness of Bayesian Neural Networks to White-Box Adversarial Attackscited by 4
  17. 2022A Manifold View of Adversarial Riskcited by 4
  18. 2022Sample Complexity Bounds for Robustly Learning Decision Lists against Evasion Attackscited by 4
  19. 2023Investigating the Corruption Robustness of Image Classifiers with Random Lp-norm Corruptionscited by 4
  20. 2024The Price of Implicit Bias in Adversarially Robust Generalizationcited by 4
  21. 2021In-distribution adversarial attacks on object recognition models using gradient-free searchcited by 3
  22. 2021Understanding Intrinsic Robustness Using Label Uncertaintycited by 3
  23. 2022Origins of Low-dimensional Adversarial Perturbationscited by 3
  24. 2025Scanning Trojaned Models Using Out-of-Distribution Samplescited by 3
  25. 2021"What's in the box?!": Deflecting Adversarial Attacks by Randomly Deploying Adversarially-Disjoint Modelscited by 2
  26. 2021On some theoretical limitations of Generative Adversarial Networkscited by 2
  27. 2022Layer-wise Regularized Adversarial Training using Layers Sustainability Analysis (LSA) frameworkcited by 2
  28. 2022Adversarial Fine-tune with Dynamically Regulated Adversarycited by 2
  29. 2022Holistic Approach to Measure Sample-level Adversarial Vulnerability and its Utility in Building Trustworthy Systemscited by 2
  30. 2024Fermi-Bose Machine achieves both generalization and adversarial robustnesscited by 2
  31. 2025Exact Upper and Lower Bounds for the Output Distribution of Neural Networks with Random Inputscited by 2
  32. 2025Rethinking the Vulnerability of Concept Erasure and a New Methodcited by 2
  33. 2025GradEscape: A Gradient-Based Evader Against AI-Generated Text Detectorscited by 2
  34. 2026The Defense Trilemma: Why Prompt Injection Defense Wrappers Fail?cited by 2
  35. 2021Image classifiers can not be made robust to small perturbationscited by 1
  36. 2022Adversarial Noises Are Linearly Separable for (Nearly) Random Neural Networkscited by 1
  37. 2022Defense Against Multi-target Trojan Attackscited by 1
  38. 2022When are Local Queries Useful for Robust Learning?cited by 1

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