mlsanityData to 7 Oct 2026

Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation

arXiv 1705.08475 ↗First posted 23 May 2017cs.LG cs.AI cs.CVcited by 182

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Abstract (arXiv)

Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high confidence. This raises concerns that such classifiers are vulnerable to attacks and calls into question their usage in safety-critical systems. We show in this paper for the first time formal guarantees on the robustness of a classifier by giving instance-specific lower bounds on the norm of the input manipulation required to change the classifier decision. Based on this analysis we propose the Cross-Lipschitz regularization functional. We show that using this form of regularization in kernel methods resp. neural networks improves the robustness of the classifier without any loss in prediction performance.

Key facts. Cited by 182 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 May 2017.

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Citing papers per year: 2021: 52; 2022: 39; 2023: 33; 2024: 22; 2025: 17; 2026: 19.

182 papers.

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  3. 2024WARM: On the Benefits of Weight Averaged Reward Modelscited by 145
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  10. 2023A Unified Algebraic Perspective on Lipschitz Neural Networkscited by 58
  11. 2021Relating Adversarially Robust Generalization to Flat Minimacited by 57
  12. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
38 more
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  5. 2021How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Reviewcited by 36
  6. 2021A Review of Formal Methods applied to Machine Learningcited by 33
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  10. 2021Noisy Feature Mixupcited by 27
  11. 2021Intriguing Properties of Input-dependent Randomized Smoothingcited by 24
  12. 2023Training robust and generalizable quantum modelscited by 21
  13. 2024H-Consistency Guarantees for Regressioncited by 21
  14. 2022Efficiently Training Low-Curvature Neural Networkscited by 19
  15. 2022Robustness in deep learning: The good (width), the bad (depth), and the ugly (initialization)cited by 18
  16. 2023Improving the Accuracy-Robustness Trade-Off of Classifiers via Adaptive Smoothingcited by 18
  17. 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
  18. 2021CounterNet: End-to-End Training of Prediction Aware Counterfactual Explanationscited by 17
  19. 2021A Unified Game-Theoretic Interpretation of Adversarial Robustnesscited by 17
  20. 2021SPADE: A Spectral Method for Black-Box Adversarial Robustness Evaluationcited by 16
  21. 2021Learning Prediction Intervals for Regression: Generalization and Calibrationcited by 16
  22. 2022A Quantitative Geometric Approach to Neural-Network Smoothnesscited by 16
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  24. 2023LipSim: A Provably Robust Perceptual Similarity Metriccited by 15
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  26. 2021Learning Security Classifiers with Verified Global Robustness Propertiescited by 14
  27. 2023Robust Weight Signatures: Gaining Robustness as Easy as Patching Weights?cited by 13
  28. 2021Learning Diverse-Structured Networks for Adversarial Robustnesscited by 12
  29. 2023Robust low-rank training via approximate orthonormal constraintscited by 12
  30. 2022Adversarial robustness of sparse local Lipschitz predictorscited by 11
  31. 2024PROSAC: Provably Safe Certification for Machine Learning Models under Adversarial Attackscited by 11
  32. 2021Understanding Generalization in Adversarial Training via the Bias-Variance Decompositioncited by 10
  33. 2022UniCR: Universally Approximated Certified Robustness via Randomized Smoothingcited by 10
  34. 2021Increasing the Confidence of Deep Neural Networks by Coverage Analysiscited by 9
  35. 2022Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systemscited by 9
  36. 2021NoiLIn: Improving Adversarial Training and Correcting Stereotype of Noisy Labelscited by 8
  37. 2021On the regularized risk of distributionally robust learning over deep neural networkscited by 8
  38. 2023Asymmetric Certified Robustness via Feature-Convex Neural Networkscited by 8

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