mlsanityData to 7 Oct 2026

Tight Certificates of Adversarial Robustness for Randomly Smoothed Classifiers

arXiv 1906.04948 ↗First posted 12 Jun 2019cs.LG stat.MLcited by 65

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Abstract (arXiv)

Strong theoretical guarantees of robustness can be given for ensembles of classifiers generated by input randomization. Specifically, an ℓ2 bounded adversary cannot alter the ensemble prediction generated by an additive isotropic Gaussian noise, where the radius for the adversary depends on both the variance of the distribution as well as the ensemble margin at the point of interest. We build on and considerably expand this work across broad classes of distributions. In particular, we offer adversarial robustness guarantees and associated algorithms for the discrete case where the adversary is ℓ0 bounded. Moreover, we exemplify how the guarantees can be tightened with specific assumptions about the function class of the classifier such as a decision tree. We empirically illustrate these results with and without functional restrictions across image and molecule datasets.

Key facts. Cited by 65 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 16; 2023: 13; 2024: 11; 2025: 9; 2026: 5.

65 papers.

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  1. 2021PatchCleanser: Certifiably Robust Defense against Adversarial Patches for Any Image Classifiercited by 63
  2. 2021PointGuard: Provably Robust 3D Point Cloud Classificationcited by 49
  3. 2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
  4. 2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
  5. 2021CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothingcited by 41
  6. 2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
  7. 2021ANCER: Anisotropic Certification via Sample-wise Volume Maximizationcited by 23
  8. 2022Double Sampling Randomized Smoothingcited by 22
  9. 2021How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implicationscited by 21
  10. 2021Center Smoothing: Certified Robustness for Networks with Structured Outputscited by 18
  11. 2022StyleFool: Fooling Video Classification Systems via Style Transfercited by 18
  12. 2022BagFlip: A Certified Defense against Data Poisoningcited by 18
38 more
  1. 2023RS-Del: Edit Distance Robustness Certificates for Sequence Classifiers via Randomized Deletioncited by 17
  2. 2023Collective Robustness Certificates: Exploiting Interdependence in Graph Neural Networkscited by 16
  3. 2024Robust Yet Efficient Conformal Prediction Setscited by 16
  4. 2024Advancing the Robustness of Large Language Models through Self-Denoised Smoothingcited by 15
  5. 2025Unveiling the Basin-Like Loss Landscape in Large Language Modelscited by 13
  6. 2023Incremental Randomized Smoothing Certificationcited by 12
  7. 2022Input-agnostic Certified Group Fairness via Gaussian Parameter Smoothingcited by 11
  8. 2023Projected Randomized Smoothing for Certified Adversarial Robustnesscited by 11
  9. 2022UniCR: Universally Approximated Certified Robustness via Randomized Smoothingcited by 10
  10. 2022CARE: Certifiably Robust Learning with Reasoning via Variational Inferencecited by 10
  11. 2022Localized Randomized Smoothing for Collective Robustness Certificationcited by 10
  12. 2023Randomized Message-Interception Smoothing: Gray-box Certificates for Graph Neural Networkscited by 10
  13. 2022MultiGuard: Provably Robust Multi-label Classification against Adversarial Examplescited by 9
  14. 2022Confidence-aware Training of Smoothed Classifiers for Certified Robustnesscited by 9
  15. 2023It Is All About Data: A Survey on the Effects of Data on Adversarial Robustnesscited by 9
  16. 2023Hierarchical Randomized Smoothingcited by 9
  17. 2023Node-aware Bi-smoothing: Certified Robustness against Graph Injection Attackscited by 8
  18. 2024Treatment of Statistical Estimation Problems in Randomized Smoothing for Adversarial Robustnesscited by 8
  19. 2021Integer-arithmetic-only Certified Robustness for Quantized Neural Networkscited by 7
  20. 2022Accelerating Certified Robustness Training via Knowledge Transfercited by 7
  21. 2022Invariance-Aware Randomized Smoothing Certificatescited by 7
  22. 2023Understanding Noise-Augmented Training for Randomized Smoothingcited by 7
  23. 2025Towards the Worst-case Robustness of Large Language Modelscited by 7
  24. 2022Certified Adversarial Robustness via Anisotropic Randomized Smoothingcited by 6
  25. 2022Smoothed Embeddings for Certified Few-Shot Learningcited by 5
  26. 2022(De-)Randomized Smoothing for Decision Stump Ensemblescited by 5
  27. 2023PECAN: A Deterministic Certified Defense Against Backdoor Attackscited by 5
  28. 2023A Certified Radius-Guided Attack Framework to Image Segmentation Modelscited by 5
  29. 2024RS-Reg: Probabilistic and Robust Certified Regression Through Randomized Smoothingcited by 4
  30. 2024SPLITZ: Certifiable Robustness via Split Lipschitz Randomized Smoothingcited by 4
  31. 2025Robust Conformal Prediction with a Single Binary Certificatecited by 4
  32. 2025One Sample is Enough to Make Conformal Prediction Robustcited by 4
  33. 2024Privacy-preserving Universal Adversarial Defense for Black-box Modelscited by 3
  34. 2023Structure-Aware Robustness Certificates for Graph Classificationcited by 2
  35. 2024Discrete Randomized Smoothing Meets Quantum Computingcited by 2
  36. 2025Reconcile Certified Robustness and Accuracy for DNN-based Smoothed Majority Vote Classifiercited by 2
  37. 2021Towards Bridging the gap between Empirical and Certified Robustness against Adversarial Examplescited by 1
  38. 2022An Overview and Prospective Outlook on Robust Training and Certification of Machine Learning Modelscited by 1

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