mlsanityData to 14 Oct 2026

Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework

arXiv 2002.09169 ↗First posted 21 Feb 2020cs.LG cs.CR math.OCcited by 46

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Abstract (arXiv)

Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing noise and only work for ℓ2 perturbation. We propose a general framework of adversarial certification with non-Gaussian noise and for more general types of attacks, from a unified functional optimization perspective. Our new framework allows us to identify a key trade-off between accuracy and robustness via designing smoothing distributions, helping to design new families of non-Gaussian smoothing distributions that work more efficiently for different ℓp settings, including ℓ1, ℓ2 and ℓ_∞ attacks. Our proposed methods achieve better certification results than previous works and provide a new perspective on randomized smoothing certification.

Key facts. Cited by 46 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 Feb 2020.

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Citing papers per year: 2021: 7; 2022: 15; 2023: 9; 2024: 9; 2025: 5; 2026: 1.

46 papers.

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  1. 2021Advances in adversarial attacks and defenses in computer vision: A surveycited by 127
  2. 2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
  3. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  4. 2021On the Certified Robustness for Ensemble Models and Beyondcited by 40
  5. 2023Text-CRS: A Generalized Certified Robustness Framework against Textual Adversarial Attackscited by 34
  6. 2021Knowledge Enhanced Machine Learning Pipeline against Diverse Adversarial Attackscited by 24
  7. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  8. 2022Double Sampling Randomized Smoothingcited by 22
  9. 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19
  10. 2024Provably Unlearnable Data Examplescited by 18
  11. 2022On Collective Robustness of Bagging Against Data Poisoningcited by 16
  12. 2024NLP Verification: Towards a General Methodology for Certifying Robustnesscited by 16
34 more
  1. 2022RetrievalGuard: Provably Robust 1-Nearest Neighbor Image Retrievalcited by 15
  2. 2023Incremental Randomized Smoothing Certificationcited by 12
  3. 2023Projected Randomized Smoothing for Certified Adversarial Robustnesscited by 11
  4. 2022UniCR: Universally Approximated Certified Robustness via Randomized Smoothingcited by 10
  5. 2022Localized Randomized Smoothing for Collective Robustness Certificationcited by 10
  6. 2022Defending Black-box Skeleton-based Human Activity Classifierscited by 9
  7. 2022Towards Robust Dataset Learningcited by 9
  8. 2022Confidence-aware Training of Smoothed Classifiers for Certified Robustnesscited by 9
  9. 2023Nonparametric Iterative Machine Teachingcited by 9
  10. 2022Formulating Robustness Against Unforeseen Attackscited by 8
  11. 2022Building Robust Ensembles via Margin Boostingcited by 8
  12. 2023Asymmetric Certified Robustness via Feature-Convex Neural Networkscited by 8
  13. 2023Nonparametric Teaching for Multiple Learnerscited by 7
  14. 2021Certified Robustness via Randomized Smoothing over Multiplicative Parameters of Input Transformationscited by 6
  15. 2022Smoothed Embeddings for Certified Few-Shot Learningcited by 6
  16. 2022Certified Adversarial Robustness via Anisotropic Randomized Smoothingcited by 6
  17. 2022(De-)Randomized Smoothing for Decision Stump Ensemblescited by 5
  18. 2023Understanding the Robustness of Randomized Feature Defense Against Query-Based Adversarial Attackscited by 4
  19. 2024RS-Reg: Probabilistic and Robust Certified Regression Through Randomized Smoothingcited by 4
  20. 2025One Sample is Enough to Make Conformal Prediction Robustcited by 4
  21. 2024Privacy-preserving Universal Adversarial Defense for Black-box Modelscited by 3
  22. 2024Discrete Randomized Smoothing Meets Quantum Computingcited by 2
  23. 2025Reconcile Certified Robustness and Accuracy for DNN-based Smoothed Majority Vote Classifiercited by 2
  24. 2022An Overview and Prospective Outlook on Robust Training and Certification of Machine Learning Modelscited by 1
  25. 2023Towards Large Certified Radius in Randomized Smoothing using Quasiconcave Optimizationcited by 1
  26. 2024Position: Towards Resilience Against Adversarial Examplescited by 1
  27. 2024Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothingcited by 1
  28. 2024Certifiably Robust Encoding Schemescited by 1
  29. 2024ARQ: A Mixed-Precision Quantization Framework for Accurate and Certifiably Robust DNNscited by 1
  30. 2025CAMP in the Odyssey: Provably Robust Reinforcement Learning with Certified Radius Maximizationcited by 1
  31. 2025Towards Strong Certified Defense with Universal Asymmetric Randomizationcited by 1
  32. 2023[Re] Double Sampling Randomized Smoothingcited by 0
  33. 2025Principal Eigenvalue Regularization for Improved Worst-Class Certified Robustness of Smoothed Classifierscited by 0
  34. 2026Provable Robustness against Backdoor Attacks via the Primal-Dual Perspective on Differential Privacycited by 0