mlsanityData to 7 Oct 2026

UniCR: Universally Approximated Certified Robustness via Randomized Smoothing

arXiv 2207.02152 ↗First posted 5 Jul 2022cs.LGcited by 10

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Abstract (arXiv)

We study certified robustness of machine learning classifiers against adversarial perturbations. In particular, we propose the first universally approximated certified robustness (UniCR) framework, which can approximate the robustness certification of any input on any classifier against any ℓp perturbations with noise generated by any continuous probability distribution. Compared with the state-of-the-art certified defenses, UniCR provides many significant benefits: (1) the first universal robustness certification framework for the above 4 'any's; (2) automatic robustness certification that avoids case-by-case analysis, (3) tightness validation of certified robustness, and (4) optimality validation of noise distributions used by randomized smoothing. We conduct extensive experiments to validate the above benefits of UniCR and the advantages of UniCR over state-of-the-art certified defenses against ℓp perturbations.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 44 of its 64 references that are in the map. First posted on arXiv 5 Jul 2022.

Builds on

44 of 64 references.

References · 44

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
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  6. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
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32 more
  1. 2019HopSkipJumpAttack: A Query-Efficient Decision-Based Attackcited by 328
  2. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 322
  3. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 311
  4. 2018Certified Defenses against Adversarial Examplescited by 305
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  6. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
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  8. 2018Sorting out Lipschitz function approximationcited by 211
  9. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
  10. 2017Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulationcited by 182
  11. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
  12. 2019Certified Robustness to Adversarial Word Substitutionscited by 164
  13. 2020Randomized Smoothing of All Shapes and Sizescited by 146
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  17. 2019Wasserstein Adversarial Examples via Projected Sinkhorn Iterationscited by 89
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  19. 2019Tight Certificates of Adversarial Robustness for Randomly Smoothed Classifierscited by 65
  20. 2019Robustness Certificates for Sparse Adversarial Attacks by Randomized Ablationcited by 59
  21. 2020Certified Robustness of Graph Neural Networks against Adversarial Structural Perturbationcited by 57
  22. 2019Certified Robustness for Top-k Predictions against Adversarial Perturbations via Randomized Smoothingcited by 54
  23. 2018Training verified learners with learned verifierscited by 50
  24. 2020Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Frameworkcited by 45
  25. 2019Provable robustness against all adversarial lp-perturbations for p≥ 1cited by 39
  26. 2018Adversarial Perturbations Against Real-Time Video Classification Systemscited by 32
  27. 2020Certified Robustness of Community Detection against Adversarial Structural Perturbation via Randomized Smoothingcited by 29
  28. 2018Procedural Noise Adversarial Examples for Black-Box Attacks on Deep Convolutional Networkscited by 21
  29. 2020Almost Tight L0-norm Certified Robustness of Top-k Predictions against Adversarial Perturbationscited by 16
  30. 2021Universal 3-Dimensional Perturbations for Black-Box Attacks on Video Recognition Systemscited by 14
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  32. 2022An Eye for an Eye: Defending against Gradient-based Attacks with Gradientscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 4; 2026: 1.

10 papers.

  1. 2024Adaptive Randomized Smoothing: Certified Adversarial Robustness for Multi-Step Defencescited by 9
  2. 2023A Certified Radius-Guided Attack Framework to Image Segmentation Modelscited by 5
  3. 2023Certifiable Black-Box Attacks with Randomized Adversarial Examples: Breaking Defenses with Provable Confidencecited by 5
  4. 2024Privacy-preserving Universal Adversarial Defense for Black-box Modelscited by 3
  5. 2024Learning Robust and Privacy-Preserving Representations via Information Theorycited by 3
  6. 2025Reconcile Certified Robustness and Accuracy for DNN-based Smoothed Majority Vote Classifiercited by 2
  7. 2025PLRV-O: Advancing Differentially Private Deep Learning via Privacy Loss Random Variable Optimizationcited by 1
  8. 2025Towards Strong Certified Defense with Universal Asymmetric Randomizationcited by 1
  9. 2026Certified vs. Empirical Adversarial Robust-ness via Hybrid Convolutions with Attention Stochasticitycited by 1
  10. 2025Principal Eigenvalue Regularization for Improved Worst-Class Certified Robustness of Smoothed Classifierscited by 0