mlsanityData to 7 Oct 2026

Certified Adversarial Robustness via Anisotropic Randomized Smoothing

arXiv 2207.05327 ↗First posted 12 Jul 2022cs.CVcited by 6

Not on the map. Why?

Abstract (arXiv)

Randomized smoothing has achieved great success for certified robustness against adversarial perturbations. Given any arbitrary classifier, randomized smoothing can guarantee the classifier's prediction over the perturbed input with provable robustness bound by injecting noise into the classifier. However, all of the existing methods rely on fixed i.i.d. probability distribution to generate noise for all dimensions of the data (e.g., all the pixels in an image), which ignores the heterogeneity of inputs and data dimensions. Thus, existing randomized smoothing methods cannot provide optimal protection for all the inputs. To address this limitation, we propose a novel anisotropic randomized smoothing method which ensures provable robustness guarantee based on pixel-wise noise distributions. Also, we design a novel CNN-based noise generator to efficiently fine-tune the pixel-wise noise distributions for all the pixels in each input. Experimental results demonstrate that our method significantly outperforms the state-of-the-art randomized smoothing methods.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 49 of its 64 references that are in the map. First posted on arXiv 12 Jul 2022.

Builds on

49 of 64 references.

References · 49

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  3. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  4. 2016Densely Connected Convolutional Networkscited by 6,691
  5. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  6. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  7. 2018A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attackscited by 1,472
  8. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,442
  9. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  10. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  11. 2017Ensemble Adversarial Training: Attacks and Defensescited by 833
  12. 2018Residual Dense Network for Image Super-Resolutioncited by 796
37 more
  1. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  2. 2020Fast is better than free: Revisiting adversarial trainingcited by 723
  3. 2019Adversarial Training for Free!cited by 638
  4. 2018Improving Transferability of Adversarial Examples with Input Diversitycited by 591
  5. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  6. 2015Empirical Evaluation of Rectified Activations in Convolutional Networkcited by 515
  7. 2017Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networkscited by 484
  8. 2018Certified Robustness to Adversarial Examples with Differential Privacycited by 462
  9. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  10. 2017Mitigating Adversarial Effects Through Randomizationcited by 382
  11. 2018Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Modelscited by 362
  12. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 322
  13. 2018Feature Denoising for Improving Adversarial Robustnesscited by 312
  14. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 311
  15. 2018Certified Defenses against Adversarial Examplescited by 305
  16. 2017Parseval Networks: Improving Robustness to Adversarial Examplescited by 288
  17. 2016Safety Verification of Deep Neural Networkscited by 262
  18. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  19. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
  20. 2017On Detecting Adversarial Perturbationscited by 232
  21. 2018Sorting out Lipschitz function approximationcited by 211
  22. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
  23. 2017Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulationcited by 182
  24. 2019Efficient Decision-based Black-box Adversarial Attacks on Face Recognitioncited by 173
  25. 2019Understanding Adversarial Attacks on Deep Learning Based Medical Image Analysis Systemscited by 151
  26. 2020Randomized Smoothing of All Shapes and Sizescited by 146
  27. 2018Scaling provable adversarial defensescited by 141
  28. 2017An approach to reachability analysis for feed-forward ReLU neural networkscited by 126
  29. 2018A Dual Approach to Scalable Verification of Deep Networkscited by 125
  30. 2018Feature Distillation: DNN-Oriented JPEG Compression Against Adversarial Examplescited by 98
  31. 2017Maximum Resilience of Artificial Neural Networkscited by 97
  32. 2020Towards Robust LiDAR-based Perception in Autonomous Driving: General Black-box Adversarial Sensor Attack and Countermeasurescited by 95
  33. 2017SafetyNet: Detecting and Rejecting Adversarial Examples Robustlycited by 76
  34. 2019Tight Certificates of Adversarial Robustness for Randomly Smoothed Classifierscited by 65
  35. 2020Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Frameworkcited by 45
  36. 2020Data-Dependent Randomized Smoothingcited by 37
  37. 2021ANCER: Anisotropic Certification via Sample-wise Volume Maximizationcited by 23

Built on by

Cited by year (2026 to 7 Oct)

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

6 papers.

  1. 2023Text-CRS: A Generalized Certified Robustness Framework against Textual Adversarial Attackscited by 32
  2. 2023Rethinking Randomized Smoothing from the Perspective of Scalabilitycited by 3
  3. 2024Robust Adaptation of Foundation Models with Black-Box Visual Promptingcited by 3
  4. 2025PLRV-O: Advancing Differentially Private Deep Learning via Privacy Loss Random Variable Optimizationcited by 1
  5. 2026Traffic-Aware Randomized Smoothing for LLM-Based Network Intrusion Detectioncited by 0
  6. 2026Faults That Fortify: CNN Adversarial Robustness via GPU Undervoltingcited by 0