mlsanityData to 14 Oct 2026

CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networks

arXiv 2109.10696 ↗First posted 22 Sep 2021cs.LG cs.AIcited by 19

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Abstract (arXiv)

In safety-critical machine learning applications, it is crucial to defend models against adversarial attacks -- small modifications of the input that change the predictions. Besides rigorously studied ℓp-bounded additive perturbations, recently proposed semantic perturbations (e.g. rotation, translation) raise a serious concern on deploying ML systems in real-world. Therefore, it is important to provide provable guarantees for deep learning models against semantically meaningful input transformations. In this paper, we propose a new universal probabilistic certification approach based on Chernoff-Cramer bounds that can be used in general attack settings. We estimate the probability of a model to fail if the attack is sampled from a certain distribution. Our theoretical findings are supported by experimental results on different datasets.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 35 of its 46 references that are in the map. First posted on arXiv 22 Sep 2021.

Builds on

35 of 46 references.

References · 35

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  3. 2013Intriguing properties of neural networkscited by 5,155
  4. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,998
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,340
  6. 2015DeepFool: a simple and accurate method to fool deep neural networkscited by 1,318
  7. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,268
  8. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
  9. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 567
  10. 2020On Adaptive Attacks to Adversarial Example Defensescited by 555
  11. 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 546
  12. 2018Certified Robustness to Adversarial Examples with Differential Privacycited by 468
23 more
  1. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 330
  2. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 328
  3. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 242
  4. 2019Kornia: an Open Source Differentiable Computer Vision Library for PyTorchcited by 232
  5. 2018Sorting out Lipschitz function approximationcited by 213
  6. 2018Spatially Transformed Adversarial Examplescited by 195
  7. 2018Certified Adversarial Robustness with Additive Noisecited by 180
  8. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 179
  9. 2018A Dual Approach to Scalable Verification of Deep Networkscited by 125
  10. 2020MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radiuscited by 114
  11. 2019Preventing Gradient Attenuation in Lipschitz Constrained Convolutional Networkscited by 87
  12. 2018Semantic Adversarial Examplescited by 86
  13. 2017Exploring the Landscape of Spatial Robustnesscited by 81
  14. 2019Robustness Certificates for Sparse Adversarial Attacks by Randomized Ablationcited by 60
  15. 2019Semantic Adversarial Attacks: Parametric Transformations That Fool Deep Classifierscited by 57
  16. 2020Certified Defense to Image Transformations via Randomized Smoothingcited by 51
  17. 2020TSS: Transformation-Specific Smoothing for Robustness Certificationcited by 49
  18. 2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
  19. 2017Geometric robustness of deep networks: analysis and improvementcited by 45
  20. 2019Robustness of Neural Networks: A Probabilistic and Practical Approachcited by 38
  21. 2020Higher-Order Certification for Randomized Smoothingcited by 37
  22. 2020Achieving robustness in classification using optimal transport with hinge regularizationcited by 27
  23. 2021DeformRS: Certifying Input Deformations with Randomized Smoothingcited by 17

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 2; 2024: 3; 2025: 5; 2026: 6.

19 papers.

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  1. 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19
  2. 2022Smoothed Embeddings for Certified Few-Shot Learningcited by 6
  3. 2025Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guidecited by 6
  4. 2022Probabilistic Verification of ReLU Neural Networks via Characteristic Functionscited by 5
  5. 2023Precise and Generalized Robustness Certification for Neural Networkscited by 4
  6. 2024RS-Reg: Probabilistic and Robust Certified Regression Through Randomized Smoothingcited by 4
  7. 2024SAVER: A Toolbox for Sampling-Based, Probabilistic Verification of Neural Networkscited by 2
  8. 2025Probabilistically Tightened Linear Relaxation-based Perturbation Analysis for Neural Network Verificationcited by 2
  9. 2024Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothingcited by 1
  10. 2025PRBench: A Standardized Probabilistic Robustness Benchmarkcited by 1
  11. 2025Non-Parametric Probabilistic Robustness: A Conservative Risk Estimator under Unknown Perturbation Distributionscited by 1
  12. 2026Semantic Robustness Certification for Vision-Language Modelscited by 1
7 more
  1. 2026Propagation of~Interval Belief Structures and~Imprecise Copulas for~Neural Network Verificationcited by 1
  2. 2023General Lipschitz: Certified Robustness Against Resolvable Semantic Transformations via Transformation-Dependent Randomized Smoothingcited by 0
  3. 2025BaB-prob: Branch and Bound with Preactivation Splitting for Probabilistic Verification of Neural Networkscited by 0
  4. 2026Towards Compact and Robust DNNs via Compression-aware Sharpness Minimizationcited by 0
  5. 2026Contract And Conquer: How to Provably Compute Adversarial Examples for a Black-Box Model?cited by 0
  6. 2026Probabilistic Verification of Voice Anti-Spoofing Modelscited by 0
  7. 2026Adversarial Detection for Pre-trained Classifiers via Lipschitz-Margin Analysis with Certificationcited by 0