mlsanityData to 14 Oct 2026

Efficient Neural Network Robustness Certification with General Activation Functions

arXiv 1811.00866 ↗First posted 2 Nov 2018cs.LG cs.CR stat.MLcited by 445

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Abstract (arXiv)

Finding minimum distortion of adversarial examples and thus certifying robustness in neural network classifiers for given data points is known to be a challenging problem. Nevertheless, recently it has been shown to be possible to give a non-trivial certified lower bound of minimum adversarial distortion, and some recent progress has been made towards this direction by exploiting the piece-wise linear nature of ReLU activations. However, a generic robustness certification for general activation functions still remains largely unexplored. To address this issue, in this paper we introduce CROWN, a general framework to certify robustness of neural networks with general activation functions for given input data points. The novelty in our algorithm consists of bounding a given activation function with linear and quadratic functions, hence allowing it to tackle general activation functions including but not limited to four popular choices: ReLU, tanh, sigmoid and arctan. In addition, we facilitate the search for a tighter certified lower bound by adaptively selecting appropriate surrogates for each neuron activation. Experimental results show that CROWN on ReLU networks can notably improve the certified lower bounds compared to the current state-of-the-art algorithm Fast-Lin, while having comparable computational efficiency. Furthermore, CROWN also demonstrates its effectiveness and flexibility on networks with general activation functions, including tanh, sigmoid and arctan.

Key facts. Cited by 445 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Nov 2018.

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Citing papers per year: 2021: 73; 2022: 72; 2023: 72; 2024: 78; 2025: 65; 2026: 85.

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  1. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 228
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  10. 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
  11. 2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
  12. 2021Improving Adversarial Robustness via Channel-wise Activation Suppressingcited by 76
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  4. 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
  5. 2021Relating Adversarially Robust Generalization to Flat Minimacited by 57
  6. 2022Certified Training: Small Boxes are All You Needcited by 52
  7. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 51
  8. 2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
  9. 2021Improved deterministic l2 robustness on CIFAR-10 and CIFAR-100cited by 47
  10. 2024Neural Network Verification with Branch-and-Bound for General Nonlinearitiescited by 47
  11. 2021Fast Certified Robust Training with Short Warmupcited by 46
  12. 2021Certified Patch Robustness via Smoothed Vision Transformerscited by 45
  13. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  14. 2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44
  15. 2022Efficient Adversarial Training without Attacking: Worst-Case-Aware Robust Reinforcement Learningcited by 43
  16. 2021CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothingcited by 42
  17. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 42
  18. 2021Reachability Analysis of Neural Feedback Loopscited by 41
  19. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  20. 2021On the Certified Robustness for Ensemble Models and Beyondcited by 40
  21. 2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
  22. 2021POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systemscited by 39
  23. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  24. 2022Don't Lie to Me! Robust and Efficient Explainability with Verified Perturbation Analysiscited by 38
  25. 2023Exploring and Exploiting Decision Boundary Dynamics for Adversarial Robustnesscited by 36
  26. 2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
  27. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  28. 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
  29. 2022DensePure: Understanding Diffusion Models towards Adversarial Robustnesscited by 33
  30. 2024Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planescited by 33
  31. 2022VeriX: Towards Verified Explainability of Deep Neural Networkscited by 30
  32. 2023Provably Bounding Neural Network Preimagescited by 29
  33. 2021Bayesian Inference with Certifiable Adversarial Robustnesscited by 26
  34. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  35. 2024Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulationcited by 25
  36. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  37. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  38. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24

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