mlsanityData to 7 Oct 2026

Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks

arXiv 1705.01320 ↗First posted 3 May 2017cs.LO cs.AI cs.LGcited by 241

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Abstract (arXiv)

We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern satisfiability modulo theory (SMT) and integer linear programming (ILP) solvers. The starting point of our approach is the addition of a global linear approximation of the overall network behavior to the verification problem that helps with SMT-like reasoning over the network behavior. We present a specialized verification algorithm that employs this approximation in a search process in which it infers additional node phases for the non-linear nodes in the network from partial node phase assignments, similar to unit propagation in classical SAT solving. We also show how to infer additional conflict clauses and safe node fixtures from the results of the analysis steps performed during the search. The resulting approach is evaluated on collision avoidance and handwritten digit recognition case studies.

Key facts. Cited by 241 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 May 2017.

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Citing papers per year: 2021: 56; 2022: 61; 2023: 37; 2024: 35; 2025: 31; 2026: 21.

241 papers.

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  1. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 224
  2. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  3. 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
  4. 2022Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Boundcited by 92
  5. 2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
  6. 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
  7. 2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
  8. 2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44
  9. 2021Certified Patch Robustness via Smoothed Vision Transformerscited by 44
  10. 2022Causality-based Neural Network Repaircited by 44
  11. 2021CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothingcited by 41
  12. 2021Reachability Analysis of Neural Feedback Loopscited by 41
38 more
  1. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 41
  2. 2021Partition-based formulations for mixed-integer optimization of trained ReLU neural networkscited by 39
  3. 2021Provable Repair of Deep Neural Networkscited by 39
  4. 2022How to Robustify Black-Box ML Models? A Zeroth-Order Optimization Perspectivecited by 39
  5. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  6. 2022Don't Lie to Me! Robust and Efficient Explainability with Verified Perturbation Analysiscited by 38
  7. 2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
  8. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  9. 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
  10. 2024Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planescited by 33
  11. 2022VeriX: Towards Verified Explainability of Deep Neural Networkscited by 30
  12. 2021Low Curvature Activations Reduce Overfitting in Adversarial Trainingcited by 29
  13. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 29
  14. 2023Provably Bounding Neural Network Preimagescited by 28
  15. 2021Reachability Is NP-Complete Even for the Simplest Neural Networkscited by 27
  16. 2021Bayesian Inference with Certifiable Adversarial Robustnesscited by 26
  17. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  18. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
  19. 2022Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopescited by 24
  20. 2021DNNV: A Framework for Deep Neural Network Verificationcited by 23
  21. 2022Individual Fairness Guarantees for Neural Networkscited by 23
  22. 2023Expressive Losses for Verified Robustness via Convex Combinationscited by 23
  23. 2023A DPLL(T) Framework for Verifying Deep Neural Networkscited by 23
  24. 2022Neural Network Verification with Proof Productioncited by 22
  25. 2022Fairify: Fairness Verification of Neural Networkscited by 22
  26. 2021Safe Control with Neural Network Dynamic Modelscited by 21
  27. 2022IBP Regularization for Verified Adversarial Robustness via Branch-and-Boundcited by 21
  28. 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
  29. 2021Neural Network Repair with Reachability Analysiscited by 19
  30. 2022NNLander-VeriF: A Neural Network Formal Verification Framework for Vision-Based Autonomous Aircraft Landingcited by 19
  31. 2023Convex Bounds on the Softmax Function with Applications to Robustness Verificationcited by 19
  32. 2021Make Sure You're Unsure: A Framework for Verifying Probabilistic Specificationscited by 18
  33. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 18
  34. 2021Latent Space Smoothing for Individually Fair Representationscited by 18
  35. 2022Verification-Aided Deep Ensemble Selectioncited by 18
  36. 2022Scalable Verification of GNN-based Job Schedulerscited by 18
  37. 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
  38. 2021DeformRS: Certifying Input Deformations with Randomized Smoothingcited by 17

50 most cited of 241 All 241 (JSON)