mlsanityData to 7 Oct 2026

Algorithms for Verifying Deep Neural Networks

arXiv 1903.06758 ↗First posted 15 Mar 2019cs.LG stat.MLcited by 221

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Abstract (arXiv)

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging to verify whether a particular network satisfies certain input-output properties. This article surveys methods that have emerged recently for soundly verifying such properties. These methods borrow insights from reachability analysis, optimization, and search. We discuss fundamental differences and connections between existing algorithms. In addition, we provide pedagogical implementations of existing methods and compare them on a set of benchmark problems.

Key facts. Cited by 221 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Mar 2019.

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Citing papers per year: 2020: 1; 2021: 37; 2022: 41; 2023: 44; 2024: 35; 2025: 39; 2026: 24.

221 papers.

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  1. 2022Safety-Enhanced Autonomous Driving Using Interpretable Sensor Fusion Transformercited by 211
  2. 2023A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validationcited by 91
  3. 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
  4. 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
  5. 2022Logic-Based Explainability in Machine Learningcited by 47
  6. 2021Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learningcited by 43
  7. 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
  8. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 41
  9. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  10. 2021OVERT: An Algorithm for Safety Verification of Neural Network Control Policies for Nonlinear Systemscited by 37
  11. 2021Neural Network Robustness as a Verification Property: A Principled Case Studycited by 35
  12. 2021Inspect, Understand, Overcome: A Survey of Practical Methods for AI Safetycited by 35
38 more
  1. 2022VeriX: Towards Verified Explainability of Deep Neural Networkscited by 30
  2. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 29
  3. 2021Verification of Image-based Neural Network Controllers Using Generative Modelscited by 27
  4. 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopescited by 26
  5. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
  6. 2023Formally Explaining Neural Networks within Reactive Systemscited by 24
  7. 2021DNNV: A Framework for Deep Neural Network Verificationcited by 23
  8. 2023A DPLL(T) Framework for Verifying Deep Neural Networkscited by 23
  9. 2024Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulationcited by 23
  10. 2022Double Sampling Randomized Smoothingcited by 22
  11. 2021Safe Control with Neural Network Dynamic Modelscited by 21
  12. 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
  13. 2022Physics guided neural networks for modelling of non-linear dynamicscited by 20
  14. 2023DiffSmooth: Certifiably Robust Learning via Diffusion Models and Local Smoothingcited by 20
  15. 2021Scaling Up Exact Neural Network Compression by ReLU Stabilitycited by 19
  16. 2022POLICE: Provably Optimal Linear Constraint Enforcement for Deep Neural Networkscited by 19
  17. 2023The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networkscited by 19
  18. 2023Enumerating Safe Regions in Deep Neural Networks with Provable Probabilistic Guaranteescited by 19
  19. 2021Make Sure You're Unsure: A Framework for Verifying Probabilistic Specificationscited by 18
  20. 2022CertiFair: A Framework for Certified Global Fairness of Neural Networkscited by 17
  21. 2021Neural Termination Analysiscited by 16
  22. 2023From Robustness to Explainability and Back Againcited by 14
  23. 2024NLP Verification: Towards a General Methodology for Certifying Robustnesscited by 14
  24. 2021Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verificationcited by 13
  25. 2022Reachability Analysis of a General Class of Neural Ordinary Differential Equationscited by 13
  26. 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)cited by 13
  27. 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
  28. 2021A Simple and Efficient Sampling-based Algorithm for General Reachability Analysiscited by 12
  29. 2022A Unified View of SDP-based Neural Network Verification through Completely Positive Programmingcited by 12
  30. 2024Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagationcited by 12
  31. 2020PILOT: Efficient Planning by Imitation Learning and Optimisation for Safe Autonomous Drivingcited by 11
  32. 2021Learning Density Distribution of Reachable States for Autonomous Systemscited by 11
  33. 2021Curriculum Learning for Safe Mapless Navigationcited by 11
  34. 2022Constrained Reinforcement Learning for Robotics via Scenario-Based Programmingcited by 11
  35. 2023Neural Abstractionscited by 11
  36. 2023Towards Verifying the Geometric Robustness of Large-scale Neural Networkscited by 11
  37. 2021Coordinate Linear Variance Reduction for Generalized Linear Programmingcited by 10
  38. 2021Benchmarking Safe Deep Reinforcement Learning in Aquatic Navigationcited by 10

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