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Introduction to Neural Network Verification

arXiv 2109.10317 ↗First posted 21 Sep 2021cs.LG cs.AI cs.PLcited by 63

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Abstract (arXiv)

Deep learning has transformed the way we think of software and what it can do. But deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security, correctness, or robustness of neural networks. This book covers foundational ideas from formal verification and their adaptation to reasoning about neural networks and deep learning.

Key facts. Cited by 63 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Sep 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 10; 2023: 12; 2024: 19; 2025: 9; 2026: 12.

63 papers.

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  1. 2024Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systemscited by 94
  2. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 29
  3. 2023Formally Explaining Neural Networks within Reactive Systemscited by 24
  4. 2022Double Sampling Randomized Smoothingcited by 22
  5. 2021Certifying Robustness to Programmable Data Bias in Decision Treescited by 21
  6. 2022Neuro-Symbolic Verification of Deep Neural Networkscited by 21
  7. 2022A Quantitative Geometric Approach to Neural-Network Smoothnesscited by 16
  8. 2023Incremental Verification of Neural Networkscited by 14
  9. 2024NLP Verification: Towards a General Methodology for Certifying Robustnesscited by 14
  10. 2022Certifiable 3D Object Pose Estimation: Foundations, Learning Models, and Self-Trainingcited by 12
  11. 2024Mask in the Mirror: Implicit Sparsificationcited by 12
  12. 2025Neural Network Verification is a Programming Language Challengecited by 12
38 more
  1. 2023Verifying Generalization in Deep Learningcited by 11
  2. 2022On Neural Network Equivalence Checking using SMT Solverscited by 10
  3. 2024How should AI decisions be explained? Requirements for Explanations from the Perspective of European Lawcited by 10
  4. 2022Safe Neurosymbolic Learning with Differentiable Symbolic Executioncited by 9
  5. 2025Systems Security Foundations for Agentic Computingcited by 9
  6. 2022Provable Fairness for Neural Network Models using Formal Verificationcited by 6
  7. 2023When to Trust AI: Advances and Challenges for Certification of Neural Networkscited by 6
  8. 2024Neural Interactive Proofscited by 6
  9. 2023Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theorycited by 5
  10. 2024Sonar-based Deep Learning in Underwater Robotics: Overview, Robustness and Challengescited by 5
  11. 2025No Soundness in the Real World: On the Challenges of the Verification of Deployed Neural Networkscited by 5
  12. 2025Beyond Benchmarks: On The False Promise of AI Regulationcited by 4
  13. 2025Faster Verified Explanations for Neural Networkscited by 4
  14. 2022Verifiable Obstacle Detectioncited by 3
  15. 2023Reliability Assurance for Deep Neural Network Architectures Against Numerical Defectscited by 3
  16. 2023DelBugV: Delta-Debugging Neural Network Verifierscited by 3
  17. 2023Detecting Violations of Differential Privacy for Quantum Algorithmscited by 3
  18. 2022CEG4N: Counter-Example Guided Neural Network Quantization Refinementcited by 2
  19. 2023On the verification of Embeddings using Hybrid Markov Logiccited by 2
  20. 2024Verifying the Generalization of Deep Learning to Out-of-Distribution Domainscited by 2
  21. 2024Wasserstein Distributionally Robust Shallow Convex Neural Networkscited by 2
  22. 2024Query languages for neural networkscited by 2
  23. 2024ROSAR: An Adversarial Re-Training Framework for Robust Side-Scan Sonar Object Detectioncited by 2
  24. 2024Learning Ensembles of Vision-based Safety Control Filterscited by 2
  25. 2025SQL4NN: Validation and expressive querying of models as datacited by 2
  26. 2026Recursive querying of neural networks via weighted structurescited by 2
  27. 2022Perception Simplex: Verifiable Collision Avoidance in Autonomous Vehicles Amidst Obstacle Detection Faultscited by 1
  28. 2023Efficient Symbolic Reasoning for Neural-Network Verificationcited by 1
  29. 2024Inferring Data Preconditions from Deep Learning Models for Trustworthy Prediction in Deploymentcited by 1
  30. 2024Outline of an Independent Systematic Blackbox Test for ML-based Systemscited by 1
  31. 2024Cyclic Sparse Training: Is it Enough?cited by 1
  32. 2024VeriFlow: Modeling Distributions for Neural Network Verificationcited by 1
  33. 2025A General Framework for Property-Driven Machine Learningcited by 1
  34. 2026Learning to Optimize by Differentiable Programmingcited by 1
  35. 2026Algebraic Invariants of Lightning Self-Attentioncited by 1
  36. 2023The Power of Typed Affine Decision Structures: A Case Studycited by 0
  37. 2023Functional trustworthiness of AI systems by statistically valid testingcited by 0
  38. 2024Robustness Verifcation in Neural Networkscited by 0

50 most cited of 63 All 63 (JSON)