mlsanityData to 14 Oct 2026

An Abstraction-Based Framework for Neural Network Verification

arXiv 1910.14574 ↗First posted 31 Oct 2019cs.FL cs.LGcited by 68

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Abstract (arXiv)

Deep neural networks are increasingly being used as controllers for safety-critical systems. Because neural networks are opaque, certifying their correctness is a significant challenge. To address this issue, several neural network verification approaches have recently been proposed. However, these approaches afford limited scalability, and applying them to large networks can be challenging. In this paper, we propose a framework that can enhance neural network verification techniques by using over-approximation to reduce the size of the network - thus making it more amenable to verification. We perform the approximation such that if the property holds for the smaller (abstract) network, it holds for the original as well. The over-approximation may be too coarse, in which case the underlying verification tool might return a spurious counterexample. Under such conditions, we perform counterexample-guided refinement to adjust the approximation, and then repeat the process. Our approach is orthogonal to, and can be integrated with, many existing verification techniques. For evaluation purposes, we integrate it with the recently proposed Marabou framework, and observe a significant improvement in Marabou's performance. Our experiments demonstrate the great potential of our approach for verifying larger neural networks.

Key facts. Cited by 68 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Oct 2019.

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Citing papers per year: 2021: 10; 2022: 21; 2023: 15; 2024: 9; 2025: 9; 2026: 4.

68 papers.

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  1. 2022Causality-based Neural Network Repaircited by 47
  2. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 42
  3. 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
  4. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  5. 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
  6. 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
  7. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
  8. 2023Towards quantum enhanced adversarial robustness in machine learningcited by 28
  9. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  10. 2022Neural Network Verification with Proof Productioncited by 22
  11. 2022Fairify: Fairness Verification of Neural Networkscited by 22
  12. 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
38 more
  1. 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
  2. 2021Probabilistic Verification of Neural Networks Against Group Fairnesscited by 17
  3. 2025RvLLM: LLM Runtime Verification with Domain Knowledgecited by 17
  4. 2022Toward Certified Robustness Against Real-World Distribution Shiftscited by 16
  5. 2021Attack as Defense: Characterizing Adversarial Examples using Robustnesscited by 14
  6. 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
  7. 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)cited by 14
  8. 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
  9. 2025Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanationscited by 13
  10. 2021Towards Practical Robustness Analysis for DNNs based on PAC-Model Learningcited by 12
  11. 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection Systemcited by 12
  12. 2022QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networkscited by 12
  13. 2023Distributionally Robust Statistical Verification with Imprecise Neural Networkscited by 12
  14. 2022Abstraction and Refinement: Towards Scalable and Exact Verification of Neural Networkscited by 11
  15. 2023Verifying Generalization in Deep Learningcited by 11
  16. 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretationcited by 11
  17. 2022Safe Neurosymbolic Learning with Differentiable Symbolic Executioncited by 9
  18. 2022QEBVerif: Quantization Error Bound Verification of Neural Networkscited by 9
  19. 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
  20. 2024Robustness Assessment of a Runway Object Classifier for Safe Aircraft Taxiingcited by 8
  21. 2024PREMAP: A Unifying PREiMage APproximation Framework for Neural Networkscited by 8
  22. 2024Provably Safe Neural Network Controllers via Differential Dynamic Logiccited by 7
  23. 2021Bisimulations for Neural Network Reductioncited by 6
  24. 2022On Optimizing Back-Substitution Methods for Neural Network Verificationcited by 6
  25. 2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
  26. 2023OccRob: Efficient SMT-Based Occlusion Robustness Verification of Deep Neural Networkscited by 5
  27. 2025Abstraction-Based Proof Production in Formal Verification of Neural Networkscited by 5
  28. 2022Boosting Robustness Verification of Semantic Feature Neighborhoodscited by 4
  29. 2024Towards Formal Verification of Deep Neural Networks for Object Detectioncited by 4
  30. 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
  31. 2023Detecting Violations of Differential Privacy for Quantum Algorithmscited by 3
  32. 2025PICID: Proof-Driven Clause Learning in Neural Network Verificationcited by 3
  33. 2025Monitoring Robustness and Individual Fairnesscited by 3
  34. 2022VPN: Verification of Poisoning in Neural Networkscited by 2
  35. 2023Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networkscited by 2
  36. 2023A Tale of Two Approximations: Tightening Over-Approximation for DNN Robustness Verification via Under-Approximationcited by 2
  37. 2025Scalable and Interpretable Verification of Image-based Neural Network Controllers for Autonomous Vehiclescited by 2
  38. 2025Verification of Bit-Flip Attacks against Quantized Neural Networkscited by 2

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