An Abstraction-Based Framework for Neural Network Verification
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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.
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- 2022Causality-based Neural Network Repaircited by 47
- 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 42
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
- 2021A Review of Formal Methods applied to Machine Learningcited by 33
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- 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
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- 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
- 2022Neural Network Verification with Proof Productioncited by 22
- 2022Fairify: Fairness Verification of Neural Networkscited by 22
- 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
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- 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
- 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)cited by 14
- 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
- 2025Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanationscited by 13
- 2021Towards Practical Robustness Analysis for DNNs based on PAC-Model Learningcited by 12
- 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection Systemcited by 12
- 2022QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networkscited by 12
- 2023Distributionally Robust Statistical Verification with Imprecise Neural Networkscited by 12
- 2022Abstraction and Refinement: Towards Scalable and Exact Verification of Neural Networkscited by 11
- 2023Verifying Generalization in Deep Learningcited by 11
- 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretationcited by 11
- 2022Safe Neurosymbolic Learning with Differentiable Symbolic Executioncited by 9
- 2022QEBVerif: Quantization Error Bound Verification of Neural Networkscited by 9
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- 2024PREMAP: A Unifying PREiMage APproximation Framework for Neural Networkscited by 8
- 2024Provably Safe Neural Network Controllers via Differential Dynamic Logiccited by 7
- 2021Bisimulations for Neural Network Reductioncited by 6
- 2022On Optimizing Back-Substitution Methods for Neural Network Verificationcited by 6
- 2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
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- 2022Boosting Robustness Verification of Semantic Feature Neighborhoodscited by 4
- 2024Towards Formal Verification of Deep Neural Networks for Object Detectioncited by 4
- 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
- 2023Detecting Violations of Differential Privacy for Quantum Algorithmscited by 3
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verificationcited by 3
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- 2022VPN: Verification of Poisoning in Neural Networkscited by 2
- 2023Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networkscited by 2
- 2023A Tale of Two Approximations: Tightening Over-Approximation for DNN Robustness Verification via Under-Approximationcited by 2
- 2025Scalable and Interpretable Verification of Image-based Neural Network Controllers for Autonomous Vehiclescited by 2
- 2025Verification of Bit-Flip Attacks against Quantized Neural Networkscited by 2
50 most cited of 68 All 68 (JSON)
- 2026Stochastic World Models for Verifying Vision-Based Neural Feedback Systems29 Sep 2026
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2026Slice and Explain: Logic-Based Explanations for Neural Networks through Domain Slicing25 Feb 2026
- 2026Talking with Verifiers: Automatic Specification Generation for Neural Network Verification13 Feb 2026
- 2025Bridging Efficiency and Safety: Formal Verification of Neural Networks with Early Exits23 Dec 2025
- 2025Correct-By-Construction: Certified Individual Fairness through Neural Network Training21 Aug 2025
- 2025Abstraction-Based Proof Production in Formal Verification of Neural Networks11 Jun 2025
- 2025Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations10 Jun 2025
- 2025Monitoring Robustness and Individual Fairness31 May 2025
- 2025RvLLM: LLM Runtime Verification with Domain Knowledge24 May 2025
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verification15 Mar 2025
- 2025Verification of Bit-Flip Attacks against Quantized Neural Networks22 Feb 2025
38 more
- 2025Scalable and Interpretable Verification of Image-based Neural Network Controllers for Autonomous Vehicles23 Jan 2025
- 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees14 Oct 2024
- 2024PREMAP: A Unifying PREiMage APproximation Framework for Neural Networks17 Aug 2024
- 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretation7 Aug 2024
- 2024Safe and Reliable Training of Learning-Based Aerospace Controllers9 Jul 2024
- 2024Towards Formal Verification of Deep Neural Networks for Object Detection1 Jul 2024
- 2024Verification-Guided Shielding for Deep Reinforcement Learning10 Jun 2024
- 2024Patch Synthesis for Property Repair of Deep Neural Networks2 Apr 2024
- 2024Provably Safe Neural Network Controllers via Differential Dynamic Logic16 Feb 2024
- 2024Robustness Assessment of a Runway Object Classifier for Safe Aircraft Taxiing8 Jan 2024
- 2023Verification of Neural Networks Local Differential Classification Privacy31 Oct 2023
- 2023Detecting Violations of Differential Privacy for Quantum Algorithms9 Sep 2023
- 2023Distributionally Robust Statistical Verification with Imprecise Neural Networks28 Aug 2023
- 2023Expediting Neural Network Verification via Network Reduction7 Aug 2023
- 2023Syntactic vs Semantic Linear Abstraction and Refinement of Neural Networks20 Jul 2023
- 2023Scaling Model Checking for DNN Analysis via State-Space Reduction and Input Segmentation (Extended Version)29 Jun 2023
- 2023QNNRepair: Quantized Neural Network Repair23 Jun 2023
- 2023Towards quantum enhanced adversarial robustness in machine learning22 Jun 2023
- 2023A Tale of Two Approximations: Tightening Over-Approximation for DNN Robustness Verification via Under-Approximation26 May 2023
- 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)5 May 2023
- 2023Fully Automatic Neural Network Reduction for Formal Verification3 May 2023
- 2023The Power of Typed Affine Decision Structures: A Case Study28 Apr 2023
- 2023Verifying Generalization in Deep Learning11 Feb 2023
- 2023Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networks10 Feb 2023
- 2023OccRob: Efficient SMT-Based Occlusion Robustness Verification of Deep Neural Networks27 Jan 2023
- 2022QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networks10 Dec 2022
- 2022Fairify: Fairness Verification of Neural Networks8 Dec 2022
- 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection System6 Dec 2022
- 2022QEBVerif: Quantization Error Bound Verification of Neural Networks6 Dec 2022
- 2022Efficient Adversarial Input Generation via Neural Net Patching30 Nov 2022
- 2022DualApp: Tight Over-Approximation for Neural Network Robustness Verification via Under-Approximation21 Nov 2022
- 2022Efficiently Finding Adversarial Examples with DNN Preprocessing16 Nov 2022
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks25 Oct 2022
- 2022Tighter Abstract Queries in Neural Network Verification23 Oct 2022
- 2022Towards Global Neural Network Abstractions with Locally-Exact Reconstruction21 Oct 2022
- 2022Boosting Robustness Verification of Semantic Feature Neighborhoods12 Sep 2022
- 2022On Optimizing Back-Substitution Methods for Neural Network Verification16 Aug 2022
- 2022Abstraction and Refinement: Towards Scalable and Exact Verification of Neural Networks2 Jul 2022
50 newest of 68 All 68 (JSON)
- 2022Causality-based Neural Network Repaircited by 47
- 2022VPN: Verification of Poisoning in Neural Networkscited by 2
- 2022VPN: Verification of Poisoning in Neural Networks8 May 2022
- 2022Causality-based Neural Network Repair20 Apr 2022
- 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 42
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
- 2021A Review of Formal Methods applied to Machine Learningcited by 33
- 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
- 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
- 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
- 2023Towards quantum enhanced adversarial robustness in machine learningcited by 28
- 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
- 2022Neural Network Verification with Proof Productioncited by 22
- 2022Fairify: Fairness Verification of Neural Networkscited by 22
- 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
- 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
12 most cited of 62 All 62 (JSON)
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2026Slice and Explain: Logic-Based Explanations for Neural Networks through Domain Slicing25 Feb 2026
- 2026Talking with Verifiers: Automatic Specification Generation for Neural Network Verification13 Feb 2026
- 2025Correct-By-Construction: Certified Individual Fairness through Neural Network Training21 Aug 2025
- 2025Abstraction-Based Proof Production in Formal Verification of Neural Networks11 Jun 2025
- 2025Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations10 Jun 2025
- 2025Monitoring Robustness and Individual Fairness31 May 2025
- 2025RvLLM: LLM Runtime Verification with Domain Knowledge24 May 2025
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verification15 Mar 2025
- 2025Verification of Bit-Flip Attacks against Quantized Neural Networks22 Feb 2025
- 2025Scalable and Interpretable Verification of Image-based Neural Network Controllers for Autonomous Vehicles23 Jan 2025
- 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees14 Oct 2024
12 newest of 62 All 62 (JSON)