Neural Network Verification with Proof Production
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Abstract (arXiv)
Deep neural networks (DNNs) are increasingly being employed in safety-critical systems, and there is an urgent need to guarantee their correctness. Consequently, the verification community has devised multiple techniques and tools for verifying DNNs. When DNN verifiers discover an input that triggers an error, that is easy to confirm; but when they report that no error exists, there is no way to ensure that the verification tool itself is not flawed. As multiple errors have already been observed in DNN verification tools, this calls the applicability of DNN verification into question. In this work, we present a novel mechanism for enhancing Simplex-based DNN verifiers with proof production capabilities: the generation of an easy-to-check witness of unsatisfiability, which attests to the absence of errors. Our proof production is based on an efficient adaptation of the well-known Farkas' lemma, combined with mechanisms for handling piecewise-linear functions and numerical precision errors. As a proof of concept, we implemented our technique on top of the Marabou DNN verifier. Our evaluation on a safety-critical system for airborne collision avoidance shows that proof production succeeds in almost all cases and requires only minimal overhead.
Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 29 of its 79 references that are in the map. First posted on arXiv 1 Jun 2022.
Builds on
29 of 79 references.
References · 29
- 2014Explaining and Harnessing Adversarial Examplescited by 7,287
- 2013Intriguing properties of neural networkscited by 5,114
- 2016End to End Learning for Self-Driving Carscited by 1,000
- 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
- 2016Safety Verification of Deep Neural Networkscited by 262
- 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
- 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
- 2016Measuring Neural Net Robustness with Constraintscited by 90
- 2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
- 2020Verification of Deep Convolutional Neural Networks Using ImageStarscited by 75
- 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
- 2019An Abstraction-Based Framework for Neural Network Verificationcited by 68
17 more
- 2018Deep Neural Network Compression for Aircraft Collision Avoidance Systemscited by 58
- 2019Quantitative Verification of Neural Networks And its Security Applicationscited by 56
- 2020An SMT-Based Approach for Verifying Binarized Neural Networkscited by 47
- 2019Fastened CROWN: Tightened Neural Network Robustness Certificatescited by 39
- 2020Parallelization Techniques for Verifying Neural Networkscited by 36
- 2020Exploiting Verified Neural Networks via Floating Point Numerical Errorcited by 35
- 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
- 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
- 2021Learning to Give Checkable Answers with Prover-Verifier Gamescited by 29
- 2020Verifying Recurrent Neural Networks using Invariant Inferencecited by 25
- 2020Global Optimization of Objective Functions Represented by ReLU Networkscited by 24
- 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
- 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
- 2020Formal Analysis and Redesign of a Neural Network-Based Aircraft Taxiing System with VerifAIcited by 21
- 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
- 2022Verification-Aided Deep Ensemble Selectioncited by 18
- 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
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Citing papers per year: 2022: 3; 2023: 4; 2024: 6; 2025: 5; 2026: 4.
22 papers.
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- 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
- 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
- 2023A DPLL(T) Framework for Verifying Deep Neural Networkscited by 23
- 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection Systemcited by 12
- 2025Neural Network Verification is a Programming Language Challengecited by 12
- 2023Verifying Generalization in Deep Learningcited by 11
- 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
- 2024Robustness Assessment of a Runway Object Classifier for Safe Aircraft Taxiingcited by 8
- 2024A Certified Proof Checker for Deep Neural Network Verification in Imandracited by 7
- 2023Towards a Certified Proof Checker for Deep Neural Network Verificationcited by 6
- 2024SoundnessBench: A Soundness Benchmark for Neural Network Verifierscited by 5
10 more
- 2025Abstraction-Based Proof Production in Formal Verification of Neural Networkscited by 5
- 2024Towards Formal Verification of Deep Neural Networks for Object Detectioncited by 4
- 2025Proof Minimization in Neural Network Verificationcited by 4
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verificationcited by 3
- 2026Incremental Neural Network Verification via Learned Conflictscited by 2
- 2024Formally Verified Approximate Policy Iterationcited by 1
- 2025Proof-Carrying Neuro-Symbolic Codecited by 1
- 2026The Luna Bound Propagator for Formal Analysis of Neural Networkscited by 0
- 2026Neural Network Verification using Partial Multi-Neuron Relaxationcited by 0
- 2026veriFIRE: an Industrial Case Study in Verifying Consistency Properties for a DNN-Based Wildfire Detection Systemcited by 0
- 2026veriFIRE: an Industrial Case Study in Verifying Consistency Properties for a DNN-Based Wildfire Detection System2 Jun 2026
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2026The Luna Bound Propagator for Formal Analysis of Neural Networks25 Mar 2026
- 2026Incremental Neural Network Verification via Learned Conflicts12 Mar 2026
- 2025Proof Minimization in Neural Network Verification11 Nov 2025
- 2025Abstraction-Based Proof Production in Formal Verification of Neural Networks11 Jun 2025
- 2025Proof-Carrying Neuro-Symbolic Code16 Apr 2025
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verification15 Mar 2025
- 2025Neural Network Verification is a Programming Language Challenge10 Jan 2025
- 2024SoundnessBench: A Soundness Benchmark for Neural Network Verifiers4 Dec 2024
- 2024Towards Formal Verification of Deep Neural Networks for Object Detection1 Jul 2024
- 2024Formally Verified Approximate Policy Iteration11 Jun 2024
10 more
- 2024A Certified Proof Checker for Deep Neural Network Verification in Imandra17 May 2024
- 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networks25 Jan 2024
- 2024Robustness Assessment of a Runway Object Classifier for Safe Aircraft Taxiing8 Jan 2024
- 2023A DPLL(T) Framework for Verifying Deep Neural Networks17 Jul 2023
- 2023Towards a Certified Proof Checker for Deep Neural Network Verification12 Jul 2023
- 2023Verifying Generalization in Deep Learning11 Feb 2023
- 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)14 Jan 2023
- 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection System6 Dec 2022
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks25 Oct 2022
- 2022Tighter Abstract Queries in Neural Network Verification23 Oct 2022
- 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
- 2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
- 2023A DPLL(T) Framework for Verifying Deep Neural Networkscited by 23
- 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection Systemcited by 12
- 2025Neural Network Verification is a Programming Language Challengecited by 12
- 2023Verifying Generalization in Deep Learningcited by 11
- 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
- 2024Robustness Assessment of a Runway Object Classifier for Safe Aircraft Taxiingcited by 8
- 2024A Certified Proof Checker for Deep Neural Network Verification in Imandracited by 7
- 2023Towards a Certified Proof Checker for Deep Neural Network Verificationcited by 6
- 2024SoundnessBench: A Soundness Benchmark for Neural Network Verifierscited by 5
12 most cited of 22 All 22 (JSON)
- 2026veriFIRE: an Industrial Case Study in Verifying Consistency Properties for a DNN-Based Wildfire Detection System2 Jun 2026
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2026The Luna Bound Propagator for Formal Analysis of Neural Networks25 Mar 2026
- 2026Incremental Neural Network Verification via Learned Conflicts12 Mar 2026
- 2025Proof Minimization in Neural Network Verification11 Nov 2025
- 2025Abstraction-Based Proof Production in Formal Verification of Neural Networks11 Jun 2025
- 2025Proof-Carrying Neuro-Symbolic Code16 Apr 2025
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verification15 Mar 2025
- 2025Neural Network Verification is a Programming Language Challenge10 Jan 2025
- 2024SoundnessBench: A Soundness Benchmark for Neural Network Verifiers4 Dec 2024
- 2024Towards Formal Verification of Deep Neural Networks for Object Detection1 Jul 2024
- 2024Formally Verified Approximate Policy Iteration11 Jun 2024
12 newest of 22 All 22 (JSON)