An SMT-Based Approach for Verifying Binarized Neural Networks
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Abstract (arXiv)
Deep learning has emerged as an effective approach for creating modern software systems, with neural networks often surpassing hand-crafted systems. Unfortunately, neural networks are known to suffer from various safety and security issues. Formal verification is a promising avenue for tackling this difficulty, by formally certifying that networks are correct. We propose an SMT-based technique for verifying Binarized Neural Networks - a popular kind of neural network, where some weights have been binarized in order to render the neural network more memory and energy efficient, and quicker to evaluate. One novelty of our technique is that it allows the verification of neural networks that include both binarized and non-binarized components. Neural network verification is computationally very difficult, and so we propose here various optimizations, integrated into our SMT procedure as deduction steps, as well as an approach for parallelizing verification queries. We implement our technique as an extension to the Marabou framework, and use it to evaluate the approach on popular binarized neural network architectures.
Key facts. Cited by 47 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Nov 2020.
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Citing papers per year: 2021: 9; 2022: 15; 2023: 8; 2024: 10; 2025: 4; 2026: 1.
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- 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
- 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
- 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
- 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
- 2023Formally Explaining Neural Networks within Reactive Systemscited by 24
- 2024Local vs. Global Interpretability: A Computational Complexity Perspectivecited by 23
- 2022Neural Network Verification with Proof Productioncited by 22
- 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
- 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19
- 2022Verification-Aided Deep Ensemble Selectioncited by 18
- 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
35 more
- 2021Neural Termination Analysiscited by 16
- 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
- 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
- 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
- 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection Systemcited by 12
- 2022QVIP: An ILP-based Formal Verification Approach for Quantized Neural Networkscited by 12
- 2024Shield Synthesis for LTL Modulo Theoriescited by 12
- 2025Neural Network Verification is a Programming Language Challengecited by 12
- 2022Constrained Reinforcement Learning for Robotics via Scenario-Based Programmingcited by 11
- 2023Verifying Generalization in Deep Learningcited by 11
- 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretationcited by 11
- 2021RoMA: a Method for Neural Network Robustness Measurement and Assessmentcited by 10
- 2022On Neural Network Equivalence Checking using SMT Solverscited by 10
- 2022QEBVerif: Quantization Error Bound Verification of Neural Networkscited by 9
- 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
- 2024Analyzing Adversarial Inputs in Deep Reinforcement Learningcited by 7
- 2021Verifying Quantized Neural Networks using SMT-Based Model Checkingcited by 6
- 2024Neural Model Checkingcited by 6
- 2023OccRob: Efficient SMT-Based Occlusion Robustness Verification of Deep Neural Networkscited by 5
- 2021QNNVerifier: A Tool for Verifying Neural Networks using SMT-Based Model Checkingcited by 4
- 2023Repairing Deep Neural Networks Based on Behavior Imitationcited by 4
- 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4
- 2022Quantization-aware Interval Bound Propagation for Training Certifiably Robust Quantized Neural Networkscited by 3
- 2022Deep Binary Reinforcement Learning for Scalable Verificationcited by 2
- 2023Architecturing Binarized Neural Networks for Traffic Sign Recognitioncited by 2
- 2024DEM: A Method for Certifying Deep Neural Network Classifier Outputs in Aerospacecited by 2
- 2022An Overview and Prospective Outlook on Robust Training and Certification of Machine Learning Modelscited by 1
- 2024Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimizationcited by 1
- 2023Evaluating robustness of support vector machines with the Lagrangian dual approachcited by 0
- 2023QNNRepair: Quantized Neural Network Repaircited by 0
- 2023Benchmarking Local Robustness of High-Accuracy Binary Neural Networks for Enhanced Traffic Sign Recognitioncited by 0
- 2025Efficient Certified Reasoning for Binarized Neural Networkscited by 0
- 2025Get Global Guarantees: On the Probabilistic Nature of Perturbation Robustnesscited by 0
- 2025On Integer Programming for the Binarized Neural Network Verification Problemcited by 0
- 2026Neural Network Verification using Partial Multi-Neuron Relaxationcited by 0
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2025On Integer Programming for the Binarized Neural Network Verification Problem1 Oct 2025
- 2025Get Global Guarantees: On the Probabilistic Nature of Perturbation Robustness26 Aug 2025
- 2025Efficient Certified Reasoning for Binarized Neural Networks25 Jun 2025
- 2025Neural Network Verification is a Programming Language Challenge10 Jan 2025
- 2024Neural Model Checking31 Oct 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
- 2024Verification-Guided Shielding for Deep Reinforcement Learning10 Jun 2024
- 2024Shield Synthesis for LTL Modulo Theories6 Jun 2024
- 2024Local vs. Global Interpretability: A Computational Complexity Perspective5 Jun 2024
- 2024Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimization27 May 2024
35 more
- 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates22 May 2024
- 2024Analyzing Adversarial Inputs in Deep Reinforcement Learning7 Feb 2024
- 2024DEM: A Method for Certifying Deep Neural Network Classifier Outputs in Aerospace4 Jan 2024
- 2023Benchmarking Local Robustness of High-Accuracy Binary Neural Networks for Enhanced Traffic Sign Recognition25 Sep 2023
- 2023Formally Explaining Neural Networks within Reactive Systems31 Jul 2023
- 2023QNNRepair: Quantized Neural Network Repair23 Jun 2023
- 2023Evaluating robustness of support vector machines with the Lagrangian dual approach5 Jun 2023
- 2023Repairing Deep Neural Networks Based on Behavior Imitation5 May 2023
- 2023Architecturing Binarized Neural Networks for Traffic Sign Recognition27 Mar 2023
- 2023Verifying Generalization in Deep Learning11 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
- 2022veriFIRE: Verifying an Industrial, Learning-Based Wildfire Detection System6 Dec 2022
- 2022QEBVerif: Quantization Error Bound Verification of Neural Networks6 Dec 2022
- 2022Quantization-aware Interval Bound Propagation for Training Certifiably Robust Quantized Neural Networks29 Nov 2022
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks25 Oct 2022
- 2022Tighter Abstract Queries in Neural Network Verification23 Oct 2022
- 2022An Overview and Prospective Outlook on Robust Training and Certification of Machine Learning Models15 Aug 2022
- 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbations5 Jul 2022
- 2022Constrained Reinforcement Learning for Robotics via Scenario-Based Programming20 Jun 2022
- 2022Neural Network Verification with Proof Production1 Jun 2022
- 2022Verifying Learning-Based Robotic Navigation Systems26 May 2022
- 2022On Neural Network Equivalence Checking using SMT Solvers22 Mar 2022
- 2022Deep Binary Reinforcement Learning for Scalable Verification11 Mar 2022
- 2022Verification-Aided Deep Ensemble Selection8 Feb 2022
- 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networks6 Jan 2022
- 2021QNNVerifier: A Tool for Verifying Neural Networks using SMT-Based Model Checking25 Nov 2021
- 2021RoMA: a Method for Neural Network Robustness Measurement and Assessment21 Oct 2021
- 2021Minimal Multi-Layer Modifications of Deep Neural Networks18 Oct 2021
- 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Results31 Aug 2021
- 2021Verifying Quantized Neural Networks using SMT-Based Model Checking10 Jun 2021
- 2021Pruning and Slicing Neural Networks using Formal Verification28 May 2021
- 2021Towards Scalable Verification of Deep Reinforcement Learning25 May 2021
- 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networks12 Mar 2021
- 2021Neural Termination Analysis7 Feb 2021
- 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
- 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
- 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
- 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
- 2023Formally Explaining Neural Networks within Reactive Systemscited by 24
- 2024Local vs. Global Interpretability: A Computational Complexity Perspectivecited by 23
- 2022Neural Network Verification with Proof Productioncited by 22
- 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
- 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19
- 2022Verification-Aided Deep Ensemble Selectioncited by 18
- 2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
12 most cited of 47 All 47 (JSON)
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2025On Integer Programming for the Binarized Neural Network Verification Problem1 Oct 2025
- 2025Get Global Guarantees: On the Probabilistic Nature of Perturbation Robustness26 Aug 2025
- 2025Efficient Certified Reasoning for Binarized Neural Networks25 Jun 2025
- 2025Neural Network Verification is a Programming Language Challenge10 Jan 2025
- 2024Neural Model Checking31 Oct 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
- 2024Verification-Guided Shielding for Deep Reinforcement Learning10 Jun 2024
- 2024Shield Synthesis for LTL Modulo Theories6 Jun 2024
- 2024Local vs. Global Interpretability: A Computational Complexity Perspective5 Jun 2024
- 2024Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimization27 May 2024
12 newest of 47 All 47 (JSON)