Pruning and Slicing Neural Networks using Formal Verification
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Abstract (arXiv)
Deep neural networks (DNNs) play an increasingly important role in various computer systems. In order to create these networks, engineers typically specify a desired topology, and then use an automated training algorithm to select the network's weights. While training algorithms have been studied extensively and are well understood, the selection of topology remains a form of art, and can often result in networks that are unnecessarily large - and consequently are incompatible with end devices that have limited memory, battery or computational power. Here, we propose to address this challenge by harnessing recent advances in DNN verification. We present a framework and a methodology for discovering redundancies in DNNs - i.e., for finding neurons that are not needed, and can be removed in order to reduce the size of the DNN. By using sound verification techniques, we can formally guarantee that our simplified network is equivalent to the original, either completely, or up to a prescribed tolerance. Further, we show how to combine our technique with slicing, which results in a family of very small DNNs, which are together equivalent to the original. Our approach can produce DNNs that are significantly smaller than the original, rendering them suitable for deployment on additional kinds of systems, and even more amenable to subsequent formal verification. We provide a proof-of-concept implementation of our approach, and use it to evaluate our techniques on several real-world DNNs.
Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). Builds on 26 of its 49 references that are in the map. First posted on arXiv 28 May 2021.
Builds on
26 of 49 references.
References · 26
- 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
- 2013Intriguing properties of neural networkscited by 5,155
- 2015Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Codingcited by 2,329
- 2016SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model sizecited by 1,060
- 2016End to End Learning for Self-Driving Carscited by 1,009
- 2016XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networkscited by 849
- 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
- 2016Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activationscited by 426
- 2016Safety Verification of Deep Neural Networkscited by 263
- 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 255
- 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 242
- 2019Algorithms for Verifying Deep Neural Networkscited by 221
14 more
- 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
- 2017An approach to reachability analysis for feed-forward ReLU neural networkscited by 127
- 2020Verification of Deep Convolutional Neural Networks Using ImageStarscited by 75
- 2019An Abstraction-Based Framework for Neural Network Verificationcited by 68
- 2021Lost in Pruning: The Effects of Pruning Neural Networks beyond Test Accuracycited by 62
- 2019Quantitative Verification of Neural Networks And its Security Applicationscited by 56
- 2020An SMT-Based Approach for Verifying Binarized Neural Networkscited by 47
- 2020Parallelization Techniques for Verifying Neural Networkscited by 36
- 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
- 2020DeepAbstract: Neural Network Abstraction for Accelerating Verificationcited by 31
- 2017Towards Proving the Adversarial Robustness of Deep Neural Networkscited by 26
- 2020Verifying Recurrent Neural Networks using Invariant Inferencecited by 26
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- 2018Toward Scalable Verification for Safety-Critical Deep Networkscited by 12
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Citing papers per year: 2021: 1; 2022: 8; 2023: 3; 2024: 2; 2025: 4; 2026: 2.
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- 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
- 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
- 2022Neural Network Verification with Proof Productioncited by 22
- 2022Verification-Aided Deep Ensemble Selectioncited by 18
- 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 16
- 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
- 2023Architecture-Preserving Provable Repair of Deep Neural Networkscited by 11
- 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
- 2022On Optimizing Back-Substitution Methods for Neural Network Verificationcited by 6
8 more
- 2022CheckINN: Wide Range Neural Network Verification in Imandra (Extended)cited by 3
- 2023DelBugV: Delta-Debugging Neural Network Verifierscited by 3
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verificationcited by 3
- 2026Incremental Neural Network Verification via Learned Conflictscited by 2
- 2025Comparing Neural Network Encodings for Logic-based Explainabilitycited by 0
- 2025Lipschitz-aware Linearity Grafting for Certified Robustnesscited by 0
- 2025On Improving Deep Active Learning with Formal Verificationcited by 0
- 2026Slice and Explain: Logic-Based Explanations for Neural Networks through Domain Slicingcited by 0
- 2026Incremental Neural Network Verification via Learned Conflicts12 Mar 2026
- 2026Slice and Explain: Logic-Based Explanations for Neural Networks through Domain Slicing25 Feb 2026
- 2025On Improving Deep Active Learning with Formal Verification16 Dec 2025
- 2025Lipschitz-aware Linearity Grafting for Certified Robustness29 Oct 2025
- 2025Comparing Neural Network Encodings for Logic-based Explainability26 May 2025
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verification15 Mar 2025
- 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates22 May 2024
- 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networks25 Jan 2024
- 2023Formally Explaining Neural Networks within Reactive Systems31 Jul 2023
- 2023DelBugV: Delta-Debugging Neural Network Verifiers29 May 2023
- 2023Architecture-Preserving Provable Repair of Deep Neural Networks7 Apr 2023
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks25 Oct 2022
8 more
- 2022Tighter Abstract Queries in Neural Network Verification23 Oct 2022
- 2022On Optimizing Back-Substitution Methods for Neural Network Verification16 Aug 2022
- 2022CheckINN: Wide Range Neural Network Verification in Imandra (Extended)21 Jul 2022
- 2022Neural Network Verification with Proof Production1 Jun 2022
- 2022Verifying Learning-Based Robotic Navigation Systems26 May 2022
- 2022Verification-Aided Deep Ensemble Selection8 Feb 2022
- 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networks6 Jan 2022
- 2021Minimal Multi-Layer Modifications of Deep Neural Networks18 Oct 2021
- 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networkscited by 42
- 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
- 2022Neural Network Verification with Proof Productioncited by 22
- 2022Verification-Aided Deep Ensemble Selectioncited by 18
- 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
- 2023Architecture-Preserving Provable Repair of Deep Neural Networkscited by 11
- 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
- 2022On Optimizing Back-Substitution Methods for Neural Network Verificationcited by 6
- 2022CheckINN: Wide Range Neural Network Verification in Imandra (Extended)cited by 3
12 most cited of 19 All 19 (JSON)
- 2026Incremental Neural Network Verification via Learned Conflicts12 Mar 2026
- 2026Slice and Explain: Logic-Based Explanations for Neural Networks through Domain Slicing25 Feb 2026
- 2025On Improving Deep Active Learning with Formal Verification16 Dec 2025
- 2025Lipschitz-aware Linearity Grafting for Certified Robustness29 Oct 2025
- 2025Comparing Neural Network Encodings for Logic-based Explainability26 May 2025
- 2025PICID: Proof-Driven Clause Learning in Neural Network Verification15 Mar 2025
- 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networks25 Jan 2024
- 2023Formally Explaining Neural Networks within Reactive Systems31 Jul 2023
- 2023DelBugV: Delta-Debugging Neural Network Verifiers29 May 2023
- 2023Architecture-Preserving Provable Repair of Deep Neural Networks7 Apr 2023
- 2022Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks25 Oct 2022
- 2022Tighter Abstract Queries in Neural Network Verification23 Oct 2022
12 newest of 19 All 19 (JSON)