Verifying Recurrent Neural Networks using Invariant Inference
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Abstract (arXiv)
Deep neural networks are revolutionizing the way complex systems are developed. However, these automatically-generated networks are opaque to humans, making it difficult to reason about them and guarantee their correctness. Here, we propose a novel approach for verifying properties of a widespread variant of neural networks, called recurrent neural networks. Recurrent neural networks play a key role in, e.g., natural language processing, and their verification is crucial for guaranteeing the reliability of many critical systems. Our approach is based on the inference of invariants, which allow us to reduce the complex problem of verifying recurrent networks into simpler, non-recurrent problems. Experiments with a proof-of-concept implementation of our approach demonstrate that it performs orders-of-magnitude better than the state of the art.
Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Apr 2020.
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Citing papers per year: 2021: 8; 2022: 8; 2023: 5; 2024: 1; 2025: 1; 2026: 2.
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- 2022Causality-based Neural Network Repaircited by 44
- 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
- 2022Neural Network Verification with Proof Productioncited by 22
- 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
- 2021Certified Robustness to Programmable Transformations in LSTMscited by 18
- 2022Verification-Aided Deep Ensemble Selectioncited by 18
- 2021Probabilistic Verification of Neural Networks Against Group Fairnesscited by 17
- 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
13 more
- 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
- 2022Tighter Abstract Queries in Neural Network Verificationcited by 8
- 2022On Optimizing Back-Substitution Methods for Neural Network Verificationcited by 6
- 2023DelBugV: Delta-Debugging Neural Network Verifierscited by 3
- 2022Toward the Analysis of Graph Neural Networkscited by 2
- 2023Model-Agnostic Reachability Analysis on Deep Neural Networkscited by 1
- 2021Permutation Invariance of Deep Neural Networks with ReLUscited by 0
- 2023Formal Verification of Long Short-Term Memory based Audio Classifiers: A Star based Approachcited by 0
- 2025LTL Verification of Memoryful Neural Agentscited by 0
- 2026Probabilistic Verification of Recurrent Neural Networks for Single and Multi-Agent Reinforcement Learningcited by 0
- 2026Neural Network Verification using Partial Multi-Neuron Relaxationcited by 0
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2026Probabilistic Verification of Recurrent Neural Networks for Single and Multi-Agent Reinforcement Learning14 May 2026
- 2025LTL Verification of Memoryful Neural Agents4 Mar 2025
- 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretation7 Aug 2024
- 2023Formal Verification of Long Short-Term Memory based Audio Classifiers: A Star based Approach16 Nov 2023
- 2023Formally Explaining Neural Networks within Reactive Systems31 Jul 2023
- 2023DelBugV: Delta-Debugging Neural Network Verifiers29 May 2023
- 2023Model-Agnostic Reachability Analysis on Deep Neural Networks3 Apr 2023
- 2023Verifying Generalization in Deep Learning11 Feb 2023
- 2022Tighter Abstract Queries in Neural Network Verification23 Oct 2022
- 2022On Optimizing Back-Substitution Methods for Neural Network Verification16 Aug 2022
- 2022Neural Network Verification with Proof Production1 Jun 2022
13 more
- 2022Verifying Learning-Based Robotic Navigation Systems26 May 2022
- 2022Causality-based Neural Network Repair20 Apr 2022
- 2022Verification-Aided Deep Ensemble Selection8 Feb 2022
- 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networks6 Jan 2022
- 2022Toward the Analysis of Graph Neural Networks1 Jan 2022
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments26 Nov 2021
- 2021RoMA: a Method for Neural Network Robustness Measurement and Assessment21 Oct 2021
- 2021Minimal Multi-Layer Modifications of Deep Neural Networks18 Oct 2021
- 2021Permutation Invariance of Deep Neural Networks with ReLUs18 Oct 2021
- 2021Probabilistic Verification of Neural Networks Against Group Fairness18 Jul 2021
- 2021Pruning and Slicing Neural Networks using Formal Verification28 May 2021
- 2021Towards Scalable Verification of Deep Reinforcement Learning25 May 2021
- 2021Certified Robustness to Programmable Transformations in LSTMs15 Feb 2021
- 2022Causality-based Neural Network Repaircited by 44
- 2022Causality-based Neural Network Repair20 Apr 2022
- 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
- 2022Neural Network Verification with Proof Productioncited by 22
- 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
- 2021Certified Robustness to Programmable Transformations in LSTMscited by 18
- 2022Verification-Aided Deep Ensemble Selectioncited by 18
- 2021Probabilistic Verification of Neural Networks Against Group Fairnesscited by 17
- 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
- 2023Verifying Generalization in Deep Learningcited by 11
12 most cited of 24 All 24 (JSON)
- 2026Neural Network Verification using Partial Multi-Neuron Relaxation28 May 2026
- 2026Probabilistic Verification of Recurrent Neural Networks for Single and Multi-Agent Reinforcement Learning14 May 2026
- 2025LTL Verification of Memoryful Neural Agents4 Mar 2025
- 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretation7 Aug 2024
- 2023Formal Verification of Long Short-Term Memory based Audio Classifiers: A Star based Approach16 Nov 2023
- 2023Formally Explaining Neural Networks within Reactive Systems31 Jul 2023
- 2023DelBugV: Delta-Debugging Neural Network Verifiers29 May 2023
- 2023Model-Agnostic Reachability Analysis on Deep Neural Networks3 Apr 2023
- 2023Verifying Generalization in Deep Learning11 Feb 2023
- 2022Tighter Abstract Queries in Neural Network Verification23 Oct 2022
- 2022On Optimizing Back-Substitution Methods for Neural Network Verification16 Aug 2022
- 2022Neural Network Verification with Proof Production1 Jun 2022
12 newest of 24 All 24 (JSON)