On the stability properties of Gated Recurrent Units neural networks
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Abstract (arXiv)
The goal of this paper is to provide sufficient conditions for guaranteeing the Input-to-State Stability (ISS) and the Incremental Input-to-State Stability (δISS) of Gated Recurrent Units (GRUs) neural networks. These conditions, devised for both single-layer and multi-layer architectures, consist of nonlinear inequalities on network's weights. They can be employed to check the stability of trained networks, or can be enforced as constraints during the training procedure of a GRU. The resulting training procedure is tested on a Quadruple Tank nonlinear benchmark system, showing satisfactory modeling performances.
Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Nov 2020.
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Citing papers per year: 2021: 3; 2022: 2; 2023: 4; 2024: 0; 2025: 3; 2026: 5.
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- 2023Deep networks for system identification: a Surveycited by 35
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
- 2021Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networkscited by 11
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systemscited by 5
- 2023Nonlinear MPC design for incrementally ISS systems with application to GRU networkscited by 5
- 2022An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX modelscited by 2
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validationcited by 1
- 2023Learning Hybrid Dynamics Models With Simulator-Informed Latent Statescited by 1
- 2025Infinity-norm-based Input-to-State-Stable Long Short-Term Memory networks: a thermal systems perspectivecited by 1
- 2026Tuning the burn-in phase in training recurrent neural networks improves their performancecited by 1
- 2026Controller Design for Structured State-space Models via Contraction Theorycited by 1
- 2022Towards lifelong learning of Recurrent Neural Networks for control designcited by 0
5 more
- 2025A Solvable Molecular Switch Model for Stable Temporal Information Processingcited by 0
- 2025Lipschitz-Based Robustness Certification for Recurrent Neural Networks via Convex Relaxationcited by 0
- 2026Embedding of Low-Dimensional Sensory Dynamics in Recurrent Networks: Implications for the Geometry of Neural Representationcited by 0
- 2026Can a Dynamic Internal Field Govern a Transformer's Cognition? Certifiability, not Superiority, in Homeostatic Compute Controlcited by 0
- 2026LoRA-RC: Reservoir Computing with Low-Rank Adaptationcited by 0
- 2026LoRA-RC: Reservoir Computing with Low-Rank Adaptation11 Sep 2026
- 2026Can a Dynamic Internal Field Govern a Transformer's Cognition? Certifiability, not Superiority, in Homeostatic Compute Control25 Aug 2026
- 2026Controller Design for Structured State-space Models via Contraction Theory8 Apr 2026
- 2026Tuning the burn-in phase in training recurrent neural networks improves their performance11 Feb 2026
- 2026Embedding of Low-Dimensional Sensory Dynamics in Recurrent Networks: Implications for the Geometry of Neural Representation26 Jan 2026
- 2025Lipschitz-Based Robustness Certification for Recurrent Neural Networks via Convex Relaxation22 Sep 2025
- 2025A Solvable Molecular Switch Model for Stable Temporal Information Processing21 Aug 2025
- 2025Infinity-norm-based Input-to-State-Stable Long Short-Term Memory networks: a thermal systems perspective14 Mar 2025
- 2023Nonlinear MPC design for incrementally ISS systems with application to GRU networks28 Sep 2023
- 2023Learning Hybrid Dynamics Models With Simulator-Informed Latent States6 Sep 2023
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validation6 Apr 2023
- 2023Deep networks for system identification: a Survey30 Jan 2023
5 more
- 2022Towards lifelong learning of Recurrent Neural Networks for control design8 Aug 2022
- 2022An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX models30 Mar 2022
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments26 Nov 2021
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systems10 Aug 2021
- 2021Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networks3 Mar 2021
- 2023Deep networks for system identification: a Surveycited by 35
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
- 2021Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networkscited by 11
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systemscited by 5
- 2023Nonlinear MPC design for incrementally ISS systems with application to GRU networkscited by 5
- 2022An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX modelscited by 2
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validationcited by 1
- 2023Learning Hybrid Dynamics Models With Simulator-Informed Latent Statescited by 1
- 2025Infinity-norm-based Input-to-State-Stable Long Short-Term Memory networks: a thermal systems perspectivecited by 1
- 2026Tuning the burn-in phase in training recurrent neural networks improves their performancecited by 1
- 2026Controller Design for Structured State-space Models via Contraction Theorycited by 1
- 2022Towards lifelong learning of Recurrent Neural Networks for control designcited by 0
12 most cited of 17 All 17 (JSON)
- 2026LoRA-RC: Reservoir Computing with Low-Rank Adaptation11 Sep 2026
- 2026Can a Dynamic Internal Field Govern a Transformer's Cognition? Certifiability, not Superiority, in Homeostatic Compute Control25 Aug 2026
- 2026Controller Design for Structured State-space Models via Contraction Theory8 Apr 2026
- 2026Tuning the burn-in phase in training recurrent neural networks improves their performance11 Feb 2026
- 2026Embedding of Low-Dimensional Sensory Dynamics in Recurrent Networks: Implications for the Geometry of Neural Representation26 Jan 2026
- 2025Lipschitz-Based Robustness Certification for Recurrent Neural Networks via Convex Relaxation22 Sep 2025
- 2025A Solvable Molecular Switch Model for Stable Temporal Information Processing21 Aug 2025
- 2025Infinity-norm-based Input-to-State-Stable Long Short-Term Memory networks: a thermal systems perspective14 Mar 2025
- 2023Nonlinear MPC design for incrementally ISS systems with application to GRU networks28 Sep 2023
- 2023Learning Hybrid Dynamics Models With Simulator-Informed Latent States6 Sep 2023
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validation6 Apr 2023
- 2023Deep networks for system identification: a Survey30 Jan 2023
12 newest of 17 All 17 (JSON)