LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification
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Abstract (arXiv)
The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a time-invariant nonlinear dynamical system. A sufficient condition guaranteeing the Input-to-State (ISS) stability property of this class of systems is provided. The ISS property entails the boundedness of the output reachable set of the LSTM. In light of this result, a novel approach for the safety verification of the network, based on the Scenario Approach, is devised. The proposed method is eventually tested on a pH neutralization process.
Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Dec 2019.
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Citing papers per year: 2021: 5; 2022: 3; 2023: 3; 2024: 0; 2025: 1; 2026: 1.
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- 2023Deep networks for system identification: a Surveycited by 37
- 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
- 2021Almost Surely Stable Deep Dynamicscited by 16
- 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 Training with Convex Loss and Regularization Functions by Extended Kalman Filteringcited by 8
- 2022Modern Machine Learning Tools for Monitoring and Control of Industrial Processes: A Surveycited by 6
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systemscited by 5
- 2022Input-to-State Stable Neural Ordinary Differential Equations with Applications to Transient Modeling of Circuitscited by 1
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validationcited by 1
- 2022Towards lifelong learning of Recurrent Neural Networks for control designcited by 0
- 2025Enhancing AI System Resiliency: Formulation and Guarantee for LSTM Resilience Based on Control Theorycited by 0
- 2026Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systems3 Oct 2026
- 2025Enhancing AI System Resiliency: Formulation and Guarantee for LSTM Resilience Based on Control Theory23 May 2025
- 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems24 Jun 2023
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validation6 Apr 2023
- 2023Deep networks for system identification: a Survey30 Jan 2023
- 2022Modern Machine Learning Tools for Monitoring and Control of Industrial Processes: A Survey22 Sep 2022
- 2022Towards lifelong learning of Recurrent Neural Networks for control design8 Aug 2022
- 2022Input-to-State Stable Neural Ordinary Differential Equations with Applications to Transient Modeling of Circuits14 Feb 2022
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments26 Nov 2021
- 2021Recurrent Neural Network Training with Convex Loss and Regularization Functions by Extended Kalman Filtering4 Nov 2021
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systems10 Aug 2021
- 2021Almost Surely Stable Deep Dynamics26 Mar 2021
1 more
- 2023Deep networks for system identification: a Surveycited by 37
- 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
- 2021Almost Surely Stable Deep Dynamicscited by 16
- 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 Training with Convex Loss and Regularization Functions by Extended Kalman Filteringcited by 8
- 2022Modern Machine Learning Tools for Monitoring and Control of Industrial Processes: A Surveycited by 6
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systemscited by 5
- 2022Input-to-State Stable Neural Ordinary Differential Equations with Applications to Transient Modeling of Circuitscited by 1
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validationcited by 1
- 2022Towards lifelong learning of Recurrent Neural Networks for control designcited by 0
- 2025Enhancing AI System Resiliency: Formulation and Guarantee for LSTM Resilience Based on Control Theorycited by 0
12 most cited of 13 All 13 (JSON)
- 2026Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systems3 Oct 2026
- 2025Enhancing AI System Resiliency: Formulation and Guarantee for LSTM Resilience Based on Control Theory23 May 2025
- 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems24 Jun 2023
- 2023Deep Long-Short Term Memory networks: Stability properties and Experimental validation6 Apr 2023
- 2023Deep networks for system identification: a Survey30 Jan 2023
- 2022Modern Machine Learning Tools for Monitoring and Control of Industrial Processes: A Survey22 Sep 2022
- 2022Towards lifelong learning of Recurrent Neural Networks for control design8 Aug 2022
- 2022Input-to-State Stable Neural Ordinary Differential Equations with Applications to Transient Modeling of Circuits14 Feb 2022
- 2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments26 Nov 2021
- 2021Recurrent Neural Network Training with Convex Loss and Regularization Functions by Extended Kalman Filtering4 Nov 2021
- 2021Recurrent Neural Network-based Internal Model Control design for stable nonlinear systems10 Aug 2021
- 2021Almost Surely Stable Deep Dynamics26 Mar 2021
12 newest of 13 All 13 (JSON)