LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification

Fabio Bonassi, Enrico Terzi, Marcello Farina, Riccardo Scattolini
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:85-94, 2020.

Abstract

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. In this work, a sufficient condition guaranteeing the Input-to-State (ISS) stability property of this system are provided. Then, a discussion on the verification of LSTM networks is provided; in particular, a dedicated approach based on the scenario algorithm is devised. The proposed method is eventually tested on a pH neutralization process.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-bonassi20a, title = {LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification}, author = {Bonassi, Fabio and Terzi, Enrico and Farina, Marcello and Scattolini, Riccardo}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {85--94}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/bonassi20a/bonassi20a.pdf}, url = {https://proceedings.mlr.press/v120/bonassi20a.html}, abstract = {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. In this work, a sufficient condition guaranteeing the Input-to-State (ISS) stability property of this system are provided. Then, a discussion on the verification of LSTM networks is provided; in particular, a dedicated approach based on the scenario algorithm is devised. The proposed method is eventually tested on a pH neutralization process.} }
Endnote
%0 Conference Paper %T LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification %A Fabio Bonassi %A Enrico Terzi %A Marcello Farina %A Riccardo Scattolini %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-bonassi20a %I PMLR %P 85--94 %U https://proceedings.mlr.press/v120/bonassi20a.html %V 120 %X 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. In this work, a sufficient condition guaranteeing the Input-to-State (ISS) stability property of this system are provided. Then, a discussion on the verification of LSTM networks is provided; in particular, a dedicated approach based on the scenario algorithm is devised. The proposed method is eventually tested on a pH neutralization process.
APA
Bonassi, F., Terzi, E., Farina, M. & Scattolini, R.. (2020). LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:85-94 Available from https://proceedings.mlr.press/v120/bonassi20a.html.

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