English

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

Systems and Control 2020-05-29 v2 Systems and Control

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. 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.

Keywords

Cite

@article{arxiv.1912.04377,
  title  = {LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification},
  author = {Fabio Bonassi and Enrico Terzi and Marcello Farina and Riccardo Scattolini},
  journal= {arXiv preprint arXiv:1912.04377},
  year   = {2020}
}

Comments

Accepted for Learning for dynamics & control (L4DC) 2020