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The goal of this paper is to analyze Long Short Term Memory (LSTM) neuralnetworks from a dynamical system perspective. The classical recursive equationsdescribing the evolution of LSTM can be recast in state space form, resultingin a time-invariant nonlinear dynamical system. A sufficient conditionguaranteeing the Input-to-State (ISS) stability property of this class ofsystems is provided. The ISS property entails the boundedness of the outputreachable set of the LSTM. In light of this result, a novel approach for thesafety verification of the network, based on the Scenario Approach, is devised.The proposed method is eventually tested on a pH neutralization process.

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