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Journal Articles Systems & Control Letters Year : 2023

Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings

Abstract

In this paper we show that neural ODE analogs of recurrent (ODE-RNN) and Long Short-Term Memory (ODE-LSTM) networks can be algorithmically embedded into the class of polynomial systems. This embedding preserves input-output behavior and can suitably be extended to other neural DE architectures. We then use realization theory of polynomial systems to provide necessary conditions for an input-output map to be realizable by an ODE-LSTM and sufficient conditions for minimality of such systems. These results represent the first steps towards realization theory of recurrent neural ODE architectures, which is is expected be useful for model reduction and learning algorithm analysis of recurrent neural ODEs.
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Dates and versions

hal-03872484 , version 1 (25-11-2022)

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Martin Gonzalez, Thibault Defourneau, Hatem Hajri, Petreczky Mihaly. Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings. Systems & Control Letters, 2023, 173. ⟨hal-03872484⟩
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