Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings

• URL: http://arxiv.org/abs/2205.11989v1
• Date: Tue, 24 May 2022 11:36:18 GMT
• Title: Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings
• Authors: Martin Gonzalez, Thibault Defourneau, Hatem Hajri, Mihaly Petreczky
• Abstract summary: We show that neural ODE analogs of recurrent (RNN) and LongTerm Memory (ODE-LSTM) networks can be algorithmically embedded into the class of systems. This embedding input-output behavior and can be extended to other DE-LSTM architectures. We then use realization theory of systems to provide necessary conditions for an input-output to be realizable by an ODE-LSTM and sufficient conditions for minimality of such systems.
• Score: 0.802904964931021
• License: http://creativecommons.org/licenses/by/4.0/
• 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 embeddeded 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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