Titre :

Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings

Auteur(s) :

Gonzalez, Martin [Auteur]
IRT SystemX
Defourneau, Thibault [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Hajri, Hatem [Auteur]
IRT SystemX
Petreczky, Mihaly [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]

Titre de la revue :

Systems and Control Letters

Pagination :

105468

Éditeur :

Elsevier

Date de publication :

2023-03

ISSN :

0167-6911

Mot(s)-clé(s) en anglais :

Realization theory Neural ODEs Recurrent Neural Networks Long Short-Term Memory System Identification
Realization theory
Neural ODEs
Recurrent Neural Networks
Long Short-Term Memory
System Identification

Discipline(s) HAL :

Mathématiques [math]/Optimisation et contrôle [math.OC]
Sciences de l'ingénieur [physics]/Automatique / Robotique

Résumé en anglais : [en]

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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL