Title :

Realization Theory Of Recurrent Neural ODEs Using Polynomial System Embeddings

Author(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]

Journal title :

Systems and Control Letters

Pages :

105468

Publisher :

Elsevier

Publication date :

2023-03

ISSN :

0167-6911

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Collections :

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

Source :

Harvested from HAL