Echo state networks are universal

This paper shows that echo state networks are universal uniform approximants in the context of discrete-time fading memory filters with uniformly bounded inputs defined on negative infinite times. This result guarantees that any fading memory input/output system in discrete time can be realized as a...

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Bibliographic Details
Published in:Neural networks 2018-12, Vol.108, p.495-508
Main Authors: Grigoryeva, Lyudmila, Ortega, Juan-Pablo
Format: Article
Language:English
Subjects:
Computer Systems - trends
Echo state networks (ESN)
Fading memory filters
Machine learning
Memory
Neural Networks (Computer)
Reservoir computing (RC)
Uniform system approximation
Universality
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Description
Summary:This paper shows that echo state networks are universal uniform approximants in the context of discrete-time fading memory filters with uniformly bounded inputs defined on negative infinite times. This result guarantees that any fading memory input/output system in discrete time can be realized as a simple finite-dimensional neural network-type state-space model with a static linear readout map. This approximation is valid for infinite time intervals. The proof of this statement is based on fundamental results, also presented in this work, about the topological nature of the fading memory property and about reservoir computing systems generated by continuous reservoir maps.
ISSN:0893-6080
1879-2782
DOI:10.1016/j.neunet.2018.08.025