Journal
NEURAL NETWORKS
Volume 108, Issue -, Pages 495-508Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2018.08.025
Keywords
Reservoir computing (RC); Universality; Echo state networks (ESN); Machine learning; Fading memory filters; Uniform system approximation
Funding
- French ANR BIPHOPROC project, France [ANR-14-OHRI-0002-02]
- Graduate School of Decision Sciences
- Young Scholar Fund AFF of the Universitat Konstanz, Germany [83980215]
- Research Commission of the Universitat Sankt Gallen, Switzerland
- Swiss National Science Foundation, Switzerland [200021_175801/1]
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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. (c) 2018 Elsevier Ltd. All rights reserved.
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