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  Re-visiting the echo state property

Yildiz, I. B., Jaeger, H., & Kiebel, S. J. (2012). Re-visiting the echo state property. Neural networks, 35, 1-9. doi:10.1016/j.neunet.2012.07.005.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-C715-8 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-5C27-A
Genre: Journal Article

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 Creators:
Yildiz, Izzet Burak1, Author              
Jaeger, Herbert2, Author
Kiebel, Stefan J.1, Author              
Affiliations:
1Department Neurology, MPI for Human Cognitive and Brain Sciences, Max Planck Society, ou_634549              
2Jacobs University Bremen, Germany, ou_persistent22              

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Free keywords: Echo state network; Spectral radius; Bifurcation; Diagonally Schur stable; Lyapunov
 Abstract: An echo state network (ESN) consists of a large, randomly connected neural network, the reservoir, which is driven by an input signal and projects to output units. During training, only the connections from the reservoir to these output units are learned. A key requisite for output-only training is the echo state property (ESP), which means that the effect of initial conditions should vanish as time passes. In this paper, we use analytical examples to show that a widely used criterion for the ESP, the spectral radius of the weight matrix being smaller than unity, is not sufficient to satisfy the echo state property. We obtain these examples by investigating local bifurcation properties of the standard ESNs. Moreover, we provide new sufficient conditions for the echo state property of standard sigmoid and leaky integrator ESNs. We furthermore suggest an improved technical definition of the echo state property, and discuss what practicians should (and should not) observe when they optimize their reservoirs for specific tasks.

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Language(s): eng - English
 Dates: 2012-06-242012-01-292012-07-122012-07-232012-11
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1016/j.neunet.2012.07.005
PMID: 22885243
Other: Epub 2012
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Title: Neural networks
Source Genre: Journal
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Publ. Info: New York : Pergamon
Pages: - Volume / Issue: 35 Sequence Number: - Start / End Page: 1 - 9 Identifier: ISSN: 0893-6080
CoNE: https://pure.mpg.de/cone/journals/resource/954925558496