English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Re-visiting the echo state property

MPS-Authors
/persons/resource/persons22662

Yildiz,  Izzet Burak
Department Neurology, MPI for Human Cognitive and Brain Sciences, Max Planck Society;

/persons/resource/persons19770

Kiebel,  Stefan J.
Department Neurology, MPI for Human Cognitive and Brain Sciences, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

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.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-C715-8
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.