Echo State Condition at the Critical Point
Department of Electrical Engineering and Advanced Institute of Manufacturing with High-Tech Innovations (AIM-HI), National Chung Cheng University, Chia-Yi 62102, Taiwan
Academic Editor: Mikhail Prokopenko
Received: 29 October 2016 / Revised: 13 December 2016 / Accepted: 15 December 2016 / Published: 23 December 2016
Recurrent networks with transfer functions that fulfil the Lipschitz continuity with
may be echo state networks if certain limitations on the recurrent connectivity are applied. It has been shown that it is sufficient if the largest singular value of the recurrent connectivity is smaller than 1. The main achievement of this paper is a proof under which conditions the network is an echo state network even if the largest singular value is one. It turns out that in this critical case the exact shape of the transfer function plays a decisive role in determining whether the network still fulfills the echo state condition. In addition, several examples with one-neuron networks are outlined to illustrate effects of critical connectivity. Moreover, within the manuscript a mathematical definition for a critical echo state network is suggested.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Mayer, N.M. Echo State Condition at the Critical Point. Entropy 2017, 19, 3.
Mayer NM. Echo State Condition at the Critical Point. Entropy. 2017; 19(1):3.
Mayer, Norbert M. 2017. "Echo State Condition at the Critical Point." Entropy 19, no. 1: 3.
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