Asymptotic Fisher Memory of Randomized Linear Symmetric Echo State Networks

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Asymptotic Fisher Memory of Randomized Linear Symmetric Echo State Networks. / Tino, Peter.

In: Neurocomputing, Vol. 298, 12.07.2018, p. 4-8.

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@article{4fbfb4d020164e37abc0e4d0943d0cda,
title = "Asymptotic Fisher Memory of Randomized Linear Symmetric Echo State Networks",
abstract = "We study asymptotic properties of Fisher memory of linear Echo State Networkswith randomized symmetric state space coupling. In particular, two reservoir constructions are considered: (1) More direct dynamic coupling construction using a class of Wigner matrices and (2) positive semi-definite dynamic coupling obtained as a product of unconstrained stochastic matrices. We show that the maximal Fisher memory is achieved when the inputto-state coupling is collinear with the dominant eigenvector of the reservoir coupling matrix. In the case of Wigner reservoirs we show that as the system size grows, the contribution to the Fisher memory of self-coupling of reservoir units is negligible. We also prove that when the input-to-state coupling is collinear with the sum of eigenvectors of the state space coupling, the expected normalized memory is four and eight time smaller than the maximal memory value for the Wigner and product constructions, respectively.",
keywords = "Fisher memory of dynamical systems, Recurrent neural network, Echo state network, Reservoir Computing",
author = "Peter Tino",
year = "2018",
month = jul
day = "12",
doi = "10.1016/j.neucom.2017.11.076",
language = "English",
volume = "298",
pages = "4--8",
journal = "Neurocomputing",
issn = "0925-2312",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Asymptotic Fisher Memory of Randomized Linear Symmetric Echo State Networks

AU - Tino, Peter

PY - 2018/7/12

Y1 - 2018/7/12

N2 - We study asymptotic properties of Fisher memory of linear Echo State Networkswith randomized symmetric state space coupling. In particular, two reservoir constructions are considered: (1) More direct dynamic coupling construction using a class of Wigner matrices and (2) positive semi-definite dynamic coupling obtained as a product of unconstrained stochastic matrices. We show that the maximal Fisher memory is achieved when the inputto-state coupling is collinear with the dominant eigenvector of the reservoir coupling matrix. In the case of Wigner reservoirs we show that as the system size grows, the contribution to the Fisher memory of self-coupling of reservoir units is negligible. We also prove that when the input-to-state coupling is collinear with the sum of eigenvectors of the state space coupling, the expected normalized memory is four and eight time smaller than the maximal memory value for the Wigner and product constructions, respectively.

AB - We study asymptotic properties of Fisher memory of linear Echo State Networkswith randomized symmetric state space coupling. In particular, two reservoir constructions are considered: (1) More direct dynamic coupling construction using a class of Wigner matrices and (2) positive semi-definite dynamic coupling obtained as a product of unconstrained stochastic matrices. We show that the maximal Fisher memory is achieved when the inputto-state coupling is collinear with the dominant eigenvector of the reservoir coupling matrix. In the case of Wigner reservoirs we show that as the system size grows, the contribution to the Fisher memory of self-coupling of reservoir units is negligible. We also prove that when the input-to-state coupling is collinear with the sum of eigenvectors of the state space coupling, the expected normalized memory is four and eight time smaller than the maximal memory value for the Wigner and product constructions, respectively.

KW - Fisher memory of dynamical systems

KW - Recurrent neural network

KW - Echo state network

KW - Reservoir Computing

U2 - 10.1016/j.neucom.2017.11.076

DO - 10.1016/j.neucom.2017.11.076

M3 - Article

VL - 298

SP - 4

EP - 8

JO - Neurocomputing

JF - Neurocomputing

SN - 0925-2312

ER -