A Local Property of the Phasor Model of Neural Networks

Masahiro AGU; Kazuo YAMANAKA; Hiroki TAKAHASHI

A Local Property of the Phasor Model of Neural Networks

Masahiro AGU, Kazuo YAMANAKA, Hiroki TAKAHASHI

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Stable phase locked states" are found amongst the equiliblia of the phasor model known as a generalized Hopfield model having complex-valued local states on the unit circle with centre at the origin. The asynchronous updating rule is assumed, and the energy decreasing characteristic is used to investigate a property of the equilibrium states. Some of the equilibria are shown to be fragile" in the sense that the energy is not locally convex. It is also shown that the local convexity of the energy is assured by a sort of consistency between the equilibrium and the connection weights.

Publication: IEICE TRANSACTIONS on Information Vol.E79-D No.8 pp.1209-1211

Publication Date: 1996/08/25

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Type of Manuscript: LETTER

Category: Bio-Cybernetics and Neurocomputing

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Masahiro AGU, Kazuo YAMANAKA, Hiroki TAKAHASHI, "A Local Property of the Phasor Model of Neural Networks" in IEICE TRANSACTIONS on Information, vol. E79-D, no. 8, pp. 1209-1211, August 1996, doi: .
Abstract: Stable phase locked states" are found amongst the equiliblia of the phasor model known as a generalized Hopfield model having complex-valued local states on the unit circle with centre at the origin. The asynchronous updating rule is assumed, and the energy decreasing characteristic is used to investigate a property of the equilibrium states. Some of the equilibria are shown to be fragile" in the sense that the energy is not locally convex. It is also shown that the local convexity of the energy is assured by a sort of consistency between the equilibrium and the connection weights.
URL: https://global.ieice.org/en_transactions/information/10.1587/e79-d_8_1209/_p

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@ARTICLE{e79-d_8_1209,
author={Masahiro AGU, Kazuo YAMANAKA, Hiroki TAKAHASHI, },
journal={IEICE TRANSACTIONS on Information},
title={A Local Property of the Phasor Model of Neural Networks},
year={1996},
volume={E79-D},
number={8},
pages={1209-1211},
abstract={Stable phase locked states" are found amongst the equiliblia of the phasor model known as a generalized Hopfield model having complex-valued local states on the unit circle with centre at the origin. The asynchronous updating rule is assumed, and the energy decreasing characteristic is used to investigate a property of the equilibrium states. Some of the equilibria are shown to be fragile" in the sense that the energy is not locally convex. It is also shown that the local convexity of the energy is assured by a sort of consistency between the equilibrium and the connection weights.},
keywords={},
doi={},
ISSN={},
month={August},}

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TY - JOUR
TI - A Local Property of the Phasor Model of Neural Networks
T2 - IEICE TRANSACTIONS on Information
SP - 1209
EP - 1211
AU - Masahiro AGU
AU - Kazuo YAMANAKA
AU - Hiroki TAKAHASHI
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 8
JA - IEICE TRANSACTIONS on Information
Y1 - August 1996
AB - Stable phase locked states" are found amongst the equiliblia of the phasor model known as a generalized Hopfield model having complex-valued local states on the unit circle with centre at the origin. The asynchronous updating rule is assumed, and the energy decreasing characteristic is used to investigate a property of the equilibrium states. Some of the equilibria are shown to be fragile" in the sense that the energy is not locally convex. It is also shown that the local convexity of the energy is assured by a sort of consistency between the equilibrium and the connection weights.
ER -