Dynamical Behavior of Neural Networks with Anti-Symmetrical Cyclic Connections

Shinya SUENAGA; Yoshihiro HAYAKAWA; Koji NAKAJIMA

doi:10.1093/ietfec/e89-a.10.2775

Dynamical Behavior of Neural Networks with Anti-Symmetrical Cyclic Connections

Shinya SUENAGA, Yoshihiro HAYAKAWA, Koji NAKAJIMA

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We show that a unit-grup, which represents a group of contiguous units with the same sign of output, is a dominant component for the dynamical behavior of a neural network with anti-symmetrical cyclie connections for the nearest neighbor connections and global connections. In transient state, it is shown that the unit-grup has the dynamics such that the amount n of units which belong to the unit-grup increases with time, and that the increasing rate of n decreases with increasing n. The dynamics cause the large difference of the number of limit-cycles between discrete and continuous time models. Additionally, the period of the limit-cycle depends on the size of the unit-grups. This dependency is obtained from computer simulations and two approximation methods. These approximations provide the lower and the upper bounds of the periods which depend on the gain of an activation function. Using these approximations, we also obtain detailed relations between a period and the other network parameters analytically.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.10 pp.2775-2786

Publication Date: 2006/10/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.10.2775

Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

Category: Oscillation, Dynamics and Chaos

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Shinya SUENAGA, Yoshihiro HAYAKAWA, Koji NAKAJIMA, "Dynamical Behavior of Neural Networks with Anti-Symmetrical Cyclic Connections" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 10, pp. 2775-2786, October 2006, doi: 10.1093/ietfec/e89-a.10.2775.
Abstract: We show that a unit-grup, which represents a group of contiguous units with the same sign of output, is a dominant component for the dynamical behavior of a neural network with anti-symmetrical cyclie connections for the nearest neighbor connections and global connections. In transient state, it is shown that the unit-grup has the dynamics such that the amount n of units which belong to the unit-grup increases with time, and that the increasing rate of n decreases with increasing n. The dynamics cause the large difference of the number of limit-cycles between discrete and continuous time models. Additionally, the period of the limit-cycle depends on the size of the unit-grups. This dependency is obtained from computer simulations and two approximation methods. These approximations provide the lower and the upper bounds of the periods which depend on the gain of an activation function. Using these approximations, we also obtain detailed relations between a period and the other network parameters analytically.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.10.2775/_p

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@ARTICLE{e89-a_10_2775,
author={Shinya SUENAGA, Yoshihiro HAYAKAWA, Koji NAKAJIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Dynamical Behavior of Neural Networks with Anti-Symmetrical Cyclic Connections},
year={2006},
volume={E89-A},
number={10},
pages={2775-2786},
abstract={We show that a unit-grup, which represents a group of contiguous units with the same sign of output, is a dominant component for the dynamical behavior of a neural network with anti-symmetrical cyclie connections for the nearest neighbor connections and global connections. In transient state, it is shown that the unit-grup has the dynamics such that the amount n of units which belong to the unit-grup increases with time, and that the increasing rate of n decreases with increasing n. The dynamics cause the large difference of the number of limit-cycles between discrete and continuous time models. Additionally, the period of the limit-cycle depends on the size of the unit-grups. This dependency is obtained from computer simulations and two approximation methods. These approximations provide the lower and the upper bounds of the periods which depend on the gain of an activation function. Using these approximations, we also obtain detailed relations between a period and the other network parameters analytically.},
keywords={},
doi={10.1093/ietfec/e89-a.10.2775},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Dynamical Behavior of Neural Networks with Anti-Symmetrical Cyclic Connections
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2775
EP - 2786
AU - Shinya SUENAGA
AU - Yoshihiro HAYAKAWA
AU - Koji NAKAJIMA
PY - 2006
DO - 10.1093/ietfec/e89-a.10.2775
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2006
AB - We show that a unit-grup, which represents a group of contiguous units with the same sign of output, is a dominant component for the dynamical behavior of a neural network with anti-symmetrical cyclie connections for the nearest neighbor connections and global connections. In transient state, it is shown that the unit-grup has the dynamics such that the amount n of units which belong to the unit-grup increases with time, and that the increasing rate of n decreases with increasing n. The dynamics cause the large difference of the number of limit-cycles between discrete and continuous time models. Additionally, the period of the limit-cycle depends on the size of the unit-grups. This dependency is obtained from computer simulations and two approximation methods. These approximations provide the lower and the upper bounds of the periods which depend on the gain of an activation function. Using these approximations, we also obtain detailed relations between a period and the other network parameters analytically.
ER -