Presentation	1995/6/30 Number of Equilibrium States in a Randomly and Symmetrically Connected Recurrent Neural Network Akira Date, Koji Kurata, Shun-ichi Amari,
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Abstract(in English)	A class of recurrent networks is considered in which w_, the connection weight from the j th to the I th element, is randomly generated under the condition w_ = w_. The expected number of equilibrium states in the network consisting of two-state threshold elements having outputs of (-1,1) or (0,1) with a variable (but uniform throughout the network) threshold is derived by a method of statistical neurodynamics. It is shown that the expected number of equilibrium states are uniquely determined by the threshold value and the equilibrium states are concentrated on the states having a specific activity level, i.e. the rate of excited neurons. For the (0,1) model, a network consisting of neurons with a threshold value adjusted to make equilibrium states in which 32% of neurons are firing has the maximum number of equilibrium states, although the combinatorial number of the states is maximum at the activity level 50%. Applications of this network as a module for memory systems are discussed.
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Keyword(in English)	random neural networks / equilibrium states / statistical neurodynamics / memory systems
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Committee	NC
Conference Date	1995/6/30(1days)
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Registration To	Neurocomputing (NC)
Language	ENG
Title (in Japanese)	(See Japanese page)
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Title (in English)	Number of Equilibrium States in a Randomly and Symmetrically Connected Recurrent Neural Network
Sub Title (in English)
Keyword(1)	random neural networks
Keyword(2)	equilibrium states
Keyword(3)	statistical neurodynamics
Keyword(4)	memory systems
1st Author's Name	Akira Date
1st Author's Affiliation	Department of Computer Science, Graduate School of Technology, Tokyo University of Agriculture and Technology()
2nd Author's Name	Koji Kurata
2nd Author's Affiliation	Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University
3rd Author's Name	Shun-ichi Amari
3rd Author's Affiliation	Department of Mathematical Engineering and Information Physics, Faculty of Engineering, University of Tokyo:RIKEN, Frontier Research System, Research on Brain Information Processing, Laboratory for Information Representation
Date	1995/6/30
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Volume (vol)	vol.95
Number (no)	135
Page	pp.pp.-
#Pages	8
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