tech report available

[Kechen Zhang]

ftp-host: cogsci.ucsd.edu
ftp-filename: /pub/tr/9402.charsys.ps.Z
size of uncompressed file: 0.55 Mb
printed pages: 21


This is the first UCSD Cognitive Science technical report available
by anonymous ftp, thanks for the help from Kathy Farrelly, Paul Maglio,
Javier Movellan, Marty Sereno, Mark Wallen and David Zipser. 

The abstract and the ftp instructions are as follows.

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	   Temporal association by Hebbian connections:
	       The method of characteristic system

			Kechen Zhang

			 June 1994
			Report 9402

		Department of Cognitive Science
              University of California, San Diego
		  La Jolla, CA 92093-0515
	 	email: kzhang at cogsci.ucsd.edu

			Abstract
While it is generally accepted that the stability of a static memory 
pattern corresponds to a certain point attractor in the dynamics of the 
underlying neural network, when temporal order is introduced and a 
sequence of memory patterns need to be retrieved successively in 
continuous time, it becomes less clear what general method should be 
used to decide whether the transient dynamics is robust or not.  In this 
paper, it is shown that such a general method can be developed if all 
the connections in the neural network are Hebbian.  This method is 
readily applied to various structures of coupled networks as well as to 
the standard temporal association model with asymmetric time-delayed 
connections.  The basic idea is to introduce new variables made of 
memory-overlap projections with alternating signs, and then circumvent 
the nonlinearity of the sigmoid function by exploiting the dynamical 
symmetry inherent in the Hebb rule.  The result is a self-contained, 
low-dimensional deterministic system.  A powerful feature of this 
approach is that it can translate questions about the stability of the 
sequential memory transitions in the original neural network into 
questions about the stability of the periodic oscillation in the 
corresponding characteristic system.  This correspondence enables direct, 
quantitative prediction of the behaviors of the original system, as being 
confirmed by computer simulations on the conjugate networks, the 
``tri-synaptic loop'' networks, and the time-delayed network.  In 
particular, the conjugate networks (consisting of two Hopfield subnets 
coupled by asymmetric Hebbian connections) offer a simple but sufficient 
structure for the storage and retrieval of sequential memory patterns 
without any additional temporal mechanisms besides the intrinsic dynamics.  
The same structure can also be used for the recognition of a temporal
sequence of sparse memory patterns.  Other topics include the storage
capacity of the conjugate networks, the exact solution of the limit
cycle in the characteristic system, the sequential retrieval at variable 
speeds, and the problem of equivalence between coupling and time delays.

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To retrieve the compressed PostScript file, do the following:

unix> ftp cogsci.ucsd.edu  
ftp> login: anonymous
ftp> password: <your full email address>
ftp> cd pub/tr
ftp> bin
ftp> ls 
ftp> get 9402.charsys.ps.Z
ftp> bye

unix> uncompress 9402.charsys.ps.Z
unix> lpr -P<printer> -s 9402.charsys.ps  (or however you print PostScript)
                             
page numbers: 0 - 20