tech report announcement

[Ken Miller]

The following tech report has been placed in the neuroprose
archive as miller.hebbian.tar.Z.  Instructions for retrieving 
and printing follow the abstract.  A slightly abridged version
of this paper has been submitted to Neural Computation.


          The Role of Constraints in Hebbian Learning
            Kenneth D. Miller and David J.C. MacKay

      Caltech Computation and Neural Systems (CNS) Program
                          CNS Memo 19                             

Models of unsupervised correlation-based (Hebbian) synaptic plasticity
are typically unstable: either all synapses grow until each reaches
the maximum allowed strength, or all synapses decay to zero strength.
A common method of avoiding these outcomes is to use a constraint that
conserves or limits the total synaptic strength over a cell.  We study
the dynamical effects of such constraints.  Two methods of enforcing a
constraint are distinguished, multiplicative and subtractive.  For
otherwise linear learning rules, multiplicative enforcement of a
constraint results in dynamics that converge to the principal
eigenvector of the operator determining unconstrained synaptic
development.  Subtractive enforcement, in contrast, leads to a final
state in which almost all synaptic strengths reach either the maximum
or minimum allowed value.  This final state is often dominated by
weight configurations other than the principal eigenvector of the
unconstrained operator.  Multiplicative enforcement yields a ``graded"
receptive field in which most mutually correlated inputs are
represented, whereas subtractive enforcement yields a receptive field
that is ``sharpened" to a few maximally-correlated inputs.  If two
equivalent input populations ({\it e.g.} two eyes) innervate a common
target, multiplicative enforcement prevents their segregation (ocular
dominance segregation) when the two populations are weakly correlated;
whereas subtractive enforcement allows segregation under these
circumstances.  An approach to understanding constraints over input
and over output cells is suggested, and some biological
implementations are discussed.

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How to retrieve and print out this paper:

unix> ftp archive.cis.ohio-state.edu
Connected to archive.cis.ohio-state.edu.
220 archive.cis.ohio-state.edu FTP server ready.
Name: anonymous
331 Guest login ok, send ident as password.
Password: [your e-mail address]
230 Guest login ok, access restrictions apply.
ftp> binary
200 Type set to I.
ftp> cd pub/neuroprose
250 CWD command successful.
ftp> get miller.hebbian.tar.Z
200 PORT command successful.
150 Opening BINARY mode data connection for miller.hebbian.tar.Z
226 Transfer complete.
480000 bytes sent in many seconds
ftp> quit
221 Goodbye.
unix> uncompress miller.hebbian.tar.Z
unix> tar xvf miller.hebbian.tar
	TO SAVE DISC SPACE, THE ABOVE TWO COMMANDS MAY BE
	REPLACED WITH THE SINGLE COMMAND
        unix> zcat miller.hebbian.tar.Z | tar xvf -
hebbian_p0-11.ps
hebbian_p12-23.ps
hebbian_p24-35.ps
unix> lpr hebbian_p24-35.ps
unix> lpr hebbian_p12-23.ps
unix> lpr hebbian_p0-11.ps