Tech Report Available

[Geoffrey Goodhill]

The following technical report version of my thesis is now available
in neuroprose:

             Correlations, Competition, and Optimality: 
      Modelling the Development of Topography and Ocular Dominance

                           CSRP 226

                       Geoffrey Goodhill
            School of Cognitive and Computing Science
                      University Of Sussex

                           ABSTRACT

There is strong biological evidence that the same mechanisms underly
the formation of both topography and ocular dominance in the visual
system. However, previous computational models of visual development
do not satisfactorily address both of these phenomena
simultaneously. In this thesis we discuss in detail several
models of visual development, focussing particularly on the form
of correlations within and between eyes. 

Firstly, we analyse the "correlational" model for ocular dominance
development recently proposed in [Miller, Keller & Stryker 1989] .
This model was originally presented for the case of identical
correlations within each eye and zero correlations between the eyes.
We relax these assumptions by introducing perturbative correlations
within and between eyes, and show that (a) the system is unstable to
non-identical perturbations in each eye, and (b) the addition of small
positive correlations between the eyes, or small negative correlations
within an eye, can cause binocular solutions to be favoured over
monocular solutions.

Secondly, we extend the elastic net model of [Goodhill 1988, Goodhill
and Willshaw 1990] for the development of topography and ocular
dominance, in particular considering its behaviour in the
two-dimensional case. We give both qualitative and quantitative
comparisons with the performance of an algorithm based on the
self-organizing feature map of Kohonen, and show that in general the
elastic net performs better. In addition we show that (a) both
algorithms can reproduce the effects of monocular deprivation, and (b)
that a global orientation for ocular dominance stripes in the elastic
net case can be produced by anisotropic boundary conditions in the
cortex.

Thirdly, we introduce a new model that accounts for the development of
topography and ocular dominance when distributed patterns of activity
are presented simultaneously in both eyes, with significant
correlations both within and between eyes. We show that stripe width
in this model can be influenced by two factors: the extent of lateral
interactions in the postsynaptic sheet, and the degree to which the
two eyes are correlated. An important aspect of this model is the form
of the normalization rule to limit synaptic strengths: we analyse this
for a simple case.

The principal conclusions of this work are as follows:

1. It is possible to formulate computational models that account for
   (a) both topography and stripe formation, and (b) ocular dominance
   segregation in the presence of *positive* correlations between
   the two eyes.

2. Correlations can be used as a ``currency'' with which to compare
   locality within an eye with correspondence between eyes. This
   leads to the novel prediction that stripe width can be influenced
   by the degree of correlation between the two eyes. 


Instructions for obtaining by anonymous ftp:

% ftp cheops.cis.ohio-state.edu
Name: anonymous
Password:neuron
ftp> binary
ftp> cd pub/neuroprose
ftp> get goodhill.thesis.tar
ftp> quit
% tar -xvf goodhill.thesis.tar  (This creates a directory called thesis)
% cd thesis
% more README

WARNING: goodhill.thesis.tar is 2.4 Megabytes, and the thesis takes up
13 Megabytes if all files are uncompressed (there are only 120 pages
- the size is due to the large number of pictures). Each file within
the tar file is individually compressed, so it is not necessary to
have 13 Meg of spare space in order to print out the thesis.

The hardcopy version is also available by requesting CSRP 226 from:

Berry Harper
School of Cognitive and Computing Sciences
University of Sussex
Falmer
Brighton BN1 9QN
GREAT BRITAIN

Please enclose a cheque for either 5 pounds sterling or 10 US dollars,
made out to "University of Sussex".


Geoffrey Goodhill
University of Edinburgh
Centre for Cognitive Science
2 Buccleuch Place
Edinburgh EH8 9LW
email: gjg at cns.ed.ac.uk