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- C. Piepenbrock
and K. Obermayer. The Effect of Intracortical Competition on the Formation
of Topographic Maps in Models of Hebbian Learning.
.
Biol. Cybern., 82:345-353, 2000.
(FTP Gzipped PostScript, 19 pages, 79 kb)
Correlation based learning models (CBL) and self-organizing maps
(SOM) are two classes of Hebbian models that have both been proposed to
explain the activity driven formation of cortical maps. Both models differ
significantly in the way lateral cortical interactions are treated leading to
different predictions for the formation of receptive fields. The linear CBL
models predict that receptive field profiles are determined by the average
values and the spatial correlations of second order of the afferent activity
patterns, wheras SOM models map stimulus features. Here we investigate a
class of models which are characterized by a variable degree of lateral
competition and which have the CBL and SOM models as limit cases. We show
that there exists a critical value for intracortical competition below which
the model exhibits CBL properties and above which feature mapping sets in.
The class of models is then analyzed with respect to the formation of
topographic maps between two layers of neurons. For Gaussian input stimuli we
find that localized receptive fields and topographic maps emerge above the
critical value for intracortical competition and we calculate this value as a
function of the size of the input stimuli and the range of the lateral
interaction function. Additionally, we show that the learning rule can be
derived via the optimization of a global cost function in a framework of
probabilistic output neurons which represent a set of input stimuli by a
sparse code.
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