LINSKER-TYPE HEBBIAN LEARNING - A QUALITATIVE-ANALYSIS ON THE PARAMETER SPACE

We developed a new method to relate the choice of system parameters to the outcomes of the unsupervised learning process in Linsker's multi- layer network model. The behavior of this model is determined by the u nderlying nonlinear dynamics that are parameterized by a set of parame ters originating from the Hebb rule and the arbor density of the synap ses. These parameters determine the presence or absence of a specific receptive field (or connection pattern) as a saturated fixed point att ractor of the model. We derived a necessary and sufficient condition t o test whether a given saturated weight vector is stable or not for an y given set of system parameters, and used this condition to determine the whole regime in the parameter space over which the given connecti on pattern is stable. The parameter space approach allows us to invest igate the relative stability of the major receptive fields reported in Linsker's simulation, and to demonstrate the crucial role played by t he localized arbor density of synapses between adjacent layers. The me thod presented here can be employed to analyze other learning and retr ieval models that use the limiter function as the constraint controlli ng the magnitude of the weight or state vectors. (C) 1997 Elsevier Sci ence Ltd.