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 underlying nonlinear dynamics that are parameterized by a set of parameters originating from the Hebb rule and the arbor density of the synapses. These parameters determine the presence or absence of a specific receptive field (or connection pattern) as a saturated fixed point attractor of the model. We derived a necessary and sufficient condition to test whether a given saturated weight vector is stable or not for any given set of system parameters, and used this condition to determine the whole regime in the parameter space over which the given connection pattern is stable. The parameter space approach allows us to investigate the relative stability of the major receptive fields reported in Linsker's simulation, and to demonstrate the crucial role played by the localized arbor density of synapses between adjacent layers. The method presented here can be employed to analyze other learning and retrieval models that use the limiter function as the constraint controlling the magnitude of the weight or state vectors. (C) 1997 Elsevier Science Ltd.