Abstract

A model describing the dynamics of the synaptic weights of a single neuron performing Hebbian learning is described. The neuron is repeatedly excited by a set of input patterns. Its response is modeled as a continuous, nonlinear function of its excitation. We study how the model forms a self-organized representation of the set of input patterns. The dynamical equations are solved directly in a few simple cases. The model is studied for random patterns by a signal to noise analysis, and by introducing a partition function and applying the replica approach. As the number of patterns is increased a first order phase transitions occurs where the neuron becomes unable to remember one pattern but rather learns to a mixture of very many patterns. The critical number of patterns for this transition scales as N b , where N is the number of synapses and b is the degree of nonlinearity. The leading order finite size corrections are calculated and compared with numerical simulations. It is shown...

Citations