Stochastic Learning in a Neural Network with Adapting Synapses.

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of N neurons and each of them is connected to K input neurons chosen at random in the network. The synapses are n-states variables which evolve in time according to Stochastic Learning rules; a parallel stochastic dynamics is assumed for neurons. Since the network maintains the same dynamics whether it is engaged in computation or in learning new memories, a very low probability of synaptic transitions is assumed. In the limit N !1 with K large and finite, the correlations of neurons and synapses can be neglected and the dynamics can be analitically calculated by flow equations for the macroscopic parameters of the system. PACS numbers: 87.10.+e, 05.20.-y 1. Introduction. In the dynamics of Attractor Neural Networks (ANNs) two processes take place: the time evolution of the neuron states and the change in strength of the connections (synapses) between neurons. Most of t..