Stochastic learning in a neural network with adapting synapses

We consider a neural network with adapting synapses whose dynamics can be analytically 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-state variables that 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→ with K large and finite, the correlations of neurons and synapses can be neglected and the dynamics can be analytically calculated by flow equations for the macroscopic parameters of the system.