Stochastic learning in a neural network with adapting synapses
Gianluca Lattanzi, G. Nardulli, G. Pasquariello, Sebastiano Stramaglia · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997
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 $N\ensuremath{\rightarrow}\ensuremath{\infty}$ 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.