Neural Networks in Which Synaptic Patterns Fluctuate with Time

We study a stochastic neural-network model in which neurons and synapses change with a priori probability p and 1–p, respectively, in the limit p0. This implies neuron activity competing with fast fluctuations of the synaptic connections—in fact, random oscillations around values given by a learning (for example, Hebb's) rule. The consequences for the system performance of a dynamics constantly checking at random the set of memorized patterns is thus studied both analytically and numerically. We describe various nonequilibrium phase transitions whose nature depends on the properties of fluctuations. We find, in particular, that under rather general conditions locally stable mixture states do not occur, and pattern recognition and retrieval processes are substantially improved for some classes of synaptic fluctuations.