Instability of frozen-in states in synchronous Hebbian neural networks

The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of frozen-in states that appear in the absence of both kinds of noise. Both, the numerical simulation procedure of Eissfeller and Opper and a new alternative procedure that allows to follow the dynamics over larger time scales have been used in this work. It is shown that synaptic noise destabilizes the frozen-in states and yields either retrieval or paramagnetic states for not too large stochastic noise. The indications are that the same results may follow in the absence of synaptic noise, for low stochastic noise.Comment: 14 pages and 4 figures; accepted for publication in J. Phys. A: Math. Ge