PARALLEL DYNAMICS OF FULLY CONNECTED Q-ISING NEURAL NETWORKS

Using a probabilistic approach, the parallel dynamics of fully connect ed e-Ising neural networks is studied for arbitrary Q. A novel recursi ve scheme is set up to determine the time evolution of the order param eters through the evolution of the distribution of the local field, ta king into account all feedback correlations. In contrast to extremely diluted and layered network architectures, the local field is no longe r normally distributed but contains a discrete part. As an illustrativ e example, an explicit analysis is carried out for the first four time steps. For the case of the Q = 2 and Q = 3 model the results are comp ared with extensive numerical simulations and excellent agreement is f ound. Finally, equilibrium fixed-point equations are derived and compa red with the thermodynamic approach based upon the replica-symmetric m ean-field approximation.