Parallel dynamics of fully connected Q-Ising neural networks

Details Parallel dynamics of fully connected Q-Ising neural networks Parallel dynamics of fully connected Q-Ising neural networks

1997-04-10

arxiv.org/abs/cond-mat/9704089v1

J.Stat.Phys. 91 (1998), 125-154

Physics

Condensed Matter

Disordered Systems and Neural Networks

26 pages incl. figures, LaTeX, uses rotate.sty and epsfig.sty

Scientific paper

Using a probabilistic approach we study the parallel dynamics of fully connected Q-Ising neural networks for arbitrary Q. A Lyapunov function is shown to exist at zero temperature. A recursive scheme is set up to determine the time evolution of the order parameters through the evolution of the distribution of the local field. As an illustrative example, an explicit analysis is carried out for the first three time steps. For the case of the Q=3 model these theoretical results are compared with extensive numerical simulations. Finally, equilibrium fixed-point equations are derived and compared with the thermodynamic approach based upon the replica-symmetric mean-field approximation.

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