Parallel dynamics of extremely diluted symmetric Q-Ising neural networks

Details Parallel dynamics of extremely diluted symmetric Q-Ising neural networks Parallel dynamics of extremely diluted symmetric Q-Ising neural networks

1998-10-28

arxiv.org/abs/cond-mat/9810386v1

J.Stat.Phys.96, 861-882 (1999)

Physics

Condensed Matter

Disordered Systems and Neural Networks

26 pages, LaTeX, including 5 figures

Scientific paper

The parallel dynamics of extremely diluted symmetric Q-Ising neural networks is studied for arbitrary Q using a probabilistic approach. In spite of the extremely diluted architecture the feedback correlations arising from the symmetry prevent a closed-form solution in contrast with the extremely diluted asymmetric model. A recursive scheme is found determining the complete time evolution of the order parameters taking into account all feedback. It is based upon the evolution of the distribution of the local field, as in the fully connected model. As an illustrative example an explicit analysis is carried out for the Q=2 and Q=3 model. These results agree with and extend the partial results existing for Q=2. For Q>2 the analysis is entirely new. Finally, equilibrium fixed-point equations are derived and a capacity-gain function diagram is obtained.

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