Dynamical properties of a randomly diluted neural network with variable activity

Details Dynamical properties of a randomly diluted neural network with variable activity Dynamical properties of a randomly diluted neural network with variable activity

1999-03-08

arxiv.org/abs/cond-mat/9903114v1

Journal of Physics A 32(16) 2983-2995 (1999)

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, 5 figures, to be published in Journal of Physics A

Scientific paper

10.1088/0305-4470/32/16/007

The subject of study is a neural network with binary neurons, randomly diluted synapses and variable pattern activity. We look at the system with parallel updating using a probabilistic approach to solve the one step dynamics with one condensed pattern. We derive restrictions on the storage capacity and the mutual information content occuring during the retrieval process. Special focus is on the constraints on the threshold for optimal performance. We also look at the effect of noisy updating, giving a dynamical version of the critical temperature, the corresponding threshold and an approximation for the time evolution for small temperatures. The description is applicable to the whole retrieval process in the limit of strong dilution. The analysis is carried out as exactly as possible and over the full parameter ranges, generalizing some former results.

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