Transient Dynamics of Sparsely Connected Hopfield Neural Networks with Arbitrary Degree Distributions

Details Transient Dynamics of Sparsely Connected Hopfield Neural Networks with Arbitrary Degree Distributions Transient Dynamics of Sparsely Connected Hopfield Neural Networks with Arbitrary Degree Distributions

2007-04-08

arxiv.org/abs/0704.1007v2

Physica A 387, 1009(2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 5 figures. Any comments are favored

Scientific paper

10.1016/j.physa.2007.09.047

Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As illustrative examples, the explicit calculations of dynamics for networks with binomial, power-law, and uniform degree distribution are performed. The results are good agreement with the extensive numerical simulations. It indicates that with the same average degree, there is a gradual improvement of network performance with increasing sharpness of its degree distribution, and the most efficient degree distribution for global storage of patterns is the delta function.

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