Topology and Dynamics of Attractor Neural Networks: The Role of Loopiness

Details Topology and Dynamics of Attractor Neural Networks: The Role of Loopiness Topology and Dynamics of Attractor Neural Networks: The Role of Loopiness

2007-03-15

arxiv.org/abs/cond-mat/0703405v3

Physica A 387, (2008) 4411-4416

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 4 figures, comments are favored

Scientific paper

10.1016/j.physa.2008.02.073

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. The large loopiness coefficient means the large probability of finding loops in the networks. We develop the recursive equations for the overlap parameters of neural networks in the term of the loopiness. It was found that the large loopiness increases the correlations among the network states at different times, and eventually it reduces the performance of neural networks. The theory is applied to several network topological structures, including fully-connected, densely-connected random, densely-connected regular, and densely-connected small-world, where encouraging results are obtained.

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