Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 37, Issue 37, Pages 8789-8799Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/37/37/002
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We study the influence of network topology on retrieval properties of recurrent neural networks, using replica techniques for dilute systems. The theory is presented for a network with an arbitrary degree distribution p(k) and applied to power-law distributions p(k) similar to k(-gamma), i.e. to neural networks on scale-free graphs. A bifurcation analysis identifies phase boundaries between the paramagnetic phase and either a retrieval phase or a spin-glass phase. Using a population dynamics algorithm, the retrieval overlap and spin-glass order parameters may be calculated throughout the phase diagram. It is shown that there is an enhancement of the retrieval properties compared with a Poissonian random graph. We compare our findings with simulations.
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