Analytic solution of attractor neural networks on scale-free graphs
I Pérez Castillo, B Wemmenhove, J P L Hatchett, A C C Coolen, N S Skantzos, T Nikoletopoulos · Journal of Physics A Mathematical and General · 2004
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 ) ∼ k −γ , 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.