Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models

Details Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models

2004-04-27

arxiv.org/abs/cond-mat/0404658v1

J. Phys. A: Math. Gen. 37 (2004) 7843

Physics

Condensed Matter

Disordered Systems and Neural Networks

17 pages, 8 figures

Scientific paper

10.1088/0305-4470/37/32/002

We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural network (Hopfield) models and we show that due to the minimisation of the frustration effects the retrieval region of the phase diagram can be significantly enlarged. Moreover, the fraction of misaligned spins is reduced by this effect, and is smaller than in the infinite connectivity regime. The main cause of this difference is found to be the non-zero fraction of sites with vanishing local field when the connectivity is finite.

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