Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models
Disordered Systems and Neural Networks
2009-11-10 v1 Statistical Mechanics
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0404658,
title = {Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models},
author = {B. Wemmenhove and N. S. Skantzos},
journal= {arXiv preprint arXiv:cond-mat/0404658},
year = {2009}
}
Comments
17 pages, 8 figures