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

TL;DR

This paper introduces an analytically solvable evolving random graph model applied to finite-connectivity Hopfield neural networks, demonstrating enlarged retrieval regions and reduced misaligned spins due to adaptive geometry effects.

Contribution

It presents a novel solvable model of adaptive random graphs applied to neural networks, revealing how slow evolution of connections enhances retrieval performance.

Findings

Enlarged retrieval region in the phase diagram.

Reduced fraction of misaligned spins.

Finite connectivity effects differ from infinite connectivity regime.

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.