Capacity of an associative memory model on random graph architectures

TL;DR

This paper investigates how the structure of different random graph architectures affects the storage capacity of Hopfield associative memory models, extending previous work beyond Erdős-Rényi graphs to include power law graphs.

Contribution

It introduces a new notion of storage capacity that accounts for graph topology and provides results for various random graph models, including power law graphs.

Findings

Storage capacity depends on graph topology.

Results extend to power law graphs.

Analysis includes non-regular random graphs.

Abstract

We analyze the storage capacity of the Hopfield models on classes of random graphs. While such a setup has been analyzed for the case that the underlying random graph model is an Erd\"{o}s-Renyi graph, other architectures, including those investigated in the recent neuroscience literature, have not been studied yet. We develop a notion of storage capacity that highlights the influence of the graph topology and give results on the storage capacity for not too irregular random graph models. The class of models investigated includes the popular power law graphs for some parameter values.