Capacity of an associative memory model on random graph architectures

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.