The storage capacity of Potts models for semantic memory retrieval

We introduce and analyze a minimal network model of semantic memory in the human brain. The model is a global associative memory structured as a collection of N local modules, each coding a feature, which can take S possible values, with a global sparseness a (the average fraction of features describing a concept). We show that, under optimal conditions, the number c of modules connected on average to a module can range widely between very sparse connectivity (c/N -> 0) and full connectivity (c = N), maintaining a global network storage capacity (the maximum number p of stored and retrievable concepts) that scales like c*S^2/a, with logarithmic corrections consistent with the constraint that each synapse may store up to a fraction of a bit.