The storage capacity of Potts models for semantic memory retrieval

We introduce and analyse 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 cM of modules connected on average to a module can range widely between very sparse connectivity (high dilution, ) and full connectivity (), maintaining a global network storage capacity (the maximum number pc of stored and retrievable concepts) that scales like pc~cMS2/a, with logarithmic corrections consistent with the constraint that each synapse may store up to a fraction of a bit.

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