The storage capacity of Potts models for semantic memory retrieval

Details The storage capacity of Potts models for semantic memory retrieval The storage capacity of Potts models for semantic memory retrieval

2005-07-05

arxiv.org/abs/cond-mat/0507111v3

J. Stat. Mech. (2005) P08010

Physics

Condensed Matter

Disordered Systems and Neural Networks

Accepted for publication in J-STAT, July 2005

Scientific paper

10.1088/1742-5468/2005/08/P08010

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.

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