The storage capacity of Potts models for semantic memory retrieval
Emilio Kropff, Alessandro Treves · Journal of Statistical Mechanics Theory and Experiment · 2005
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 c M 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 p c of stored and retrievable concepts) that scales like p c ∼ c M S 2 / a , with logarithmic corrections consistent with the constraint that each synapse may store up to a fraction of a bit.