Reducing a cortical network to a Potts model yields storage capacity estimates

TL;DR

This paper analyzes how reducing a cortical network to a Potts model with local feedback can estimate storage capacity, providing insights into phase transitions and implications for human semantic memory.

Contribution

It establishes the correspondence between cortical networks and Potts models, introducing a local feedback term and deriving capacity estimates for both fully connected and partially connected networks.

Findings

The local feedback term influences storage capacity.

Capacity estimates are derived using replica analysis.

Implications for human semantic memory are discussed.

Abstract

An autoassociative network of Potts units, coupled via tensor connections, has been proposed and analysed as an effective model of an extensive cortical network with distinct short- and long-range synaptic connections, but it has not been clarified in what sense it can be regarded as an effective model. We draw here the correspondence between the two, which indicates the need to introduce a local feedback term in the reduced model, i.e., in the Potts network. An effective model allows the study of phase transitions. As an example, we study the storage capacity of the Potts network with this additional term, the local feedback $w$, which contributes to drive the activity of the network towards one of the stored patterns. The storage capacity calculation, performed using replica tools, is limited to fully connected networks, for which a Hamiltonian can be defined. To extend the results to the case of intermediate partial connectivity, we also derive the self-consistent signal-to-noise analysis for the Potts network; and finally we discuss implications for semantic memory in humans.