Frontal Latching Networks and the neuronal basis of infinite recursion

Alessandro Treves
SISSA, Trieste, Italy
and
NTNU, Trondheim, Norway

Abstract

Understanding the neural basis of higher cognitive functions, such as those involved in language, in planning, in logics, what the Greeks would have called "logos", requires as a very prerequisite a shift from mere localization, which has been popular with imaging research, to an analysis of network operation. A recent proposal points at infinite recursion as the core of several higher functions, and thus challenges cortical network theorists to describe network behavior that could subserve infinite recursion. Considering a class of reduced models of large semantic associative networks, whose storage capacity can be studied analytically with statistical physics methods, I have simulated their dynamics, once the units are endowed with a simple model of firing frequency adaptation. I find that such models naturally display latching dynamics, i.e. they hop from one attractor to the next following a stochastic process based on the correlations among attractors. I propose here that such latching dynamics may be associated with a network capacity for combinatorial recursion. More interestingly it turns out, from the simulations and from analytical arguments, that infinite latching only occurs after a phase transition, once the network connectivity becomes sufficiently extensive to support structured transition probabilities between global network states. The crucial development endowing a semantic system with a non-random dynamics would thus be an increase in connectivity, perhaps to be identified with the dramatic increase in spine numbers recently observed in the basal dendrites of pyramidal cells in Old World monkey and particularly in human frontal cortex.

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