Phase Transitions in a Neural Model of Problem Solving

Abstract

In order to model the process of acquisition of competence by children in solving problems of addition between integer numbers, we introduced a generalization of a celebrated neural network model, the Harmony Theory proposed by Smolensky. The generalization consists in allowing a variable number of atoms of knowledge, as well as variable strengths associated to them. The variation of these quantities depends on the rightness of the answer given by the network to a particular addition problem. We monitored the average values of correctly solved problems and the maximum values of ∆C/∆T, C being the specific heat and T the temperature, as defined by Smolensky, in order to find evidence for phase transitions in a simulated learning process. We found only partial evidence of such phase transitions. Besides, the network performance was strongly dependent on the structuration of initial dotation of knowledge atoms.