Mathematical Analysis of Learning Behavior of Neuronal Models

Abstract

In this paper, we wish to analyze the convergence behavior of a number of neuronal plasticity models. Recent neurophysiological research suggests that the neuronal behavior is adaptive. In particular, memory stored within a neuron is associated with the synaptic weights which are varied or adjusted to achieve learning. A number of adaptive neuronal models have been proposed in the literature. Three specific models will be analyzed in this paper, specifically the Hebb model, the Sutton-Barto model, and the most recent trace model. In this paper we will examine the conditions for convergence, the position of conver(cid:173) gence and the rate at convergence, of these models as they applied to classical conditioning. Simulation results are also presented to verify the analysis.