14 - Dynamics of Supervised Learning with Restricted Training Sets

Summary

Abstract

We study the dynamics of supervised learning in layered neural networks, in the regime where the size p of the training set is proportional to the number N of inputs. Here the local fields are no longer described by Gaussian distributions. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the relevant performance measures, incorporating the theory of complete training sets in the limit p/N → ∞ as a special case. For simplicity we restrict ourselves here to single-layer networks and realizable tasks.

Introduction

In the last few years much progress has been made in the analysis of the dynamics of supervised learning in layered neural networks, using the strategy of statistical mechanics: by deriving from the microscopic dynamical equations a set of closed laws describing the evolution of suitably chosen macroscopic observables (dynamic order parameters) in the limit of an infinite system size [e.g. Kinzel & Rujan (1990), Kinouchi & Caticha (1992), Biehl & Schwarze (1992, 1995), Saad & Solla (1995)]. A recent review and more extensive guide to the relevant references can be found in Mace & Coolen (1998a).