Learning of correlated patterns by simple perceptrons

TL;DR

This paper investigates how statistical correlations among input patterns affect the learning performance of simple perceptrons in a teacher-student setup, extending a methodology to analyze correlated patterns.

Contribution

It introduces an extension of a previous methodology to analyze the impact of input pattern correlations on perceptron learning in a teacher-student framework.

Findings

Correlations among input patterns influence learning efficiency.

Enhanced orthogonality of input patterns can optimize learning performance.

The methodology provides insights into pattern correlation effects on perceptron learning.

Abstract

Learning behavior of simple perceptrons is analyzed for a teacher-student scenario in which output labels are provided by a teacher network for a set of possibly correlated input patterns, and such that teacher and student networks are of the same type. Our main concern is the effect of statistical correlations among the input patterns on learning performance. For this purpose, we extend to the teacher-student scenario a methodology for analyzing randomly labeled patterns recently developed in {\em J. Phys. A: Math. Theor.} {\bf 41}, 324013 (2008). This methodology is used for analyzing situations in which orthogonality of the input patterns is enhanced in order to optimize the learning performance.