A canonical ensemble approach to graded-response perceptrons

TL;DR

This paper investigates graded-response perceptrons using a canonical ensemble approach, comparing different error measures and analyzing replica-symmetry-breaking effects to understand their retrieval capabilities.

Contribution

It introduces soft error measures for perceptrons with graded outputs and evaluates their performance and symmetry-breaking effects, extending previous models.

Findings

Soft error measures improve retrieval properties.

Performance varies between linear, quadratic, and rigid error measures.

Replica-symmetry-breaking effects are significant in these models.

Abstract

Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner-Derrida canonical ensemble approach. Soft non- negative error measures are introduced allowing for extended retrieval properties. In particular, the performance of these systems for a linear and quadratic error measure, corresponding to the perceptron respectively the adaline learning algorithm, is compared with the performance for a rigid error measure, simply counting the number of errors. Replica-symmetry-breaking effects are evaluated.