文档介绍：
DISCRETE
APPLIED
MATHEMATICS
Discrete Applied Mathelnatics 69 (I 996) 33-60
Representation theory and invariant neural networks ”
Jeffrey Wood *, John Shawe-Taylor
Received 5 April 1994; revised 19 December 1994
Abstract
A feedforward neural network is a computational device used for pattern recognition. In many
recognition problems, certain transformations exist which, when applied to a pattern, leave its
classification unchanged. Invariance under a given group of transformations is therefore typically
a desirable property of pattern classifiers. In this paper, we present a methodology, based on
representation theory, for the construction of a neural network invariant under any given finite
linear group. Such networks show improved generalization abilities and may also learn faster
than corresponding networks without in-built invariance.
We hope in the future to generalize this theory to approximate invariance under continuous
groups.
1. Introduction
A typical property of a pattern recognition problem is the invariance of the classi-
fication under certain transformations of the input pattern. By constructing the pattern
recognition system in such a way that the invariance is in-built a priori, it should bc
possible to speed training and/or improve the generalization performance of the system.
Numerous papers have been written on the subject of invariant pattern recognition
(see for example [6,10,17,19]), but few make use of the wealth of highly applicable
material in the field of group theory. [n this paper we apply standard representation
theory to obtain a nu