Representation theory and invariant neural networks

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.