Neural network complexity classification based on the problem

Abstract

This paper presents a complexity power study of different artificial neural networks (ANNs) structures, specifically the feedforward and the recurrent neural networks. We use the 'order of a predicate' concept to classify a problem in a given class and show that the neural network structure, determined by its topology (direct or recurrent) and the presence or absence of hidden neurons, must be considered when dealing with different problem classes. ANNs problems' complexity and computability are dealt and it is shown how the presence or absence of a hidden layer of neurons restricts the modeling ability of a given neural network structure. In order to do that, a classical binary problem is presented and it is shown how to deal with it when using a feedforward and a recurrent neural network structure with and without a hidden layer.