The Computational Capabilities of Neural Networks

Abstract

The (artificial) neural networks represent a widely applied computational paradigm that is an alternative to the conventional computers in many areas of artificial intelligence. By analogy with classical models of computation such as Turing machines which are useful for understanding the computational potential and limits of conventional computers, the capability of neural networks to realize general computations have been studied for more than decade and many relevant results have been achieved [1, 2, 3, 5]. The neural networks are classified into a computational taxonomy according to the restrictions that are imposed on their parameters. Thus, various models are obtained which have different computational capabilities and enrich the traditional repertoire of computational means. In particular, the computational power of neural networks have been investigated by comparing their variants with each other and with more traditional computational tools including finite automata, Turing machines, Boolean circuits, etc. The aim of this approach is to find out what is, in principle, or efficiently, computable by particular neural networks, and how to optimally implement required functions.

Research partially supported by project LN00A056 of The Ministry of Education of the Czech Republic.