Neural networks for computation: number representations and programming complexity

Abstract

Methods for using neural networks for computation are considered. The success of such networks in finding good solutions to complex problems is found to be dependent on the number representation schemes used. Redundant schemes are found to offer advantages in terms of convergence. Neural networks are applied to the combinatorial optimization problem known as the Hitchcock problem and signal processing problems, such as matrix inversion and Fourier transformation. The concept of programming complexity is introduced. It is shown that for some computational problems, the programming complexity may be so great as to limit the utility of neural networks, while for others the investment of computation in programming the network is justified. Simulations of neural networks using a digital computer are presented.