The Use of Wiener-Volterra Methods in the Analysis and Synthesis of Simulated Neural Networks

Abstract

This paper applies the Wiener-Volterra method of system analysis to some simple simulated neural networks. It then shows that a broad class of more complicated systems can be decomposed into these simple networks and that the overall system Wiener-Volterra representation is the algebraic composition of the representations for the simple networks. A simulated neural network as used here consists of a collection of elements each of which has a relatively simple transfer function. These elements accept input from outside the system and from other elements, process it, and pass the resulting output to other elements and to the system output. The word neural in the name comes from the parallel, distributed nature of the system: the transfer functions of the elements are neither claimed nor constrained to match the transfer functions of nerve cells. However, by choosing the transfer function of the elements properly, these networks can be used as models for physiologic neural networks. Such simulated networks are useful in that by proper configuration they can mimic a wide range of systems and in some cases, by allowing a correction term to be fed back to modify the interconnections or the elements, the network can ‘learn’ the proper configuration itself.