On the design of feedforward neural networks for binary mappings

Abstract

This paper presents a new design technique that builds a feedforward net for an arbitrary set of binary associations. The key idea of the technique is to treat the set of associations as a binary matrix mapping, and to decompose the mapping into a cascade of the so-called primitive operations. There are only three different types of primitive operations, each of which is easily realizable into a simple feedforward subnet. The mapping, thus the set of associations, can then be readily realized by cascading the simple feedforward subnets that realize the primitive operations. The new technique has the important advantage that the computation time spent in constructing the realization is proportional to k · n, compared to k · 2 n typical of many conventional direct design approaches, where k is the number of given binary patterns, n the dimension of the patterns. Further, the generated feedforward net has k · n number of neurons, the same order of magnitude compared to many conventional methods. With such a substantial reduction in computational time, the technique can be readily employed in constructing feedforward nets for binary association problems of extremely large size.