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A Two Layer Paradigm Capable of Forming Arbitrary Decision Regions in Input Space

Deolalikar, Vinay

HPL-2001-63R1

Keyword(s): artificial neural networks; classification regions; bithreshold neuron; bithreshold logic; 2-layer networks

Abstract: It is well know that a 2-layer perceptron network with threshold neurons is incapable of forming arbitrary decision regions in input space, while a 3-layer perceptron has that capability. In this paper, the effect of replacing the output neuron in a 2-layer perceptron by a bithreshold element is studied. The limitations of this modified 2-layer perceptron are observed. Results on the separating capabilities of a pair of parallel hyperplanes are obtained. Based on these, a new 2-layer neural paradigm based on increasing the dimensionality of the output of the first layer is proposed and is shown to be capable of forming any arbitrary decision region in input space. Then a type of logic called bithreshold logic, based on the bithreshold neuron transfer function, is studied. Results on limits of switching function realizability using bithreshold gates are obtained. Notes: Copyright 2001 IEEE. Reprinted, with permission, from IEEE Transactions on Neural Networks

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