A two-layer paradigm capable of forming arbitrary decision regions in input space

Author

Deolalikar, Vinay

Author_Institution

Inf. Theor. Res. Group, Hewlett Packard Res. Labs., Palo Alto, CA, USA

Volume

13

Issue

1

fYear

2002

fDate

1/1/2002 12:00:00 AM

Firstpage

15

Lastpage

21

Abstract

It is well known that a two-layer perceptron network with threshold neurons is incapable of forming arbitrary decision regions in input space, while a three-layer perceptron has that capability. The effect of replacing the output neuron in a two-layer perceptron with a bithreshold element is studied. The limitations of this modified two-layer perceptron are observed. Results on the separating capabilities of a pair of parallel hyperplanes are obtained. Based on these, a new two-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 the limits of switching function realizability using bithreshold gates are obtained

Keywords

decision theory; feedforward neural nets; multilayer perceptrons; threshold logic; transfer functions; arbitrary decision region; arbitrary decision regions; bithreshold element; bithreshold neuron transfer function; classification regions; input space; modified two-layer perceptron; output neuron; parallel hyperplanes; switching function realizability; three-layer perceptron; threshold neurons; two layer paradigm; two-layer neural paradigm; two-layer perceptron network; Feeds; Function approximation; Intelligent networks; Logic; Multilayer perceptrons; Neural networks; Neurons; Pattern recognition; Speech recognition; Transfer functions;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.977261

Filename

977261