Connectionistic models of Boolean category representation
type: Item
instance of: scholarly article
title: Connectionistic models of Boolean category representation
zbMATH Open document ID: 0601.68058
DOI: 10.1007/BF00355545
published in: Biological Cybernetics
publication date: 1986-01-01T00:00:00Z
review text: Several distinct connectionistic/neural representations capable of computing arbitrary Boolean functions are described and discussed in terms of possible tradeoffs between time, space, and expressive clarity. It is suggested that the ability of a threshold logic unit (TLU) to represent prototypical groupings has significant advantages for representing real world categories. Upper and lower bounds on the number of nodes needed for Boolean completeness are demonstrated. The necessary number of nodes is shown to increase exponentially with the number of input features, the exact rate of increase depending on the representation scheme. In addition, in non-recurrent networks, connection weights are shown to increase exponentially with a linear reduction in the number of nodes below approximately \(2^ d\). This result suggests that optimum memory efficiency may require unacceptable learning time. Finally, two possible extensions to deal with non-Boolean values are considered.
Mathematics Subject Classification ID: 68T05
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 94C10
Mathematics Subject Classification ID: 94C15
zbMATH DE Number: 3970133
zbMATH Keywords: computing arbitrary Boolean functions
zbMATH Keywords: threshold logic unit
zbMATH Keywords: TLU
zbMATH Keywords: Boolean completeness
Wikidata QID: Q52143334
author: Steven Hampson
author: Dennis James Volper
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00355545
OpenAlex ID: W1985452896
description: scientific article; zbMATH DE number 3970133