Multilayer neural networks and polyhedral dichotomies

We study the number of hidden layers required by a multilayer neural network with threshold units to compute a dichotomy from ℝd to {0,1}, defined by a finite set of hyperplanes. We show that this question is far more intricate than computing Boolean functions, although this well-known problem is un...

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Bibliographic Details
Published inAnnals of mathematics and artificial intelligence Vol. 24; no. 1-4; pp. 115 - 128
Main Authors Kenyon, Claire, Paugam-Moisy, Hélène
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.01.1998
Subjects
Boolean functions
Dichotomies
Hyperplanes
Multilayers
Neural networks
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Summary:We study the number of hidden layers required by a multilayer neural network with threshold units to compute a dichotomy from ℝd to {0,1}, defined by a finite set of hyperplanes. We show that this question is far more intricate than computing Boolean functions, although this well-known problem is underlying our research. We present advanced results on the characterization of dichotomies, from ℝ2 to {0,1}, which require two hidden layers to be exactly realized.
ISSN:1012-2443
1573-7470
DOI:10.1023/A:1018997115206