Multilayer neural networks and polyhedral dichotomies

Authors
Kenyon, C Paugam-Moisy, H
Citation
C. Kenyon et H. Paugam-moisy, Multilayer neural networks and polyhedral dichotomies, ANN MATH A, 24(1-4), 1998, pp. 115-128
Citations number
18
Categorie Soggetti
Engineering Mathematics
Journal title
ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
ISSN journal
10122443 → ACNP
Volume
24
Issue
1-4
Year of publication
1998
Pages
115 - 128
Database
ISI
SICI code
1012-2443(1998)24:1-4<115:MNNAPD>2.0.ZU;2-1
Abstract
We study the number of hidden layers required by a multilayer neural networ k with threshold units to compute a dichotomy from R-d to {0, 1}, defined b y a finite set of hyperplanes. We show that this question is far more intri cate than computing Boolean functions, although this well-known problem is underlying our research. We present advanced results on the characterizatio n of dichotomies, from R-2 to {0, 1}, which require two hidden layers to be exactly realized.