ESTIMATES OF THE NUMBER OF HIDDEN UNITS AND VARIATION WITH RESPECT TOHALF-SPACES

Authors
KURKOVA V KAINEN PC KREINOVICH V
Citation
V. Kurkova et al., ESTIMATES OF THE NUMBER OF HIDDEN UNITS AND VARIATION WITH RESPECT TOHALF-SPACES, Neural networks, 10(6), 1997, pp. 1061-1068
Citations number
22
Categorie Soggetti
Mathematical Methods, Biology & Medicine","Computer Sciences, Special Topics","Computer Science Artificial Intelligence",Neurosciences,"Physics, Applied
Journal title
Neural networks → ACNP
ISSN journal
08936080
Volume
10
Issue
6
Year of publication
1997
Pages
1061 - 1068
Database
ISI
SICI code
0893-6080(1997)10:6<1061:EOTNOH>2.0.ZU;2-Z
Abstract
We estimate variation with respect to half-spaces in terms of ''flows through hyperplanes''. Our estimate is derived from an integral repres entation for smooth compactly supported multivariable functions proved using properties of the Heaviside and delta distributions. Consequent ly we obtain conditions which guarantee approximation error rate of or der O(1/root n) by one-hidden-layer networks with n sigmoidal perceptr ons. (C) 1997 Elsevier Science Ltd.