Startseite Überblick A-Z Suche Kontakt

 Lehrstuhl Mathematik & Informatik Lower Bounds on the Complexity of Approximating Continuous Functions by Sigmoidal Neural Networks

 Unser Angebot: Mitarbeiter | Forschung | Lehre
 Startseite » Mitarbeiter » M. Schmitt » Lower Bounds on the Complexity of Approximating Continuous Functions by Sigmoidal Neural Networks

 Lower Bounds on the Complexity of Approximating Continuous Functions by Sigmoidal Neural Networks
We calculate lower bounds on the size of sigmoidal neural networks that approximate continuous functions. In particular, we show that for the approximation of polynomials the network size has to grow as \$\Omega((\log k)^{1/4})\$ where \$k\$ is the degree of the polynomials. This bound is valid for any input dimension, i.e. independently of the number of variables. The result is obtained by introducing a new method employing upper bounds on the Vapnik-Chervonenkis dimension for proving lower bounds on the size of networks that approximate continuous functions.

 Seitenanfang | Diese Seite drucken Letzte Änderung: 03.02.2003 | Ansprechpartner: Webmaster