Integral Transforms Induced by Heaviside Perceptrons

Autoři: RNDr. Věra Kůrková, DSc.
Rok vydání: 2020
Typ publikace: Kapitola v monografii
Periodikum: Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy, etc. Methods and Their Applications
Projekty: Modelová složitost neuronových, radiálních a jádrových sítí
Schopnosti a omezení mělkých a hlubokých sítí
Bibliografická citace: KŮRKOVÁ, Věra, KAINEN, P.C. Integral Transforms Induced by Heaviside Perceptrons. In: KOSHELEVA, O., SHARY, S., XIANG, G., ZAPATRIN, R., eds. Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy, etc. Methods and Their Applications. Cham: Springer, 2020, S. 631-649. Studies in Computational Intelligence, 835. ISBN 978-3-030-31040-0
Dostupné z: doi:10.1007/978-3-030-31041-7_36
DOI: 10.1007/978-3-030-31041-7_36
ID: 485562

Abstrakt

We investigate an integral transform with kernel induced by perceptrons with the Heaviside activation function. Representation theorems are given expressing sufficiently smooth functions as “infinite Heaviside perceptron networks”. The representation is exploited to obtain estimates of rates of approximation of these functions by networks with increasing numbers of units.