Year: 2022
Author: Yahong Yang, Yang Xiang
Journal of Machine Learning, Vol. 1 (2022), Iss. 4 : pp. 342–372
Abstract
In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of the neural network is $\mathcal{O}(1/\sqrt{m})$ where $m$ is the size of networks. In other words, the error of the network is no dependence on the dimensionality respecting to the number of the nodes in neural networks. The key idea of the approximation is to define a Barron space of functionals.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jml.221018
Journal of Machine Learning, Vol. 1 (2022), Iss. 4 : pp. 342–372
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Functionals Neural networks Infinite dimensional spaces Barron spectral space Fourier series.