Approximation in shiftinvariant spaces with deep ReLU neural networks
Abstract
We study the expressive power of deep ReLU neural networks for approximating functions in dilated shiftinvariant spaces, which are widely used in signal processing, image processing, communications and so on. Approximation error bounds are estimated with respect to the width and depth of neural networks. The network construction is based on the bit extraction and datafitting capacity of deep neural networks. As applications of our main results, the approximation rates of classical function spaces such as Sobolev spaces and Besov spaces are obtained. We also give lower bounds of the $L^p (1\le p \le \infty)$ approximation error for Sobolev spaces, which show that our construction of neural network is asymptotically optimal up to a logarithmic factor.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.11949
 Bibcode:
 2020arXiv200511949Y
 Keywords:

 Computer Science  Machine Learning;
 Mathematics  Numerical Analysis;
 Statistics  Machine Learning
 EPrint:
 doi:10.1016/j.neunet.2022.06.013