Pointwise convergence of Fourier series and deep neural network for the indicator function of d-dimensional ball
Not on the map. Why?
Abstract (arXiv)
In this paper, we clarify the crucial difference between a deep neural network and the Fourier series. For the multiple Fourier series of periodization of some radial functions on ℝd, Kuratsubo (2010) investigated the behavior of the spherical partial sum and discovered the third phenomenon other than the well-known Gibbs-Wilbraham and Pinsky phenomena. In particular, the third one exhibits prevention of pointwise convergence. In contrast to it, we give a specific deep neural network and prove pointwise convergence.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 6 of its 24 references that are in the map. First posted on arXiv 17 Apr 2023.
Builds on
6 of 24 references.
References · 6
- 2016Error bounds for approximations with deep ReLU networkscited by 567
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
- 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 160
- 2019On the minimax optimality and superiority of deep neural network learning over sparse parameter spacescited by 24
- 2020Estimation error analysis of deep learning on the regression problem on the variable exponent Besov spacecited by 13
- 2019Optimal Function Approximation with Relu Neural Networkscited by 9
Built on by
Not cited yet.