Pointwise convergence of Fourier series and deep neural network for the indicator function of d-dimensional ball
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909231286845440 |
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| author | Kawasumi, Ryota Yoneda, Tsuyoshi |
| author_facet | Kawasumi, Ryota Yoneda, Tsuyoshi |
| contents | 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 $\mathbb{R}^d$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08172 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pointwise convergence of Fourier series and deep neural network for the indicator function of d-dimensional ball Kawasumi, Ryota Yoneda, Tsuyoshi Machine Learning Information Theory Analysis of PDEs 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 $\mathbb{R}^d$, 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. |
| title | Pointwise convergence of Fourier series and deep neural network for the indicator function of d-dimensional ball |
| topic | Machine Learning Information Theory Analysis of PDEs |
| url | https://arxiv.org/abs/2304.08172 |