Approximation of functionals on Korobov spaces with Fourier Functional Networks
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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Detail(s)
Original language | English |
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Article number | 106922 |
Journal / Publication | Neural Networks |
Volume | 182 |
Online published | 20 Nov 2024 |
Publication status | Published - Feb 2025 |
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DOI | DOI |
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Link to Scopus | https://www.scopus.com/record/display.uri?eid=2-s2.0-85210137000&origin=recordpage |
Permanent Link | https://scholars.cityu.edu.hk/en/publications/publication(8757be00-7a3d-4b05-8635-0c74b4e17fb4).html |
Abstract
Learning from functional data with deep neural networks has become increasingly useful, and numerous neural network architectures have been developed to tackle high-dimensional problems raised in practical domains. Despite the impressive practical achievements, theoretical foundations underpinning the ability of neural networks to learn from functional data largely remain unexplored. In this paper, we investigate the approximation capacity of a functional neural network, called Fourier Functional Network, consisting of Fourier neural operators and deep convolutional neural networks with a great reduction in parameters. We establish rates of approximating by Fourier Functional Networks nonlinear continuous functionals defined on Korobov spaces of periodic functions. Finally, our results demonstrate dimension-independent convergence rates, which overcomes the curse of dimension. © 2024 The Authors.
Research Area(s)
- Approximation theory, Convolutional neural network, Fourier neural operator, Korobov space, Neural network
Citation Format(s)
Approximation of functionals on Korobov spaces with Fourier Functional Networks. / Liu, Peilin; Liu, Yuqing; Zhou, Xiang et al.
In: Neural Networks, Vol. 182, 106922, 02.2025.
In: Neural Networks, Vol. 182, 106922, 02.2025.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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