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Approximation of Functionals by Neural Network without Curse of Dimensionality. (arXiv:2205.14421v3 [math.NA] UPDATED)
Aug. 11, 2022, 1:11 a.m. | Yahong Yang, Yang Xiang
cs.LG updates on arXiv.org arxiv.org
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 $O(1/\sqrt{m})$ where $m$ is
the size of networks, which overcomes the curse of dimensionality. The key idea
of the approximation is to define a Barron spectral space of functionals.
approximation arxiv dimensionality math network neural network
More from arxiv.org / cs.LG updates on arXiv.org
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