Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms
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Abstract (arXiv)
This paper establishes the nearly optimal rate of approximation for deep neural networks (DNNs) when applied to Korobov functions, effectively overcoming the curse of dimensionality. The approximation results presented in this paper are measured with respect to Lp norms and H1 norms. Our achieved approximation rate demonstrates a remarkable "super-convergence" rate, outperforming traditional methods and any continuous function approximator. These results are non-asymptotic, providing error bounds that consider both the width and depth of the networks simultaneously.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 27 of its 52 references that are in the map. First posted on arXiv 8 Nov 2023.
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27 of 52 references.
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15 more
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