Spectral Barron space and deep neural network approximation

09/02/2023

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by   Yulei Liao, et al.

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We prove the sharp embedding between the spectral Barron space and the Besov space. Given the spectral Barron space as the target function space, we prove a dimension-free result that if the neural network contains L hidden layers with N units per layer, then the upper and lower bounds of the L^2-approximation error are 𝒪(N^-sL) with 0 < sL≤ 1/2, where s is the smoothness index of the spectral Barron space.