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Higher Order Approximation Rates for ReLU CNNs in Korobov Spaces
arXiv:2501.11275v2 Announce Type: replace Abstract: This paper investigates the L_p approximation error for higher order Korobov functions using deep convolutional neural networks (CNNs) with ReLU act
arXiv:2501.11275v2 Announce Type: replace Abstract: This paper investigates the L_p approximation error for higher order Korobov functions using deep convolutional neural networks (CNNs) with ReLU activation. For target functions having a mixed derivative of order m+1 in each direction, we improve classical approximation rate of second order to (m+1)-th order (modulo a logarithmic factor) in terms of the depth of CNNs. The key ingredient in our analysis is approximate representation of high-order sparse grid basis functions by CNNs. The results suggest that higher order expressivity of CNNs does not severely suffer from the curse of dimensionality.
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Source: arXiv cs.LG | 2026-04-24