AI RESEARCH
Higher Order Approximation Rates for ReLU CNNs in Korobov Spaces
arXiv CS.LG
•
ArXi:2501.11275v2 Announce Type: replace This paper investigates the $L_p$ approximation error for higher order Korobo 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.