4 papers
Shallow neural network approximation in mixed Sobolev spaces
Yuwen Li, Guozhi Zhang
We investigate the best approximation of mixed Sobolev spaces by shallow neural networks with neurons and general activation functions. We first establish an activation-i…
Nearly optimal Kolmogorov widths under holomorphic mappings
Yuwen Li, Guozhi Zhang
This paper establishes essentially optimal asymptotic bounds for Kolmogorov widths under holomorphic mappings between complex Banach spaces. Given a compact parameter set whose Kol…
Some Super-approximation Rates of ReLU Neural Networks for Korobov Functions
Yuwen Li, Guozhi Zhang
This paper examines the and norm approximation errors of ReLU neural networks for Korobov functions. In terms of network width and depth, we derive nearly optimal sup…
Higher Order Approximation Rates for ReLU CNNs in Korobov Spaces
Yuwen Li, Guozhi Zhang
This paper investigates the approximation error for higher order Korobov functions using deep convolutional neural networks (CNNs) with ReLU activation. For target functions…