Spectral Barron Space for Deep Neural Network Approximation
Yulei Liao, Pingbing Ming · SIAM Journal on Mathematics of Data Science · 2025
Abstract. We prove the sharp embedding between the spectral Barron space and the Besov space with embedding constants independent of the input dimension. Given the spectral Barron space as the target function space, we prove a dimension-free convergence result that if the neural network contains [Formula: see text] hidden layers with [Formula: see text] units per layer, then the upper and lower bounds of the [Formula: see text]-approximation error are [Formula: see text] with [Formula: see text], where [Formula: see text] is the smoothness index of the spectral Barron space.