Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art
machine learning methods are based on neural networks (NNs). Lacking, however, is a …

Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space
to model functions by neural networks as the curse of dimensionality (CoD) cannot be …

The aim of this expository paper is to explain to graduate students and beginning
researchers in the field of mathematics, statistics and engineering the fundamental concept …

We study the approximation capacity of some variation spaces corresponding to shallow
ReLU k neural networks. It is shown that sufficiently smooth functions are contained in these …

A ridge is a function that is characterized by a one-dimensional profile (activation) and a
multidimensional direction vector. Ridges appear in the theory of neural networks as …

Reproducing Kernel Hilbert spaces (RKHS) have been a very successful tool in various
areas of machine learning. Recently, Barron spaces have been used to prove bounds on the …

It is shown that over-parameterized neural networks can achieve minimax optimal rates of
convergence (up to logarithmic factors) for learning functions from certain smooth function …

This paper introduces a novel theoretical framework for the analysis of vector-valued neural
networks through the development of vector-valued variation spaces, a new class of …

Sparsity of a learning solution is a desirable feature in machine learning. Certain
reproducing kernel Banach spaces (RKBSs) are appropriate hypothesis spaces for sparse …

Studying the function spaces defined by neural networks helps to understand the
corresponding learning models and their inductive bias. While in some limits neural …