We develop a variational framework to understand the properties of functions learned by
fitting deep neural networks with rectified linear unit (ReLU) activations to data. We propose …

Deep learning is a topic of considerable current interest. The availability of massive data
collections and powerful software resources has led to an impressive amount of results in …

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 …

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 …

This paper explores the implicit bias of overparameterized neural networks of depth greater
than two layers. Our framework considers a family of networks of varying depths that all have …

We study the theory of neural network (NN) from the lens of classical nonparametric
regression problems with a focus on NN's ability to adaptively estimate functions with …

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 …

Spectral Barron spaces have received considerable interest recently, as it is the natural
function space for approximation theory of two-layer neural networks with a dimension-free …

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 …

We investigate the distributional extension of the-plane transform in and of related operators.
We parameterize the-plane domain as the Cartesian product of the Stiefel manifold of …