In this article, we review the literature on statistical theories of neural networks from three
perspectives: approximation, training dynamics, and generative models. In the first part …

Deep neural networks (DNNs) trained with the logistic loss (also known as the cross entropy
loss) have made impressive advancements in various binary classification tasks. Despite the …

Convolutional neural networks (CNNs) have gained immense popularity in recent years,
finding their utility in diverse fields such as image recognition, natural language processing …

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 …

Constructing the architecture of a neural network is a challenging pursuit for the machine
learning community, and the dilemma of whether to go deeper or wider remains a persistent …

We derive a novel approximation error bound with explicit prefactor for Sobolev-regular
functions using deep convolutional neural networks (CNNs). The bound is non-asymptotic in …

In recent years, functional neural networks have been proposed and studied in order to
approximate nonlinear continuous functionals defined on L p ([-1, 1] s) for integers s≥ 1 and …

Readability of Chinese texts considered in this paper is a multi-class classification problem
with 12 grade classes corresponding to 6 grades in primary schools, 3 grades in middle …

We study approximation and learning capacities of convolutional neural networks (CNNs)
with one-side zero-padding and multiple channels. Our first result proves a new …

The great success of deep learning poses an urgent challenge to establish the theoretical
basis for its working mechanism. Recently, research on the convergence of deep neural …