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 …

Real-world data often exhibit low-dimensional geometric structures and can be viewed as
samples near a low-dimensional manifold. This paper studies nonparametric regression of …

There has been a growing interest in expressivity of deep neural networks. However, most of
the existing work about this topic focuses only on the specific activation function such as …

We perform a study on the generalization ability of the wide two-layer ReLU neural network
on $\mathbb {R} $. We first establish some spectral properties of the neural tangent kernel …

Accurate individual tree detection by unmanned aerial vehicles (UAVs) is a critical technique
for smart forest management and serves as the foundation for evaluating ecological …

Recent studies have shown that computed tomography (CT) scan images can characterize
COVID-19 disease in patients. Several deep learning (DL) methods have been proposed for …

In this paper, we perform deep neural networks for learning stationary ψ-weakly dependent
processes. Such weak-dependence property includes a class of weak dependence …

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 …

Most of existing statistical theories on deep neural networks have sample complexities
cursed by the data dimension and therefore cannot well explain the empirical success of …