Reinforcement learning (RL) is one of the most vibrant research frontiers in machine
learning and has been recently applied to solve a number of challenging problems. In this …

Diffusion models achieve state-of-the-art performance in various generation tasks. However,
their theoretical foundations fall far behind. This paper studies score approximation …

While efficient distribution learning is no doubt behind the groundbreaking success of
diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the …

Federated learning faces huge challenges from model overfitting due to the lack of data and
statistical diversity among clients. To address these challenges, this paper proposes a novel …

We describe the new field of the mathematical analysis of deep learning. This field emerged
around a list of research questions that were not answered within the classical framework of …

We explore the methodology and theory of reward-directed generation via conditional
diffusion models. Directed generation aims to generate samples with desired properties as …

This paper establishes the optimal approximation error characterization of deep rectified
linear unit (ReLU) networks for smooth functions in terms of both width and depth …

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 …

The limitations and high false-negative rates (30%) of COVID-19 test kits have been a
prominent challenge during the 2020 coronavirus pandemic. Manufacturing those kits and …

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 …