* indicates equal contribution or alphabetical author order.

A spectral-based analysis of the separation between two-layer neural networks and linear methods Lei Wu, Jihao Long Accepted by Journal of Machine Learning Research, 2022

Learning a single neuron for non-monotonic activation functions Lei Wu In International Conference on Artificial Intelligence and Statistics (AISTATS), 2022

A qualitative study of the dynamic behavior of adaptive gradient algorithms Chao Ma*, Lei Wu*, Weinan E Mathematical and Scientific Machine Learning (MSML), 2021

Towards a mathematical understanding of neural network-based machine learning: what we know and what we don't Weinan E*, Chao Ma*, Stephan Wojtowytsch*, Lei Wu* CSIAM Trans. Appl. Math., 2020

Machine learning based non-Newtonian fluid model with molecular fidelity Huan Lei, Lei Wu, Weinan E Physical Review E, 2020

Machine learning from a continuous viewpoint, I Weinan E*, Chao Ma*, Lei Wu* Science China Mathematics, 2020

The slow deterioration of the generalization error of the random feature model Chao Ma*, Lei Wu*, Weinan E Mathematical and Scientific Machine Learning (MSML), 2020

The Barron space and flow-induced function spaces for neural network models Weinan E*, Chao Ma*, Lei Wu* Constructive Approximation, 2021

A comparative analysis of the optimization and generalization property of two-layer neural network and random feature models under gradient descent dynamics Weinan E*, Chao Ma*, Lei Wu* Science China Mathematics, 2020

The generalization error of minimum-norm solutions for over-parameterized neural networks Weinan E*, Chao Ma*, Lei Wu* Journal of Pure and Applied Functional Analysis, 2020

Global convergence of gradient descent for deep linear residual networks Lei Wu*, Qingcan Wang*, Chao Ma Neural Information Processing Systems (NeurIPS), 2019

A priori estimates of the population risk for two-layer neural networks Weinan E*, Chao Ma*, Lei Wu* Communications in Mathematical Sciences, 2019

The anisotropic noise in stochastic gradient descent: Its behavior of escaping from minima and regularization effects Zhanxing Zhu, Jingfeng Wu, Bing Yu, Lei Wu, Jinwen Ma International Conference on Machine Learning (ICML), 2019

How SGD selects the global minima in over-parameterized learning: A stability perspective Lei Wu, Chao Ma, Weinan E Advances in Neural Information Processing Systems (NeurIPS), 2018

Towards understanding and improving the transferability of adversarial examples in deep neural networks Lei Wu, Zhanxing Zhu Asian Conference on Machine Learning (ACML), 2020 [arXiv version]

Irreversible samplers from jump and continuous Markov processes Yi-An Ma, Emily B Fox, Tianqi Chen, Lei Wu Statistics and Computing, 2018

Towards understanding generalization of deep learning: perspective of loss landscapes Lei Wu, Zhanxing Zhu, Weinan E Workshop on Principled Approaches to Deep Learning, ICML2017

Smoothed dissipative particle dynamics model for mesoscopic multiphase flows in the presence of thermal fluctuations Huan Lei, Nathan A Baker, Lei Wu, Gregory K Schenter, Christopher J Mundy, Alexandre M Tartakovsky Physical Review E, 2016

Complexity measures for neural networks with general activation functions using path-based norms Zhong Li, Chao Ma, Lei Wu arxiv preprint, 2020.

The quenching-activation behavior of the gradient descent dynamics for two-layer neural network models Chao Ma*, Lei Wu*, Weinan E arXiv Preprint, 2020.

Analysis of the gradient descent algorithm for a deep neural network model with skip-connections Weinan E*, Chao Ma*, Lei Wu* arXiv preprint, 2019