Publications and Preprints
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
Weinan E, Chao Ma, Stephan Wojtowytsch, and Lei Wu, arXiv:2009.10713, PDFComplexity Measures for Neural Networks with General Activation Functions Using Path-based Norms
Zhong Li, Chao Ma, Lei Wu, arXiv:2009.06132. PDFA Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms
Chao Ma, Lei Wu, Weinan E, arXiv:2009.06125. PDFThe Slow Deterioration of the Generalization Error of the Random Feature Model
Chao Ma, Lei Wu, Weinan E, Mathematical and Scientific Machine Learning, 373-389. PDFThe Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models
Chao Ma, Lei Wu, Weinan E, arXiv:2006.14450. PDFA Priori Estimates of the Generalization Error for Autoencoders
Zehao Dou, Weinan E, Chao Ma, ICASSP 2020, 3327-3331. LinkA mean-field analysis of deep resnet and beyond: Towards provable optimization via overparameterization from depth
Yuping Lu, Chao Ma, Yulong LU, Jianfeng Lu, Lexing Ying, ICML 2020. PDFOn the generalization properties of minimum-norm solutions for over-parameterized neural network models
Weinan E, Chao Ma, Lei Wu, arXiv:1912.06987. PDFModeling subgrid-scale force and divergence of heat flux of compressible isotropic turbulence by artificial neural network
Chenyue Xie, Ke Li, Chao Ma, Jianchun Wang, Physical Review Fluids 4(10), 104605. LinkHeterogeneous Multireference Alignment for Images With Application to 2D Classification in Single Particle Reconstruction
Chao Ma, Tamir Bendory, Nicolas Boumal, Fred Sigworth, Amit Singer, IEEE Transactions on Image Processing 29, 1699-1710. PDFUniformly Accurate Machine Learning Based Hydrodynamic Models for Kinetic Equations
Jiequn Han, Chao Ma, Zheng Ma, Weinan E, Proceedings of the National Academy of Sciences (2019): 201909854. PDFBarron Spaces and the Flow-induced Function Spaces for Neural Network Models
Weinan E, Chao Ma, Lei Wu, arXiv:1906.08039. PDFArtificial neural network approach to large-eddy simulation of compressible isotropic turbulence
Chenyue Xie, Jianchun Wang, Ke Li, Chao Ma, Phys. Rev. E 99, 053113, LinkA priori estimates of the population risk for residual networks
Weinan E, Chao Ma, Qingcan Wang, Communications in Mathematical Sciences, PDFAnalysis of the gradient descent algorithm for a deep neural network model with skip-connections
Weinan E, Chao Ma, Qingcan Wang, Lei Wu, arXiv:1904.05263, PDFA 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, arXiv:1904.04326, PDFMachine learning from a continuous viewpoint, I
Weinan E, Chao Ma, Lei Wu, Science China Mathematics (2020): 1-34, PDFA priori estimates of the population risk for two-layer neural networks
Weinan E, Chao Ma, Lei Wu, Communications in Mathematical Sciences 17 (5), 1407-1425, PDFGlobal convergence of gradient descent for deep linear residual networks
Lei Wu, Qingcan Wang, Chao Ma, Neurips 2019, PDFGlobally Convergent Levenberg-Marquardt Method For Phase Retrieval
Chao Ma, Xin Liu, Zaiwen Wen, IEEE Transactions on Information Theory 65 (4), 2343-2359, LinkModel Reduction with Memory and the Machine Learning of Dynamical Systems
Chao Ma, Jianchun Wang, Weinan E, Commun. Comput. Phys., 25 (2019), pp. 947-9628, PDFHow SGD Selects the Global Minima in Over-parameterized Learning: A Stability Perspective
Lei Wu, Chao Ma, Weinan E, Neurips 2018, PDFBispectrum Inversion with Application to Multireference Alignment
Tamir Bendory, Nicolas, Boumal, Chao Ma, Zhizhen Zhao, Amit Singer, IEEE Transactions on Signal Processing 66.4 (2017): 1037-1050, PDF
Talks and Presentations
A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms, symposium on machine learning and dynamical systems, 09/2020
The Slow Deterioration of the Generalization Error of the Random Feature Model, UC Berkeley, 09/2020
The Slow Deterioration of the Generalization Error of the Random Feature Model, MSML 2020, 07/2020
A-priori Estimates of Population Risks for Neural Networks Models, Shanghai Jiao Tong University, 03/2020
A-priori estimates of population risks for neural networks models, Chinese Academy of Sciences, 07/2019
Appropriate function spaces for two-layer neural network and residual network models, Peking University, 06/2019