Publications and Preprints

  1. The Sobolev Regularization Effect of Stochastic Gradient Descent
    Chao Ma, Lexing Ying, arXiv 2105.13462, PDF

  2. Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural Networks
    Yuqing Li, Tao Luo, Chao Ma, arXiv: 2103.16355, PDF

  3. Achieving Adversarial Robustness Requires An Active Teacher
    Chao Ma, Lexing Ying, arXiv: 2012.07233, PDF

  4. Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning
    Pan Zhou, Jiashi Feng, Chao Ma, Caiming Xiong, Steven HOI, Neurips 2020, PDF

  5. 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, PDF

  6. Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms
    Zhong Li, Chao Ma, Lei Wu, arXiv:2009.06132. PDF

  7. A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms
    Chao Ma, Lei Wu, Weinan E, arXiv:2009.06125. PDF

  8. The Slow Deterioration of the Generalization Error of the Random Feature Model
    Chao Ma, Lei Wu, Weinan E, Mathematical and Scientific Machine Learning, 373-389. PDF

  9. The Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models
    Chao Ma, Lei Wu, Weinan E, arXiv:2006.14450. PDF

  10. A Priori Estimates of the Generalization Error for Autoencoders
    Zehao Dou, Weinan E, Chao Ma, ICASSP 2020, 3327-3331. Link

  11. A 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. PDF

  12. On the generalization properties of minimum-norm solutions for over-parameterized neural network models
    Weinan E, Chao Ma, Lei Wu, arXiv:1912.06987. PDF

  13. Modeling 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. Link

  14. Heterogeneous 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. PDF

  15. Uniformly 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. PDF

  16. Barron Spaces and the Flow-induced Function Spaces for Neural Network Models
    Weinan E, Chao Ma, Lei Wu, arXiv:1906.08039. PDF

  17. Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence
    Chenyue Xie, Jianchun Wang, Ke Li, Chao Ma, Phys. Rev. E 99, 053113, Link

  18. A priori estimates of the population risk for residual networks
    Weinan E, Chao Ma, Qingcan Wang, Communications in Mathematical Sciences, PDF

  19. Analysis 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, PDF

  20. 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, arXiv:1904.04326, PDF

  21. Machine learning from a continuous viewpoint, I
    Weinan E, Chao Ma, Lei Wu, Science China Mathematics (2020): 1-34, PDF

  22. A 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, PDF

  23. Global convergence of gradient descent for deep linear residual networks
    Lei Wu, Qingcan Wang, Chao Ma, Neurips 2019, PDF

  24. Globally Convergent Levenberg-Marquardt Method For Phase Retrieval
    Chao Ma, Xin Liu, Zaiwen Wen, IEEE Transactions on Information Theory 65 (4), 2343-2359, Link

  25. Model Reduction with Memory and the Machine Learning of Dynamical Systems
    Chao Ma, Jianchun Wang, Weinan E, Commun. Comput. Phys., 25 (2019), pp. 947-9628, PDF

  26. How SGD Selects the Global Minima in Over-parameterized Learning: A Stability Perspective
    Lei Wu, Chao Ma, Weinan E, Neurips 2018, PDF

  27. Bispectrum 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

  1. A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms, symposium on machine learning and dynamical systems, 09/2020

  2. The Slow Deterioration of the Generalization Error of the Random Feature Model, UC Berkeley, 09/2020

  3. The Slow Deterioration of the Generalization Error of the Random Feature Model, MSML 2020, 07/2020

  4. A-priori Estimates of Population Risks for Neural Networks Models, Shanghai Jiao Tong University, 03/2020

  5. A-priori estimates of population risks for neural networks models, Chinese Academy of Sciences, 07/2019

  6. Appropriate function spaces for two-layer neural network and residual network models, Peking University, 06/2019