Chao Ma

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Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

Lei Wu, E. Weinan, Chao Ma, 2020, CSIAM Transactions on Applied Mathematics.

Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence.

Chao Ma, C. Xie, Jianchun Wang, 2019, Physical review. E.

A Priori Estimates of the Population Risk for Residual Networks

E. Weinan, Chao Ma, Qingcan Wang, 2019, ArXiv.

Modeling subgrid-scale force and divergence of heat flux of compressible isotropic turbulence by artificial neural network

Chao Ma, C. Xie, Jianchun Wang, 2019, Physical Review Fluids.

Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't pdf

E Weinan, Stephan Wojtowytsch, Lei Wu, 2020, CSIAM Transactions on Applied Mathematics.

The Slow Deterioration of the Generalization Error of the Random Feature Model

E Weinan, Lei Wu, Chao Ma, 2020, MSML.

Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning

Pan Zhou, Caiming Xiong, Jiashi Feng, 2020, NeurIPS.

A Priori Estimates for Two-layer Neural Networks

E Weinan, Chao Ma, Lei Wu, 2018 .

Uniformly accurate machine learning-based hydrodynamic models for kinetic equations

Chao Ma, Weinan E, Jiequn Han, 2019, Proceedings of the National Academy of Sciences.

How SGD Selects the Global Minima in Over-parameterized Learning : A Dynamical Stability Perspective

Lei Wu, Chao Ma, 2018 .

The Multiscale Structure of Neural Network Loss Functions: The Effect on Optimization and Origin

Lei Wu, Chao Ma, Lexing Ying, 2022, ArXiv.

Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning pdf

E Weinan, Pan Zhou, Jiashi Feng, 2020, NeurIPS.

Cycloastragenol Attenuates Osteoclastogenesis and Bone Loss by Targeting RANKL-Induced Nrf2/Keap1/ARE, NF-κB, Calcium, and NFATc1 Pathways

W. He, Chao Ma, Jiake Xu, 2022, Frontiers in Pharmacology.

Generalization Error Bounds for Deep Neural Networks Trained by SGD

Chao Ma, Ming Wang, 2022, ArXiv.

Correcting Convexity Bias in Function and Functional Estimate

Chao Ma, Lexing Ying, 2022, 2208.07996.

The Asymmetric Maximum Margin Bias of Quasi-Homogeneous Neural Networks

S. Ganguli, Chao Ma, D. Kunin, 2022, ArXiv.

Revealing Spatial-temporal Taxi Demand Patterns after Vaccination in COVID-19 Pandemic

Chao Ma, Yunlong Zhang, Zihao Li, 2022, 2210.02624.

A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics

Lei Wu, W. E, Chao Ma, 2020, Science China Mathematics.

Beyond the Quadratic Approximation: The Multiscale Structure of Neural Network Loss Landscapes

Lei Wu, Chao Ma, Lexing Ying, 2022, Journal of Machine Learning.

Early Stage Convergence and Global Convergence of Training Mildly Parameterized Neural Networks

Chao Ma, Ming Wang, 2022, Neural Information Processing Systems.

A Qualitative Study of the Dynamic Behavior for Adaptive Gradient Algorithms

Lei Wu, E. Weinan, Chao Ma, 2020, MSML.

A Priori Estimates of the Generalization Error for Two-layer Neural Networks pdf

Lei Wu, E Weinan, Chao Ma, 2018, Communications in Mathematical Sciences.

Bispectrum Inversion With Application to Multireference Alignment

Zhizhen Zhao, Amit Singer, Tamir Bendory, 2017, IEEE Transactions on Signal Processing.

Globally Convergent Levenberg-Marquardt Method for Phase Retrieval

Zaiwen Wen, Chao Ma, Xin Liu, 2019, IEEE Transactions on Information Theory.

A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics

Lei Wu, E Weinan, Chao Ma, 2019, Science China Mathematics.

On Linear Stability of SGD and Input-Smoothness of Neural Networks

Lexing Ying, Chao Ma, Chao Ma, 2021, NeurIPS.

Barron Spaces and the Compositional Function Spaces for Neural Network Models pdf

Lei Wu, E Weinan, Chao Ma, 2019, ArXiv.

N A ] 2 6 Se p 20 20 Machine Learning from a Continuous Viewpoint

Lei Wu, Chao Ma, Weinan, 2021 .

Machine learning from a continuous viewpoint, I

Lei Wu, E. Weinan, Chao Ma, 2019, Science China Mathematics.

A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth

Chao Ma, Lexing Ying, Yiping Lu, 2020, ICML.

Provably convergent quasistatic dynamics for mean-field two-player zero-sum games

Chao Ma, Lexing Ying, 2022, ICLR.

The Asymmetric Maximum Margin Bias of Quasi-Homogeneous Neural Networks

S. Ganguli, Chao Ma, D. Kunin, 2022, ICLR.

On the Generalization Properties of Minimum-norm Solutions for Over-parameterized Neural Network Models pdf

E Weinan, Chao Ma, Lei Wu, 2019, ArXiv.

Model Reduction with Memory and the Machine Learning of Dynamical Systems pdf

E Weinan, Jianchun Wang, Chao Ma, 2018, Communications in Computational Physics.

Causal-Discovery Performance of ChatGPT in the context of Neuropathic Pain Diagnosis

Chao Ma, Ruibo Tu, Cheng Zhang, 2023, ArXiv.

Understanding Causality with Large Language Models: Feasibility and Opportunities

Paul N. Bennett, Chao Ma, Stefan Bauer, 2023, ArXiv.

Identifiable Generative Models for Missing Not at Random Data Imputation pdf

Chao Ma, Cheng Zhang, Chao Ma, 2021, NeurIPS.

Generalization Error Bounds for Deep Neural Networks Trained by SGD

Chao Ma, Ming Wang, 2022, ArXiv.

Heterogeneous Multireference Alignment for Images With Application to 2D Classification in Single Particle Reconstruction

Amit Singer, Tamir Bendory, Nicolas Boumal, 2018, IEEE Transactions on Image Processing.

The Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models pdf

E Weinan, Lei Wu, Chao Ma, 2020, ArXiv.

Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections pdf

Lei Wu, E Weinan, Chao Ma, 2019, ArXiv.

Mathematical Theory of Neural Network Models for Machine Learning

Chao Ma, 2020 .

A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms pdf

E Weinan, Lei Wu, Chao Ma, 2020, ArXiv.

Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms pdf

Lei Wu, Chao Ma, Zhong Li, 2020, ArXiv.

The Generalization Error of the Minimum-norm Solutions for Over-parameterized Neural Networks

Lei Wu, Chao Ma, 2021 .

Rademacher complexity and the generalization error of residual networks

E. Weinan, Chao Ma, Qingcan Wang, 2020 .

Early Stage Convergence and Global Convergence of Training Mildly Parameterized Neural Networks

Chao Ma, Ming Wang, 2022, NeurIPS.

Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning

Chao Ma, Joel Jennings, Matthew Ashman, 2023, ICLR.

Uniformly accurate machine learning-based hydrodynamic models for kinetic equations

W. E, Chao Ma, Jiequn Han, 2019, Proceedings of the National Academy of Sciences.

A priori estimates of the population risk for two-layer neural networks

Lei Wu, Chao Ma, Wu Lei, 2018, Communications in Mathematical Sciences.

How SGD Selects the Global Minima in Over-parameterized Learning : A Dynamical Stability Perspective

Lei Wu, Chao Ma, 2018 .

A Priori Estimates of the Generalization Error for Autoencoders

E Weinan, Chao Ma, Zehao Don, 2020, ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

Achieving Adversarial Robustness Requires An Active Teacher pdf

Chao Ma, Lexing Ying, Chao Ma, 2020, Journal of Computational Mathematics.