How SGD Selects the Global Minima in Over-parameterized Learning: A Dynamical Stability Perspective. - Lei Wu; Chao Ma 012; Weinan E (NeurIPS, 2018)

Model Reduction with Memory and the Machine Learning of Dynamical Systems. - Chao Ma 012; Jianchun Wang; Weinan E (CoRR, 2018)

A Priori Estimates of the Generalization Error for Two-layer Neural Networks. - Weinan E; Chao Ma 012; Lei Wu (CoRR, 2018)

Bispectrum Inversion With Application to Multireference Alignment. - Tamir Bendory; Nicolas Boumal; Chao Ma 012; Zhizhen Zhao 001; Amit Singer (IEEE Trans. Signal Process., 2018)

Global Convergence of Gradient Descent for Deep Linear Residual Networks. - Lei Wu; Qingcan Wang; Chao Ma 012 (NeurIPS, 2019)

A Priori Estimates of the Population Risk for Residual Networks. - Weinan E; Chao Ma 012; Qingcan Wang (CoRR, 2019)

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 012; Lei Wu (CoRR, 2019)

Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections. - Weinan E; Chao Ma 012; Qingcan Wang; Lei Wu (CoRR, 2019)

Barron Spaces and the Compositional Function Spaces for Neural Network Models. - Weinan E; Chao Ma 012; Lei Wu (CoRR, 2019)

On the Generalization Properties of Minimum-norm Solutions for Over-parameterized Neural Network Models. - Weinan E; Chao Ma 012; Lei Wu (CoRR, 2019)

Machine Learning from a Continuous Viewpoint. - Weinan E; Chao Ma 012; Lei Wu (CoRR, 2019)

Globally Convergent Levenberg-Marquardt Method for Phase Retrieval. - Chao Ma 012; Xin Liu 001; Zaiwen Wen (IEEE Trans. Inf. Theory, 2019)

A Priori Estimates of the Generalization Error for Autoencoders. - Zehao Don; Weinan E; Chao Ma 012 (ICASSP, 2020)

A Mean Field Analysis Of Deep ResNet And Beyond: Towards Provably Optimization Via Overparameterization From Depth. - Yiping Lu 001; Chao Ma 012; Yulong Lu; Jianfeng Lu 001; Lexing Ying (ICML, 2020)

The Slow Deterioration of the Generalization Error of the Random Feature Model. - Chao Ma 012; Lei Wu; Weinan E (MSML, 2020)

Towards Theoretically Understanding Why Sgd Generalizes Better Than Adam in Deep Learning. - Pan Zhou 002; Jiashi Feng; Chao Ma 012; Caiming Xiong; Steven Chu-Hong Hoi; Weinan E (NeurIPS, 2020)

A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth. - Yiping Lu 001; Chao Ma 012; Yulong Lu; Jianfeng Lu 001; Lexing Ying (CoRR, 2020)

The Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models. - Chao Ma 012; Lei Wu; Weinan E (CoRR, 2020)

Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms. - Zhong Li 004; Chao Ma 012; Lei Wu (CoRR, 2020)

Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't. - Weinan E; Chao Ma 012; Stephan Wojtowytsch; Lei Wu (CoRR, 2020)

Achieving Adversarial Robustness Requires An Active Teacher. - Chao Ma 012; Lexing Ying (CoRR, 2020)

Heterogeneous Multireference Alignment for Images With Application to 2D Classification in Single Particle Reconstruction. - Chao Ma 012; Tamir Bendory; Nicolas Boumal; Fred J. Sigworth; Amit Singer (IEEE Trans. Image Process., 2020)

A Qualitative Study of the Dynamic Behavior for Adaptive Gradient Algorithms. - Chao Ma 012; Lei Wu; Weinan E (MSML, 2021)

On Linear Stability of SGD and Input-Smoothness of Neural Networks. - Chao Ma 012; Lexing Ying (NeurIPS, 2021)

The Sobolev Regularization Effect of Stochastic Gradient Descent. - Chao Ma 012; Lexing Ying (CoRR, 2021)

A Riemannian Mean Field Formulation for Two-layer Neural Networks with Batch Normalization. - Chao Ma 012; Lexing Ying (CoRR, 2021)

Provably convergent quasistatic dynamics for mean-field two-player zero-sum games. - Chao Ma 012; Lexing Ying (ICLR, 2022)

The Multiscale Structure of Neural Network Loss Functions: The Effect on Optimization and Origin. - Chao Ma 012; Lei Wu; Lexing Ying (CoRR, 2022)

Why self-attention is Natural for Sequence-to-Sequence Problems? A Perspective from Symmetries. - Chao Ma 012; Lexing Ying (CoRR, 2022)

Understanding the Generalization Benefits of Late Learning Rate Decay. - Yinuo Ren; Chao Ma 012; Lexing Ying (AISTATS, 2024)