111 citations · 753 across the 34 of their papers we have counts for
8 papers · 1 filter
Machine Learning from a Continuous Viewpoint
Weinan E, Chao Ma, Lei Wu
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analys…
The Generalization Error of the Minimum-norm Solutions for Over-parameterized Neural Networks
Weinan E, Chao Ma, Lei Wu
We study the generalization properties of minimum-norm solutions for three over-parametrized machine learning models including the random feature model, the two-layer neural networ…
Global Convergence of Gradient Descent for Deep Linear Residual Networks
Lei Wu, Qingcan Wang, Chao Ma
We analyze the global convergence of gradient descent for deep linear residual networks by proposing a new initialization: zero-asymmetric (ZAS) initialization. It is motivated by…
Uniformly Accurate Machine Learning Based Hydrodynamic Models for Kinetic Equations
Jiequn Han, Chao Ma, Zheng Ma +1
A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approxim…
The Barron Space and the Flow-induced Function Spaces for Neural Network Models
Weinan E, Chao Ma, Lei Wu
One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a q…
Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections
Weinan E, Chao Ma, Qingcan Wang +1
The behavior of the gradient descent (GD) algorithm is analyzed for a deep neural network model with skip-connections. It is proved that in the over-parametrized regime, for a suit…
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
A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are…
A Priori Estimates of the Population Risk for Residual Networks
Weinan E, Chao Ma, Qingcan Wang
Optimal a priori estimates are derived for the population risk, also known as the generalization error, of a regularized residual network model. An important part of the regularize…