Machine learning from a continuous viewpoint,I  

作　　者：Weinan E Chao Ma Lei Wu 

机构地区：[1]Department of Mathematics,Princeton University,Princeton,NJ 08544,USA [2]The Program in Applied and Computational Mathematics,Princeton University,Princeton,NJ 08544,USA [3]Beijing Institute of Big Data Research,Beijing 100871,China

出　　处：《Science China Mathematics》2020年第11期2233-2266,共34页中国科学：数学（英文版）

基　　金：supported by a gift to Princeton University from iFlytek and the Office of Naval Research(ONR)Grant(Grant No.N00014-13-1-0338)。

摘　　要：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 analysis.We demonstrate that conventional machine learning models and algorithms,such as the random feature model,the two-layer neural network model and the residual neural network model,can all be recovered(in a scaled form)as particular discretizations of different continuous formulations.We also present examples of new models,such as the flow-based random feature model,and new algorithms,such as the smoothed particle method and spectral method,that arise naturally from this continuous formulation.We discuss how the issues of generalization error and implicit regularization can be studied under this framework.

关 键 词：machine learning continuous formulation flow-based model gradient flow particle approximation 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] O241[自动化与计算机技术—控制科学与工程]