Strong Overall Error Analysis for the Training of Artificial Neural Networks Via Random Initializations  

作　　者：Arnulf Jentzen Adrian Riekert 

机构地区：[1]School of Data Science and Shenzhen Research Institute of Big Data,The Chinese University of Hong Kong,Shenzhen,People’s Republic of China [2]Applied Mathematics:Institute for Analysis and Numerics,University of Münster,Münster,Germany

出　　处：《Communications in Mathematics and Statistics》2024年第3期385-434,共50页数学与统计通讯（英文）

基　　金：funded by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)under Germany’s Excellence Strategy EXC 2044-390685587;Mathematics Münster:Dynamics-Geometry-Structure。

摘　　要：Although deep learning-based approximation algorithms have been applied very successfully to numerous problems,at the moment the reasons for their performance are not entirely understood from a mathematical point of view.Recently,estimates for the convergence of the overall error have been obtained in the situation of deep supervised learning,but with an extremely slow rate of convergence.In this note,we partially improve on these estimates.More specifically,we show that the depth of the neural network only needs to increase much slower in order to obtain the same rate of approximation.The results hold in the case of an arbitrary stochastic optimization algorithm with i.i.d.random initializations.

关 键 词：Deep learning Artificial intelligence Empirical risk minimization Optimization 

分 类 号：O17[理学—数学]