两隐层前向神经网络表示能力的一些研究  

Some studies about expressive powers of feed-forward neural networks with two hidden layers

作　　者：肖颖敏 陈志祥 XIAO Yingmin;CHEN Zhixiang(School of Mathematical,Physical and Information Science,Shaoxing University,Shaoxing,Zhejiang 312000)

机构地区：[1]绍兴文理学院数理信息学院,浙江绍兴312000

出　　处：《绍兴文理学院学报》2025年第2期48-57,86,共11页Journal of Shaoxing University

摘　　要：多隐层网络表示能力的刻画一直是深度学习中重要而亟待解决的数理难题。本文就两隐层网络情形进行一些探讨。一方面,对两个隐层都以幂函数为激活函数,以及第一隐层增加一个ReLU激活函数的网络的表示能力进行了初步的探索和描述;另一方面,对以一类sigmoidal为激活函数的两隐层网络的输出进行了刻画。The characterization of expressive powers of multi-hidden layer networks has always been an important and urgent mathematical problem to be solved in deep learning.This article discusses the situation of the two hidden layers networks.On the one hand,the representation ability of the two-hidden layer network with the power function as the activation function and the network with the first hidden layer added to the ReLU activation function is preliminarily explored and described.On the other hand,the output of the two-hidden layer network with a class of sigmoidal activation functions is characterized.

关 键 词：神经网络 激活函数 表示能力 逼近 

分 类 号：O241.5[理学—计算数学]