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一类前向人工神经网络的L^(p)逼近误差估计

The Estimation of Error of L^(p)Approximation for a Class of Feedforward Artificial Neural Networks
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摘要 本文构造了一类激活函数由Sigmoid函数生成的单隐层前向人工神经网络.我们使用Steklov平均函数并以目标函数的光滑模作为度量工具,估计该神经网络逼近L^(p)可积函数的速度,得到该网络L^(p)逼近的Jackson型定理. This paper constructs a class of single hidden layer feedforward artificial neural networks with activation functions generated by Sigmoid functions.By using the Steklov mean function and the smoothness of modulus of the target function as metric tools,the error that the networks approximate the L^(p)integrable function is estimated,and the Jackson type theorem of the L^(p)approximation is obtained.
作者 俞斌 叶海良 曹飞龙 YU Bin;YE Hailiang;CAO Feilong(College of Sciences,China Jiliang University,Hangzhou 310018,China)
机构地区 中国计量大学理学院
出处 《应用数学》 北大核心 2025年第3期896-904,共9页 Mathematica Applicata
基金 国家自然科学基金(62176244)。
关键词 前向人工神经网络 逼近 光滑模 L^(p)空间 Feedforward artificial neural network Approximation Modulus of smoothness L^(p)space
分类号 O174.41 [理学—基础数学]
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