四层前向神经网络作为通用逼近器的一致性分析  

Uniformity Analyses for Four-Layer Feedforward Neural Networks as Universal Approximators

作　　者：刘普寅[1] 张汉江[1] 

机构地区：[1]国防科技大学数学系,湖南长沙410073

出　　处：《模糊系统与数学》2000年第4期36-43,共8页Fuzzy Systems and Mathematics

基　　金：National Science Foundation(69974041).

摘　　要：如果转移函数σ:R→ R是 Tauber-Wiener函数 ,即σ∈ (TW) ,本文给出了四层前向神经网络 ∑pi=1vi(∑qj=1uijσ(Aij. x +θij) )作为通用逼近器的一致性分析 ,且选取了该网络具有某类特殊性质的连结权。例如 ,若 f,g是连续函数 ,且 f≤g,则相应的连结权关于 f,g是递增的 ,等等。最后为验证结论 ,给出了一个模拟例子。If the transitive function σ:R→R is a Tauber Wiener function, i.e. σ∈(TW), the uniformity of the four layer feedforward neural network ∑pi=1v i(∑qj=1u ij σ(A ij ·x+θ ij )) as a universal approximator is analysed. Some connection weights of the neural network with special conditions are selected. For instance,if f,g are continuous functions and f≤g,the connection weights corresponding respectively with f,g are increasing, etc. Finally a simulation example illustrates our conclusions.

关 键 词：四层前向神经网络 通用逼近器 保序算子 

分 类 号：O174.41[理学—数学] TP18[理学—基础数学]