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

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.