关于前馈多层神经网络多维函数逼近能力的一个定理

A NOVEL THEOREM ON THE MULTI-DIMENSIONAL FUNCTION APPROXIMATION ABILITY OF FEED FORWARD MULTI-LAYER NEURAL NETWORKS

本文首次证明了前馈神经网络多维函数逼近能力的一个重要定理:当隐层神经元数目足够多时,其多维函数逼近能力与维数无关.也就是说我们只需研究其一维函数逼近能力,所得的结论完全适合于多维情形,该定理大大简化了前馈多层神经网络函数逼近问题的分析难度。本文还给出了该定理的一个应用。

This paper presents a novel theorem on the multi-dimensional function approximation ability of feed forward multi-layer neural networks (FFMLNN), which states that the function approximation ability of FFMLNN is independent of the dimension of the function to be approximated when the number of the hidden units is sufficiently large. This theorem simplifies greatly the analysis of the function approximation ability of FFMLNN because one needs only to study the one dimensional function approximation ability of FFMLNN. An application of the proposed theorem is given.