A NOVEL THEOREM ON THE MULTI-DIMENSIONAL FUNCTION APPROXIMATION ABILITY OF FEED FORWARD MULTI-LAYER NEURAL NETWORKS
关于前馈多层神经网络多维函数逼近能力的一个定理

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.