多层前馈神经网络隐单元数目上界的证明

A Proof of the Upper Bounds of the Number of Hidden Units in Multistory Feedforward Neural Networks

摘要: 研究前馈神经网络隐单元数目的上蜀和如何利用样本集的特性减少所需的隐单元个数。利用Ｓｉｇｍｏｉｄ函数的两端极限特性，使每个隐单元表示１～２个样本。在样本集具有局部单调性的情况下，可以用有〖（ｐ－１）／２〗个隐单元的３层前馈神经网络以任意小的误差表示ｐ个目标值。对一般的样本集，所需的隐单元数为〖（ｐ－１）／２〗～（ｐ－１）个。

Abstract: To investigate the upper bound of the number of the hidden units in feedforward nerual networks and how to utilize the property of the patterns set to reduce the needed number. The property of the two unequal limits at infinities of Sigmoid function was used to make one hidden unit to represent one to two patterns. When the patterns set possesses the property of local monotone, the upper bound is BHDG1,K*2W( p -1)/2BHDG1,WK*2. In general, the upper bound ranges from BHDG1,K*2W( p -1)/2BHDG1,WK*2 to ( p -1).