关于前馈神经网络的激活函数与认知能力

讨论了目前前馈神经网络研究中存在的一些问题 ,给出了前馈神经网络的一种数学框架。在这种框架下 ,提出了网络神经元激活函数的选取原则 ,给出了前馈神经网络认知能力的概念 ,证明了静态前馈神经网络的认知能力是有限的。指出了网络的认知能力与激活函数、隐层神经元个数的选取都有关 ,并提出了隐层神经元个数的选取原则。最后 ,给出了前馈神经网络泛化能力的概念 ,指出前馈网络的泛化能力是有条件的。

The Activation Functions and Cognitive Ability of Feedforward Neural Networks

In this paper, we discuss some problems of feedforward neural networks (FNN). A mathematical theory is introduced for the feedforward neural networks. And then a principle to select an activation function for the neurons of the FNN is given. The concept of the cognitive ability of the FNN is introduced. It is proved that the cognitive ability of a static FNN is limited. And it is pointed out that the cognitive ability of the FNN is interrelated with the activation function and the number of the neurons of the FNN. A principle to determine the number of the neurons of the FNN is given. Finally, a concept of the generalized ability of the FNN is introduced and some results are obtained.