论文部分内容阅读
文中研究一类多元周期Lebesgue平方可积函数SF_d与神经网络集合Π_(φ,n,d)=(?)之间偏差dist(SF_d,Π_(φ,n,d))的估计问题.特别地,利用Fourier变换、逼近论等方法给出dist(SF_d,Π_(φ,n,d))的下界估计,即dist(?).所获下界估计仅与神经网络隐层的神经元数目有关,与目标函数及输入的维数无关.该估计也进一步揭示了神经网络逼近速度与其隐层拓扑结构之间的关系.
In this paper, we study the estimation problem of the dist (SF_d, Π_ (φ, n, d)) of a class of multivariate periodic Lebesgue square integrable function SF_d and neural network set Π_ (φ, n, d) , The lower bound estimate of dist (SF_d, Π_ (φ, n, d)) is given by Fourier transform and approximation theory, which is called dist (?). The obtained lower bound estimation is only related to the number of neurons in hidden layer of neural network, Which has nothing to do with the objective function and the input dimension.The estimation also further reveals the relationship between the approximation speed of neural network and its hidden layer topology.