Constructive Estimation of Approximation for trigonometric Neural Networks
Constructive Estimation of Approximation for trigonometric Neural Networks
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DOI：
10.1142/s021969131250021x
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发表时间：
2012-05
期刊：
影响因子：
--
通讯作者：
Jianjun Wang;Wei-hong Xu;Bin Zou
中科院分区：
文献类型：
--
作者：
Jianjun Wang;Wei-hong Xu;Bin Zou
对于具有三角权系数的三层人工神经网络，本文给出了逼近2π周期p阶Lebesgue可积函数L2 pi ^{p}的上界和下界.我们得到的定理提供了这些近似网络的显式方程表示，其隐藏层单元的数量的规格，近似的下界估计，以及近似的本质阶。所得结果不仅刻画了神经网络逼近的内在性质，而且揭示了神经网络精度（速度）与隐层神经元数目之间的内在关系。
For the three-layer artificial neural networks with trigonometric weights coefficients, the upper bound and lower bound of approximating 2π-periodic pth-order Lebesgue integrable functions $L_{2\pi}^{p}$ are obtained in this paper. Theorems we obtained provide explicit equational representations of these approximating networks, the specification for their numbers of hidden-layer units, the lower bound estimation of approximation, and the essential order of approximation. The obtained results not only characterize the intrinsic property of approximation of neural networks, but also uncover the implicit relationship between the precision (speed) and the number of hidden neurons of neural networks.