Kainen Paul C, Kůrková Vera
Department of Mathematics, Georgetown University, Washington, DC 20057-1233, USA.
Neural Comput. 2009 Oct;21(10):2970-89. doi: 10.1162/neco.2009.04-08-745.
Complexity of one-hidden-layer networks is studied using tools from nonlinear approximation and integration theory. For functions with suitable integral representations in the form of networks with infinitely many hidden units, upper bounds are derived on the speed of decrease of approximation error as the number of network units increases. These bounds are obtained for various norms using the framework of Bochner integration. Results are applied to perceptron networks.
利用非线性逼近和积分理论的工具研究了单隐藏层网络的复杂性。对于具有无限多个隐藏单元的网络形式的具有适当积分表示的函数，随着网络单元数量的增加，推导出了逼近误差减小速度的上界。使用博赫纳积分框架针对各种范数获得了这些界。结果应用于感知器网络。
