球面神经网络的构造与逼近

Construction and Approximation of Spherical Neural Networks

研究球面神经网络的构造与逼近问题.利用球面广义的de la Vallee Poussin平均、球面求积公式及改进的单变量Cardaliaguet-Euvrard神经网络算子,构造具logistic激活函数的单隐层前向网络,并给出了Jackson型误差估计.

This paper studies the problem of the construction and approximation of spherical neural networks. Using generalized de la Vallee Poussin means of sphere, spherical quadrature rules and modified univariate Cardaliaguet-Euvrard neural network operators, we construct feed-forward networks of one hidden layer with logistic activation function, and give the error estimates of Jackson type.