Abstract: Based on the approximation theory of Fourier-series working in square integrable space, a Fourier neuronal network was constructed by using activation functions of the complex exponential form. Then a weightsdirectdetermination method was derived to decide the neuralnetwork weights immediately, which remedied the weaknesses of conventional BP neural networks such as small convergence rate, easily converging to local minimum and possibly lengthy or oscillatory learning process. A hidden-neurons-growing algorithm was presented to adjust the neural-network structure adaptively. Theoretical analysis and simulation results substantiate further that the presented Fourier neural network and algorithm could have good properties of high-precision learning, noise-suppressing and discontinuous-function approximating.

Key words: Fourier series, weights-direct-determination, feed-forward neural network, growing algorithm, complex-exponent

摘要： 以平方可积空间上的复指数Fourier级数作为激励函数构造了新型Fourier神经元网络，并推导出采用加号逆表示的网络权值直接确定公式，克服了传统BP神经网络收敛速度慢、易陷于局部极小点、迭代学习易发生振荡等缺陷。并在此基础上构造了隐神经元衍生算法，克服了传统BP神经网络难以确定最优网络拓扑结构的缺点。理论分析及仿真实验表明，该复指数Fourier神经元网络能够一步计算网络最优权值且能自适应调整网络结构，对随机加性噪声具有抑制作用，并能高精度逼近非连续函数。

关键词: Fourier级数, 前向神经网络, 权值直接确定, 衍生算法, 复指数