∑-π型神经网络中误差曲面与学习效率研究

STUDIES ON ERROR SURFACES AND LEARNING EFFICIENCY IN ∑-π NEURAL NETWORK

∑－π型神经网络是由具有高阶神经网络特性的单元构成的无隐层网络。研究了∑－π型神经网络中的误差曲面和学习效率，给出了理论推导和分析。对于典型的ＸＯＲ问题，分别使用ＢＰ网络和∑－π网络进行了计算机模拟计算。结果表明，ＢＰ网络中误差曲面存在大量的平台（ｆｌａｔ）和梯阶（ｓｔａｉｒ－ｓｔｅｐ），∑－π网络中误差曲面变化梯度较大，因此具有较快的学习收敛速率，能克服ＢＰ网络的不足。按文中所用模拟计算方法，可以建立∑－π网络和ＢＰ网络中学习参数与学习效率、误差曲面特性之间关系数据库，有利于∑－π网络和ＢＰ网络的参数优选、加速收敛和硬件实现。还讨论了∑－π网络和ＢＰ网络的神经生物学基础。

?π neural network is a no-hidden-layer network formed by the units with properties of higher-order neural network model. In the present study, the author investigated the error surfaces and learning efficiency in ∑-π neural network, gave the theoretical analyses and studied XOR problem by means of computer simulation calculations using BP network and ∑-π network separately to compare the 2 networks. The results s ow the divergence of error surfaces in ∑-π network is greater than that in BP network and there is no stair-step and flat, which often appear in BP network. Therefore ∑-π network, with faster convergence rate, can compement the shortcoming of BP network. We can use these calculation methods to build a data bank to relate learning parameters, to learning efficiency and error surfaces, so as to optimize the parameters in the 2 networks and help speed convergence and the realization of hardware. The neurobiological bases of BP and ∑-π networks are discussed.