前向代数神经网络的函数逼近理论及学习算法

ON FORWARD ALGEBRA NEURAL NETWORKS FUNCTION APPROXIMATION THEORY AND LEARNING ALGORTHMS

文中对ＭＰ神经元模型进行了推广，定义了多项式代数神经元、多项式代数神经网络，将多项式代数融入代数神经网络，分析了前向多项式代数神经网络函数逼近能力及理论依据，设计出了一类双输入单输出的前向４层多项式代数神经网络模型，由该模型构成的网络能够逼近于给定的二元多项式到预定的精度．给出了在Ｐ－ａｄｉｃ意义下的多项式代数神经网络函数逼近整体学习算法，在学习的过程中，不存在局部极小，通过实例表明，该算法有效．最后，指出ＦＬＡＮＮ中函数展开型网络均可由神经元的激发函数变换来实现，为近似符号网络计算提供一新理论和方法．

In this paper,the MP neurons are popularized, the concepts of polynomials algebra neurons and polynomials algebra neural networks are firstly proposed, and polynomials algebra neural networks are mixed together with algebra neural networks. An analysis is made of forward algebra neural networks function approximate capability and theory foundation, and a kind of double inputs and single output four layers forward algebra neurons are designed, which can approximate a given double variable polynomials function, satisfying the given precision. A learning algorithm of algebra neural networks under p-adic is designed. This method can escape local minimum during the learning process. Finally, examples illustrate its efficiency. It is pointed out that function link artificial neural networks can be accomplished by means of activation functions of neurons, thus providing a new theory and method in approximate symbol networks computation.