同伦BP网络理论与算法

ＢＰ网络和算法是使用最广泛的神经网络模型之一，但由于它使用梯度算法，因而存在有固有的局域极小及收敛速度慢等问题。本文首先把一ＢＰ网络的优化问题变换为一非线性方程的求解，然后将同伦思想引入到神经网络学习训练之中，提出了相应的同伦ＢＰ网络理论与算法，它具有全局收敛的优点，同时具有比传统梯度法收敛速度快一个数量级以上和克服病态的能力，在ＢＰ梯度法不收敛时它也能给出正确解答。本文的理论证明和计算机仿真实验

Homotopy BP Neural Network:Theory and Algorithm

Theory and algorithm of the homotopy BP neural network are proposed in the paper,the error minimization problem in a BP neural network is transfered to the solving system of an associated nonlinear equation,and the globally minimum error and the faster convergence speeds can be obtained by the homotopy BP algorithm.It is checked by results obtained with theoretical analysis and computer simulation.