Abstract: In this paper, a new gradient training algorithm is presented to train the recurrent pi-sigma neural networks, in which a penalty is added to the conventional error function. The algorithm can not only improve the generalization of neural networks, but also avoid the slow convergence caused by the case that the original weights are chosen too small, achieving a better convergence compared to the traditional gradient algorithm without the penalty term. Moreover, the convergence of the algorithm is also studied, and finally the simulated experimental results indicates that the algorithm is efficient.

Key words: recurrent pi-sigma neural networks, gradient algorithm, penalty, convergence

摘要： 传统的梯度算法存在收敛速度过慢的问题，针对这个问题，提出一种将惩罚项加到传统误差函数的梯度算法以训练递归pi-sigma神经网络，算法不仅提高了神经网络的泛化能力，而且克服了因网络初始权值选取过小而导致的收敛速度过慢的问题，相比不带惩罚项的梯度算法提高了收敛速度。从理论上分析了带惩罚项的梯度算法的收敛性，并通过实验验证了算法的有效性。

关键词: 递归pi-sigma神经网络, 梯度算法, 惩罚项, 收敛性