一种新的联想记忆系统及其学习收敛性

New Associative Memory System and Its Learning Convergence

提出了一种新的联想记忆系统——基于牛顿前向插公式的联想记忆系统（ＮＦＩ－ＡＭＳ），用以实现在任意阶多变量多项式函数的高精度逼近，设计了相应的学习方法，并证明了在通常情况下对于任意多变量连续函数，ＮＦＩ－ＡＭＳ的学习总是以任意精度收敛的．该系统较之传统的ＣＭＡＣ类型的ＡＭＳ，具有所需供学习的样本点较少，学习精度高和存储单元空间较小的优点，且比多层ＢＰ网络具有学习算法简单和收敛速度快的特点，可望在智能控制与信号处理，模式识别中得到应用．

A new high order Associative Memory System based on Newton forword interpolation formula (NFI AMS) used for implementing the high precision approximation to multi variable polynomial functions with arbitrarily given order is proposed.The learning algorithm of NFI AMS is designed.Moreover,it is proved that the NFI AMS learning always converges to a given multivariable continuous function with arbitrary accuracy under a wide condition.The AMS possesses the advantages over conventional CMAS type AMS less learning sample points,high precision of learning and much less required memory size,and also the advantages over multi layer BP neural networks in much less computational effort for training and fast convergence rate.The systems of NFI AMS has great potential in the application areas of intelligent control and signal processing,process modelling and pattern recognition.