Hopfield网的初等关联分析及仿真试验

Elementary Connected Analysis for Hopfield Networks

关于Ｈｏｐｆｉｅｌｄ网的输出转移轨迹、吸引子、吸引域和如何逃离局部极小点等问题，尤其是对具有一般的权系数和偏置的网络，一直没有得到很好的解决。本文首先定义了Ｈｏｐｆｉｅｌｄ网的初等关联网络，分析了初等关联网络的性质，找出了具有关联关系的网络输出转移轨迹之间存在的关联关系和规律，使得如果已知了一个网络的输出转移轨迹，利用这一规律可以很容易地得出与其相关联的网络的输出转移轨迹，并给出了它们的吸引子之间关系的结论，为Ｈｏｎｆｉｌｅｄ网络的局部极小点的逃离、最不容错网络的判断提供了方法，对网络的进一步分析和设计提供了一种新的方法和途径。所进行的大量计算机仿真实验验证了这一规律的存在。

The elementary connected network of a Hop field network is defined, the properties of any two elementary connected networks analyzed, and the relationship (or called connected law) between the output transferences of any two elementary connected networks found out, with which the output transference of a Hopfield network can be easily deduced by that of any network which is elementary connected with it. The realtionship of the attractors between any two elementary connected networks is derived out which is helpful for the escapement from the local minimum point and for Judgement of whether a Hopfield network is with no tolerant ability to input data. Finally, computer simulation results are presented which are in accordance whith the connected law.