二进前向网络的结构优化设计

ｎ维超立方体顶点的分类问题是人工神经网络研究中的重要问题之一。若对ｎ维超立方体的顶点进行正确分类，同时保证网络具有最好的稳健能力，则任两个不同类顶点连线的中点都应是分割这两顶点的超平面上的点。基于这样的思想，本文导出了使网络稳健能力最强的分类超平面的标准方程，给出了网络各层节点之间连接权值和阈值的可能值。其连接权值仅需取＋１、－１和０，阈值仅需取１２加上〔－ｎ，ｎ－１〕上的整数，从而可获得最优的网络结构、最少的隐节点数目、最大的稳健能力，这样结构的网络易于训练，并不易进入局部极小点。

The Optimal Structure Design for Feedforward Neural Networks

In order to realize a correct classification of vertices on n dimensional hypercube with a binary neural network with maximal robustness,the median point on the line of any two adjacent vertices falling into different classes must be in the hyperplane classifying the two vertices.Based on this,the standard equation of the hyperplane is induced,and the possible values of connection weights and biases of the neurons in the network are given,which result in the optimal structure,the least number of hidden nodes and the maximal robustness,and make the network much easier to train and difficult to fall into local minimum.