关键词: 二进神经网络，布尔函数，奇偶校验问题，蚁群算法

Abstract: Binary neural network can completely express arbitrary Boolean function, but more isolated nodes such as parity problem are difficult to implement with simple network structure. According to this problem, we presented a learning algorithm to realize 13oolcan function such as parity problems with many isolated samples. 13y means of the ant colony algorithm, we obtained the optimized core nodes and the extension order of true and false nodes, by combing the geometrical algorithm, we gave the steps of how to expand the classifier hyperplanes with the optimized core nodes, so this algorithm can reduce the number of hidden neurons in network, and the expression of the hidden neurons and the output neuron are also given. Finally,this algorithm is validated to be effective through examples.

Key words: Binary neural networks, Boolean function, Parity problems, Ant colony algorithm