二进神经网络中汉明球的逻辑意义及一般判别方法

剖析二进神经元的逻辑意义对二进神经网络的规则提取是十分重要的，在布尔空间中，汉明球是一种线性可分的空间结构，如何从汉明球中提取出具有清晰逻辑意义的规则是二进神经网络研究的一个问题，通过对MofN规则表达形式的扩展，分析了汉明球的逻辑意义，提出了表达汉明球逻辑意义的LEM规则和GEM规则方法，并且讨论了汉明球和汉明补球的等价性，另一个重要的结果是证明了二进神经元和汉明球等价的充要条件，从而建立了判别汉明球的一般方法。

LOGICAL MEANING OF HAMMING SPHERE AND ITS GENERAL JUDGEMENT METHOD IN BINARY NEURAL NETWORKS

For extracting rules from binary neural networks, it is important to analyze logical meaning of neurons. Hamming sphere is a kind of structure in Boolean space. How to extract rules which express clear logical meaning from Hamming sphere is a problem in binary neural network research. In this paper, clear logical meaning of Hamming sphere is dug out by modifying the MofN rule form to LEM and GEM rule forms, which are proposed as two new rule forms, and also the equivalent relation between a Hamming sphere and a Hamming complementary sphere is discussed. Another important result is that a necessary and sufficient condition for a Hamming sphere equivalent to a binary neuron is proved. By that necessary and sufficient condition, a method of judging a Hamming sphere is established.