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.