一类离散Hopfield网络的吸引特性研究
APPROACHES ON ATTRACTION CHARACTORISTICS OF A KIND OF DISCRETE HOPFIELD NETWORKS
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摘要: 该文以n维超立方体为大规模局域连接模型的离散Hopfield网络(简称An网)为研究对象,深入讨论了这种网络的吸引特性,包括吸引子/吸引环的结构和吸引半径等,得出了具有相同结构的吸引子/吸引环具有相同的吸引特性和吸引半径,并给出了它们的吸引半径;进一步地,本文将上述讨论扩展到较为一般的离散Hopfield网络,讨论了它们的吸引子/吸引环与An网的吸引子/吸引环相同(或部分相同)的条件,以及相应的吸引子/吸引环的吸引半径,得出了迁移越大,保留An网吸引子/吸引环的数目越少,且吸引半径越小的结论。Abstract: This paper studies the attraction characteristics of a kind of symmetric discrete Hopfield neural networks, the network with ri-cube as its structure and connection situation, called n-cube network. The structure of the attraction states/cycles and their attraction diameters are explored. The result is that the attraction region is of same size and so is the attraction diameters for the attraction states/cycles with same attraction structure. Furthermore, the above result is extended to a more general asymmetric discrete Hopfield network and the conditions for the network to be (or partially to be) with the same attraction states/cycles as those of n-cube network are studied, and its attraction diameters are presented.
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