On permutation symmetries of hopfield model neural network

• Main Authors: Jiyang Dong, Shenchu Xu, Zhenxiang Chen, Boxi Wu
• Format: Article
• Language: English
• Published: Hindawi Limited 2001-01-01
• Series: Discrete Dynamics in Nature and Society
• Subjects: Discrete hopfield neural network; Permutation symmetries; Associative memory; Storable patterns set.
• Online Access: http://dx.doi.org/10.1155/S1026022601000139
• ISSN: 1026-0226; 1607-887X

Discrete Hopfield neural network (DHNN) is studied by performing permutation operations on the synaptic weight matrix. The storable patterns set stored with Hebbian learning algorithm in a network without losing memories is studied, and a condition which makes sure all the patterns of the storable patterns set have a same basin size of attraction is proposed. Then, the permutation symmetries of the network are studied associating with the stored patterns set. A construction of the storable patterns set satisfying that condition is achieved by consideration of their invariance under a point group.