Discrete Dynamics in Nature and Society
Volume 6 (2001), Issue 2, Pages 129-136

On permutation symmetries of hopfield model neural network

Jiyang Dong, Shenchu Xu, Zhenxiang Chen, and Boxi Wu

Department of Physics, Xiamen University, Xiamen 361005, China

Received 29 July 2000

Copyright © 2001 Jiyang Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.