On permutation symmetries of hopfield model neural network
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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1026022601000139 |
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| _version_ | 1850225820929359872 |
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| author | Jiyang Dong Shenchu Xu Zhenxiang Chen Boxi Wu |
| author_facet | Jiyang Dong Shenchu Xu Zhenxiang Chen Boxi Wu |
| author_sort | Jiyang Dong |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5b7b579e47ad486e993f176c6ae6d491 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5b7b579e47ad486e993f176c6ae6d4912025-08-20T02:05:13ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2001-01-016212913610.1155/S1026022601000139On permutation symmetries of hopfield model neural networkJiyang Dong0Shenchu Xu1Zhenxiang Chen2Boxi Wu3Department of Physics, Xiamen University, Xiamen 361005, ChinaDepartment of Physics, Xiamen University, Xiamen 361005, ChinaDepartment of Physics, Xiamen University, Xiamen 361005, ChinaDepartment of Physics, Xiamen University, Xiamen 361005, ChinaDiscrete 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.http://dx.doi.org/10.1155/S1026022601000139Discrete hopfield neural network; Permutation symmetries; Associative memory; Storable patterns set. |
| spellingShingle | Jiyang Dong Shenchu Xu Zhenxiang Chen Boxi Wu On permutation symmetries of hopfield model neural network Discrete Dynamics in Nature and Society Discrete hopfield neural network; Permutation symmetries; Associative memory; Storable patterns set. |
| title | On permutation symmetries of hopfield model neural network |
| title_full | On permutation symmetries of hopfield model neural network |
| title_fullStr | On permutation symmetries of hopfield model neural network |
| title_full_unstemmed | On permutation symmetries of hopfield model neural network |
| title_short | On permutation symmetries of hopfield model neural network |
| title_sort | on permutation symmetries of hopfield model neural network |
| topic | Discrete hopfield neural network; Permutation symmetries; Associative memory; Storable patterns set. |
| url | http://dx.doi.org/10.1155/S1026022601000139 |
| work_keys_str_mv | AT jiyangdong onpermutationsymmetriesofhopfieldmodelneuralnetwork AT shenchuxu onpermutationsymmetriesofhopfieldmodelneuralnetwork AT zhenxiangchen onpermutationsymmetriesofhopfieldmodelneuralnetwork AT boxiwu onpermutationsymmetriesofhopfieldmodelneuralnetwork |