摘要 :
Symmetry is a powerful tool to reduce the freedom degrees of a problem. However, the applicability of the symmetry tool strongly depends on the possibility to calculate the symmetries of the system. General searching methods, e.g....
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Symmetry is a powerful tool to reduce the freedom degrees of a problem. However, the applicability of the symmetry tool strongly depends on the possibility to calculate the symmetries of the system. General searching methods, e.g., ergodic searching, is unpractical for a high-dimensional system since the order of the symmetric group grows with n, where n is the dimension of the system. We propose an approach based on genetic algorithms to search for the symmetric permutations of a binary patterns set. Calculations for five kinds of dimensional pattern set are also given. Results show that the majority of symmetric permutations can be found within an acceptable time for a high-dimensional pattern set by the new approach, which makes it possible to study and design high-dimensional artificial neural networks by the method of symmetry.
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摘要 :
Symmetry is a powerful tool to reduce the freedom degrees of a problem. However, the applicability of the symmetry tool strongly depends on the possibility to calculate the symmetries of the system. General searching methods, e.g....
展开
Symmetry is a powerful tool to reduce the freedom degrees of a problem. However, the applicability of the symmetry tool strongly depends on the possibility to calculate the symmetries of the system. General searching methods, e.g., ergodic searching, is unpractical for a high-dimensional system since the order of the symmetric group grows with n, where n is the dimension of the system. We propose an approach based on genetic algorithms to search for the symmetric permutations of a binary patterns set. Calculations for five kinds of dimensional pattern set are also given. Results show that the majority of symmetric permutations can be found within an acceptable time for a high-dimensional pattern set by the new approach, which makes it possible to study and design high-dimensional artificial neural networks by the method of symmetry.
收起
摘要 :
Symmetry is a powerful tool to reduce the freedom degrees of a problem. However, the applicability of the symmetry tool strongly depends on the possibility to calculate the symmetries of the system. General searching methods, e.g....
展开
Symmetry is a powerful tool to reduce the freedom degrees of a problem. However, the applicability of the symmetry tool strongly depends on the possibility to calculate the symmetries of the system. General searching methods, e.g., ergodic searching, is unpractical for a high-dimensional system since the order of the symmetric group grows with n!, where n is the dimension of the system. In this paper, we propose an approach based on Genetic Algorithms to search for the symmetric permutations of a binary patterns set. Calculations for five kinds of dimensional pattern set are also given. Results show that the majority of symmetric permutations can be found within an acceptable time for a high-dimensional pattern set by the new approach, which makes it possible study and design the high-dimensional artificial neural networks by the method of symmetry.
收起
摘要 :
Symmetry is a powerful tool to reduce the freedom degrees of a problem. However, the applicability of the symmetry tool strongly depends on the possibility to calculate the symmetries of the system. General searching methods, e.g....
展开
Symmetry is a powerful tool to reduce the freedom degrees of a problem. However, the applicability of the symmetry tool strongly depends on the possibility to calculate the symmetries of the system. General searching methods, e.g., ergodic searching, is unpractical for a high-dimensional system since the order of the symmetric group grows with n!, where n is the dimension of the system. In this paper, we propose an approach based on Genetic Algorithms to search for the symmetric permutations of a binary patterns set. Calculations for five kinds of dimensional pattern set are also given. Results show that the majority of symmetric permutations can be found within an acceptable time for a high-dimensional pattern set by the new approach, which makes it possible study and design the high-dimensional artificial neural networks by the method of symmetry.
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