Quantum Effects in Neural Networks
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概要
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We develop the statistical rnechanics of the Hopfield model in a transverse field to investigatehow quantum fluctuations affect the rnacroscopic behavior of neural networks, When the numberof embedded patterns is finite, the Trotter decomposition reduces the problem to that of a randomIsing model. It turns out that the effects of quanturn fluctuations on macroscopic variables playthe same roles as those of thermal fluctuations. For an extensive number of embedded patterns,we apply the replica method to the Trotter-decomposed system. The result is summarized asa ground-state phase diagram drawn in terms of the number of patterns per site, a, and thestrength of the transverse field, ,2s. The phase diagrarn coincides very accurately with that ofthe conventional classical Hopfield model if we replace the temperature T in the latter modelby A. Quantum fluctuations are thtrs concluded to be quite similar to thermal fluctuations indetermination of the macroscopic behavior of the present model.
- 社団法人日本物理学会の論文
- 1996-12-15
著者
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NONOMURA Yoshihiko
The Institute of Physical and Chemical Research (RIKEN)
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Nonomura Yoshihiko
Department Of Physics Tokyo Institute Of Technology:institute Of Physical And Chemical Research
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Nonomura Yoshihiko
Magnetic Materials Laboratory Institute Of Physical And Chemical Research (riken)
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Nonomura Yoshihiko
Department Of Physics Faculty Of Science University Of Tokyo
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Nishimori Hidetoshi
Department Of Physics Facuilty Of Science Tokyo Institute Of Technology
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Nonomura Yoshihiko
Magnetic Materials Laboratory,Institute of Physical and Chemical Research (RIKEN)
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NONOMURA Yoshihiko
Computational Materials Science Center, National Institute for Materials Science
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