Quantum Effects in Neural Networks
Quantum Effects in Neural Networks
复制标题
神经网络中的量子效应
DOI：
10.1143/jpsj.65.3780
复制
发表时间：
1996
影响因子：
1.7
通讯作者：
Y. Nonomura
中科院分区：
文献类型：
--
作者：
H. Nishimori;Y. Nonomura
我们发展了横场中Hopfield模型的统计力学，以研究量子涨落如何影响神经网络的宏观行为。当嵌入模式的数量是有限的，特罗特分解减少了问题的随机伊辛模型。结果表明，量子涨落对宏观变量的影响与热涨落的作用相同。对于大量的嵌入模式，我们应用复制方法的Trotter分解系统。结果总结为根据每个位置的图案数量α和横向场强度Δ绘制的基态相图。如果用Δ代替经典Hopfield模型中的温度T，则相图与经典Hopfield模型的相图非常吻合。因此，量子涨落的结论是非常相似的热涨落在确定本模型的宏观行为。
We develop the statistical mechanics of the Hopfield model in a transverse field to investigate how quantum fluctuations affect the macroscopic behavior of neural networks. When the number of embedded patterns is finite, the Trotter decomposition reduces the problem to that of a random Ising model. It turns out that the effects of quantum fluctuations on macroscopic variables play the 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 as a ground-state phase diagram drawn in terms of the number of patterns per site, α, and the strength of the transverse field, Δ. The phase diagram coincides very accurately with that of the conventional classical Hopfield model if we replace the temperature T in the latter model by Δ. Quantum fluctuations are thus concluded to be quite similar to thermal fluctuations in determination of the macroscopic behavior of the present model.