Transient dynamics for sequence processing neural networks
Transient dynamics for sequence processing neural networks
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DOI：
10.1088/0305-4470/35/2/306
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发表时间：
2002-01-18
期刊：
影响因子：
--
通讯作者：
Okada, M
中科院分区：
文献类型：
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作者：
Kawamura, M;Okada, M
本文用路径积分方法和统计神经动力学方法讨论了序列联想记忆模型的瞬态动力学的一个精确解。虽然路径积分方法有能力给出一个精确的解决方案的瞬态动力学，只有静态性能已被讨论的顺序联想记忆。通过分析串扰噪声的相关性，我们成功地导出了瞬态动力学的精确宏观描述。令人惊讶的是，这个精确解的序参数方程是完全等效的统计神经动力学，这是一个近似理论，假设串扰噪声服从高斯分布。为了检验我们的理论研究结果，我们数值计算得到的串扰噪声的累积量。我们验证了三阶和四阶累积量等于零，并且即使在非检索情况下串扰噪声也呈正态分布。我们表明，我们的理论得到的结果与计算机模拟得到的结果一致。我们还发现宏观不稳定态与分界线完全重合。
An exact solution of the transient dynamics fora sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact solution of the transient dynamics, only stationary properties have been discussed for the sequential associative memory. We have succeeded in deriving an exact macroscopic description of the transient dynamics by analysing the correlation of crosstalk noise. Surprisingly, the order parameter equations of this exact solution are completely equivalent to those of the statistical neurodynamics, which is an approximation theory that assumes crosstalk noise to obey the Gaussian distribution. In order to examine our theoretical findings, we numerically obtain cumulants of the crosstalk noise. We verify that the third- and fourth-order cumulants are equal to zero, and that the crosstalk noise is normally distributed even in the non-retrieval case. We show that the results obtained by our theory agree with those obtained by computer simulations. We have also found that the macroscopic unstable state completely coincides with the separatrix.