The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles
The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles
复制标题
DOI：
10.1088/0305-4470/37/25/002
复制
发表时间：
2004-06-25
期刊：
影响因子：
--
通讯作者：
Okada, M
中科院分区：
文献类型：
--
作者：
Mimura, K;Kawamura, M;Okada, M
利用路径积分分析方法，给出了存储无限个有限步极限环的联想记忆模型瞬态动力学的精确解。在假定麦克斯韦构造正确的情况下，我们成功地从具有延迟自相互作用的有限步序列处理模型的宏观递推方程中导出了有序参数的稳态方程。我们还通过信噪分析（SCSNA）推导了稳态方程。信噪分析必须假设自旋输入的串扰噪声服从高斯分布。另一方面，路径积分方法不需要对串扰噪声进行高斯近似。我们发现，在动力学是确定性的情况下，当我们假设麦克斯韦构造方差时，对于稳态，信噪分析和路径积分分析都给出了完全相同的结果。我们已经展示了存储容量（alpha(c)）对每一个极限环(l)的模式数的依赖性。在l = 1时，存储容量为Hopfield模型中的alpha(c) = 0.138。存储容量随步数单调增加，在l近似或等于10时收敛到alpha(c) = 0.269。只要极限环的阶数为l = O(1)，有限步序列处理模型的原始性质就会出现。
An exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps is shown by means of the path-integral analysis. Assuming the Maxwell construction ansatz, we have succeeded in deriving the stationary state equations of the order parameters from the macroscopic recursive equations with respect to the finite-step sequence processing model which has retarded self-interactions. We have also derived the stationary state equations by means of the signal-to-noise analysis (SCSNA). The signal-to-noise analysis must assume that crosstalk noise of an input to spins obeys a Gaussian distribution. On the other hand, the path-integral method does not require such a Gaussian approximation of crosstalk noise. We have found that both the signal-to-noise analysis and the path-integral analysis give completely the same result with respect to the stationary state in the case where the dynamics is deterministic, when we assume the Maxwell construction ansatz. We have shown the dependence of the storage capacity (alpha(c)) on the number of patterns per one limit cycle (l). At l = 1, the storage capacity is alpha(c) = 0.138 as in the Hopfield model. The storage capacity monotonically increases with the number of steps, and converges to alpha(c) = 0.269 at l similar or equal to 10. The original properties of the finite-step sequence processing model appear as long as the number of steps of the limit cycle has order l = O(1).