论文标题
通过离散耦合分析Hopfield模型
Analysis of the Hopfield Model with Discrete Coupling
论文作者
论文摘要
对高速ISING计算的特定硬件的需求不断增长，这促使需要确定准确性如何取决于具有物理资源有限的硬件实现。例如，在数字硬件（例如现场可编程的门阵列）中，随着代表耦合强度的位数降低，集成的ISING旋转的密度和计算速度可以提高，而计算精度则较低。为了优化准确性效率的权衡，我们必须根据代表耦合强度的钻头数量来估计Ising计算机的性能变化。在这项研究中，我们通过与离散耦合专注于Hopfield模型来解决此问题。 Hopfield模型是一个规范的Ising计算模型。先前的研究已经通过统计力学方法分析了一些非线性函数（例如符号）对Hopfield模型绘制耦合强度的效果，但没有详细介绍耦合强度的效果。在这里，我们通过使用副本方法来得出了与离散耦合的Hopfield模型的顺序参数方程，并阐明了代表耦合强度和关键内存能力的位数之间的关系。在本文中，我们使用了与一般非线性耦合（Sompolinsky（1986））的Hopfield模型的复制方法，以多位离散的耦合强度分析模型，并且我们将模型的De almeida-the-de almeida-the the de almeida-the the de almeida-the the the the and-Almeide coupling与一般非线性耦合。
Growing demand for high-speed Ising-computing-specific hardware has prompted a need for determining how the accuracy depends on a hardware implementation with physically limited resources. For instance, in digital hardware such as field-programmable gate arrays, as the number of bits representing the coupling strength is reduced, the density of integrated Ising spins and the speed of computing can be increased while the calculation accuracy becomes lower. To optimize the accuracy-efficiency trade-off, we have to estimate the change in performance of the Ising computing machine depending on the number of bits representing the coupling strength. In this study, we tackle this issue by focusing on the Hopfield model with discrete coupling. The Hopfield model is a canonical Ising computing model. Previous studies have analyzed the effect of a few nonlinear functions (e.g. sign) for mapping the coupling strength on the Hopfield model with statistical mechanics methods, but not the effect of discretization of the coupling strength in detail. Here, we derived the order parameter equations of the Hopfield model with discrete coupling by using the replica method and clarified the relationship between the number of bits representing the coupling strength and the critical memory capacity. In this paper, we used the replica method for the Hopfield model with general nonlinear coupling (Sompolinsky (1986)) to analyze the model with a multi-bit discrete coupling strength, and we novelly derived the de Almeida-Thouless line of the model with general nonlinear coupling.
