Monte Carlo Study of Complex Information Processing Models

我们在这个项目中的目的是开发用于分析统计力学和信息处理中常用的概率模型的大规模相空间的数值工具，并通过使用这些工具来阐明其统计性质。特别是，一种扩展的系综蒙特卡罗(MC)方法作为一种有用的概率算法得到了积极的应用。主要成果如下：1.MC方法和分析工具的发展：提出了一种新的MC算法--群体退火法，作为模拟退火法对有限温度采样算法的改进。此外，我们还开发了一种评估自由能差的方法，并将主成分分析(PCA)等多元分析应用于大规模模拟数据。后一个例子是Sourlas代码的PCA研究，在该研究中，适当的稳定解自动从模拟数据中的许多亚稳态解2中分离出来。开发人员…信息论的更多发展：调查传播是最近在信息处理领域发展起来的一种概率算法。虽然该方法已被应用于许多模型，但其性能和有效性仍鲜为人知。提出了一种利用MC方法确定测量传播中先验未知的模型参数的方法，并发现该方法适用于随机多体相互作用模型。自旋玻璃物理：通过大规模的MC模拟，我们发现了低温自旋玻璃态的特殊性质，例如，在弱微扰下的脆性和手性玻璃相的存在。此外，我们还发现了扩展的标度公式，这些公式在很大范围内表达了热力学可观测值的前序。3D双峰伊辛自旋玻璃的数据说明了这种扩展的标度，使得从标度分析中得到的不同可观测值的临界参数的估计是一致的。较少

Our aim in this project is to develop numerical tools for analyzing large-scale phase space of probabilistic models which are commonly discussed in statistical-mechanics and information processing, and to clarify their statistical properties by using the tools. Particularly, an extended ensemble Monte Carlo (MC) method has been employed actively as a useful probabilistic algorithm. Main achievements are as follows :1. Development of MC methods and analysis tools : We have proposed a new MC algorithm called "population annealing", which is regarded as a modified way of the simulated annealing to an algorithm for finite-temperature sampling. In addition, we have developed a way to evaluate free-energy difference and have applied multivariate analysis such as principal component analysis (PCA) to large-scale simulation data. A latter example is a PCA study of Sourlas codes, in which a proper stable solution is automatically separated from many metastable solutions in simulation data2. Dev … More elopment in information theory : Survey propagation is a recently developed probabilistic algorithm in the field of information processing. While the method has been already applied to many models, its performance and validity are still poorly understood. We have developed a way for determining a model parameter which is unknown a priori in the survey propagation by using MC method and have found that it works in a random multi-body interaction model.3. Spin glass physics : By large-scale MC simulations, we have found peculiar properties of low-temperature spin glass states which are, for example, fragility under weak perturbation and the existence of chiral glass phase. In addition, we discover extended scaling formulae which express to leading order of thermodynamic observables over a wide range. The extended scaling, illustrated by data on the 3d bimodal Ising spin glass, leads to consistency for the estimates of critical parameters obtained from scaling analyses for different observables. Less