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Monte Carlo Study of Complex Information Processing Models

复杂信息处理模型的蒙特卡罗研究

基本信息

批准号：
14084204
负责人：
HUKUSHIMA Koji
金额：
$ 4.03万
依托单位：
University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14084204/
关键词：
Monte Carlo Method Extended Ensemble Spin Glass Phase Transition Condensed Matter Information theory Probabilistic approach 情報基礎エイジング現象最適化

项目摘要

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

我们该项目的目标是开发数值工具来分析统计力学和信息处理中常见的概率模型的大规模相空间，并使用这些工具阐明其统计特性。特别地，扩展集成蒙特卡罗（MC）方法已被积极采用作为有用的概率算法。主要成果如下： 1． MC方法和分析工具的开发：我们提出了一种新的MC算法，称为“群体退火”，它被视为模拟退火对有限温度采样算法的修改方式。此外，我们还开发了一种评估自由能差异的方法，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，其中适当的稳定解自动从模拟数据中的许多亚稳态解中分离出来。 Dev … More 信息论中的发展：调查传播是信息处理领域最近开发的概率算法。尽管该方法已经应用于许多模型，但其性能和有效性仍然知之甚少。我们开发了一种利用MC方法来确定测量传播中先验未知的模型参数的方法，并发现它适用于随机多体相互作用模型。 3．自旋玻璃物理：通过大规模MC模拟，我们发现了低温自旋玻璃态的特殊性质，例如弱扰动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，可以在很宽的范围内表达热力学可观测量的主导顺序。通过 3d 双峰伊辛自旋玻璃上的数据说明的扩展标度可以使从不同可观测值的标度分析中获得的关键参数估计值保持一致。较少的