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题名: Nonbacktracking operator for the Ising model and its applications in systems with multiple states
作者: Zhang, P
刊名: PHYSICAL REVIEW E
出版日期: 2015
卷号: 91, 期号:4, 页码:42120
学科分类: Physics
DOI: http://dx.doi.org/10.1103/PhysRevE.91.042120
通讯作者: Zhang, P (reprint author), Santa Fe Inst, Santa Fe, NM 87501 USA.
文章类型: Article
英文摘要: The nonbacktracking operator for a graph is the adjacency matrix defined on directed edges of the graph. The operator was recently shown to perform optimally in spectral clustering in sparse synthetic graphs and have a deep connection to belief propagation algorithm. In this paper we consider nonbacktracking operator for Ising model on a general graph with a general coupling distribution and study the spectrum of this operator analytically. We show that spectral algorithms based on this operator is equivalent to belief propagation algorithm linearized at the paramagnetic fixed point and recovers replica-symmetry results on phase boundaries obtained by replica methods. This operator can be applied directly to systems with multiple states like Hopfield model. We show that spectrum of the operator can be used to determine number of patterns that stored successfully in the network, and the associated eigenvectors can be used to retrieve all the patterns simultaneously. We also give an example on how to control the Hopfield model, i.e., making network more sparse while keeping patterns stable, using the nonbacktracking operator and matrix perturbation theory.
类目[WOS]: Physics, Fluids & Plasmas ;  Physics, Mathematical
关键词[WOS]: ATTRACTOR NEURAL-NETWORKS ;  SPIN-GLASS MODEL ;  DYNAMICS ;  HOPFIELD ;  MEMORY
收录类别: SCI
项目资助者: AFOSR ;  DARPA [FA9550-12-1-0432]
语种: 英语
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/21028
Appears in Collections:理论物理所2015年知识产出_期刊论文

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Recommended Citation:
Zhang, P. Nonbacktracking operator for the Ising model and its applications in systems with multiple states[J]. PHYSICAL REVIEW E,2015,91(4):42120.
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