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Nonbacktracking operator for the Ising model and its applications in systems with multiple states
Zhang, P; Zhang, P (reprint author), Santa Fe Inst, Santa Fe, NM 87501 USA.
2015
发表期刊PHYSICAL REVIEW E
卷号91期号:4页码:42120
文章类型Article
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.
学科领域Physics
资助者AFOSR ; AFOSR ; AFOSR ; AFOSR ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; AFOSR ; AFOSR ; AFOSR ; AFOSR ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432]
DOIhttp://dx.doi.org/10.1103/PhysRevE.91.042120
关键词[WOS]ATTRACTOR NEURAL-NETWORKS ; SPIN-GLASS MODEL ; DYNAMICS ; HOPFIELD ; MEMORY
收录类别SCI
语种英语
资助者AFOSR ; AFOSR ; AFOSR ; AFOSR ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; AFOSR ; AFOSR ; AFOSR ; AFOSR ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432] ; DARPA [FA9550-12-1-0432]
WOS类目Physics, Fluids & Plasmas ; Physics, Mathematical
引用统计
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/21028
专题理论物理所SCI论文
通讯作者Zhang, P (reprint author), Santa Fe Inst, Santa Fe, NM 87501 USA.
推荐引用方式
GB/T 7714
Zhang, P,Zhang, P . Nonbacktracking operator for the Ising model and its applications in systems with multiple states[J]. PHYSICAL REVIEW E,2015,91(4):42120.
APA Zhang, P,&Zhang, P .(2015).Nonbacktracking operator for the Ising model and its applications in systems with multiple states.PHYSICAL REVIEW E,91(4),42120.
MLA Zhang, P,et al."Nonbacktracking operator for the Ising model and its applications in systems with multiple states".PHYSICAL REVIEW E 91.4(2015):42120.
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