Message passing algorithms for the Hopfield network reconstruction: Threshold behavior and limitation

Journal Article · Mon Nov 15 04:00:00 EST 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.82.056111· OSTI ID:21502848

Haiping, Huang ^[1]

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1. Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China)

The Hopfield network is reconstructed as an inverse Ising problem by passing messages. The applied susceptibility propagation algorithm is shown to improve significantly on other mean-field-type methods and extends well into the low-temperature region. However, this iterative algorithm is limited by the nature of the supplied data. Its performance deteriorates as the data become highly magnetized, and this method finally fails in the presence of the frozen type data where at least two of its magnetizations are equal to 1 in absolute value. On the other hand, a threshold behavior is observed for the susceptibility propagation algorithm and the transition from good reconstruction to poor one becomes sharper as the network size increases.

• OSTI ID: 21502848
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) Journal Issue: 5 Vol. 82; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
97 MATHEMATICS AND COMPUTING
ALGORITHMS
CALCULATION METHODS
ITERATIVE METHODS
MAGNETIZATION
MATHEMATICAL LOGIC
MEAN-FIELD THEORY
PERFORMANCE