Reconstructing the Hopfield network as an inverse Ising problem

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

DOI:https://doi.org/10.1103/PHYSREVE.81.036104· OSTI ID:21344716

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)

We test four fast mean-field-type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low-temperature regime, the simulated annealing technique is adopted. Although performances of these network reconstruction algorithms on the simulated network of spiking neurons are extensively studied recently, the analysis of Hopfield networks is lacking so far. For the Hopfield network, we found that, in the retrieval phase favored when the network wants to memory one of stored patterns, all the reconstruction algorithms fail to extract interactions within a desired accuracy, and the same failure occurs in the spin-glass phase where spurious minima show up, while in the paramagnetic phase, albeit unfavored during the retrieval dynamics, the algorithms work well to reconstruct the network itself. This implies that, as an inverse problem, the paramagnetic phase is conversely useful for reconstructing the network while the retrieval phase loses all the information about interactions in the network except for the case where only one pattern is stored. The performances of algorithms are studied with respect to the system size, memory load, and temperature; sample-to-sample fluctuations are also considered.

• OSTI ID: 21344716
• 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: 3 Vol. 81; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
ANIMAL CELLS
ANNEALING
COMPUTERIZED SIMULATION
EQUILIBRIUM
FAILURES
FLUCTUATIONS
HEAT TREATMENTS
MAGNETISM
MATHEMATICAL LOGIC
MEAN-FIELD THEORY
NERVE CELLS
PARAMAGNETISM
PERFORMANCE
SIMULATION
SOMATIC CELLS
SPIN GLASS STATE
VARIATIONS