Neural-network model composed of multidimensional spin neurons

Journal Article · Tue Jan 31 23:00:00 EST 1995 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.51.1538· OSTI ID:6644999

Nakamura, Y; Torii, K; Munakata, T ^[1]

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1. Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-01 (Japan)

As an extension of the Hopfield model, we propose a neural network composed of [ital D]-dimensional spin neurons ([ital D][ge]1). Our model is equivalent to the Hopfield model in the case of [ital D]=1 and is related to the clock neural network in the case of [ital D]=2. We derive the free energy of our model using the replica symmetric theory. When a finite number of patterns are embedded they are found to be retrievable if the tempeature [ital T] is lower than 1/[ital D]. The phase diagram and the storage capacity of the network are also obtained with the storage capacity [alpha][sub [ital c]]=0.0743 ([ital D]=2) and [alpha][sub [ital c]]=0.0432 ([ital D]=3) for [ital T]=0.

• OSTI ID: 6644999
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 51:2; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CRYSTAL MODELS
DIAGRAMS
ENERGY
FREE ENERGY
FUNCTIONS
HAMILTONIAN FUNCTION
ISING MODEL
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL MODELS
MECHANICS
NEURAL NETWORKS
PHASE DIAGRAMS
PHYSICAL PROPERTIES
STATISTICAL MECHANICS
THERMODYNAMIC PROPERTIES