Finite-dimensional neural networks storing structured patterns

Hidetoshi Nishimori, W. Whyte, D. Sherrington

研究成果: Article査読

5 被引用数 (Scopus)

抄録

We investigate thermodynamic properties of neural networks defined on a finite-dimensional lattice designed to store and retrieve patterns with structure. Our aim is to draw phase diagrams with axes of temperature and a parameter controlling the structure of patterns. Gauge symmetry is used to derive various exact or rigorous results on the properties of the system. These results put strong constraints on the possible phase diagrams. We also use Peierls arguments to prove the existence of a ferromagnetic phase and of a phase with finite overlap order in certain regions of the phase diagram. Our conclusion on the phase diagram is that, first, if the number of embedded patterns is smaller than a critical value, the system has in general three phases: a paramagnetic phase, a retrieval phase, and a ferromagnetic phase accompanied by finite overlap order. For larger numbers of embedded patterns, a ferromagnetic phase without overlap order appears in addition. The retrieval phase without ferromagnetic order may be replaced by a spin glass phase for large numbers of embedded patterns.

本文言語English
ページ(範囲)3628-3642
ページ数15
ジャーナルPhysical Review E
51
4
DOI
出版ステータスPublished - 1995
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • 凝縮系物理学

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