Statistical Mechanics of Mexican-Hat-Type Horizontal Connection

• Takiyama Ken

  Graduate School of Frontier Sciences, The University of Tokyo

• Naruse Yasushi

  Kobe Advanced ICT Research Center

• Okada Masato

  Graduate School of Frontier Sciences, The University of Tokyo Brain Science Institute

Abstract

We propose a multi-hypercolumn model consisting of M hypercolumns. Adjacent hypercolumns interact with each other through horizontal connections. This model consists of inter-hypercolumn and intra-hypercolumn Mexican-hat-type interactions. We analyze our model using statistical–mechanical methods. In this model, we theoretically show that the free energy is equivalent to the posterior distribution in the Bayesian framework in extremely weak inter-hypercolumn interactions. A numerical experiment supports this equivalence. The results of this study reveal the relationship between a microscopic neural structure and a macroscopic computational theory.

Journal

• Journal of the Physical Society of Japan

  Journal of the Physical Society of Japan 78 (6), 064002-064002, 2009

  THE PHYSICAL SOCIETY OF JAPAN

Keywords

• hypercolumn
• horizontal connection
• Mexican hat
• statistical mechanics
• Bayesian inference
• image restoration
• von-Mises distribution

Details

• CRID: 1390001204196449920
• NII Article ID: 130005437406
• NII Article ID: 10025960971
• NII Article ID: 210000107826
• NII Book ID: AA00704814
• DOI: 10.1143/jpsj.78.064002
• ISSN: 13474073
• ISSN: 00319015
• NDL BIB ID: 10252237
• Web Site: http://id.ndl.go.jp/bib/10252237
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I10252237
• Web Site: https://journals.jps.jp/doi/pdf/10.1143/JPSJ.78.064002
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed