Spontaneous symmetry breaking and the formation of columnar structures in the primary visual cortex II --- Local organization of orientation modules

1996/11/05 by Kengo Yamagishi, Yamagishi, Kengo
Computer Science · Neuroscience · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Neural dynamics and brain function #Topological and Geometric Data Analysis #Visual perception and processing mechanisms #adap-org #nlin.AO

paper · pdf · doi:10.48550/arxiv.adap-org/9611002

36 pages Latex2.09 and eps figures. Needs epsf.sty, amssym.def, and Type1 TeX-fonts of BlueSky Res. for correct typo in graphics files

arxiv created 1996/11/05 · openalex publication_date 1996/11/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Self-organization of orientation-wheels observed in the visual cortex is discussed from the view point of topology. We argue in a generalized model of Kohonen's feature mappings that the existence of the orientation-wheels is a consequence of Riemann-Hurwitz formula from topology. In the same line, we estimate partition function of the model, and show that regardless of the total number N of the orientation-modules per hypercolumn the modules are self-organized, without fine-tuning of parameters, into definite number of orientation-wheels per hypercolumn if N is large.

Citations

• Self-organized formation of topologically correct feature maps

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