title: A mathematical analysis of the development of oriented receptive fields in Linsker's model.
abstract: We consider Linsker's neural network model and study how oriented receptive fields (RFs) are developed at layer F-->G mathematically. We concentrate on the Mexican-hat correlation function and show that this function determines the spatial frequency of RFs. We also focus on the role of the arbor function. Two types of arbor functions, a Gaussian type and a step type, are considered, and it is shown that the Gaussian arbor function develops center-surround RFs while the step arbor function enables the development of multi-lobed RFs in addition to center-surround RFs. The roles of Linsker's parameters k1, k2 are also discussed.
authors.affiliation: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Japan. tyam@is.titech.ac.jp
authors.forename: Tadashi
authors.initials: T
authors.lastname: Yamazaki
mesh_terms: D005583:Fourier Analysis; D008954:Models, Biological; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D009949:Orientation / Q000502:physiology; D014794:Visual Fields / Q000502:physiology*