A mathematical analysis of the development of oriented receptive fields in Linsker's model

Authors:
Tadashi Yamazaki
Affiliations:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Meguro, Tokyo 152-8552, Japan
Venue:
Neural Networks
Year:
2002

Citing 1
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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.