A mathematical analysis of the development of oriented receptive fields in Linsker's model
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.
mathematical analysis development oriented receptive field linsker mexican-hat correlation function arbor function self-organization correlation based model