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.