Modeling of auditory spatial receptive fields with spherical approximation functions.

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Abstract
A spherical approximation technique is presented that affords a mathematical characterization of a virtual space receptive field (VSRF) based on first-spike latency in the auditory cortex of cat. Parameterizing directional sensitivity in this fashion is much akin to the use of difference-of-Gaussian (DOG) functions for modeling neural responses in visual cortex. Artificial neural networks and approximation techniques typically have been applied to problems conforming to a multidimensional Cartesian input space. The problem with using classical planar Gaussians is that radial symmetry and consistency on the plane actually translate into directionally dependent distortion on spherical surfaces. An alternative set of spherical basis functions, the von Mises basis function (VMBF), is used to eliminate spherical approximation distortion. Unlike the Fourier transform or spherical harmonic expansions, the VMBFs are nonorthogonal, and hence require some form of gradient-descent search for optimal estimation of parameters in the modeling of the VSRF. The optimization equations required to solve this problem are presented. Three descriptive classes of VSRF (contralateral, frontal, and ipsilateral) approximations are investigated, together with an examination of the residual error after parameter optimization. The use of the analytic receptive field model in computational models of population coding of sound direction is discussed, together with the importance of quantifying receptive field gradients. Because spatial hearing is by its very nature three dimensional or, more precisely, two dimensional (directional) on the sphere, we find that spatial receptive field models are best developed on the sphere.