MODELING OF AUDITORY SPATIAL RECEPTIVE-FIELDS WITH SPHERICAL APPROXIMATION FUNCTIONS

A spherical approximation technique is presented that affords a mathem atical characterization of a virtual space receptive field (VSRF) base d on first-spike latency in the auditory cortex of cat. Parameterizing directional sensitivity in this fashion is much akin to the use of di fference-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 multidimensio nal Cartesian input space. The problem with using classical planar Gau ssians is that radial symmetry and consistency on the plane actually t ranslate 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 distort ion. Unlike the Fourier transform or spherical harmonic expansions, th e VMBFs are nonorthogonal, and hence require some form of gradient-des cent search for optimal estimation of parameters in the modeling of th e 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 exa mination of the residual error after parameter optimization. The use o f the analytic receptive field model in computational models of popula tion coding of sound direction is discussed, together with the importa nce of quantifying receptive field gradients. Because spatial hearing is by its very nature three dimensional or, more precisely, two dimens ional (directional) on the sphere, we find that spatial receptive fiel d models are best developed on the sphere.