Approximation by Spherical Neural Networks with Sigmoidal Functions.

This paper addresses the approximation by feed-forward neural networks (FNNs) with sigmoidal active functions on the unit sphere. Firstly, some nice properties of typical logistic function are derived, and the function and its derivatives are taken as active functions to construct spherical FNNs approximation operators, where the spherical Cesáro mean is employed as a key link in constructing the operators. Subsequently, by using spherical quadrature formula and Marcinkiewicz-Zygmund type inequality, the error of the operators approximating continuous spherical function is estimated, and a Jackson type theorem is established by means of the best polynomial approximation. [ABSTRACT FROM AUTHOR]