Asymptotic Expansion for Neural Network Operators of the Kantorovich Type and High Order of Approximation

Abstract In this paper, we study the rate of pointwise approximation for neural network operators Kantorovich type. This result is obtained proving a certain asymptotic expansion above and then by establishing Voronovskaja type formula. A central role in resuts played truncated algebraic moments density functions generated suitable sigmoidal functions. Furthermore, to improve convergence, consider finite linear combinations operators, also latter case, obtain theorem. Finally, concrete examples activation have been deeply discussed, together with case rectified unit (ReLu) function, very used connection deep networks.