The construction and approximation of feedforward neural network with hyperbolic tangent function

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.