Neural networks in infinite domain as positive linear operators

Abstract. Neural network operators in infinite domain are interpreted as positive linear operators and related general theory applies to them. These operators are induced by a symmetrized density function deriving from the parametrized and deformed hyperbolic tangent activation function. We are acting on the space of continuous and bounded functions on the real line to the reals. We study quantitatively the rate of convergence of these neural network operators to the unit operator. Our inequalities involve the modulus of continuity of the function under approximation or its derivative.