George A. Anastassiou
Generalized Logistic Neural Networks as Positive Linear Operators over Infinite Domain
Neural Parallel and Scientific Computations 33 (2025) 39-54

https://doi.org/10.46719/NPSC2025.33.03

ABSTRACT.
Generalized Logistic 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, deformed and symmetrized Generalized Logistic 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 under initial conditions.

AMS (MOS) Subject Classification: 41A17, 41A25, 41A36

Keywords and phrases: Neural Network operators, Positive linear Operators, modulus of continuity, quantitative approximation to the unit, infinite domain,. generalized logistic activation function.