Neural Networks as Positive Linear Operators
Year: 2025
Type: article
Abstract: Basic neural network operators are interpreted as positive linear operators and the 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. I explore the space of continuous functions on a compact interval of the real line to the reals. I study quantitatively the rate of convergence of these neural network operators to the unit operator. The studied inequalities involve the modulus of continuity of the function under approximation or its derivative. I produce uniform and Lp, p≥1, approximation results via these inequalities. The convexity of functions is also taken into consideration.
Source: Mathematics
DOI: 10.3390/math13071112
Author: George A. Anastassiou
Institution: University of Memphis
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4408927556