Multivariate Generalized Logistic Neural Networks on Infinite Domain as Positive Linear Operators and a Taste of Measure Theory
DOI:
https://doi.org/10.65135/atsf.2026.7Keywords:
Multivariate neural network operators, quantitative approximation to the unit, infinite domain, probability measure, generalized logistic functionAbstract
We study a family of multivariate neural network operators on the infinite domain, constructed via a symmetrized generalized logistic activation function. These operators are treated as positive linear mappings acting on bounded and continuous functions. We establish quantitative approximation results in terms of moduli of continuity and Frechet derivatives. The operators are also examined within a probabilistic framework, highlighting their connections to measure theory.
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