Max-Min Neural Network Operators For Approximation of Multivariate Functions

• URL: http://arxiv.org/abs/2601.07886v1
• Date: Mon, 12 Jan 2026 06:14:05 GMT
• Title: Max-Min Neural Network Operators For Approximation of Multivariate Functions
• Authors: Abhishek Yadav, Uaday Singh, Feng Dai,
• Abstract summary: We develop a framework for approximation by max-min neural network operators.<n>We establish pointwise and uniform convergence theorems and derive estimates for the order of approximation.
• Score: 4.5657111459153885
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we develop a multivariate framework for approximation by max-min neural network operators. Building on the recent advances in approximation theory by neural network operators, particularly, the univariate max-min operators, we propose and analyze new multivariate operators activated by sigmoidal functions. We establish pointwise and uniform convergence theorems and derive quantitative estimates for the order of approximation via modulus of continuity and multivariate generalized absolute moment. Our results demonstrate that multivariate max-min structure of operators, besides their algebraic elegance, provide efficient and stable approximation tools in both theoretical and applied settings.

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