提出多变量最大最小神经网络算子，实现高效稳定函数逼近。
Max-Min Neural Network Operators For Approximation of Multivariate Functions
- 基于Sigmoid激活的多变量最大最小神经算子框架
- 证明了逐点与一致收敛性，并给出逼近阶量化估计
- 理论与应用兼具，适合函数逼近研究者参考
本文构建了基于最大最小神经网络算子的多变量函数逼近框架。在近期单变量最大最小算子进展基础上，我们提出并分析了由Sigmoid函数激活的新多变量算子。建立了逐点与一致收敛定理，并通过连续性模和多变量广义绝对矩推导出逼近阶的定量估计。结果表明，多变量最大最小结构不仅具有代数美感，更在理论与实际应用中提供了高效且稳定的逼近工具。
原文摘要 · Abstract (English)
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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