提出新型神经网络算子，提升函数逼近精度与收敛速度。
Convergence Analysis of Max-Min Exponential Neural Network Operators in Orlicz Space
- 采用最大最小策略构建指数型神经网络算子。
- 在Orlicz空间中实现点态与一致收敛，理论证明收敛阶数。
- 适合研究函数逼近与神经网络泛化能力的学者。
本文提出一种基于最大最小策略的指数型神经网络算子，用于函数逼近。将该框架扩展至Max Min Kantorovich型指数神经网络算子，并研究其逼近性质。针对单变量函数，分析了点态与一致收敛性。通过对数模连续性刻画收敛阶，给出相应的收敛速率估计。进一步在Orlicz空间设定下考察了Max Min Kantorovich型算子的收敛行为。通过合适的核函数与Sigmoid激活函数，提供图形化展示函数逼近误差。
原文摘要 · Abstract (English)
In this current work, we propose a Max Min approach for approximating functions using exponential neural network operators. We extend this framework to develop the Max Min Kantorovich-type exponential neural network operators and investigate their approximation properties. We study both pointwise and uniform convergence for univariate functions. To analyze the order of convergence, we use the logarithmic modulus of continuity and estimate the corresponding rate of convergence. Furthermore, we examine the convergence behavior of the Max Min Kantorovich type exponential neural network operators within the Orlicz space setting. We provide some graphical representations to illustrate the approximation error of the function through suitable kernel and sigmoidal activation functions.
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