EML树可逼近任意高阶光滑函数，为函数拟合提供新理论框架。
EML Trees Are Universal Approximators
- 用树结构组合EML函数，实现函数逼近
- 能逼近W^{k,∞}类函数，理论上具有通用性
- 提出可学习的算法，适合理论研究与优化问题
最近提出的EML（Exp-Minus-Log）函数是NAND门的连续模拟，可作为构建基本函数的组合单元。本文研究了EML函数的树状组合表达能力，证明此类树对W^{k,∞}类函数（k∈ℕ）具有通用逼近性，借鉴经典神经网络逼近理论，并通过显式构造模仿多项式表示的EML树实现。进一步提出一种配备可调参数的EML树学习算法，并在实际优化问题中验证其可行性。结果确立了EML树作为函数逼近的理论基础框架。
原文摘要 · Abstract (English)
The recently introduced EML (Exp-Minus-Log) function acts as continuous analogue of NAND gates, providing a compositional building block capable of representing elementary functions. In this work, we study the expressive power of tree-structured compositions of EML functions. We show that such trees enjoy a universal approximation property for functions in $W^{k, \infty}$ for $k \in \mathbb N$, drawing on classical neural network approximation arguments while exploiting the ability to explicitly construct EML trees that mimic polynomial representations. We further propose a learning algorithm for EML-type trees equipped with fitting parameters, and demonstrate its feasibility in practical optimization problems. Our results establish EML trees as a theoretically grounded framework for function approximation.
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