发表机构
Jagiellonian University（雅盖隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文枚举并分类EML算子的多种变体，澄清常见误解，并提出用有理函数替代矩阵运算的莫比乌斯层及激活函数eml(x,1/x)，以在神经网络的有理推广中评估所有初等函数。
AI 中文摘要
EML算子的发现足以评估标准的显式纯超越初等函数，已在多个科学学科中引发广泛兴趣和讨论。然而，大多数作者聚焦于二元EML算子本身，而如今已知许多性质略有不同的相似变体。本文试图通过枚举和分类这些变体来弥补这一空白。我们还借此机会澄清与EML算子相关的常见误解。主要目标——在尽可能接近已被证实的神经网络架构（该架构将矩阵乘法与单一单变量非线性激活函数相结合）中进行符号回归——仍然遥不可及。相反，我们提出一个莫比乌斯层，用有理函数替代矩阵运算，并展示最近发现的激活函数eml(x,1/x)，该函数允许分别恢复exp(x)和ln(x)，从而在神经网络的有理推广中评估所有初等函数。
英文摘要
The discovery of the EML operator, sufficient to evaluate the standard explicit purely transcendental elementary functions, has led to considerable interest and discussion across multiple scientific disciplines. However, most authors have focused on the binary EML itself, while numerous similar variants with slightly different properties are now known. This article attempts to close this gap by enumerating and classifying them. We also take this opportunity to clarify common misconceptions related to the EML operator. The principal goal, symbolic regression within an architecture as close as possible to proven neural networks which combine matrix multiplication with a single univariate non-linear activation function, remains beyond reach. Instead, we propose a Möbius layer, with rational functions replacing matrix operations, and showcase the recently discovered activation function eml(x,1/x), which allows exp(x) and ln(x) to be recovered separately, and hence all elementary functions to be evaluated within a rational generalization of the neural network.
Comments25 pages, 2 figures, see also the TNG Big Techday conference recording at https://youtu.be/8942GJdrCYI?si=Q4XO0ZlQRK9JDAvK. Wolfram Mathematica implementation of a Goldstern-type single operator in the Appendix. Follow-up to arXiv:2603.21852
