Diversity of EML-type operators

Abstract: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.

25 pages, 2 figures, see also the TNG Big Techday conference recording at this https URL. Wolfram Mathematica implementation of a Goldstern-type single operator in the Appendix. Follow-up to arXiv:2603.21852

Symbolic Computation (cs.SC); Machine Learning (cs.LG); Logic (math.LO)

I.2.6; F.4.1; G.1.2

arXiv:2609.11210 [cs.SC]

(or arXiv:2609.11210v1 [cs.SC] for this version)

https://doi.org/10.48550/arXiv.2609.11210 arXiv-issued DOI via DataCite (pending registration)