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.
Related
- Stability of Serrin-Type Overdetermined Problems for the p-Laplacian and Related Operators
- Weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels
- The Dry Ten Martini Problem for subcritical Type I operators
- Eigenvectors and Eigenvalues of p-Curvature Operators for KZ--type Differential Connections
- Multilinear rough singular integral operators may not be of the weak type at the endpoint
BibTeX
@misc{odrzywolek2026diversity,
title = {{Diversity of EML-type operators}},
author = {Andrzej Odrzywołek},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11210},
eprint = {2609.11210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11210},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diversity of EML-type operators
AU - Andrzej Odrzywołek
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11210
UR - https://arxiv.org/abs/2609.11210
AB - 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.
ER -