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Life sciences · Preprint
arXiv · September 10, 2026
Posted before peer review. The findings may change or fail to hold.
This is a preprint presenting a mathematical and computational framework for operators and activation functions in neural network architectures. It classifies variants of the EML operator and proposes a Möbius layer using rational functions, but reports no empirical validation, performance metrics, or clinical application.
Preprint.
EML operator variants with different properties are enumerated and classified A Möbius layer is proposed using rational functions as an alternative to matrix operations The activation function eml(x,1/x) allows separate recovery of exp(x) and ln(x)
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This is an unreviewed preprint describing mathematical operators and their properties; it reports no empirical data, clinical outcomes, or experimental validation of claims.
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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.
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