EML Trees Are Universal Approximators
2026-06-22 • Machine Learning
Machine LearningNeural and Evolutionary ComputingSymbolic Computation
AI summaryⓘ
The authors study a new mathematical function called EML, which works like a smooth version of logical NAND gates and can be combined in tree structures to represent different functions. They prove that these EML trees can approximate a wide range of functions accurately, using ideas similar to those from neural networks. The authors also develop a way to train these trees on data and show it works in practice. Overall, their work supports using EML trees as a solid method for approximating functions.
EML functionNAND gatefunction approximationuniversal approximationneural networkstree structuresW^{k, ∞} function spacepolynomial representationlearning algorithmoptimization
Authors
Joe Germany, Elie Abdo, Joseph Bakarji
Abstract
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.