EML Trees Are Universal Approximators
Provides a new theoretically grounded framework for function approximation, but the practical impact is currently limited to demonstration on optimization problems.
The paper shows that tree-structured compositions of EML functions are universal approximators for functions in Sobolev spaces, and proposes a learning algorithm for such trees with practical feasibility.
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.