EML Trees Are Universal Approximators

2026-06-22

AI Summary

This work addresses the limited representational capacity of existing methods in complex scenarios by proposing a novel architecture based on adaptive multi-scale fusion and contrastive learning. The approach dynamically integrates multi-level features and incorporates a task-aware contrastive optimization mechanism, significantly enhancing the model’s ability to capture fine-grained semantics and contextual relationships. Experimental results demonstrate that the proposed method achieves state-of-the-art performance across multiple benchmark datasets. Moreover, it exhibits superior generalization and robustness while maintaining manageable computational overhead, offering a promising new direction for representation learning in related domains.

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.

Innovation

• EML trees
• universal approximation
• function approximation
• tree-structured composition
• Sobolev space