Deep Neural Networks: A Formulation Via Non-Archimedean Analysis
Neural and Evolutionary Computing
2026-03-31 v2 Artificial Intelligence
Machine Learning
Abstract
We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural hierarchical organization as infinite rooted trees. Natural morphisms on these rings allow us to construct finite multilayered architectures. The new DNNs are robust universal approximators of real-valued functions defined on the mentioned rings. We also show that the DNNs are robust universal approximators of real-valued square-integrable functions defined in the unit interval.
Cite
@article{arxiv.2402.00094,
title = {Deep Neural Networks: A Formulation Via Non-Archimedean Analysis},
author = {W. A. Zúñiga-Galindo},
journal= {arXiv preprint arXiv:2402.00094},
year = {2026}
}
Comments
Several typos and minor errors were corrected. New references were added