Deep Neural Networks: A Formulation via Non-Archimedean Analysis

Authors

• Wilson A. Zuniga-Galindo, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

7-27-2026

Abstract

We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified by using numbers in the ring of integers of non-Archimedean 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.

Comments

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Recommended Citation

Zúñiga-Galindo, Wilson A. "Deep neural networks: a formulation via non-archimedean analysis." Journal of Fourier Analysis and Applications 32, no. 4 (2026): 77. https://doi.org/10.1007/s00041-026-10290-y

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Journal of Fourier Analysis and Applications

DOI

10.1007/s00041-026-10290-y