Deep Neural Networks: A Formulation Via Non-Archimedean Analysis

Authors

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

Document Type

Article

Publication Date

2024

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.

Recommended Citation

Zúñiga-Galindo, W. A. "Deep Neural Networks: A Formulation Via Non-Archimedean Analysis." arXiv preprint arXiv:2402.00094 (2024).