Deep Neural Networks: A Formulation via Non-Archimedean Analysis
Abstract
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.
Fields of Study & Subjects
Computational Physics and Python Applications
Neural Networks and Applications
Publication details
- Journal / source
- Journal of Fourier Analysis and Applications
- Publisher
- Springer Science and Business Media LLC
- Volume
- 32
- Issue
- 4
- Publication date
- 27 July 2026
- Language
- EN