Deep Neural Networks: A Formulation Via Non-Archimedean Analysis
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 8 of its 42 references that are in the map. First posted on arXiv 31 Jan 2024.
Builds on
8 of 42 references.
References · 8
- 2018Universality of Deep Convolutional Neural Networkscited by 176
- 2021The Principles of Deep Learning Theorycited by 173
- 2019Deep Neural Network Approximation Theorycited by 93
- 2021The staircase property: How hierarchical structure can guide deep learningcited by 62
- 2019Approximation spaces of deep neural networkscited by 51
- 2021Unified field theoretical approach to deep and recurrent neuronal networkscited by 20
- 2022p-Adic Statistical Field Theory and Deep Belief Networkscited by 2
- 2023Hierarchical Wilson-Cowan Models and Connection Matricescited by 2
Built on by
Citing papers per year: 2026: 1.
1 paper.