[2402.00094] Deep Neural Networks: A Formulation Via Non-Archimedean Analysis

Computer Science > Neural and Evolutionary Computing arXiv:2402.00094 (cs) [Submitted on 31 Jan 2024 (v1), last revised 30 Mar 2026 (this version, v2)] Title:Deep Neural Networks: A Formulation Via Non-Archimedean Analysis Authors:W. A. Zúñiga-Galindo View a PDF of the paper titled Deep Neural Networks: A Formulation Via Non-Archimedean Analysis, by W. A. Z\'u\~niga-Galindo View PDF HTML (experimental) 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. Comments: Subjects: Neural and Evolutionary Computing (cs.NE); Artificial Intelligence (cs.AI); Machine Learning (cs.LG) MSC classes: Primary 68T07, 65D15, Secondary 41A30, 11S85 Cite as: arXiv:2402.00094 [cs.NE]   (or arXiv:2402.00094v2 [cs.NE] for this version)   https://doi.org/10.48550/arXiv.2402.00094 Focus to learn more arXiv-issued DOI via DataCite Submission history From: W. A. Zuniga-Galindo [view email] [v1] Wed, 31 Jan 2024 14:49:44 UTC (25 KB) [v2] Mon, 3...