--> Mathematics > Number Theory arXiv:2603.29905 (math) [Submitted on 31 Mar 2026] Title: $p$-adic Character Neural Network Authors: Tomoki Mihara View a PDF of the paper titled $p$-adic Character Neural Network, by Tomoki Mihara View PDF HTML (experimental) Abstract: We propose a new frame work of $p$-adic neural network. Unlike the original $p$-adic neural network by S.\ Albeverio, A.\ Khrennikov, and B.\ Tirrozi using a family of characteristic functions indexed by hyperparameters of precision as activation functions, we use a single injective $p$-adic character on the topological Abelian group $\mathbb{Z}_p$ of $p$-adic integers as an activation function. We prove the $p$-adic universal approximation theorem for this formulation of $p$-adic neural network, and reduce it to the feasibility problem of polynomial equations over the finite ring of integers modulo a power of $p$. Subjects: Number Theory (math.NT) ; Machine Learning (cs.LG) Cite as: arXiv:2603.29905 [math.NT] (or arXiv:2603.29905v1 [math.NT] for this version) https://doi.org/10.48550/arXiv.2603.29905 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tomoki Mihara [ view email ] [v1] Tue, 31 Mar 2026 15:50:10 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled $p$-adic Character Neural Network, by Tomoki Mihara View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2026-03 Change to browse by: cs cs.LG math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation &times; loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) Links to Code Toggle Papers with Code ( What is Papers with Code? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? )