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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.29905 |
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| _version_ | 1866917375295619072 |
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| author | Mihara, Tomoki |
| author_facet | Mihara, Tomoki |
| contents | 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 $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29905 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $p$-adic Character Neural Network Mihara, Tomoki Number Theory Machine Learning 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 $p$. |
| title | $p$-adic Character Neural Network |
| topic | Number Theory Machine Learning |
| url | https://arxiv.org/abs/2603.29905 |