Related papers: $p$-adic Character Neural Network

$p$-adic Character Neural Network

URL: http://arxiv.org/abs/2603.29905v1
Date: Tue, 31 Mar 2026 15:50:10 GMT
Title: $p$-adic Character Neural Network
Abstract summary: We use a single injective $p$-adic character on the topological Abelian group $mathbbZ_p$ as an activation function.<n>We prove the $p$-adic universal approximation for this formulation of $p$-adic neural network, and reduce it to the feasibility problem of equations over the finite ring of integers modulo a power of $p$.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 $p$.

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