$p$-adic Character Neural Network

ArXi:2603.29905v1 Announce Type: cross We propose a new frame work of $p$-adic neural network. Unlike the original $p$-adic neural network by S.\ Albeverio, A.\ Khrenniko, 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.