Abstract
A method for approximating continuous functions \(\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}\) by a linear superposition of continuous functions \(\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}\) is presented and a polynomial regression model is constructed that allows approximating such functions with any degree of accuracy. A physical interpretation of such a model is given and possible methods for its training are discussed. The proposed model can be considered as a simple alternative to possible \(p\) -adic models based on neural network architecture.
