p-Adic Polynomial Regression as Alternative to Neural Network for Approximating p-Adic Functions of Many Variables

A method for approximating continuous functions Z₏^n₏ by a linear superposition of continuous functions Z₏₏ 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.