$p$-Adic Polynomial Regression as Alternative to Neural Network for Approximating $p$-Adic Functions of Many Variables
This provides a simpler method for approximating p-adic functions, which is incremental and domain-specific to mathematical analysis.
The paper tackles the problem of approximating continuous p-adic functions of many variables by proposing a polynomial regression model as an alternative to neural networks, achieving any desired degree of accuracy.
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.