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

• URL: http://arxiv.org/abs/2503.23488v2
• Date: Tue, 01 Apr 2025 08:48:08 GMT
• Title: $p$-Adic Polynomial Regression as Alternative to Neural Network for Approximating $p$-Adic Functions of Many Variables
• Authors: Alexander P. Zubarev,
• Abstract summary: A regression model is constructed that allows approximating continuous functions with any degree of accuracy.<n>The proposed model can be considered as a simple alternative to possible $p$-adic models based on neural network architecture.
• Score: 55.2480439325792
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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