What does this research mean for the field?

$$p$$-adic polynomial regression can effectively detect digitwise noise in data. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The research aims to develop a novel framework for p-adic optimization as a limit of the least squares method to facilitate polynomial regression.

March 15, 2026

p-Adic Polynomial Regression Detecting Digitwise Noise

Key Points

The research aims to develop a novel framework for p-adic optimization as a limit of the least squares method to facilitate polynomial regression.
Formulated p-adic optimization as an infinitesimal limit of least squares method.
Introduced several algorithms for dealing with p-adic optimization.
Addressed a maximal feasible subsystem problem over the finite field F_p.
Employed heuristic approaches to tackle the inherent complexity of the optimization.
Proposed algorithms show potential for efficient digitwise noise detection.
Demonstrated the effectiveness of p-adic regression under sparse noise conditions.
Found that heuristic methods can effectively approximate solutions to complex optimization problems.

Abstract

We propose a new formulation of p -adic optimisation as the infinitesimal limit of the least squares method, and introduce several algorithms for p -adic optimisation. Since the optimisation problem includes the maximal feasible subsystem problem of linear equations over the finite field Fₚ, which is APX-complete, i. e. complete for the class of problems which allow constant-factor approximations, by E. Amaldi and V. Kann, we mainly deal with heuristic approaches to the p -adic optimisation under mild assumptions. In particular, we deal with p -adic polynomial regression under the assumption that noise occurs digitwise sparsely.

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p-Adic Polynomial Regression Detecting Digitwise Noise

Key Points

Abstract

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