Studying number theory with deep learning: a case study with the Möbius and squarefree indicator functions

2025/02/14 by David Lowry-Duda, Lowry-Duda, David
Mathematics · #Analytic Number Theory Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Number Theory (math.NT) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2502.10335

openalex publication_date 2025/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Building on work of Charton, we train small transformer models to calculate the Möbius function μ(n) and the squarefree indicator function μ²(n). The models attain nontrivial predictive power. We apply a mixture of additional models and feature scoring to give a theoretical explanation.

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