English

Studying number theory with deep learning: a case study with the M\"obius and squarefree indicator functions

Number Theory 2025-07-29 v2 Machine Learning

Abstract

Building on work of Charton, we train small transformer models to calculate the M\"{o}bius function μ(n)\mu(n) and the squarefree indicator function μ2(n)\mu^2(n). The models attain nontrivial predictive power. We apply a mixture of additional models and feature scoring to give a theoretical explanation.

Cite

@article{arxiv.2502.10335,
  title  = {Studying number theory with deep learning: a case study with the M\"obius and squarefree indicator functions},
  author = {David Lowry-Duda},
  journal= {arXiv preprint arXiv:2502.10335},
  year   = {2025}
}
R2 v1 2026-06-28T21:44:43.085Z