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

Abstract

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