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

Abstract

Building on work of Charton, we train small transformer models to calculate the Möbius function $\hat{I}¼(n)$ and the squarefree indicator function $\hat{I}{¼}^2(n)$. The models attain nontrivial predictive power. We apply a mixture of additional models and feature scoring to give a theoretical explanation.