Studying number theory with deep learning: a case study with the Möbius and squarefree indicator functions
This work addresses the problem of applying deep learning to number theory, which is significant for researchers in the field of mathematics and computer science, and is an incremental step in this area.
This study tackled the problem of calculating the Möbius function and the squarefree indicator function using deep learning, resulting in small transformer models with nontrivial predictive power. The models were able to attain this power, although no specific numbers are given.
Building on work of Charton, we train small transformer models to calculate the Möbius function $μ(n)$ and the squarefree indicator function $μ^2(n)$. The models attain nontrivial predictive power. We apply a mixture of additional models and feature scoring to give a theoretical explanation.