Studying number theory with deep learning: a case study with the M"obius and squarefree indicator functions
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Abstract (arXiv)
Building on work of Charton, we train small transformer models to calculate the M"obius 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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 8 of its 22 references that are in the map. First posted on arXiv 14 Feb 2025.
Builds on
8 of 22 references.
References · 8
- 2020Generative Language Modeling for Automated Theorem Provingcited by 388
- 2015Neural GPUs Learn Algorithmscited by 121
- 2021Linear algebra with transformerscited by 63
- 2020Teaching Temporal Logics to Neural Networkscited by 51
- 2023Learning the greatest common divisor: explaining transformer predictionscited by 33
- 2021Transformer-based Machine Learning for Fast SAT Solvers and Logic Synthesiscited by 9
- 2013Detecting squarefree numberscited by 2
- 2024Transformers to Predict the Applicability of Symbolic Integration Routinescited by 2
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Citing papers per year: 2026: 1.
1 paper.
- 2026On (not) learning the M"obius functioncited by 0
- 2026On (not) learning the M"obius function25 Apr 2026