Statistical analysis of 250,000 Boyd Mahler-measure constants reveals p-adic valuation laws (P(v_p = r) ≈ p^{-r} for p ≥ 5) and a lower-bound conjecture at p = 2, with a conditional proof on a subfamily.
Int2Int: a framework for mathematics with transformers
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abstract
This paper documents Int2Int, an open source code base for using transformers on problems of mathematical research, with a focus on number theory and other problems involving integers. Int2Int is a complete PyTorch implementation of a transformer architecture, together with training and evaluation loops, and classes and functions to represent, generate and decode common mathematical objects. Ancillary code for data preparation, and Jupyter Notebooks for visualizing experimental results are also provided. This document presents the main features of Int2Int, serves as its user manual, and provides guidelines on how to extend it. Int2Int is released under the MIT licence, at https://github.com/f-charton/Int2Int.
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Machine learning the arithmetic of Boyd's Mahler measure conjectures
Statistical analysis of 250,000 Boyd Mahler-measure constants reveals p-adic valuation laws (P(v_p = r) ≈ p^{-r} for p ≥ 5) and a lower-bound conjecture at p = 2, with a conditional proof on a subfamily.