Can small transformers learn the language of Coxeter groups?

The field of mechanistic interpretability is well-suited to collaborative projects between mathematicians and AI researchers. This work describes one such project. We trained a small transformer to learn the language of the Coxeter group affine A2, best known as the symmetries of the tiling of the Euclidean plane by equilateral triangles. We then formulated and proved a word-theoretic conjecture about affine A2 after observing the attention patterns of the trained model.