# Coxeter groups

A small transformer with a single attention layer was trained to predict the left and right descent sets of elements of the infinite Coxeter group Ã₂, meaning the possible first and last letters of minimal-length words. Test accuracy improved as training data moved from random words to reduced words to ShortLex normal-form words: the random-word and reduced-word datasets each began deteriorating at some length, while the set of all 1,998 ShortLex words of length at most 36 never deteriorated. From the trained model's attention patterns, the researchers formulated and independently proved two word-theory propositions about right and left descent sets.

A small transformer with a single attention layer was trained to predict the left and right descent sets of elements of the infinite Coxeter group Ã₂, meaning the possible first and last letters of minimal-length words. Test accuracy improved as training data moved from random words to reduced words to ShortLex normal-form words: the random-word and reduced-word datasets each began deteriorating at some length, while the set of all 1,998 ShortLex words of length at most 36 never deteriorated. From the trained model's attention patterns, the researchers formulated and independently proved two word-theory propositions about right and left descent sets.