Abstract
GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens. Viewing this sensitivity as a geometric property, we derive an so(n)-valued 1-form that depends only on the geometry of the token embeddings. Despite this purely geometric origin, we show that its curvature is semantically meaningful: On chess reasoning tasks, the curvature couples to the world model of an off-the-shelf instruction-tuned model, with transformations clustering by board region and respecting piece importance. Our findings suggest that token space geometry directly reflects how models internally represent problems.