A geometric relation of the error introduced by sampling a language model's output distribution to its internal state
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 $\mathfrak{so}(n)$-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 repre...
| Authors | Albert F. Modenbach |
|---|---|
| Primary category | cs.LG |
| Published | 6 May 2026 |
| Last updated at source | 9 May 2026 |
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