A geometric relation of the error introduced by sampling a language model's output distribution to its internal state

• URL: http://arxiv.org/abs/2605.04899v2
• Date: Sat, 09 May 2026 14:24:36 GMT
• Title: A geometric relation of the error introduced by sampling a language model's output distribution to its internal state
• Abstract summary: GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens.<n>Our findings suggest that token space geometry directly reflects how models internally represent problems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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 $\mathfrak{so}(n)$-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 represent problems.

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