Abstract
In autoregressive large language models (LLMs), temporal straightening offers an account of how the next-token prediction objective shapes representations. Models learn to progressively straighten the representational trajectory of input sequences across layers, potentially facilitating next-token prediction via linear extrapolation. However, a direct link between this trajectory and token-level behavior has been missing. We provide such a link by relating contextual curvature-a geometric measure of how sharply the representational trajectory bends over recent context-to next-token entropy. Across two models (GPT-2 XL and Pythia-2.8B), contextual curvature is correlated with entropy, and this relationship emerges during training. Perturbation experiments reveal selective dependence: manipulating curvature through trajectory-aligned interventions reliably modulates entropy, while geometrically misaligned perturbations have no effect. Finally, regularizing representations to be straighter during training modestly reduces token-level entropy without degrading validation loss. These results identify trajectory curvature as a task-aligned representational feature that influences behavioral uncertainty in LLMs.
Explore similar work
May 6, 2026cs.LG
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.
Albert F. Modenbach
Jun 23, 2026cs.CL
Contextual entrainment, which is a newly discovered phenomenon in large language models (LLMs), refers to the tendency of a model to assign higher probabilities to tokens that appear in its context. In this work, we extend this phenomenon from the token level to the sentence level by examining the per-token mean log-probability of a sentence instead of the probabilities of individual tokens. We investigate sentence-level contextual entrainment across 26 LLMs from seven families and two datasets, which cover both subjective and objective tasks. We find that sentence-level contextual entrainment exists. This means that the sentences in the prompt (even if they are counterfactual statements) can significantly increase their probability during model inference time. As the model size increases, contextual entrainment gradually decreases. We also find that contextual entrainment is controlled by 2% to 4% of the attention heads. Turning off these attention heads can effectively mitigate contextual entrainment without hurting the model's performance.
Yang Liu, Chenhui Chu
Jun 2, 2026cs.LG
Large language models hallucinate confidently, making uncertainty quantification (UQ) essential for reliable deployment. Existing methods rely predominantly on token-level signals, leaving the geometric structure of intermediate hidden states underused. In this paper, we take the geometric complexity of hidden-state matrices as a measure of the global uncertainty of LLMs, while treating token-level uncertainty estimation as a local metric. We show that hidden-state geometric entropy (global uncertainty) and token-level entropy (local uncertainty) are statistically near-orthogonal, capturing distinct failure regimes for reliability prediction. In particular, global geometry recovers the confident-but-wrong failure mode that local signals systematically miss. Building on this, we propose Global-Local Uncertainty (GLU), an unsupervised, single-pass score that fuses the two signals via a multiplicative gate. Across three model families and six benchmarks, GLU matches or outperforms all unsupervised baselines while requiring only a single forward pass and remaining length-normalized and architecture-agnostic.
Johanne Medina, Tianyi Zhou, Keivin Isufaj +2