Representational Curvature Modulates Behavioral Uncertainty in Large Language Models
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.
Full article excerpt tap to expand
Computer Science > Artificial Intelligence arXiv:2604.23985 (cs) [Submitted on 27 Apr 2026] Title:Representational Curvature Modulates Behavioral Uncertainty in Large Language Models Authors:Jack King, Evelina Fedorenko, Eghbal A. Hosseini View a PDF of the paper titled Representational Curvature Modulates Behavioral Uncertainty in Large Language Models, by Jack King and 2 other authors View PDF HTML (experimental) 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. Subjects: Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG) Cite as: arXiv:2604.23985 [cs.AI] (or arXiv:2604.23985v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2604.23985 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Eghbal Hosseini [view email] [v1] Mon, 27 Apr 2026 03:00:47 UTC (7,172 KB) Full-text links: Access Paper: View a PDF of the paper titled Representational Curvature Modulates Behavioral Uncertainty in Large Language Models, by Jack King and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: cs.AI < prev | next > new | recent | 2026-04 Change to browse by: cs cs.CL cs.LG References & Citations NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are…
This excerpt is published under fair use for community discussion. Read the full article at arXiv.org.
Discussion
0 commentsMore from arXiv.org