@inproceedings{sun-etal-2026-llm,
title = "{LLM} Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals",
author = "Sun, Lihao and
Dong, Hang and
Qiao, Bo and
Lin, Qingwei and
Zhang, Dongmei and
Rajmohan, Saravan",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.acl-long.1237/",
pages = "26872--26887",
ISBN = "979-8-89176-390-6",
abstract = "This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC{--}AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior."
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%0 Conference Proceedings
%T LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals
%A Sun, Lihao
%A Dong, Hang
%A Qiao, Bo
%A Lin, Qingwei
%A Zhang, Dongmei
%A Rajmohan, Saravan
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F sun-etal-2026-llm
%X This work characterizes large language models’ chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC–AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.
%U https://aclanthology.org/2026.acl-long.1237/
%P 26872-26887
Markdown (Informal)
[LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://aclanthology.org/2026.acl-long.1237/) (Sun et al., ACL 2026)
ACL