@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://preview.aclanthology.org/ingest-acl/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."
}