← 研踪 PaperTrailACL Anthology · ACL 2026:acl:2026.acl-long.1237 · 记录 #1
LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals
来源日期（仅到月份） 2026-07
来源记录日期 2026-07
雷达观测 2026-11-01 21:54
摘要
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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记录 #1 · 2026-07 · 最新观测版本
LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals
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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