LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals

• URL: http://arxiv.org/abs/2604.05655v1
• Date: Tue, 07 Apr 2026 09:55:50 GMT
• Title: LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals
• Abstract summary: This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space.<n>We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth.
• Score: 41.161787849343824
• License: http://creativecommons.org/licenses/by/4.0/
• 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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