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Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning

arXiv · AI, language, vision and robotics · article · Aug 31, 2026 · UTC

LLM agents need to sustain goal-consistent reasoning across long multi-turn interactions under strict resource constraints. However, as the multi-turn context accumulates, it can destabilize the underlying LLM's internal representation of task-relevant information from earlier turns, blurring the boundary between constructive reasoning and representation drift. We formulate multi-turn reasoning as a hidden-state trajectory of the underlying LLM that is characterized via two complementary signals: temporal curvature that captures the directional consistency of turn-to-turn updates, and variance

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