这篇论文用几何方法追踪LLM推理轨迹，能提前发现错误路径，提升任务成功率还降低token成本。
研究人员提出通过几何信号追踪LLM隐藏状态轨迹，包括时间曲率和方差斜率。在四项任务和三种底层模型上，这些信号能在任务完成前区分正确与错误推理路径。研究将每个任务分解为读、写、回应、转移四个动作链，发现不同信号能区分各种链模式。实验表明，该方法在τ-Bench上将任务成功率从24.1%提升至39.6%，同时减少11.2%的token消耗。
Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning
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 slope which measures the expansion or contraction of the exploration space. Across four tasks and three underlying LLMs, we observed that these geometric signals distinguish between correct and incorrect episodes prior to completion. We further decompose each episode into three-action chains formed from four actions (Read, Write, Respond, Transfer) and show that separability is action-dependent, with different signals distinguishing various chain patterns. Our experiments demonstrate that trajectory geometry can identify critical turns in the reasoning process, increasing task success rates on $τ$-Bench from 24.1% to 39.6% while reducing token cost by 11.2%.