通过分析隐藏状态轨迹几何，提升大模型多轮推理的稳定性与效率。
Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning
- 用轨迹曲率与方差斜率量化多轮推理中的状态演化规律。
- 提前识别错误推理路径，使任务成功率从24.1%提升至39.6%。
- 适用于需要长程稳定推理的智能体系统，如自动规划与复杂问答。
大模型代理在资源受限条件下需维持多轮交互中的目标一致性推理。然而，随着上下文积累，底层大模型对早期任务信息的内部表征会逐渐失真，模糊了有效推理与表征漂移的边界。本文将多轮推理建模为底层大模型的隐藏状态轨迹，通过两个互补信号刻画：时间曲率（捕捉逐轮更新的方向一致性）和方差斜率（衡量探索空间的扩张或收缩）。在四个任务和三个基础大模型上，我们发现这些几何信号可在任务完成前区分正确与错误的推理过程。进一步将每个推理过程分解为由四类动作（读取、写入、回应、传递）构成的三步链，发现可分离性依赖具体动作，不同信号能区分不同链模式。实验表明，轨迹几何可识别推理中的关键转折点，在τ-Bench上将任务成功率从24.1%提升至39.6%，同时降低11.2%的令牌消耗。
原文摘要 · Abstract (English)
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 $\tau$-Bench from 24.1% to 39.6% while reducing token cost by 11.2%.
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