Hidden-State Trajectories for Adaptive Reasoning
Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning
This method improves LLM reasoning efficiency across tasks, reducing costs while increasing success rates, making it valuable for developers working with constrained resources.
Researchers developed geometric signals to track LLM hidden-state trajectories across multi-turn interactions. The approach uses temporal curvature and variance slope to distinguish between correct and incorrect reasoning episodes. On τ-Bench, this method increased task success rates from 24.1% to 39.6% while reducing token cost by 11.2%. The signals show different effectiveness across action chains of Read, Write, Respond, and Transfer actions.
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%.