Title: Off-Trajectory Reasoning: Can LLMs Collaborate on Reasoning Trajectory?
Primary area: foundation or frontier models, including LLMs
Keywords: large langage models; language model reasoning; multi-model collaboration; off-trajectory reasoning

Abstract: Reasoning LLMs are trained to verbalize their thinking process, yielding strong gains on complex tasks. This transparency also opens a promising direction: multiple reasoners can directly collaborate on each other's thinking on a shared trajectory, yielding better inference efficiency and exploration. A key prerequisite, however, is the ability to assess usefulness and build on another model's partial thinking —we call this *off-trajectory reasoning*. Our paper investigates a critical question: can standard *solo-reasoning* training pipelines yield desired *off-trajectory* behaviors? We propose twin tests that capture the two extremes of the off-trajectory spectrum, namely 
**Recoverability**, which tests whether LLMs can backtrack from ``distractions'' induced by misleading reasoning traces, and **Guidability**, which tests their ability to build upon correct reasoning from stronger collaborators. Our study evaluates 15 open-weight LLMs (1.5B—32B) and reveals a counterintuitive finding — "stronger" LLMs on benchmarks are often more fragile under distraction. Moreover, all models tested fail to effectively leverage guiding steps from collaborators on problems beyond their inherent capabilities, with solve rates remaining under 9.2%. Finally, we conduct control studies to isolate the effects of three factors in post-training on these behaviors: the choice of distillation teacher, the use of RL, and data selection strategy. Our results provide actionable insights for training natively strong reasoning collaborators; e.g., we find that sub-optimal recoverability behaviors of teacher models are transferred to distilled students even if the distilled data trajectories are correct. Taken together, this work lays the groundwork for evaluating multi-model collaborations under shared reasoning, while revealing limitations of off-the-shelf reasoning LLMs.

TL;DR: We propose twin tests to study LLM off-trajectory reasoning