Measuring Off-Trajectory Math Reasoning of LLMs

Reasoning LLMs are trained to verbalize their thinking process, yielding strong gains on math benchmarks. 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%. This work lays the groundwork for evaluating multi-model collaborations under shared reasoning, while revealing limitations of off-the-shelf reasoning LLMs.