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Letting a stronger teacher write corrections directly into a student's reasoning traces nearly doubled hard-logic-game accuracy, from 19.5 to 35.6 percent

AspireAI community · arXiv
Reinforcement learning from verifiable rewards stalls on hard reasoning because when every rollout in a group fails, the reward carries no learning signal. PIVOT separates two mechanisms that each fail alone: trajectory-level intervention, which improves the chance of reaching reward-bearing trajectories, and token-level supervision, which gives dense targets. It inserts teacher-generated corrections into student rollouts and applies token-level KL supervision to those segments alongside the RLVR objective. On hard logic games the reverse-KL variant nearly doubled mean avg@8 from 19.5 percent for the best-performing baseline to 35.6 percent, and on the hard math split it lifted a base model that solved 5.04 percent of problems to 23.05 percent. The paper also reports where to intervene: middle-of-trajectory corrections beat prefix corrections on all three games, and spreading a fixed teacher token budget across more rollouts made results monotonically worse.
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