PIVOT：通过在线教师纠正的渐进式干预
PIVOT: Progressive Intervention via Online Teacher Correction
Zhihao Yang, Boyuan Zheng, Puhui Tan, Yukun Chen, Kuan Zhang, Longze Chen, Jiaming Li, Renke Shan 等 10 位作者
AI 速览：PIVOT 将教师生成的纠正片段插入学生 rollout，并对这些片段施加 token 级 KL 监督，与 RLVR 目标联合训练，以缓解困难推理任务中稀疏奖励无学习信号的问题。
Reinforcement learning from verifiable rewards (RLVR) is limited by sparse outcome-level feedback on hard reasoning tasks: when all rollouts in a group fail, rewards provide no learning signal. Stronger teachers can provide additional guidance, but this raises a central question: how can such signals be incorporated into RLVR to support successful rollouts while remaining learnable for the student? We distinguish two complementary mechanisms: trajectory-level intervention, which improves access to reward-bearing trajectories, and token-level supervision, which provides dense targets to guide student learning. Our controlled experiments show that either mechanism alone can remain insufficient, motivating their combination. We therefore introduce PIVOT, which inserts teacher-generated corrections into student rollouts and applies token-level KL supervision to these segments alongside the RLVR objective. Beyond their combination, we systematically analyze where to intervene and how to supervise, yielding a recipe for effective guidance. Across hard logic games and mathematical reasoning benchmarks, PIVOT consistently outperforms existing methods, nearly doubling mean avg@8 on logic games from 19.5% for the best-performing baseline to 35.6%.