RLVR 泛化失效研究：模型在 OOD 场景下会退回暴力枚举
Not All Reasoning Generalizes: A Case Study on Learning Generalizable Reasoning Strategies in RLVR
这篇论文把 RLVR 泛化失效拆得很清楚：模型看着会推导，换个分布就偷偷改成枚举。想搞懂训练出真实推理能力的人建议看。
论文用可求解方程的受控框架研究 RLVR 的泛化能力，其中 f 为非双射字符串函数。实验发现模型在分布内任务上保持高准确率并采用结构化推导，但在更解数、更长 y 等 OOD 漂移下会放弃推导、退化成暴力枚举，准确率大幅下降。这种失效既非基座能力不足也非 reward hacking，而是推理策略本身没有泛化。作者提出的间接干预方法是与双射反演任务共同训练，虽然这些任务并非更难且离 OOD 评估更远，却能显著恢复正确策略。论文还给出理论分析：仅靠结果奖励的 RLVR 可以隐式地为有效推理策略分配更多信用，无需过程监督。
Not All Reasoning Generalizes: A Case Study on Learning Generalizable Reasoning Strategies in RLVR
Reinforcement learning with verifiable rewards (RLVR) can enable generalizable improvement for large language model (LLM) reasoning. This paper studies how to incentivize such generalization via reasoning strategies. We study this question with a controllable equation-solving framework: finding multiple inputs x for equations f(x)=y, where f is a non-bijective string function. This setting makes reasoning strategies observable while supporting a clear definition of easy-to-hard out-of-distribution (OOD) shifts, e.g., more solutions, longer y, etc. We uncover a subtle RLVR failure: it teaches the model to solve in-distribution tasks with high accuracy and structured step-by-step derivation, yet under OOD shifts, the same model abandons derivation and collapses to ineffective brute-force enumeration, causing sharp accuracy drops. This observation reveals the deeper challenges of RLVR generalization as it is neither incapable base model nor reward hacking, since the model succeeds in-distribution with the correct reasoning strategy. The key to mitigating this failure is an indirect intervention that surprisingly helps: co-training with bijective inversion tasks. Although these bijective tasks are actually not uniformly harder and even further from the non-bijective OOD evaluation, they make derivation more certain and substantially restore the correct strategy and accuracy under OOD shifts. This effect further motivates our theoretical analysis: outcome-only RLVR can shape reasoning processes through implicitly crediting the effective reasoning strategies more, even without process supervision. To conclude, our analysis framework and findings systematically reveal the crucial role and incentivization of reasoning strategies in RLVR generalization under OOD shifts. Code is available at https://github.com/ziqipang/rl_meta_thinking.