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 gene…