Reinforcement learning struggles to generalize reasoning strategies out of distribution
Not All Reasoning Generalizes: A Case Study on Learning Generalizable Reasoning Strategies in RLVR
Machine Learning
Summary
Sometimes, AI models can learn to solve problems really well when the problems look like what they've seen before. But when the problems change in unexpected ways, these models often stop using their smart step-by-step thinking and guess around randomly, which makes them worse. The authors studied this by having models solve equations in different ways and found a way to help by training on a slightly different type of problem. This additional training helped models keep using good reasoning even when the problems changed, improving their accuracy.
What this means in practice
- •For machine learning engineers: Improve robustness of AI reasoning systems by including complementary training tasks that preserve logical strategies under data shifts.
- •For automated reasoning software teams: Develop equation-solving tools that maintain effective stepwise solving methods even when faced with novel or more complex equations.
Authors
Ziqi Pang, Yu-Xiong Wang
Abstract
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.