When Domains Interact: Asymmetric and Order-Sensitive Cross-Domain Effects in Reinforcement Learning for Reasoning

Group Relative Policy Optimization (GRPO) has become a key technique for improving reasoning abilities in large language models, yet its behavior under different domain sequencing strategies is poorly understood. In particular, the impact of sequential (one domain at a time) versus mixed-domain (multiple domain at a time) training in GRPO has not been systematically studied. We provide the first systematic analysis of training-order effects across math, science, logic, and puzzle reasoning tasks. We found (1) single-domain generalization is highly asymmetric: training on other domains improves math reasoning by approximately 25% accuracy, while yielding negligible transfer to logic and puzzle; (2) cross-domain interactions are highly order-dependent: training in the order mathrightarrowscience achieves 83% / 41% accuracy on math / science, while reversing the order to sciencerightarrowmath degrades performance to 77% / 25%; (3) no single strategy is universally optimal in multi-domain training: sequential training favors math (up to 84%), mixed training favors science and logic, and poor ordering can incur large performance gaps (from 70% to 56%). Overall, our findings demonstrate that GRPO under multi-domain settings exhibits pronounced asymmetry, order sensitivity, and strategy dependence, highlighting the necessity of domain-aware and order-aware training design.