ROAM-GRPO: Enforcing Reasoning Diversity in GRPO via Routed Off-mode Approach Mining

Supervised fine-tuning (SFT) paired with Reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant recipe for post-training LLMs on complex reasoning tasks, but has been shown to collapse the policy into a low-diversity mode. Repeated LLM outputs are nearly identical, and pass@k accuracy converges or degrades as a result. We propose ROAM-GRPO (Routed Off-mode Approach Mining for GRPO), an augmentation to the GRPO algorithm which incentivizes exploration of distinct reasoning strategies and aims to increase output creativity during evaluation. ROAM-GRPO detects well-solved problems during training and transfers them to an “off-mode” track. The model is prompted to produce distinct solution strategies to such problems, which are verified for logical validity and distinctness by an LLM judge and subsequently self-distilled into the policy. Training Qwen3.5-2b on a 1000-episode slice of the MATH lvl5 dataset, ROAM-GRPO implementation increases peak pass@16 by $4.7\%$ and correct embedding cosine distance by ~1.5-2x on a difficult evaluation set.