BODHI: Do LLMs Branch Out and Discover Heterogeneous Inferences?

Reinforcement Learning with Verifiable Rewards (RLVR) has become a widely adopted technique for enhancing the reasoning ability of Large Language Models (LLMs). However, the effectiveness of RLVR strongly depends on the capability of base models. This issue arises because it requires the model to have sufficient capability to perform high-quality exploration, which involves both effectiveness and diversity. Unfortunately, existing methods address this issue by imitating expert trajectories, which improve effectiveness but neglect diversity. To address this, we argue that the expert only needs to provide guidance only at critical decision points rather than the entire reasoning path. Based on this insight, we propose MENTOR: Mixed-policy Expert Navigation for Token-level Optimization of Reasoning, a framework that provides expert guidance only at critical decision points to perform effective and diverse exploration in RLVR. Extensive experiments show that MENTOR enables models capture the essence of expert strategies rather than surface imitation, thereby performing high-quality exploration and achieving superior overall performance. Our code is available online.

Reinforcement Learning with Verifiable Rewards (RLVR) has been central to the recent success of Large Reasoning Models. However, while RLVR significantly improves single-sample accuracy, it often fails to expand the model's intrinsic reasoning coverage (pass@k) due to limited exploration during training. To address this, we optimize the structural design of train-time rollouts to enhance pass@k. Our analysis identifies three key design principles: (1) difficulty-adaptive rollout can play an important role in expanding pass@k, beyond serving as an efficiency heuristic; (2) tree-based rollout outperforms parallel sampling in discovering correct answers; and (3) sentence-entropy-guided forking overcomes the localization phenomenon of token-level branching to maximize semantic diversity. Building on these insights, we propose DATPO (Difficulty-Adaptive Sentence-entropy-guided Tree-structured Policy Optimization). DATPO integrates difficulty-adaptive tree search with a sibling-diversity advantage term, explicitly promoting semantic diversity to expand reasoning coverage during training. Experiments on mathematical reasoning benchmarks demonstrate that DATPO outperforms baselines especially in pass@k, which directly translates to superior test-time scaling performance.

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models, but prompt groups with identical rollout rewards consume generation budget without effective learning signals. Pre-rollout prompt selection can reduce this waste by screening prompts before rollout generation. However, existing pre-rollout methods struggle to balance exploitation and exploration: repeatedly exploiting historically informative prompts can narrow training coverage, whereas broader exploration can lower the fraction of informative prompts. To address these limitations, we introduce LEEPS, a Latent-Guided Explore--Exploit Prompt Sampler that adaptively balances the reuse of previously observed informative prompts with continued exploration of uncertain ones. LEEPS partitions candidates into exploit and explore portfolios and adaptively allocates rollout budget according to their recent non-trivial ratios. It further uses representation-space neighbors and historical rollout outcomes to prioritize uncertain prompts likely to yield non-zero reward variance, thereby making exploration more targeted without additional rollouts. Across six mathematical reasoning benchmarks, LEEPS achieves the highest average score at both model scales, with relative gains of 2.6% and 3.7% over the strongest baseline for Qwen2.5-Math-1.5B and 7B, respectively, and generally improves faster during the training process. It also achieves the highest average score across the three evaluated OOD general-reasoning benchmarks at both model scales and adds only about 2 seconds of online sampling overhead per training step. Code is available at https://github.com/ShuangLiangX/LEEPS.