# BODHI: Do LLMs Branch Out and Discover Heterogeneous Inferences?

arXiv: https://arxiv.org/abs/2608.02867 · HTML: https://mlsanity.com/paper/2608.02867/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 40 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 26 of 26)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [TreePO: Bridging the Gap of Policy Optimization and Efficacy and Inference Efficiency with Heuristic Tree-based Modeling](https://mlsanity.com/paper/2508.17445/) (2025)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [A Configurable Library for Generating and Manipulating Maze Datasets](https://mlsanity.com/paper/2309.10498/) (2023)
- [Diversity-Incentivized Exploration for Versatile Reasoning](https://mlsanity.com/paper/2509.26209/) (2025)
- [What Makes a Good Reasoning Chain? Uncovering Structural Patterns in Long Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.22148/) (2025)
- [Revisiting Entropy in Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2511.05993/) (2025)
- [DRA-GRPO: Your GRPO Needs to Know Diverse Reasoning Paths for Mathematical Reasoning](https://mlsanity.com/paper/2505.09655/) (2025)
- [Semantic-Space Exploration and Exploitation in RLVR for LLM Reasoning](https://mlsanity.com/paper/2509.23808/) (2025)
- [Rewarding the Rare: Uniqueness-Aware RL for Creative Problem Solving in LLMs](https://mlsanity.com/paper/2601.08763/) (2026)
- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [Reinforced Efficient Reasoning via Semantically Diverse Exploration](https://mlsanity.com/paper/2601.05053/) (2026)
- [Local Coherence or Global Validity? Investigating RLVR Traces in Math Domains](https://mlsanity.com/paper/2510.18176/) (2025)
- [Curriculum Reinforcement Learning Can Incentivize Reasoning Capacity in LLMs Beyond the Base Model](https://mlsanity.com/paper/2606.22317/) (2026)
- [SD-E2: Semantic Exploration for Reasoning Under Token Budgets](https://mlsanity.com/paper/2601.17982/) (2026)
- [KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?](https://mlsanity.com/paper/2507.11408/) (2025)

## Built on by (most cited first, 2 of 2)

- [Locked at the Entrance, Open Inside: Where RLVR Narrows the Solution Space](https://mlsanity.com/paper/2608.29188/) (2026)
- [Reasoning Concentrates Errors, and Self-Consistency Never Notices](https://mlsanity.com/paper/2609.32035/) (2026)

## Abstract (arXiv)

Although reinforcement learning with verifiable rewards (RLVR) has improved the performance of large language models (LLMs) across a variety of reasoning tasks, there is significant debate as to whether RLVR expands the reasoning capability boundary, or just improves sampling efficiency. In this paper, we investigate the nature of test-time exploration in RLVR-trained LLMs by employing controlled maze-solving experiments and extracting a tree structure from mathematical reasoning traces (BODHI-Trees) based on semantic equivalence. This helps us delineate between entropy arising from stylistic variations and genuine inferential branching. Our findings demonstrate that the policy entropy collapse observed in RLVR models is not merely syntactic, and is accompanied by a significant reduction in semantic branching entropy. While RLVR improves adherence to environmental constraints and backtracking capabilities, it constricts the space of continuations; we provide evidence suggesting that this might be responsible for the sample efficiency gains of RLVR, albeit at the cost of genuine rollout diversity.