# ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs

arXiv: https://arxiv.org/abs/2506.18896 · HTML: https://mlsanity.com/paper/2506.18896/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 35 of its 69 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 30 of 35)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [A Survey on Knowledge Distillation of Large Language Models](https://mlsanity.com/paper/2402.13116/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [A Survey on Data Selection for Language Models](https://mlsanity.com/paper/2402.16827/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Method](https://mlsanity.com/paper/2402.17193/) (2024)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning](https://mlsanity.com/paper/2502.18080/) (2025)
- [Critique-out-Loud Reward Models](https://mlsanity.com/paper/2408.11791/) (2024)
- [Synthetic Data (Almost) from Scratch: Generalized Instruction Tuning for Language Models](https://mlsanity.com/paper/2402.13064/) (2024)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [Learning to Plan & Reason for Evaluation with Thinking-LLM-as-a-Judge](https://mlsanity.com/paper/2501.18099/) (2025)
- [ReasonFlux: Hierarchical LLM Reasoning via Scaling Thought Templates](https://mlsanity.com/paper/2502.06772/) (2025)
- [Co-Evolving LLM Coder and Unit Tester via Reinforcement Learning](https://mlsanity.com/paper/2506.03136/) (2025)

## Built on by (most cited first, 30 of 47)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [OpenClaw-RL: Train Any Agent Simply by Talking](https://mlsanity.com/paper/2603.10165/) (2026)
- [Revolutionizing Reinforcement Learning Framework for Diffusion Large Language Models](https://mlsanity.com/paper/2509.06949/) (2025)
- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [Agentic Reinforcement Learning with Implicit Step Rewards](https://mlsanity.com/paper/2509.19199/) (2025)
- [Demystifying Reinforcement Learning in Agentic Reasoning](https://mlsanity.com/paper/2510.11701/) (2025)
- [Beyond Correctness: Harmonizing Process and Outcome Rewards through RL Training](https://mlsanity.com/paper/2509.03403/) (2025)
- [Hard2Verify: A Step-Level Verification Benchmark for Open-Ended Frontier Math](https://mlsanity.com/paper/2510.13744/) (2025)
- [SOD: Step-wise On-policy Distillation for Small Language Model Agents](https://mlsanity.com/paper/2605.07725/) (2026)
- [Attention as a Compass: Efficient Exploration for Process-Supervised RL in Reasoning Models](https://mlsanity.com/paper/2509.26628/) (2025)
- [Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment](https://mlsanity.com/paper/2601.14249/) (2026)
- [Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner](https://mlsanity.com/paper/2507.23317/) (2025)
- [Hybrid Reward Normalization for Process-supervised Non-verifiable Agentic Tasks](https://mlsanity.com/paper/2509.25598/) (2025)
- [Save the Good Prefix: Precise Error Penalization via Process-Supervised RL to Enhance LLM Reasoning](https://mlsanity.com/paper/2601.18984/) (2026)
- [Search-R2: Enhancing Search-Integrated Reasoning via Actor-Refiner Collaboration](https://mlsanity.com/paper/2602.03647/) (2026)
- [Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning](https://mlsanity.com/paper/2605.02913/) (2026)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [Fin-PRM: A Domain-Specialized Process Reward Model for Financial Reasoning in Large Language Models](https://mlsanity.com/paper/2508.15202/) (2025)
- [Reward Modeling for Reinforcement Learning-Based LLM Reasoning: Design, Challenges, and Evaluation](https://mlsanity.com/paper/2602.09305/) (2026)
- [StructVRM: Aligning Multimodal Reasoning with Structured and Verifiable Reward Models](https://mlsanity.com/paper/2508.05383/) (2025)
- [NIRVANA: Structured Pruning Reimagined for Large Language Model Compression](https://mlsanity.com/paper/2509.14230/) (2025)
- [PRInTS: Reward Modeling for Long-Horizon Information Seeking](https://mlsanity.com/paper/2511.19314/) (2025)
- [Retrospective Progress-Aware Self-Refinement for LLM Agent Training](https://mlsanity.com/paper/2606.14302/) (2026)
- [From Chatbot to Digital Colleague: The Paradigm Shift Toward Persistent Autonomous AI](https://mlsanity.com/paper/2606.14502/) (2026)
- [CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2507.15698/) (2025)
- [TaTToo: Tool-Grounded Thinking PRM for Test-Time Scaling in Tabular Reasoning](https://mlsanity.com/paper/2510.06217/) (2025)
- [Characterizing, Evaluating, and Optimizing Complex Reasoning](https://mlsanity.com/paper/2602.08498/) (2026)
- [Rewarding the Scientific Process: Process-Level Reward Modeling for Agentic Data Analysis](https://mlsanity.com/paper/2604.24198/) (2026)
- [ReasoningFlow: Discourse Structures for Understanding LLM Reasoning Traces](https://mlsanity.com/paper/2606.05402/) (2026)
- [From Absolute to Relative: Rethinking Reward Shaping in Group-Based Reinforcement Learning](https://mlsanity.com/paper/2601.23058/) (2026)

## Abstract (arXiv)

Process Reward Models (PRMs) have recently emerged as a powerful framework for supervising intermediate reasoning steps in large language models (LLMs). Previous PRMs are primarily trained on model final output responses and struggle to evaluate intermediate thinking trajectories robustly, especially in the emerging setting of trajectory-response outputs generated by frontier reasoning models like Deepseek-R1. In this work, we introduce ReasonFlux-PRM, a novel trajectory-aware PRM explicitly designed to evaluate the trajectory-response type of reasoning traces. ReasonFlux-PRM incorporates both step-level and trajectory-level supervision, enabling fine-grained reward assignment aligned with structured chain-of-thought data. We adapt ReasonFlux-PRM to support reward supervision under both offline and online settings, including (i) selecting high-quality model distillation data for downstream supervised fine-tuning of smaller models, (ii) providing dense process-level rewards for policy optimization during reinforcement learning, and (iii) enabling reward-guided Best-of-N test-time scaling. Empirical results on challenging downstream benchmarks such as AIME, MATH500, and GPQA-Diamond demonstrate that ReasonFlux-PRM-7B selects higher quality data than strong PRMs (e.g., Qwen2.5-Math-PRM-72B) and human-curated baselines. Furthermore, our derived ReasonFlux-PRM-7B yields consistent performance improvements, achieving average gains of 12.1% in supervised fine-tuning, 4.5% in reinforcement learning, and 6.3% in test-time scaling. We also release our efficient ReasonFlux-PRM-1.5B for resource-constrained applications and edge deployment. Project: https://github.com/Gen-Verse/ReasonFlux