# Retrieval-Augmented Process Reward Model for Generalizable Mathematical Reasoning

arXiv: https://arxiv.org/abs/2502.14361 · HTML: https://mlsanity.com/paper/2502.14361/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Retrieval-augmented generation / [Agentic RAG, agents and memory](https://mlsanity.com/rag/agentic-rag-agents-and-memory/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 28 of 28)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [Leveraging Passage Retrieval with Generative Models for Open Domain Question Answering](https://mlsanity.com/paper/2007.01282/) (2020)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence](https://mlsanity.com/paper/2406.11931/) (2024)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [LLM Critics Help Catch LLM Bugs](https://mlsanity.com/paper/2407.00215/) (2024)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [OpenR: An Open Source Framework for Advanced Reasoning with Large Language Models](https://mlsanity.com/paper/2410.09671/) (2024)
- [Evaluating Mathematical Reasoning Beyond Accuracy](https://mlsanity.com/paper/2404.05692/) (2024)
- [LLM Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedback](https://mlsanity.com/paper/2406.14024/) (2024)

## Built on by (most cited first, 23 of 23)

- [GenPRM: Scaling Test-Time Compute of Process Reward Models via Generative Reasoning](https://mlsanity.com/paper/2504.00891/) (2025)
- [A Comprehensive Survey of Reward Models: Taxonomy, Applications, Challenges, and Future](https://mlsanity.com/paper/2504.12328/) (2025)
- [A Survey of Process Reward Models: From Outcome Signals to Process Supervisions for Large Language Models](https://mlsanity.com/paper/2510.08049/) (2025)
- [Synergizing RAG and Reasoning: A Systematic Review](https://mlsanity.com/paper/2504.15909/) (2025)
- [StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models](https://mlsanity.com/paper/2509.22558/) (2025)
- [Med-PRM: Medical Reasoning Models with Stepwise, Guideline-verified Process Rewards](https://mlsanity.com/paper/2506.11474/) (2025)
- [Is PRM Necessary? Problem-Solving RL Implicitly Induces PRM Capability in LLMs](https://mlsanity.com/paper/2505.11227/) (2025)
- [Adaptive Milestone Reward for GUI Agents](https://mlsanity.com/paper/2602.11524/) (2026)
- [Can Knowledge-Graph-based Retrieval Augmented Generation Really Retrieve What You Need?](https://mlsanity.com/paper/2510.16582/) (2025)
- [Reward Modeling for Reinforcement Learning-Based LLM Reasoning: Design, Challenges, and Evaluation](https://mlsanity.com/paper/2602.09305/) (2026)
- [CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2507.15698/) (2025)
- [NL-Debugging: Exploiting Natural Language as an Intermediate Representation for Code Debugging](https://mlsanity.com/paper/2505.15356/) (2025)
- [ToolPRM: Fine-Grained Inference Scaling of Structured Outputs for Function Calling](https://mlsanity.com/paper/2510.14703/) (2025)
- [MassTool: A Multi-Task Search-Based Tool Retrieval Framework for Large Language Models](https://mlsanity.com/paper/2507.00487/) (2025)
- [Arbitrage: Efficient Reasoning via Advantage-Aware Speculation](https://mlsanity.com/paper/2512.05033/) (2025)
- [When Distance Distracts: Representation Distance Bias in BT-Loss for Reward Models](https://mlsanity.com/paper/2512.06343/) (2025)
- [Training Data Efficiency in Multimodal Process Reward Models](https://mlsanity.com/paper/2602.04145/) (2026)
- [Process Reward Agents for Steering Knowledge-Intensive Reasoning](https://mlsanity.com/paper/2604.09482/) (2026)
- [Fusing Bidirectional Chains of Thought and Reward Mechanisms A Method for Enhancing Question-Answering Capabilities of Large Language Models for Chinese Intangible Cultural Heritage](https://mlsanity.com/paper/2505.08167/) (2025)
- [Constraint-Rectified Training for Efficient Chain-of-Thought](https://mlsanity.com/paper/2602.12526/) (2026)
- [EvoOptiGraph: Weakness-Driven Coevolution via Graph-Based Structural Generation for Optimization Modeling](https://mlsanity.com/paper/2606.26578/) (2026)
- [ThinkRetrieve: Retrieval-Augmented Reasoning Traces for Test-Time Scaling](https://mlsanity.com/paper/2608.10928/) (2026)
- [Learning Process Rewards via Reasoning State Propagation](https://mlsanity.com/paper/2609.39220/) (2026)

## Abstract (arXiv)

While large language models (LLMs) have significantly advanced mathematical reasoning, Process Reward Models (PRMs) have been developed to evaluate the logical validity of reasoning steps. However, PRMs still struggle with out-of-distribution (OOD) challenges. This paper identifies key OOD issues, including step OOD, caused by differences in reasoning patterns across model types and sizes, and question OOD, which arises from dataset shifts between training data and real-world problems. To address these issues, we introduce Retrieval-Augmented Process Reward Model (RetrievalPRM), a novel framework designed to tackle these OOD issues. By utilizing a two-stage retrieval-enhanced mechanism, RetrievalPRM retrieves semantically similar questions and steps as a warmup, enhancing PRM's ability to evaluate target steps and improving generalization and reasoning consistency across different models and problem types. Our extensive experiments demonstrate that RetrievalPRM outperforms existing baselines across multiple real-world datasets. Our open-source contributions include a retrieval-enhanced dataset, a tuning framework for PRM training, and the RetrievalPRM model, establishing a new standard for PRM performance.