# Evaluating Robustness of Reward Models for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2410.01729 · HTML: https://mlsanity.com/paper/2410.01729/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 62 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## 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, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [Prometheus 2: An Open Source Language Model Specialized in Evaluating Other Language Models](https://mlsanity.com/paper/2405.01535/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Secrets of RLHF in Large Language Models Part I: PPO](https://mlsanity.com/paper/2307.04964/) (2023)
- [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024)
- [Regularizing Hidden States Enables Learning Generalizable Reward Model for LLMs](https://mlsanity.com/paper/2406.10216/) (2024)
- [Common 7B Language Models Already Possess Strong Math Capabilities](https://mlsanity.com/paper/2403.04706/) (2024)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [LLMs cannot find reasoning errors, but can correct them given the error location](https://mlsanity.com/paper/2311.08516/) (2023)
- [Evaluating Mathematical Reasoning Beyond Accuracy](https://mlsanity.com/paper/2404.05692/) (2024)
- [Empirical Design in Reinforcement Learning](https://mlsanity.com/paper/2304.01315/) (2023)
- [Coffee-Gym: An Environment for Evaluating and Improving Natural Language Feedback on Erroneous Code](https://mlsanity.com/paper/2409.19715/) (2024)

## Built on by (most cited first, 22 of 22)

- [RewardBench 2: Advancing Reward Model Evaluation](https://mlsanity.com/paper/2506.01937/) (2025)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [AceMath: Advancing Frontier Math Reasoning with Post-Training and Reward Modeling](https://mlsanity.com/paper/2412.15084/) (2024)
- [Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2504.12501/) (2025)
- [Web-Shepherd: Advancing PRMs for Reinforcing Web Agents](https://mlsanity.com/paper/2505.15277/) (2025)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [Rethinking Reward Model Evaluation: Are We Barking up the Wrong Tree?](https://mlsanity.com/paper/2410.05584/) (2024)
- [VerifyBench: Benchmarking Reference-based Reward Systems for Large Language Models](https://mlsanity.com/paper/2505.15801/) (2025)
- [On the Robustness of Reward Models for Language Model Alignment](https://mlsanity.com/paper/2505.07271/) (2025)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)
- [Reward Modeling for Reinforcement Learning-Based LLM Reasoning: Design, Challenges, and Evaluation](https://mlsanity.com/paper/2602.09305/) (2026)
- [Why is Your Language Model a Poor Implicit Reward Model?](https://mlsanity.com/paper/2507.07981/) (2025)
- [J1: Exploring Simple Test-Time Scaling for LLM-as-a-Judge](https://mlsanity.com/paper/2505.11875/) (2025)
- [Confidence as a Reward: Transforming LLMs into Reward Models](https://mlsanity.com/paper/2510.13501/) (2025)
- [Scaling Large Reasoning Models beyond Human Supervision: A Path toward Superintelligence](https://mlsanity.com/paper/2608.31075/) (2026)
- [SelfCheck-Eval: A Multi-Module Framework for Zero-Resource Hallucination Detection in Large Language Models](https://mlsanity.com/paper/2502.01812/) (2025)
- [RoleRMBench & RoleRM: Towards Reward Modeling for Profile-Based Role Play in Dialogue Systems](https://mlsanity.com/paper/2512.10575/) (2025)
- [EVALUESTEER: Measuring Reward Model Steerability Towards Values and Preferences](https://mlsanity.com/paper/2510.06370/) (2025)
- [Uncovering Factor Level Preferences to Improve Human-Model Alignment](https://mlsanity.com/paper/2410.06965/) (2024)
- [Cheems: A Practical Guidance for Building and Evaluating Chinese Reward Models from Scratch](https://mlsanity.com/paper/2502.17173/) (2025)
- [Long-form RewardBench: Evaluating Reward Models for Long-form Generation](https://mlsanity.com/paper/2603.12963/) (2026)
- [Who Sets the Pace of Judge Hacking? Judge Capability versus the Policy-Judge Gap](https://mlsanity.com/paper/2610.15778/) (2026)

## Abstract (arXiv)

Reward models are key in reinforcement learning from human feedback (RLHF) systems, aligning the model behavior with human preferences. Particularly in the math domain, there have been plenty of studies using reward models to align policies for improving reasoning capabilities. Recently, as the importance of reward models has been emphasized, RewardBench is proposed to understand their behavior. However, we figure out that the math subset of RewardBench has different representations between chosen and rejected completions, and relies on a single comparison, which may lead to unreliable results as it only see an isolated case. Therefore, it fails to accurately present the robustness of reward models, leading to a misunderstanding of its performance and potentially resulting in reward hacking. In this work, we introduce a new design for reliable evaluation of reward models, and to validate this, we construct RewardMATH, a benchmark that effectively represents the robustness of reward models in mathematical reasoning tasks. We demonstrate that the scores on RewardMATH strongly correlate with the results of optimized policy and effectively estimate reward overoptimization, whereas the existing benchmark shows almost no correlation. The results underscore the potential of our design to enhance the reliability of evaluation, and represent the robustness of reward model. We make our code and data publicly available.