# Uncertainty-Aware Step-wise Verification with Generative Reward Models

arXiv: https://arxiv.org/abs/2502.11250 · HTML: https://mlsanity.com/paper/2502.11250/

## 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 23 of its 28 references that are in the map.
- First posted on arXiv 16 Feb 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, 23 of 23)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [NV-Embed: Improved Techniques for Training LLMs as Generalist Embedding Models](https://mlsanity.com/paper/2405.17428/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [PandaLM: An Automatic Evaluation Benchmark for LLM Instruction Tuning Optimization](https://mlsanity.com/paper/2306.05087/) (2023)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Improving Reward Models with Synthetic Critiques](https://mlsanity.com/paper/2405.20850/) (2024)
- [Improving Uncertainty Quantification in Large Language Models via Semantic Embeddings](https://mlsanity.com/paper/2410.22685/) (2024)
- [Deep Bayesian Active Learning for Preference Modeling in Large Language Models](https://mlsanity.com/paper/2406.10023/) (2024)
- [How to Fix a Broken Confidence Estimator: Evaluating Post-hoc Methods for Selective Classification with Deep Neural Networks](https://mlsanity.com/paper/2305.15508/) (2023)

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

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [StepSearch: Igniting LLMs Search Ability via Step-Wise Proximal Policy Optimization](https://mlsanity.com/paper/2505.15107/) (2025)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)
- [From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centered](https://mlsanity.com/paper/2506.07461/) (2025)
- [Know What You Don't Know: Uncertainty Calibration of Process Reward Models](https://mlsanity.com/paper/2506.09338/) (2025)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [InfoPO: Information-Driven Policy Optimization for User-Centric Agents](https://mlsanity.com/paper/2603.00656/) (2026)
- [Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner](https://mlsanity.com/paper/2507.23317/) (2025)
- [More Bang for the Buck: Process Reward Modeling with Entropy-Driven Uncertainty](https://mlsanity.com/paper/2503.22233/) (2025)
- [Towards Agents That Know When They Don't Know: Uncertainty as a Control Signal for Structured Reasoning](https://mlsanity.com/paper/2509.02401/) (2025)
- [SSR: Socratic Self-Refine for Large Language Model Reasoning](https://mlsanity.com/paper/2511.10621/) (2025)
- [On the Limits of Test-Time Compute: Sequential Reward Filtering for Better Inference](https://mlsanity.com/paper/2512.04558/) (2025)
- [Grounding the Score: Explicit Visual Premise Verification for Reliable Vision-Language Process Reward Models](https://mlsanity.com/paper/2603.16253/) (2026)
- [Reasoning Path and Latent State Analysis for Multi-view Visual Spatial Reasoning: A Cognitive Science Perspective](https://mlsanity.com/paper/2512.02340/) (2025)
- [Predicting and improving test-time scaling laws via reward tail-guided search](https://mlsanity.com/paper/2602.01485/) (2026)
- [Diagnosing Multi-step Reasoning Failures in Black-box LLMs via Stepwise Confidence Attribution](https://mlsanity.com/paper/2605.19228/) (2026)
- [The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2606.22792/) (2026)
- [Verify, Repair, Repeat, or Stop? Robust Stopping for Noisy Verify-Repair Loops in LLM Agents](https://mlsanity.com/paper/2607.17641/) (2026)
- [One-Token Verification for Reasoning Correctness Estimation](https://mlsanity.com/paper/2603.01025/) (2026)
- [Granularity-Regulated Adaptive Computational Efficiency for Optimal Verification in Test-Time Scaling](https://mlsanity.com/paper/2606.19354/) (2026)
- [VeriBound: PAC-Bayesian Generalization Bounds for Process Reward Models Trained with Formal Verification Tools](https://mlsanity.com/paper/2606.20740/) (2026)
- [Rewarding Better Thinking for LLM Preference Alignment](https://mlsanity.com/paper/2607.19824/) (2026)

## Abstract (arXiv)

Complex multi-step reasoning tasks, such as solving mathematical problems, remain challenging for large language models (LLMs). While outcome supervision is commonly used, process supervision via process reward models (PRMs) provides intermediate rewards to verify step-wise correctness in solution traces. However, as proxies for human judgement, PRMs suffer from reliability issues, including susceptibility to reward hacking. In this work, we propose leveraging uncertainty quantification (UQ) to enhance the reliability of step-wise verification with generative reward models for mathematical reasoning tasks. We introduce CoT Entropy, a novel UQ method that outperforms existing approaches in quantifying a PRM's uncertainty in step-wise verification. Our results demonstrate that incorporating uncertainty estimates improves the robustness of judge-LM PRMs, leading to more reliable verification.