# Know What You Don't Know: Uncertainty Calibration of Process Reward Models

arXiv: https://arxiv.org/abs/2506.09338 · HTML: https://mlsanity.com/paper/2506.09338/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 11 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, 24 of 24)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling](https://mlsanity.com/paper/2502.06703/) (2025)
- [To Believe or Not to Believe Your LLM](https://mlsanity.com/paper/2406.02543/) (2024)
- [PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Models](https://mlsanity.com/paper/2501.03124/) (2025)
- [Evaluating Mathematical Reasoning Beyond Accuracy](https://mlsanity.com/paper/2404.05692/) (2024)
- [Calibrating Language Models with Adaptive Temperature Scaling](https://mlsanity.com/paper/2409.19817/) (2024)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [Thermometer: Towards Universal Calibration for Large Language Models](https://mlsanity.com/paper/2403.08819/) (2024)
- [Think Smarter not Harder: Adaptive Reasoning with Inference Aware Optimization](https://mlsanity.com/paper/2501.17974/) (2025)
- [Uncertainty-Aware Step-wise Verification with Generative Reward Models](https://mlsanity.com/paper/2502.11250/) (2025)
- [Rollout Roulette: A Probabilistic Inference Approach to Inference-Time Scaling of LLMs using Particle-Based Monte Carlo Methods](https://mlsanity.com/paper/2502.01618/) (2025)
- [Experts Don't Cheat: Learning What You Don't Know By Predicting Pairs](https://mlsanity.com/paper/2402.08733/) (2024)
- [Uncertainty Quantification in Detection Transformers: Object-Level Calibration and Image-Level Reliability](https://mlsanity.com/paper/2412.01782/) (2024)

## Built on by (most cited first, 21 of 21)

- [E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testing](https://mlsanity.com/paper/2512.03109/) (2025)
- [Environment Scaling for Interactive Agentic Experience Collection: A Survey](https://mlsanity.com/paper/2511.09586/) (2025)
- [Overconfidence and Calibration in Medical VQA: Empirical Findings and Hallucination-Aware Mitigation](https://mlsanity.com/paper/2604.02543/) (2026)
- [Fail-Fast, Restart-Smart: Early Failure Prediction and Restart for SWE Agentic Tasks](https://mlsanity.com/paper/2608.03222/) (2026)
- [Mitigating Premature Exploitation in Particle-based Monte Carlo for Inference-Time Scaling](https://mlsanity.com/paper/2510.05825/) (2025)
- [Grounding the Score: Explicit Visual Premise Verification for Reliable Vision-Language Process Reward Models](https://mlsanity.com/paper/2603.16253/) (2026)
- [TrajSelector: Harnessing Latent Representations for Efficient and Effective Best-of-N in Large Reasoning Model](https://mlsanity.com/paper/2510.16449/) (2025)
- [LLM Reasoning with Process Rewards for Outcome-Guided Steps](https://mlsanity.com/paper/2604.02341/) (2026)
- [Efficient Paths and Dense Rewards: Probabilistic Flow Reasoning for Large Language Models](https://mlsanity.com/paper/2601.09260/) (2026)
- [Conformal Certification of Reasoning Trace Prefixes](https://mlsanity.com/paper/2605.30085/) (2026)
- [Critic Experience Bank: Self-Evolving Step-Level Confidence Estimation for LLM Agents](https://mlsanity.com/paper/2607.12397/) (2026)
- [Intrinsic Selection and Particle Resampling for Inference-Time Scaling Beyond Domain Verifiability](https://mlsanity.com/paper/2606.08850/) (2026)
- [AI Achieves a Perfect LSAT Score](https://mlsanity.com/paper/2604.10034/) (2026)
- [PAC-CF: Calibrating Irreversible Frontier Pruning in LLM-Guided Search](https://mlsanity.com/paper/2604.14345/) (2026)
- [Distributional Process Reward Models: Calibrated Prediction of Future Rewards via Conditional Optimal Transport](https://mlsanity.com/paper/2605.06785/) (2026)
- [Process Rewards with Learned Reliability](https://mlsanity.com/paper/2605.15529/) (2026)
- [Configurable Reward Model for Balanced Safety Alignment](https://mlsanity.com/paper/2605.30487/) (2026)
- [Turning Intent into Specifications: A Benchmark and an Interactive User-Assistant Agent](https://mlsanity.com/paper/2606.20585/) (2026)
- [The Exceedance Design Effect: Effective Sample Size for Thresholds under Clustering](https://mlsanity.com/paper/2608.21262/) (2026)
- [Reliable Self-Evolution with Imperfect Proxy Rewards](https://mlsanity.com/paper/2610.02975/) (2026)
- [Learning More by Training Less: Uncertainty-Guided Progressive Contraction for Efficient Reasoning Post-Training](https://mlsanity.com/paper/2610.12933/) (2026)

## Abstract (arXiv)

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated. Specifically, they tend to overestimate the success probability that a partial reasoning step will lead to a correct final answer, particularly when smaller LLMs are used to complete the reasoning trajectory. To address this, we present a calibration approach -- performed via quantile regression -- that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the compute budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective IAS, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.