# Quantifying and Understanding Uncertainty in Large Reasoning Models

arXiv: https://arxiv.org/abs/2604.13395 · HTML: https://mlsanity.com/paper/2604.13395/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 20 of 20)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [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)
- [LLaVA-CoT: Let Vision Language Models Reason Step-by-Step](https://mlsanity.com/paper/2411.10440/) (2024)
- [WebThinker: Empowering Large Reasoning Models with Deep Research Capability](https://mlsanity.com/paper/2504.21776/) (2025)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [LMM-R1: Empowering 3B LMMs with Strong Reasoning Abilities Through Two-Stage Rule-Based RL](https://mlsanity.com/paper/2503.07536/) (2025)
- [Reliable Post hoc Explanations: Modeling Uncertainty in Explainability](https://mlsanity.com/paper/2008.05030/) (2020)
- [CLEVR-Math: A Dataset for Compositional Language, Visual and Mathematical Reasoning](https://mlsanity.com/paper/2208.05358/) (2022)
- [NILE : Natural Language Inference with Faithful Natural Language Explanations](https://mlsanity.com/paper/2005.12116/) (2020)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [Topology of Reasoning: Understanding Large Reasoning Models through Reasoning Graph Properties](https://mlsanity.com/paper/2506.05744/) (2025)
- [CoT-UQ: Improving Response-wise Uncertainty Quantification in LLMs with Chain-of-Thought](https://mlsanity.com/paper/2502.17214/) (2025)
- [CP-Router: An Uncertainty-Aware Router Between LLM and LRM](https://mlsanity.com/paper/2505.19970/) (2025)
- [Do not Abstain! Identify and Solve the Uncertainty](https://mlsanity.com/paper/2506.00780/) (2025)
- [Towards Modeling Uncertainties of Self-explaining Neural Networks via Conformal Prediction](https://mlsanity.com/paper/2401.01549/) (2024)
- [Teaching Language Models to Reason with Tools](https://mlsanity.com/paper/2510.20342/) (2025)
- [Towards Unveiling Predictive Uncertainty Vulnerabilities in the Context of the Right to Be Forgotten](https://mlsanity.com/paper/2508.07458/) (2025)
- [Quantifying Uncertainty in Natural Language Explanations of Large Language Models for Question Answering](https://mlsanity.com/paper/2509.15403/) (2025)
- [Uncertainty-aware Language Guidance for Concept Bottleneck Models](https://mlsanity.com/paper/2602.23495/) (2026)

## Abstract (arXiv)

Large Reasoning Models (LRMs) have recently demonstrated significant improvements in complex reasoning. While quantifying generation uncertainty in LRMs is crucial, traditional methods are often insufficient because they do not provide finite-sample guarantees for reasoning-answer generation. Conformal prediction (CP) stands out as a distribution-free and model-agnostic methodology that constructs statistically rigorous uncertainty sets. However, existing CP methods ignore the logical connection between the reasoning trace and the final answer. Additionally, prior studies fail to interpret the origins of uncertainty coverage for LRMs as they typically overlook the specific training factors driving valid reasoning. Notably, it is challenging to disentangle reasoning quality from answer correctness when quantifying uncertainty, while simultaneously establishing theoretical guarantees for computationally efficient explanation methods. To address these challenges, we first propose a novel methodology that quantifies uncertainty in the reasoning-answer structure with statistical guarantees. Subsequently, we develop a unified example-to-step explanation framework using Shapley values that identifies a provably sufficient subset of training examples and their key reasoning steps to preserve the guarantees. We also provide theoretical analyses of our proposed methods. Extensive experiments on challenging reasoning datasets verify the effectiveness of the proposed methods.