# BARREL: Boundary-Aware Reasoning for Factual and Reliable LRMs

arXiv: https://arxiv.org/abs/2505.13529 · HTML: https://mlsanity.com/paper/2505.13529/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 18 May 2025.

## 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, 27 of 27)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [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)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Self-critiquing models for assisting human evaluators](https://mlsanity.com/paper/2206.05802/) (2022)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [Investigating the Factual Knowledge Boundary of Large Language Models with Retrieval Augmentation](https://mlsanity.com/paper/2307.11019/) (2023)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [Large Language Models Must Be Taught to Know What They Don't Know](https://mlsanity.com/paper/2406.08391/) (2024)
- [LLM Internal States Reveal Hallucination Risk Faced With a Query](https://mlsanity.com/paper/2407.03282/) (2024)
- [Rejection Improves Reliability: Training LLMs to Refuse Unknown Questions Using RL from Knowledge Feedback](https://mlsanity.com/paper/2403.18349/) (2024)
- [Rewarding Doubt: A Reinforcement Learning Approach to Calibrated Confidence Expression of Large Language Models](https://mlsanity.com/paper/2503.02623/) (2025)
- [Can AI Assistants Know What They Don't Know?](https://mlsanity.com/paper/2401.13275/) (2024)
- [FLAME: Factuality-Aware Alignment for Large Language Models](https://mlsanity.com/paper/2405.01525/) (2024)
- [Learning to Trust Your Feelings: Leveraging Self-awareness in LLMs for Hallucination Mitigation](https://mlsanity.com/paper/2401.15449/) (2024)
- [Knowledge Boundary of Large Language Models: A Survey](https://mlsanity.com/paper/2412.12472/) (2024)
- [Don't Just Say "I don't know"! Self-aligning Large Language Models for Responding to Unknown Questions with Explanations](https://mlsanity.com/paper/2402.15062/) (2024)
- [Trade-offs in Large Reasoning Models: An Empirical Analysis of Deliberative and Adaptive Reasoning over Foundational Capabilities](https://mlsanity.com/paper/2503.17979/) (2025)
- [UAlign: Leveraging Uncertainty Estimations for Factuality Alignment on Large Language Models](https://mlsanity.com/paper/2412.11803/) (2024)

## Built on by (most cited first, 8 of 8)

- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [BAPO: Boundary-Aware Policy Optimization for Reliable Agentic Search](https://mlsanity.com/paper/2601.11037/) (2026)
- [Know More, Know Clearer: A Meta-Cognitive Framework for Knowledge Augmentation in Large Language Models](https://mlsanity.com/paper/2602.12996/) (2026)
- [Abstention as an Action Can Kill Both the Reward Gradient and the KL Anchor: Collapse Law and Repair for Error-Penalized Reinforcement Learning](https://mlsanity.com/paper/2608.00301/) (2026)
- [REIN: Bridging the Gap between Reasoning and Reliability via Reflection and Abstention Alignment](https://mlsanity.com/paper/2608.07931/) (2026)
- [From Refuse to Richness: Rubric Rewards for Long-Form Hallucination Reinforcement Learning](https://mlsanity.com/paper/2608.12337/) (2026)
- [Decision Potential Surface: A Theoretical and Practical Approximation of Large Language Model Decision Boundary](https://mlsanity.com/paper/2510.03271/) (2025)
- [Enhancing Reliability across Short and Long-Form QA via Reinforcement Learning](https://mlsanity.com/paper/2512.08944/) (2025)

## Abstract (arXiv)

Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities in mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with "I don't know". Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL-a novel framework that promotes concise and boundary-aware factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeek-R1-Distill-Llama-8B from 39.33% to 61.48%, while still achieving accuracy comparable to models finetuned on reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System 2 LRMs.