# Double-Checker: Enhancing Reasoning of Slow-Thinking LLMs via Self-Critical Fine-Tuning

arXiv: https://arxiv.org/abs/2506.21285 · HTML: https://mlsanity.com/paper/2506.21285/

## Key facts

- Cited by 2 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 30 of its 51 references that are in the map.
- First posted on arXiv 26 Jun 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, 30 of 30)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [Verify-and-Edit: A Knowledge-Enhanced Chain-of-Thought Framework](https://mlsanity.com/paper/2305.03268/) (2023)
- [Levels of AGI for Operationalizing Progress on the Path to AGI](https://mlsanity.com/paper/2311.02462/) (2023)
- [Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't](https://mlsanity.com/paper/2503.16219/) (2025)
- [Critique Fine-Tuning: Learning to Critique is More Effective than Learning to Imitate](https://mlsanity.com/paper/2501.17703/) (2025)
- [Think Twice: Enhancing LLM Reasoning by Scaling Multi-round Test-time Thinking](https://mlsanity.com/paper/2503.19855/) (2025)
- [Teaching Language Models to Critique via Reinforcement Learning](https://mlsanity.com/paper/2502.03492/) (2025)
- [DeepCritic: Deliberate Critique with Large Language Models](https://mlsanity.com/paper/2505.00662/) (2025)
- [Beyond the Last Answer: Your Reasoning Trace Uncovers More than You Think](https://mlsanity.com/paper/2504.20708/) (2025)
- [Can We Verify Step by Step for Incorrect Answer Detection?](https://mlsanity.com/paper/2402.10528/) (2024)
- [UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2501.13766/) (2025)
- [Dancing with Critiques: Enhancing LLM Reasoning with Stepwise Natural Language Self-Critique](https://mlsanity.com/paper/2503.17363/) (2025)

## Built on by (most cited first, 2 of 2)

- [Thinking-Free Policy Initialization Makes Distilled Reasoning Models More Effective and Efficient Reasoners](https://mlsanity.com/paper/2509.26226/) (2025)
- [Teaching Large Language Models When Not to Know: Learning Temporal Critique for Ex-Ante Reasoning](https://mlsanity.com/paper/2605.14636/) (2026)

## Abstract (arXiv)

While slow-thinking large language models (LLMs) exhibit reflection-like reasoning, commonly referred to as the "aha moment:, their ability to generate informative critiques and refine prior solutions remains limited. In this paper, we introduce Double-Checker, a principled framework designed to enhance the reasoning capabilities of slow-thinking LLMs by fostering explicit self-critique and iterative refinement of their previous solutions. By fine-tuning on our curated 1,730 self-critical instances, Double-Checker empowers long-CoT LLMs to iteratively critique and refine their outputs during inference until they evaluate their solutions as correct under self-generated critiques. We validate the efficacy of Double-Checker across a comprehensive suite of reasoning benchmarks, demonstrating that iterative self-critique significantly enhances the reasoning capabilities of long-CoT LLMs. Notably, our Double-Checker increases the pass@1 performance on challenging AIME benchmarks from 4.4% to 18.2% compared to the original long-CoT LLMs. These results highlight a promising direction for developing more trustworthy and effective LLMs capable of structured self-critique. Our codes and data are available at https://github.com/XinXU-USTC/DoubleChecker