# Critique Fine-Tuning: Learning to Critique is More Effective than Learning to Imitate

arXiv: https://arxiv.org/abs/2501.17703 · HTML: https://mlsanity.com/paper/2501.17703/

## Key facts

- Cited by 63 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 50 of its 57 references that are in the map.
- First posted on arXiv 29 Jan 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 50)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Multitask Prompted Training Enables Zero-Shot Task Generalization](https://mlsanity.com/paper/2110.08207/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)

## Built on by (most cited first, 30 of 63)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback](https://mlsanity.com/paper/2506.03106/) (2025)
- [LongCat-Flash Technical Report](https://mlsanity.com/paper/2509.01322/) (2025)
- [LLMs are Greedy Agents: Effects of RL Fine-tuning on Decision-Making Abilities](https://mlsanity.com/paper/2504.16078/) (2025)
- [Enhancing LLM Reasoning with Iterative DPO: A Comprehensive Empirical Investigation](https://mlsanity.com/paper/2503.12854/) (2025)
- [Heimdall: test-time scaling on the generative verification](https://mlsanity.com/paper/2504.10337/) (2025)
- [OpenCodeReasoning-II: A Simple Test Time Scaling Approach via Self-Critique](https://mlsanity.com/paper/2507.09075/) (2025)
- [Genius: A Generalizable and Purely Unsupervised Self-Training Framework For Advanced Reasoning](https://mlsanity.com/paper/2504.08672/) (2025)
- [Self-Correction Bench: Uncovering and Addressing the Self-Correction Blind Spot in Large Language Models](https://mlsanity.com/paper/2507.02778/) (2025)
- [Fostering Video Reasoning via Next-Event Prediction](https://mlsanity.com/paper/2505.22457/) (2025)
- [Language Models Can Learn from Verbal Feedback Without Scalar Rewards](https://mlsanity.com/paper/2509.22638/) (2025)
- [XRPO: Pushing the limits of GRPO with Targeted Exploration and Exploitation](https://mlsanity.com/paper/2510.06672/) (2025)
- [Sherlock: Self-Correcting Reasoning in Vision-Language Models](https://mlsanity.com/paper/2505.22651/) (2025)
- [CLPO: Curriculum Learning meets Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2509.25004/) (2025)
- [Co-PatcheR: Collaborative Software Patching with Component(s)-specific Small Reasoning Models](https://mlsanity.com/paper/2505.18955/) (2025)
- [SpatiaLab: Can Vision-Language Models Perform Spatial Reasoning in the Wild?](https://mlsanity.com/paper/2602.03916/) (2026)
- [Shadow-FT: Tuning Instruct Model via Training on Paired Base Model](https://mlsanity.com/paper/2505.12716/) (2025)
- [RefineCoder: Iterative Improving of Large Language Models via Adaptive Critique Refinement for Code Generation](https://mlsanity.com/paper/2502.09183/) (2025)
- [Can Language Models Falsify? Evaluating Algorithmic Reasoning with Counterexample Creation](https://mlsanity.com/paper/2502.19414/) (2025)
- [Critique-Coder: Enhancing Coder Models by Critique Reinforcement Learning](https://mlsanity.com/paper/2509.22824/) (2025)
- [ScaleDiff: Scaling Difficult Problems for Advanced Mathematical Reasoning](https://mlsanity.com/paper/2509.21070/) (2025)
- [Retrieval is Not Enough: Enhancing RAG Reasoning through Test-Time Critique and Optimization](https://mlsanity.com/paper/2504.14858/) (2025)
- [Aletheia: What Makes RLVR For Code Verifiers Tick?](https://mlsanity.com/paper/2601.12186/) (2026)
- [Bootstrapping Exploration with Group-Level Natural Language Feedback in Reinforcement Learning](https://mlsanity.com/paper/2603.04597/) (2026)
- [SWE-Review: Closing the Loop on Issue Resolution with Agentic Code Review](https://mlsanity.com/paper/2607.06065/) (2026)
- [MetaSC: Test-Time Safety Specification Optimization for Language Models](https://mlsanity.com/paper/2502.07985/) (2025)
- [Teaching LLMs How to Learn with Contextual Fine-Tuning](https://mlsanity.com/paper/2503.09032/) (2025)
- [PrefixMemory-Tuning: Modernizing Prefix-Tuning by Decoupling the Prefix from Attention](https://mlsanity.com/paper/2506.13674/) (2025)
- [A Stitch in Time Saves Nine: Proactive Self-Refinement for Language Models](https://mlsanity.com/paper/2508.12903/) (2025)

## Abstract (arXiv)

Supervised Fine-Tuning (SFT) is commonly used to train language models to imitate annotated responses for given instructions. In this paper, we propose Critique Fine-Tuning (CFT), a method more effective than SFT for reasoning tasks. Instead of simply imitating correct responses, CFT trains models to critique noisy responses, inspired by human learning processes that emphasize critical thinking, deeper analysis, and nuanced understanding - traits often overlooked by standard SFT. To validate the effectiveness of CFT, we construct multiple critique datasets (e.g., WebInstruct, MetaMath, NuminaMath), where GPT-4o serves as the teacher to generate critiques in the form of ([query; noisy response], critique). Experiments on these datasets demonstrate that CFT consistently outperforms SFT by 4-10% across six mathematical reasoning benchmarks, and is effective across different base models including Qwen2.5, Qwen2.5-Math, and DeepSeek-Math. Notably, our model Qwen2.5-Math-CFT only requires 1 hour of training on 8 x H100 over the 50K examples, yet matches or outperforms strong competitors like Qwen2.5-Math-Instruct on most benchmarks, which use over 2M samples. Moreover, it matches the performance of SimpleRL, which is a DeepSeek-r1 replication trained with 140 x more compute. Experiments on IF_Eval and MT-Bench further demonstrate that CFT can significantly enhance the model's general generation and instruction-following capabilities, outperforming the Qwen2.5-Math-Instruct by a large margin. Ablation studies show that CFT is robust to noisy response sources and teacher critique models. These findings highlight that CFT offers a more effective alternative to advance the reasoning of language models.