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

Supervised Fine-Tuning (SFT) is commonly used to train language models to imitate annotated responses for given instructions. In this paper, we challenge this paradigm and propose Critique Fine-Tuning (CFT), a strategy where models learn to critique noisy responses rather than simply imitate correct ones. Inspired by human learning processes that emphasize critical thinking, CFT encourages deeper analysis and nuanced understanding-traits often overlooked by standard SFT. To validate the effectiveness of CFT, we construct a 50K-sample dataset from WebInstruct, using GPT-4o as the teacher to generate critiques in the form of ([query; noisy response], critique). CFT on this dataset yields a consistent 4-10% improvement over SFT on six math benchmarks with different base models like Qwen2.5, Qwen2.5-Math and DeepSeek-Math. We further expand to MetaMath and NuminaMath datasets and observe similar gains over SFT. Notably, our model Qwen2.5-Math-CFT only requires 1 hour training on 8xH100 over the 50K examples. It can match or outperform strong competitors like Qwen2.5-Math-Instruct on most benchmarks, which use over 2M samples. Moreover, it can match the performance of SimpleRL, which is a deepseek-r1 replication trained with 140x more compute. Ablation studies show that CFT is robust to the source of noisy response and teacher critique model. Through these findings, we argue that CFT offers a more effective alternative to advance the reasoning of language models.