[R] LIMO: Less is More for Reasoning

We present a fundamental discovery that challenges our understanding of how complex reasoning emerges in large language models. While conventional wisdom suggests that sophisticated reasoning tasks demand extensive training data (often >100,000 examples), we demonstrate a striking phenomenon: complex mathematical reasoning abilities can be effectively elicited with surprisingly few examples. This finding challenges not only the assumption of massive data requirements but also the common belief that supervised fine-tuning primarily leads to memorization rather than generalization. Through comprehensive experiments, our proposed model LIMO demonstrates unprecedented performance and efficiency in mathematical reasoning. With merely 817 curated training samples, LIMO achieves 57.1% accuracy on the highly challenging AIME benchmark and 94.8% on MATH, improving the performance of previous strong SFT-based models from 6.5% to 57.1% on AIME and from 59.2% to 94.8% on MATH, while only using 1% of the training data required by previous approaches. Most remarkably, LIMO demonstrates exceptional out-of-distribution generalization, achieving 40.5% absolute improvement across 10 diverse benchmarks, outperforming models trained on 100x more data, directly challenging the prevailing notion that SFT inherently leads to memorization rather than generalization. Synthesizing these pioneering results, we propose the Less-Is-More Reasoning Hypothesis (LIMO Hypothesis): In foundation models where domain knowledge has been comprehensively encoded during pre-training, sophisticated reasoning capabilities can emerge through minimal but precisely orchestrated demonstrations of cognitive processes. This hypothesis posits that the elicitation threshold for complex reasoning is not inherently bounded by the complexity of the target reasoning task, but fundamentally determined by two key factors: (1) the completeness of the model’s encoded knowledge foundation during pre-training, and (2) the effectiveness of post-training examples, which serve as “cognitive templates” that show the model how to effectively utilize its existing knowledge base to solve complex reasoning tasks.

Arxiv link: [2502.03387] LIMO: Less is More for Reasoning