Long Is More Important Than Difficult for Training Reasoning Models

TL;DR

The paper challenges the prevailing view that problem difficulty is the primary driver of reasoning performance in large language models, showing that reasoning length is the key factor. It demonstrates a data-length scaling law in which model accuracy improves nearly linearly as reasoning length increases, and provides a simple synthesis method to generate arbitrarily long reasoning data. By constructing the Long1K dataset and fine-tuning a strong base model to Long1K-32B, the authors achieve state-of-the-art or competitive results on MATH500 and GPQA Diamond with only 1,000 training samples, and release the model, code, and data openly. These results imply that dataset design and training strategies should prioritize extended reasoning sequences over forcing difficulty, enabling scalable improvements in reasoning capabilities.

Abstract

Difficult problems, which often result in long reasoning traces, are widely recognized as key factors for enhancing the performance of reasoning models. However, such high-challenge problems are scarce, limiting the size of available datasets. In this paper, we propose a simple method to decouple the reliance on problem difficulty. First, we empirically demonstrate that reasoning length, rather than problem difficulty, primarily influences the performance of trained models. Second, we identify a scaling law on reasoning length, showing that model performance increases in a log-linear fashion as the reasoning data length grows. Finally, we introduce a straightforward technique to generate reasoning data of arbitrary length, and show that synthesized data is effective for training reasoning models. After fine-tuning the Qwen2.5-32B-Instruct language model on our Long1K dataset, we present our model, Long1K-32B, which achieves remarkable performance with only 1,000 training samples, achieving 95.6\% accuracy on MATH, and 71.1\% on GPQA outperforming DeepSeek-R1-Distill-Qwen-32B. The model, code, and dataset are all open-sourced, available at https://huggingface.co/ZTss/LONG1.

Figures (6)

• Figure 1: (a) Accuracy comparison of Qwen2.5-7B-Instruct and Qwen2.5-32B-Instruct after training on Long Problems(Composite) and Difficult Problems(Composite). (b) Accuracy comparison of Qwen2.5-7B-Instruct and Qwen2.5-32B-Instruct after training on Long Problems(Double) and Difficult Problems(Single).
• Figure 2: Test results of models trained under different reasoning length levels on MATH500 and GPQA Diamond.
• Figure 3: This is the prompt for extracting mathematical knowledge points.
• Figure 4: This is an example of extracting mathematical knowledge points.
• Figure 5: This is a prompt for Long Problem (Composite) based on multiple mathematical concepts.