README.md

---
base_model: Qwen/Qwen2.5-1.5B
language:
- en
pipeline_tag: text-generation
library_name: transformers
license: apache-2.0
license_link: https://huggingface.co/Qwen/Qwen2.5-Math-1.5B/blob/main/LICENSE
---

# Qwen2.5-Math-1.5B

> [!Warning]
> <div align="center">
> <b>
> 🚨 Qwen2.5-Math mainly supports solving English and Chinese math problems through CoT and TIR. We do not recommend using this series of models for other tasks.
> </b>
> </div>

## Introduction

In August 2024, we released the first series of mathematical LLMs - [Qwen2-Math](https://qwenlm.github.io/blog/qwen2-math/) - of our Qwen family. A month later, we have upgraded it and open-sourced **Qwen2.5-Math** series, including base models **Qwen2.5-Math-1.5B/7B/72B**, instruction-tuned models **Qwen2.5-Math-1.5B/7B/72B-Instruct**, and mathematical reward model **Qwen2.5-Math-RM-72B**. 
                                                                              
Unlike Qwen2-Math series which only supports using Chain-of-Thught (CoT) to solve English math problems, Qwen2.5-Math series is expanded to support using both CoT and Tool-integrated Reasoning (TIR) to solve math problems in both Chinese and English. The Qwen2.5-Math series models have achieved significant performance improvements compared to the Qwen2-Math series models on the Chinese and English mathematics benchmarks with CoT. 
![](http://qianwen-res.oss-accelerate-overseas.aliyuncs.com/Qwen2.5/qwen2.5-math-pipeline.jpeg)

While CoT plays a vital role in enhancing the reasoning capabilities of LLMs, it faces challenges in achieving computational accuracy and handling complex mathematical or algorithmic reasoning tasks, such as finding the roots of a quadratic equation or computing the eigenvalues of a matrix. TIR can further improve the model's proficiency in precise computation, symbolic manipulation, and algorithmic manipulation. Qwen2.5-Math-1.5B/7B/72B-Instruct achieve 79.7, 85.3, and 87.8 respectively on the MATH benchmark using TIR. 

## Model Details


For more details, please refer to our [blog post](https://qwenlm.github.io/blog/qwen2.5-math/) and [GitHub repo](https://github.com/QwenLM/Qwen2.5-Math).


## Requirements
* `transformers>=4.37.0` for Qwen2.5-Math models. The latest version is recommended.

> [!Warning]
> <div align="center">
> <b>
> 🚨 This is a must because <code>transformers</code> integrated Qwen2 codes since <code>4.37.0</code>.
> </b>
> </div>

For requirements on GPU memory and the respective throughput, see similar results of Qwen2 [here](https://qwen.readthedocs.io/en/latest/benchmark/speed_benchmark.html).

## Quick Start

> [!Important]
>
> **Qwen2.5-Math-1.5B-Instruct** is an instruction model for chatting;
>
> **Qwen2.5-Math-1.5B** is a base model typically used for completion and few-shot inference, serving as a better starting point for fine-tuning.

## Citation

If you find our work helpful, feel free to give us a citation.

```
@article{yang2024qwen2,
  title={Qwen2 technical report},
  author={Yang, An and Yang, Baosong and Hui, Binyuan and Zheng, Bo and Yu, Bowen and Zhou, Chang and Li, Chengpeng and Li, Chengyuan and Liu, Dayiheng and Huang, Fei and others},
  journal={arXiv preprint arXiv:2407.10671},
  year={2024}
}
```