---
license: apache-2.0
language:
- en
metrics:
- accuracy
pipeline_tag: text-generation
tags:
- code
- math
---
# MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs

This is a model for the paper "[MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs](https://arxiv.org/pdf/2402.16352.pdf)".




## News

- **[2024-02-26]** Our paper is now accessible at [ArXiv Paper](https://arxiv.org/pdf/2402.16352.pdf).

## Introduction

Large language models (LLMs) have exhibited great potential in mathematical reasoning. However, there remains a performance gap in this area between existing open-source models and closed-source models such as GPT-4. 

In this paper, we introduce **MathGenie**, a novel method for generating diverse and reliable math problems from a small-scale problem-solution dataset (denoted as *seed data*). We augment the ground-truth solutions of our seed data and train a back-translation model to translate the augmented solutions back into new questions. Subsequently, we generate code-integrated solutions for the new questions. To ensure the correctness of the code-integrated solutions, we employ rationale-based strategy for solution verification. 

Various pretrained models, ranging from 7B to 70B, are trained on the newly curated data to test the effectiveness of the proposed augmentation technique, resulting in a family of models known as *MathGenieLM*. These models consistently outperform previous open-source models across five representative mathematical reasoning datasets, achieving state-of-the-art performance. In particular, MathGenieLM-InternLM2 achieves an accuracy of 87.7% on GSM8K and 55.7% on MATH, securing the best overall score among open-source language models.

You can refer to the [project homepage](https://mathgenie.github.io/) and [the paper](https://arxiv.org/pdf/2402.16352.pdf) for more details.

## Usage

### Models

Our [MathGenie-InterLM-20B](https://huggingface.co./MathGenie/MathGenie-InterLM-20B) model is available at Huggingface now.
Our [MathGenie-Mixtral-8x7B](https://huggingface.co./MathGenie/MathGenie-Mixtral-8x7B) model is available at Huggingface now.

| Base Model   | Model                                                        |
| ------------ | ------------------------------------------------------------ |
| InternLM-20B | [MathGenie-InterLM-20B](https://huggingface.co./MathGenie/MathGenie-InterLM-20B) |
| Mixtral-8x7B | [MathGenie-Mixtral-8x7B](https://huggingface.co./MathGenie/MathGenie-Mixtral-8x7B) |

### Inference & Evaluation

**template**

```
{% for message in messages %}
{% if message['role'] == 'user' %}
{{ '<|user|>' }}{% elif message['role'] == 'system' %}
{{ '<|system|>' }}{% elif message['role'] == 'assistant' %}
{{ '<|assistant|>' }}{% endif %}
{% for block in message['content'] %}
{% if block['type'] == 'text' %}
{{ '<|text|>' }}{% elif block['type'] == 'code' %}
{{ '<|code|>' }}{% elif block['type'] == 'execution' %}
{{ '<|execution|>' }}{% endif %}
{{ block['content'] + '<|endofblock|>' }}{% endfor %}
{{ '<|endofmessage|>' }}{% endfor %}
```

Please refer to the [MathCoder repo](https://github.com/mathllm/MathCoder) for the detailed code for inference and evaluation of our MathGenieLM models.

## Citation

If you find this paper helpful to your research, please kindly cite this BibTex:

```
@misc{lu2024mathgenie,
			title={MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs}, 
      author={Zimu Lu and Aojun Zhou and Houxing Ren and Ke Wang and Weikang Shi and Junting Pan and Mingjie Zhan and Hongsheng Li},
      year={2024},
      eprint={2402.16352},
      archivePrefix={arXiv},
      primaryClass={cs.CL}
}
```

```
@inproceedings{
			wang2024mathcoder,
			title={MathCoder: Seamless Code Integration in {LLM}s for Enhanced Mathematical Reasoning},
			author={Ke Wang and Houxing Ren and Aojun Zhou and Zimu Lu and Sichun Luo and Weikang Shi and Renrui Zhang and Linqi Song and Mingjie Zhan and Hongsheng Li},
			booktitle={The Twelfth International Conference on Learning Representations},
			year={2024},
			url={https://openreview.net/forum?id=z8TW0ttBPp}
}
```