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license: apache-2.0
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---
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---
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license: apache-2.0
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language:
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- en
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metrics:
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- accuracy
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pipeline_tag: text-generation
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tags:
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- code
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- math
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---
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# MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs
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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)".
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## News
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- **[2024-02-26]** Our paper is now accessible at [ArXiv Paper](https://arxiv.org/pdf/2402.16352.pdf).
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## Introduction
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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.
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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.
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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.
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You can refer to the [project homepage](https://mathgenie.github.io/) and [the paper](https://arxiv.org/pdf/2402.16352.pdf) for more details.
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## Usage
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### Models
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Our [MathGenie-InterLM-20B](https://huggingface.co/MathGenie/MathGenie-InterLM-20B) model is available at Huggingface now.
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Our [MathGenie-Mixtral-8x7B](https://huggingface.co/MathGenie/MathGenie-Mixtral-8x7B) model is available at Huggingface now.
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| Base Model | Model |
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| ------------ | ------------------------------------------------------------ |
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| InternLM-20B | [MathGenie-InterLM-20B](https://huggingface.co/MathGenie/MathGenie-InterLM-20B) |
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| Mixtral-8x7B | [MathGenie-Mixtral-8x7B](https://huggingface.co/MathGenie/MathGenie-Mixtral-8x7B) |
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### Inference & Evaluation
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Please refer to the [MathCoder repo](https://github.com/mathllm/MathCoder) for the detailed code for inference and evaluation of our MathGenieLM models.
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## Citation
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If you find this paper helpful to your research, please kindly cite this BibTex:
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```
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@misc{lu2024mathgenie,
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title={MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs},
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author={Zimu Lu and Aojun Zhou and Houxing Ren and Ke Wang and Weikang Shi and Junting Pan and Mingjie Zhan and Hongsheng Li},
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year={2024},
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eprint={2402.16352},
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archivePrefix={arXiv},
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primaryClass={cs.CL}
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}
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```
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```
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@inproceedings{
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wang2024mathcoder,
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title={MathCoder: Seamless Code Integration in {LLM}s for Enhanced Mathematical Reasoning},
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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},
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booktitle={The Twelfth International Conference on Learning Representations},
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year={2024},
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url={https://openreview.net/forum?id=z8TW0ttBPp}
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}
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```
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