MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs
This is the official repository for the paper "MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs".
[Homepage] [ArXiv Paper] [Huggingface Models] [Github]
- [2024-02-26] Our paper is now accessible at ArXiv Paper.
- [2024-03-] Our MathGenie-InterLM-20B model is available at Huggingface now.
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.
Framework of MathGenie. Iterative Solution Augmentation augments human-annotated solutions in GSM8K and MATH to create new solutions, as shown in Step 1. These solutions are then back-translated to new questions using Question Back-translation, demonstrated in Step 2. Then reliable code-integrated solutions are curated using Verification-Based Solution Filtering, by generating solutions and filtering them using verification rationales, as shown in Step 3.
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.
Main results of MathGenieLM, compared to various open-source and closed-source models on 2 in-domain datasets (GSM8K, MATH), and 3 out-of-domain datasets (SVAMP, Simuleq, Mathematics).
You can refer to the project homepage and the paper for more details.
Our MathGenie-InterLM-20B model is available at Huggingface now.
| Base Model | Model |
|---|---|
| InternLM-20B | MathGenie-InterLM-20B |
Please refer to the MathCoder repo for the detailed code for inference and evaluation of our MathGenieLM models.
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}
}