ToRA: A Tool-Integrated Reasoning Agent
for Mathematical Problem Solving
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[📜 Paper] •
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Repo for "ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving"
🔥 News
- [2023/10/08] 🔥🔥🔥 All ToRA models released at HuggingFace!!!
- [2023/09/29] ToRA paper, repo, and website released.
💡 Introduction
ToRA is a series of Tool-integrated Reasoning Agents designed to solve challenging mathematical reasoning problems by interacting with tools, e.g., computation libraries and symbolic solvers. ToRA series seamlessly integrate natural language reasoning with the utilization of external tools, thereby amalgamating the analytical prowess of language and the computational efficiency of external tools.
| Model | Size | GSM8k | MATH | AVG@10 math tasks† |
|---|---|---|---|---|
| GPT-4 | - | 92.0 | 42.5 | 78.3 |
| GPT-4 (PAL) | - | 94.2 | 51.8 | 86.4 |
| ToRA-7B | 7B | 68.8 | 40.1 | 62.4 |
| ToRA-Code-7B | 7B | 72.6 | 44.6 | 66.5 |
| ToRA-13B | 13B | 72.7 | 43.0 | 65.9 |
| ToRA-Code-13B | 13B | 75.8 | 48.1 | 71.3 |
| ToRA-Code-34B* | 34B | 80.7 | 51.0 | 74.8 |
| ToRA-70B | 70B | 84.3 | 49.7 | 76.9 |
*ToRA-Code-34B is currently the first and only open-source model to achieve over 50% accuracy (pass@1) on the MATH dataset, which significantly outperforms GPT-4’s CoT result (51.0 vs. 42.5), and is competitive with GPT-4 solving problems with programs. By open-sourcing our codes and models, we hope more breakthroughs will come!
†10 math tasks include GSM8k, MATH, GSM-Hard, SVAMP, TabMWP, ASDiv, SingleEQ, SingleOP, AddSub, and MultiArith.
⚡️ Training
The models are trained on ToRA-Corpus 16k, which contains tool-integrated reasoning trajectories of MATH and GSM8k from GPT-4.
We use imitation learning (i.e., SFT) to fine-tune the models, and then apply our proposed output space shaping to improve tool-integrated reasoning behaviors. Please refer to the paper for more details.
🪁 Inference & Evaluation
Please refer to ToRA's GitHub repo for inference, evaluation, and training code.
☕️ Citation
If you find this repository helpful, please consider citing our paper:
@misc{gou2023tora,
title={ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving},
author={Zhibin Gou and Zhihong Shao and Yeyun Gong and yelong shen and Yujiu Yang and Minlie Huang and Nan Duan and Weizhu Chen},
year={2023},
eprint={2309.17452},
archivePrefix={arXiv},
primaryClass={cs.CL}
}
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