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home / papers / 2024 / MARIO: MAth Reasoning with code Interpreter Output - A Reproducible Pipeline

MARIO: MAth Reasoning with code Interpreter Output - A Reproducible Pipeline

Paper · 2024 · Minpeng Liao, Chengxi Li, Wei Luo et al.

Summary

Code-centric math solvers such as PoT or ToRA compute accurately, but they often ignore real-world sense. For example, they may return a negative number of cups. MARIO addresses this with a solution format that mixes natural-language reasoning with Python snippets run by a code interpreter.

The authors built the corpus from GSM8K and MATH training problems:

  • GPT-3.5 and GPT-4 produced initial solutions using ReAct-style prompts.
  • Human reviewers fixed GSM8K discrepancies and easy final-answer errors in MATH.
  • A Llemma-34B model, fine-tuned on this seed data, sampled extra solutions for MATH problems that were still unsolved.
  • MetaMath questions added further positive and negative samples.

Training starts from Llemma with full-parameter SFT. A LoRA multi-task stage then teaches the same model to both generate solutions and score them as an outcome value model (OVM). At inference, an outlier-free OVM selection step picks the best answer.

The authors report state-of-the-art MATH results for models around 7B and good out-of-domain generalization. The work matters because the full pipeline, code and checkpoints are released for reproducibility.

Key points

  • Coverage of the training sets:
    • GPT annotation gave correct solutions for 98.3% of GSM8K, and human review brought it to full coverage.
    • MATH coverage rose from 66.7% (GPT) to 83.9% (human fixes) and then to 93.8% (self-training sampling).
  • Data ablation on Llemma-7B (GSM8K / MATH accuracy):
    • GPT-only data, 23.9K: 66.3 / 40.2
    • With human corrections, 26.9K: 67.1 / 43.5
    • With MetaMath augmentation, 82K: 70.1 / 47.0
  • Single deployed model: the value classifier is a light binary head trained with LoRA, so one model handles both generating and verifying solutions.
  • Criticism of GSM-Hard: the authors argue it is a flawed benchmark, because its altered numbers can yield physically impossible answers (negative ages, fractional people).
  • Annotation cost: GPT-4 charges about $0.01 per GSM8K solution and $0.025 per MATH solution, plus roughly 80 hours of manual correction.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🏢Alibaba GroupHangzhou · China201 works · 17,172 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 18,614 worksArtificial Intelligence · 17,965 worksArts and Humanities · 17,450 worksLanguage and Linguistics · 17,296 worksComputational Theory and Mathematics · 321 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,685 works

Cite

Cite as Minpeng Liao, Chengxi Li, Wei Luo, Wu Jing and Kai Fan. 2024. MARIO: MAth Reasoning with code Interpreter Output - A Reproducible Pipeline. Findings of the Association for Computational Linguistics: ACL 2024.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2024.findings-acl.53 · arXiv 2401.08190

@inproceedings{liao2024mario,
  title = {{MARIO: MAth Reasoning with code Interpreter Output - A Reproducible Pipeline}},
  author = {Minpeng Liao, Chengxi Li, Wei Luo, Wu Jing and Kai Fan},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2024},
  year = {2024},
  doi = {10.18653/v1/2024.findings-acl.53},
  eprint = {2401.08190},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.18653/v1/2024.findings-acl.53}
}

References

43 references, 33 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Rohan Anil, Andrew M Dai, Orhan Firat, Melvin Johnson, Dmitry Lepikhin, Alexandre Passos, Siamak Shakeri, Emanuel Taropa, Paige Bailey, Zhifeng Chen, et al. 2023. Palm 2 technical report. arXiv preprint arXiv:2305.10403.
  2. Anonymous. 2023. Solving challenging math word problems using GPT-4 code interpreter with code-based self-verification. In Submitted to The Twelfth International Conference on Learning Representations. Under review.
  3. Anthropic. 2023. Model card and evaluations for claude models. find
  4. Zhangir Azerbayev, Hailey Schoelkopf, Keiran Paster, Marco Dos Santos, Stephen McAleer, Albert Q Jiang, Jia Deng, Stella Biderman, and Sean Welleck. 2023. Llemma: An open language model for mathematics. arXiv preprint arXiv:2310.10631.
  5. Jinze Bai, Shuai Bai, Yunfei Chu, Zeyu Cui, Kai Dang, Xiaodong Deng, Yang Fan, Wenbin Ge, Yu Han, Fei Huang, Binyuan Hui, Luo Ji, Mei Li, Junyang Lin, Runji Lin, Dayiheng Liu, Gao Liu, Chengqiang Lu, Keming Lu, Jianxin Ma, Rui Men, Xingzhang Ren, Xuancheng Ren, Chuanqi Tan, Sinan Tan, Jianhong Wenhu… find
  6. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. 2021a. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168.
  7. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. 2021b. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168.
  8. Tri Dao. 2023. FlashAttention-2: Faster attention with better parallelism and work partitioning.
  9. DeepSeek. 2023. Deepseek coder: Let the code write itself. https://github.com/deepseek-ai/ DeepSeek-Coder. ↗
  10. Yao Fu, Hao Peng, Litu Ou, Ashish Sabharwal, and Tushar Khot. 2023. Specializing smaller language models towards multi-step reasoning. In Proceedings of the 40th International Conference on Machine Learning, volume 202 of Proceedings of Machine Learning Research, pages 10421–10430. PMLR.
  11. Luyu Gao, Aman Madaan, Shuyan Zhou, Uri Alon, Pengfei Liu, Yiming Yang, Jamie Callan, and Graham Neubig. 2023. Pal: Program-aided language models. In International Conference on Machine Learning, pages 10764–10799. PMLR. find
  12. Jianping Gou, Baosheng Yu, Stephen J. Maybank, and Dacheng Tao. 2021. Knowledge distillation: A survey. International Journal of Computer Vision, 129(6):1789–1819. find
  13. Zhibin Gou, Zhihong Shao, Yeyun Gong, yelong shen, Yujiu Yang, Minlie Huang, Nan Duan, and Weizhu Chen. 2023. Tora: A tool-integrated reasoning agent for mathematical problem solving.
  14. Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. 2021. Measuring mathematical problem solving with the math dataset. NeurIPS.
  15. Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. 2015. Distilling the knowledge in a neural network.
  16. Namgyu Ho, Laura Schmid, and Se-Young Yun. 2023. Large language models are reasoning teachers. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 14852–14882, Toronto, Canada. Association for Computational Linguistics.
  17. Edward J Hu, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. 2021. Lora: Low-rank adaptation of large language models. In International Conference on Learning Representations.
  18. Muhammad Khalifa, Lajanugen Logeswaran, Moontae Lee, Honglak Lee, and Lu Wang. 2023. GRACE: Discriminator-guided chain-of-thought reasoning. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 15299–15328, Singapore. Association for Computational Linguistics. find
  19. Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yutaka Matsuo, and Yusuke Iwasawa. 2023. Large language models are zero-shot reasoners.
  20. Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, Ambrose Slone, Cem Anil, Imanol Schlag, Theo Gutman-Solo, et al. 2022. Solving quantitative reasoning problems with language models. Advances in Neural Information Processing Systems, 35:3843– 3857.
  21. Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. 2023. Let’s verify step by step. arXiv preprint arXiv:2305.20050.
  22. Haipeng Luo, Qingfeng Sun, Can Xu, Pu Zhao, Jian-guang Lou, Chongyang Tao, Xiubo Geng, Qingwei Lin, Shifeng Chen, and Dongmei Zhang. 2023. Wizardmath: Empowering mathematical reasoning for large language models via reinforced evol-instruct. arXiv preprint arXiv:2308.09583.
  23. Aman Madaan, Niket Tandon, Prakhar Gupta, Skyler Hallinan, Luyu Gao, Sarah Wiegreffe, Uri Alon, Nouha Dziri, Shrimai Prabhumoye, Yiming Yang, Sean Welleck, Bodhisattwa Prasad Majumder, Shashank Gupta, Amir Yazdanbakhsh, and Peter Clark. 2023. Self-refine: Iterative refinement with self-feedback. find
  24. Zhihong Shao, Fei Huang, and Minlie Huang. 2022. Chaining simultaneous thoughts for numerical reasoning. In Findings of the Association for Computational Linguistics: EMNLP 2022, pages 2533–2547, Abu Dhabi, United Arab Emirates. Association for Computational Linguistics. find
  25. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Mingchuan Zhang, YK Li, Y Wu, and Daya Guo. 2024. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300.
  26. Gemini Team, Rohan Anil, Sebastian Borgeaud, Yonghui Wu, Jean-Baptiste Alayrac, Jiahui Yu, Radu Soricut, Johan Schalkwyk, Andrew M Dai, Anja Hauth, et al. 2023. Gemini: a family of highly capable multimodal models. arXiv preprint arXiv:2312.11805.
  27. Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. 2023. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288.
  28. Ke Wang, Houxing Ren, Aojun Zhou, Zimu Lu, Sichun Luo, Weikang Shi, Renrui Zhang, Linqi Song, Mingjie Zhan, and Hongsheng Li. 2023a. Mathcoder: Seamless code integration in llms for enhanced mathematical reasoning.
  29. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. 2023b. Self-consistency improves chain of thought reasoning in language models. In The Eleventh International Conference on Learning Representations.
  30. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. 2022. Chain-of-thought prompting elicits reasoning in large language models. Advances in Neural Information Processing Systems, 35:24824–24837.
  31. R OpenAI. 2023. Gpt-4 technical report. arXiv, pages 2303–08774.
  32. Samyam Rajbhandari, Olatunji Ruwase, Jeff Rasley, Shaden Smith, and Yuxiong He. 2021. Zero-infinity: Breaking the gpu memory wall for extreme scale deep learning. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’21, New York, NY, US…
  33. Baptiste Roziere, Jonas Gehring, Fabian Gloeckle, Sten Sootla, Itai Gat, Xiaoqing Ellen Tan, Yossi Adi, Jingyu Liu, Tal Remez, Jérémy Rapin, et al. 2023. Code llama: Open foundation models for code. arXiv preprint arXiv:2308.12950.
  34. Tianwen Wei, Liang Zhao, Lichang Zhang, Bo Zhu, Lijie Wang, Haihua Yang, Biye Li, Cheng Cheng, Weiwei Lü, Rui Hu, et al. 2023. Skywork: A more open bilingual foundation model. arXiv preprint arXiv:2310.19341.
  35. Yixuan Weng, Minjun Zhu, Fei Xia, Bin Li, Shizhu He, Shengping Liu, Bin Sun, Kang Liu, and Jun Zhao. 2023. Large language models are better reasoners with self-verification. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 2550–2575, Singapore. Association for Computat…
  36. Yuxi Xie, Kenji Kawaguchi, Yiran Zhao, Xu Zhao, Min-Yen Kan, Junxian He, and Qizhe Xie. 2023. Decomposition enhances reasoning via self-evaluation guided decoding. find
  37. Zhen Yang, Ming Ding, Qingsong Lv, Zhihuan Jiang, Zehai He, Yuyi Guo, Jinfeng Bai, and Jie Tang. 2023. Gpt can solve mathematical problems without a calculator. arXiv preprint arXiv:2309.03241. find
  38. Shunyu Yao, Jeffrey Zhao, Dian Yu, Nan Du, Izhak Shafran, Karthik R Narasimhan, and Yuan Cao. 2022. React: Synergizing reasoning and acting in language models. In The Eleventh International Conference on Learning Representations.
  39. Fei Yu, Anningzhe Gao, and Benyou Wang. 2023a. Outcome-supervised verifiers for planning in mathematical reasoning. arXiv preprint arXiv:2311.09724.
  40. Longhui Yu, Weisen Jiang, Han Shi, Jincheng Yu, Zhengying Liu, Yu Zhang, James T Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu. 2023b. Metamath: Bootstrap your own mathematical questions for large language models. arXiv preprint arXiv:2309.12284.
  41. Zheng Yuan, Hongyi Yuan, Chengpeng Li, Guanting Dong, Keming Lu, Chuanqi Tan, Chang Zhou, and Jingren Zhou. 2023. Scaling relationship on learning mathematical reasoning with large language models.
  42. Xiang Yue, Xingwei Qu, Ge Zhang, Yao Fu, Wenhao Huang, Huan Sun, Yu Su, and Wenhu Chen. 2023. Mammoth: Building math generalist models through hybrid instruction tuning. arXiv preprint arXiv:2309.05653.
  43. Aojun Zhou, Ke Wang, Zimu Lu, Weikang Shi, Sichun Luo, Zipeng Qin, Shaoqing Lu, Anya Jia, Linqi Song, Mingjie Zhan, et al. 2023. Solving challenging math word problems using gpt-4 code interpreter with code-based self-verification. arXiv preprint arXiv:2308.07921.

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