---
title: "To Code or not to Code? Adaptive Tool Integration for Math"
description: "Math-focused language models can reason in natural language (CoT) or offload… 9.4 points on AIME. 37 references, cited by 7 papers here."
authors: ["Haozhe Wang", "Long Li", "Chao Qu", "Weidi Xu", "Fengming Zhu", "Wei Chu", "Fangzhen Lin"]
year: 2025
venue: "Findings of the Association for Computational Linguistics: ACL 2025"
source: "https://aclanthology.org/2025.findings-acl.159/"
doi: "10.18653/v1/2025.findings-acl.159"
arxiv: "2502.00691"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/wang-2025-code-or-not-code-adaptive/"
---
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# To Code or not to Code? Adaptive Tool Integration for Math Language Models via Expectation-Maximization

**Authors:** [Haozhe Wang](https://md.research.elamur.ai/free/en/authors/haozhe-wang/), [Long Li](https://md.research.elamur.ai/free/en/authors/long-li/), [Chao Qu](https://md.research.elamur.ai/free/en/authors/chao-qu/), [Weidi Xu](https://md.research.elamur.ai/free/en/authors/weidi-xu/), Fengming Zhu, [Wei Chu](https://md.research.elamur.ai/free/en/authors/wei-chu/) and [Fangzhen Lin](https://md.research.elamur.ai/free/en/authors/fangzhen-lin/) · **Year:** 2025 · **Venue:** [Findings of the Association for Computational Linguistics: ACL 2025](https://md.research.elamur.ai/free/en/venues/findings/) ([Findings of the Association for Computational Linguistics 2025](https://md.research.elamur.ai/free/en/venues/findings/2025/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2025.findings-acl.159/) · [PDF](https://aclanthology.org/2025.findings-acl.159.pdf) · [DOI 10.18653/v1/2025.findings-acl.159](https://doi.org/10.18653/v1/2025.findings-acl.159) · [arXiv 2502.00691](https://arxiv.org/abs/2502.00691) · [OpenAlex](https://openalex.org/W4412888798)

**Citations:** 2 citations (OpenAlex, 2026-10-14) · [7](https://md.research.elamur.ai/free/en/papers/wang-2025-code-or-not-code-adaptive/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Math-focused language models can reason in natural language (CoT) or offload computation to Python, but current hybrid systems such as Mammoth, Deepseek-Math and Qwen-2.5-Math decide poorly when to use code. They either wait for an explicit instruction or follow fixed templates learned through supervised fine-tuning. The authors aim for autonomous code integration (AutoCode), where the model itself judges whether code will help, given its own abilities. They found that standard RL such as PPO explores the space of CoT/code mixtures too narrowly. To fix this, they treat the code-triggering choice as a latent variable in an Expectation-Maximization loop:

- **E-step:** the model is probed with both CoT and code prefixes. The value of each choice is estimated from multiple rollouts, and the training data is reweighted toward the more promising strategy.
- **M-step:** off-policy RL updates both the tool-use decision and the reasoning itself.

Built on Qwen-2.5-Base, the resulting 7B model raises MATH500 accuracy from 60.4% to 71.4% and trains more efficiently than SFT or RL baselines. This matters because it shows that tool-use policy can be learned rather than hand-specified.

## Key points
- The 7B AutoCode model gains about 11 points on MATH500 (60.4% → 71.4%) and 9.4 points on AIME, without o1-style long CoT.
- Existing models choose between CoT and code at near-chance level (about 50%). For example, DeepseekMath-Instruct-7B loses 11.54% accuracy when left to decide on its own.
- AutoCode4Math-Qwen2.5 picks the right strategy 89.53% of the time and beats explicitly code-prompted performance by 7%.
- Under SFT+RL training, per-query code usage drifts toward the extremes (always or never), which the authors read as evidence of weak exploration.
- Code, models and data are released at github.com/HaozheH3/AutoCode. The method has only been evaluated on mathematics.

*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

- [Hong Kong University of Science and Technology](https://md.research.elamur.ai/free/en/universities/hong-kong-university-of-science-and-technology/) — University, Hong Kong, China · 183 works · 27,600 citations

📚 Shelves (7): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 19,503 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 18,805 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 17,959 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 17,789 works · [➗ Mathematics](https://md.research.elamur.ai/free/en/shelves/mathematics/) · 233 works · [🧮 Computational Theory and Mathematics](https://md.research.elamur.ai/free/en/shelves/computer-science/computational-theory-and-mathematics/) · 496 works · [➗ Applied Mathematics](https://md.research.elamur.ai/free/en/shelves/mathematics/applied-mathematics/) · 73 works

🧭 Topics (1): [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · 4,145 works

## Cite

Cite as: Haozhe Wang, Long Li, Chao Qu, Weidi Xu, Fengming Zhu, Wei Chu and Fangzhen Lin. 2025. To Code or not to Code? Adaptive Tool Integration for Math Language Models via Expectation-Maximization. Findings of the Association for Computational Linguistics: ACL 2025.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{wang2025code,
  title = {{To Code or not to Code? Adaptive Tool Integration for Math Language Models via Expectation-Maximization}},
  author = {Haozhe Wang, Long Li, Chao Qu, Weidi Xu, Fengming Zhu, Wei Chu and Fangzhen Lin},
  booktitle = {Findings of the Association for Computational Linguistics: ACL 2025},
  year = {2025},
  doi = {10.18653/v1/2025.findings-acl.159},
  eprint = {2502.00691},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.18653/v1/2025.findings-acl.159}
}
```

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*Updated 3 November 2026*