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Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning

Paper · 2025 · Maggie Huan, Yuetai Li, Tuney Zheng et al.

Summary

The paper asks whether the rapid gains reasoning-tuned LLMs show on math benchmarks such as MATH and AIME reflect broader problem-solving skill or narrow specialization. The authors evaluated more than 20 open-weight reasoning models on three task groups: math, other reasoning (science QA, coding, medical QA, agent planning) and non-reasoning tasks (conversational QA, instruction following, hallucination detection). They introduced a Transferability Index, which measures how much of a model's math improvement carries over to other groups. Across model families and sizes, the training method was the most consistent predictor of transfer. RL-tuned models carried their gains over, while SFT-tuned models often lost general abilities. A controlled experiment on Qwen3-14B-Base, trained on the same math data with either SFT or RL, confirmed this pattern. Analyses of hidden-state PCA, KL divergence and token rank shift showed that SFT moves internal representations and output distributions much further from the base model. The findings call into question post-training recipes that depend heavily on SFT with distilled reasoning traces.

Key points

  • Benchmarks:
    • Math: MATH500, AIME24, AIME25 and OlympiadBench.
    • Other reasoning: GPQA-Diamond, LiveCodeBench, ACPBench and HeadQA.
    • Non-reasoning: CoQA, IFEval, HaluEval and MC-TACO.
  • Transferability Index (TI): per-benchmark gains over the base model are z-normalized, compressed with a signed square root, and weighted toward harder tasks. Each group's score is then expressed as a ratio to the math group's score.
  • Controlled study (UniReason models):
    • Training data came from MATH and DeepScaler.
    • SFT targets were Qwen3-32B chain-of-thought traces, kept only if their final answer was correct (rejection sampling).
    • RL used GRPO with answer correctness as the reward.
  • Results on Qwen3-14B-Base:
    • Math average: base 27.7, RL 53.8, best SFT 49.8.
    • Non-reasoning average: base 45.7, RL 53.2, SFT 21.1 (think) and 29.0 (no-think).
    • TI on non-reasoning tasks: RL +52.2, SFT −104.1 and −278.9.
  • Ablation: the sampling distribution, credit assignment and negative gradients support generalization in RL, while KL regularization has only a subtle effect.

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

 Fields, topics and concepts

Cite

Cite as Maggie Huan, Yuetai Li, Tuney Zheng, Xiaoyu Xu, Seungone Kim, Minxin Du, Radha Poovendran, Graham Neubig and Xiang Yue. 2025. Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning. arXiv:2507.00432.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2507.00432 · arXiv 2507.00432

@misc{huan2025does,
  title = {{Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning}},
  author = {Maggie Huan, Yuetai Li, Tuney Zheng, Xiaoyu Xu, Seungone Kim, Minxin Du, Radha Poovendran, Graham Neubig and Xiang Yue},
  year = {2025},
  doi = {10.48550/arxiv.2507.00432},
  eprint = {2507.00432},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2507.00432}
}

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