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Give me a hint: Can LLMs take a hint to solve math problems?

Paper · 2024 · Vansh Agrawal, Pratham Singla, Amitoj Singh Miglani et al.

Summary

The authors ask whether LLMs solve competition-style math better when they receive a short, problem-specific nudge rather than worked examples. They borrow the idea from tutoring, where a teacher points a student in the right direction without giving away the full solution. Gemini 1.5 Flash was shown each question with its final answer and asked to write a hint. The hint was then added to the target prompt. This approach was compared with baseline, one-shot, few-shot and chain-of-thought (CoT) prompting, and with misleading (adversarial) and unrelated (random) hints, for 17 prompt variants in total. Eleven LLMs were tested: base, instruction-tuned, math-tuned and closed-source models. The test set was a 700-problem subset of the MATH dataset. Hinting gave the best average accuracy and CoT the weakest among the non-adversarial methods. Bad hints pushed accuracy below CoT. The work suggests that light guidance can beat full worked examples, but models are easily misled by wrong context.

Key points

  • The evaluation used 7 MATH topics with 100 problems each, at difficulty levels 1–5. The 11 models comprised 9 open-source models plus GPT-4o-mini and Gemini Flash.
  • In Table 2, hinting lifted closed-source models from 0.6685 to 0.7186 and math-tuned models from 0.6180 to 0.6485. Base models dropped from 0.5385 to 0.5104, which the authors attribute to weak instruction following.
  • Adversarial hints hurt every model category. Random hints were especially damaging for base models, which fell to 0.2871.
  • Qwen-2-Math-Instruct came close to GPT-4o-mini and led the 7B/8B group, while Mistral-Instruct ranked lowest in that group.
  • The study has several limitations:
    • The problem sample is small.
    • Answers were graded by an LLM.
    • Hints were generated with access to the correct answer.
    • No models larger than about 8B parameters among the open-source set were tested.

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

🎓Indian Institute of Technology RoorkeeRoorkee · India3 works · 6 citations

 Fields, topics and concepts

📚 Shelves 6The 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 worksMathematics · 189 worksApplied Mathematics · 52 works

🧭 Topics 1Research subjects and languages the work is about.Language models & pretraining · 3,894 works

Cite

Cite as Vansh Agrawal, Pratham Singla, Amitoj Singh Miglani, Shivank Garg and Ayush Mangal. 2024. Give me a hint: Can LLMs take a hint to solve math problems?. arXiv:2410.05915.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2410.05915 · arXiv 2410.05915

@misc{agrawal2024give,
  title = {{Give me a hint: Can LLMs take a hint to solve math problems?}},
  author = {Vansh Agrawal, Pratham Singla, Amitoj Singh Miglani, Shivank Garg and Ayush Mangal},
  year = {2024},
  doi = {10.48550/arxiv.2410.05915},
  eprint = {2410.05915},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2410.05915}
}

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