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A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning

Iddo Drori1,2, Sarah Zhang3, Reece Shuttleworth1

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Proceedings of the National Academy of Sciences of the United States of America
|August 2, 2022
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Summary

A neural network fine-tuned on code can solve university math problems with 81% accuracy, significantly outperforming previous AI models. This AI also explains solutions and generates new math questions, marking a milestone for higher education.

Keywords:
and generating questionsansweringexplainingmathematics coursesneural networks

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Area of Science:

  • Artificial Intelligence
  • Computer Science
  • Mathematics Education

Background:

  • Traditional AI models struggle with complex mathematical reasoning and problem-solving.
  • Existing language models show limited success in solving university-level mathematics problems.

Purpose of the Study:

  • To develop an AI capable of solving university mathematics course problems at a human level.
  • To evaluate the effectiveness of program synthesis using a code-fine-tuned neural network for mathematical problem-solving.
  • To assess the AI's ability to explain solutions and generate novel mathematics questions.

Main Methods:

  • Utilized OpenAI's Codex transformer, fine-tuned on code, for program synthesis.
  • Employed few-shot learning to enable the model to solve problems with minimal examples.
  • Curated datasets from MIT and Columbia University mathematics courses, alongside the MATH dataset for advanced problems.
  • Executed synthesized programs to automatically solve and generate solutions (including plots and equations) for mathematics problems.

Main Results:

  • Achieved 81% automatic accuracy in solving university-level mathematics course problems.
  • Significantly surpassed GPT-3's performance (18.8% zero-shot, 30.8% few-shot) on the same datasets.
  • Improved state-of-the-art automatic solution accuracy from 8.8% to 81.1% on benchmark topics.
  • Demonstrated human-level performance in explaining solutions and generating questions.

Conclusions:

  • Program synthesis with a code-fine-tuned neural network is highly effective for solving complex mathematics problems.
  • This AI approach represents a significant advancement in automated mathematical reasoning and educational tools.
  • The model's capabilities in solving, explaining, and generating problems offer scalable solutions for higher education.