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A geometric neural solving method based on a diagram text information fusion analysis.

Bin Ma1, Pengpeng Jian1, Cong Pan2

  • 1North China University of Water Resources and Electric Power, Zhengzhou, 450046, China.

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This study introduces an improved AI method for solving geometry problems by enhancing feature extraction from diagrams and text. The new approach boosts performance on datasets like PGPS9K, improving geometric problem-solving capabilities.

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Area of Science:

  • Artificial Intelligence
  • Computer Science
  • Mathematics Education

Background:

  • Geometric problem solving in AI education faces challenges due to difficulties in integrating diagrammatic and textual information.
  • Current methods suffer from poor feature extraction from geometry diagrams and inadequate fusion of multi-modal information, hindering performance.
  • Effective geometric reasoning requires combining mathematical theorems, logical representation, and solution execution.

Purpose of the Study:

  • To develop an improved AI-driven method for geometric problem solving by addressing limitations in feature extraction and information fusion.
  • To enhance the semantic representation of cross-modal information through auxiliary tasks and pre-training strategies.
  • To improve the accuracy and effectiveness of AI systems in solving geometry problems presented in diverse formats.

Main Methods:

  • An improved diagram parser, DenseNet, was proposed for effective geometry diagram feature extraction.
  • A structural and semantic pre-training strategy was employed for text description parsing to ensure consistent interpretation.
  • Information fusion was achieved by connecting modal labels and processing through an encoder, guided by multi-modal information.

Main Results:

  • The proposed method demonstrated improved performance on the PGPS9K dataset, with an average improvement of 1.3%.
  • Effectiveness was further validated through comparisons with the Geometry3K dataset, confirming the robustness of the approach.
  • Enhanced semantic representation and information fusion led to more accurate geometric knowledge generation and program execution.

Conclusions:

  • The developed AI method significantly improves geometric problem-solving capabilities by effectively integrating visual and textual data.
  • The integration of an improved diagram parser and advanced pre-training strategies enhances the AI's ability to understand and solve complex geometry problems.
  • This research offers a promising direction for advancing AI in mathematical education and automated reasoning systems.