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<p>To address the challenges of high specialization and fragmented learning resources in Geometric Algebra (GA), this paper introduces a multi-task Geometric Algebraic Large Language Model (GAGPT), which is built upon a GA vector base, a GA knowledge graph, and a GA multi-tasking agent. Additionally, to facilitate interactive GA teaching, the paper proposes the development of two specialized agents: a GA knowledge Q&amp;A agent and a GA interactive exercises agent. The GAGPT is equipped with comprehensive GA contextual background information by constructing a GA vector base from an extensively curated GA corpus. A GA Knowledge Graph is developed from the selected corpus to provide the model with the necessary GA rules. In the GA knowledge Q&amp;A experiment, the accuracy of both formula-based and concept-based quizzes was improved by 46% and 42%, respectively, when compared to GPT-4o. Moreover, in the experiment involving the gradual generation of GA exercises, GAGPT demonstrated superior performance, while GPT-4o, despite utilizing the appropriate GA calculation formulas, made computational errors that led to incorrect results.</p>

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GAGPT and Its Application to the Interactive Learning of Geometric Algebra

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Jian Wang,
  • Pei Du,
  • Zhuo Zhao,
  • Wen Luo,
  • Zhaoyuan Yu,
  • Linwang Yuan

摘要

To address the challenges of high specialization and fragmented learning resources in Geometric Algebra (GA), this paper introduces a multi-task Geometric Algebraic Large Language Model (GAGPT), which is built upon a GA vector base, a GA knowledge graph, and a GA multi-tasking agent. Additionally, to facilitate interactive GA teaching, the paper proposes the development of two specialized agents: a GA knowledge Q&A agent and a GA interactive exercises agent. The GAGPT is equipped with comprehensive GA contextual background information by constructing a GA vector base from an extensively curated GA corpus. A GA Knowledge Graph is developed from the selected corpus to provide the model with the necessary GA rules. In the GA knowledge Q&A experiment, the accuracy of both formula-based and concept-based quizzes was improved by 46% and 42%, respectively, when compared to GPT-4o. Moreover, in the experiment involving the gradual generation of GA exercises, GAGPT demonstrated superior performance, while GPT-4o, despite utilizing the appropriate GA calculation formulas, made computational errors that led to incorrect results.