Large Language Model for Geometric Algebra: A Preliminary Attempt

Geometric algebra serves as the unified language of mathematics, physics, and engineering in the 21st century. Coinciding with the era of artificial intelligence, the utilization of a Large Language Model (LLM) can significantly benefit the learning and application of geometric algebra. This study develops a representative application called PrivateGPT, based on the ggml-ggml-nous-gpt4-vicuna-13b model, to explore the integration of geometric algebra and LLM by building a knowledge base of geometric algebra expertise. The Geometric Algebra Knowledge Base was created by collecting 20,711 papers and data, categorizing them by topics. This application possesses the capability of iterative refinement, enhancing its understanding and reasoning of geometric algebra knowledge. It accomplishes the textual summarization of research content, methods, innovations, and conclusions. It facilitates the development of tailored learning plans for students from diverse fields to acquire knowledge of geometric algebra in their specific domains. Additionally, we compared the performance of PrivateGPT and ChatGPT in providing personalized learning paths for the same group of learners and evaluated their responses through a questionnaire survey. The results showed that PrivateGPT has an advantage in devising tailored learning plans for learners from various disciplines.