Abstract
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.
Supported by the National Natural Science Foundation of China (No. 42130103, 42230406 and 41930404).
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References
Lasenby, J., Lasenby, A.N., Doran, C.J.L.: A unified mathematical language for physics and engineering in the 21st century. Philos. Trans. R. Soc. London Series A-Math. Phys. Eng. Sci. 358(1765), 21–39 (2000). https://doi.org/10.1098/rsta.2000.0517
Hitzer, E., Nitta, T., Kuroe, Y.: Applications of Clifford’s geometric algebra. Adv. Appl. Clifford Algebras 23(2), 377–404 (2013). https://doi.org/10.1007/s00006-013-0378-4
Cooper, G.: Examining science education in ChatGPT: an exploratory study of generative artificial intelligence. J. Sci. Educ. Technol. 32(3), 444–452 (2023). https://doi.org/10.1007/s10956-023-10039-y
LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. Nature 521(7553), 436–444 (2015). https://doi.org/10.1038/nature14539
Touvron, H., et al.: LLaMA: open and efficient foundation language models. arXiv:2302.13971 (2023)
Devlin, J., Chang, M. W., Lee, K., Toutanova, K.: Bert: pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805 (2018)
Bauer, E., et al.: Using natural language processing to support peer‐feedback in the age of artificial intelligence: a cross‐disciplinary framework and a research agenda. Br. J. Educ. Technol. 107–125 (2023). https://doi.org/10.1111/bjet.13336
Sorin, V., Barash, Y., Konen, E., Klang, E.: Large language models for oncological applications. J. Cancer Res. Clin. Oncol. 363, 1287–1289 (2023). https://doi.org/10.1007/s00432-023-04824-w
Brants, T., Popat, A. C., Xu, P., Och, F. J., Dean, J.: Large Language Models in Machine Translation. 2007
Kung, T.H., et al.: Performance of ChatGPT on USMLE: potential for AI-assisted medical education using large language models. PLOS Digit. Health 2(2), e0000198 (2023). https://doi.org/10.1371/journal.pdig.0000198
Oh, N., Choi, G.-S., Lee, W.Y.: ChatGPT goes to the operating room: Evaluating GPT-4 performance and its potential in surgical education and training in the era of large language models. Ann. Surg. Treat. Res. 104(5), 269–273 (2023)
Lee, H.: The rise of CHATGPT: exploring its potential in medical education. Anat. Sci. Educ. (2023)
Kraus, M., et al.: Enhancing large language models with climate resources arXiv preprint arXiv:2304.00116 (2023)
Chroma. https://www.trychroma.com/
Hu, E.J., et al.: Lora: low-rank adaptation of large language models. arXiv preprint arXiv:2106.09685 (2021)
Lester, B., Al-Rfou, R., Constant, N.: The power of scale for parameter-efficient prompt tuning. arXiv preprint arXiv:2104.08691 (2021)
Hu, S., et al.: Knowledgeable prompt-tuning: incorporating knowledge into prompt verbalizer for text classification. arXiv preprint arXiv:2108.02035 (2021)
Lasenby, J.: Guide to Geometric Algebra in Practice, 1st edn. Springer, New York (2011). https://doi.org/10.1007/978-0-85729-811-9
Colapinto, P.: Articulating space: geometric algebra for parametric design-symmetry, kinematics, and curvature. Ph.D. University of California, Santa Barbara (2016)
Dorst, L., Daniel, F., Stephen, M.: Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry, 1st edn. Elsevier, San Francisco (2009)
Hosny Eid, A.: Introducing geometric algebra to geometric computing software developers: a computational thinking approach. arXiv:1705.06668 (2017)
Jeannette, M.W.: Computational thinking. Commun. ACM 49(3), 33–35 (2006)
Luo, W., et al.: Multilevel declassification method for geographic vector field data: a geometric algebra approach. Adv. Appl. Clifford Algebras 32(5), 52–72 (2022)
Magnenat-Thalmann, N., et al.: Advances in Computer Graphics, 1st edn. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-89029-2
Breuils, S., Tachibana, K., Hitzer, E.: New applications of Clifford’s geometric algebra. Adv. Appl. Clifford Algebras 32(2), 17–56 (2022)
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Wang, J. et al. (2024). Large Language Model for Geometric Algebra: A Preliminary Attempt. In: Sheng, B., Bi, L., Kim, J., Magnenat-Thalmann, N., Thalmann, D. (eds) Advances in Computer Graphics. CGI 2023. Lecture Notes in Computer Science, vol 14498. Springer, Cham. https://doi.org/10.1007/978-3-031-50078-7_19
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