TITLE:
Advanced Applications of Fundamental Mathematics in Large Language Processing Models
AUTHORS:
Meng Guo
KEYWORDS:
Basic Mathematics, Large Language Model (LLM), Linear Algebra, Optimization Theory, Attention Mechanism, Interpretability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.5,
May
15,
2026
ABSTRACT: Large Language Models (LLMs), as a core technology in the field of artificial intelligence, rely heavily on fundamental mathematical theories for their underlying architecture, training optimization, inference mechanisms, and performance improvement. This article systematically summarizes the advanced applications of basic mathematical branches such as linear algebra, probability theory and mathematical statistics, functional analysis, optimization theory, information theory, topology, etc. in large language models. It deeply analyzes the implementation principles of mathematical theory in key links such as word embedding, attention mechanism, model training, inference optimization, and interpretability analysis. Combined with the international cutting-edge research results in the past five years, it elaborates on the core role of basic mathematics in breaking through the performance of large language models, improving theories, and expanding scenarios. At the same time, summarizing the bottlenecks currently faced by the application of mathematical theories, and looking forward to the research direction of deep integration between basic mathematics and large language models in the future, providing mathematical theoretical references and technical ideas for the theoretical research and engineering practice of large language models.