Exploring the Specific Applications of Mathematical Models in the Field of Artificial Intelligence

Against the backdrop of the continuous evolution of artificial intelligence technology and increasingly complex application scenarios, mathematical models, as fundamental tools for system construction, play a critical role in the evolution and optimization of intelligent algorithms. This study systematically explores the specific applications of mathematical models in the field of artificial intelligence and establishes an analytical framework encompassing modeling paradigms, system structures, and methodological mechanisms. It focuses on analyzing the functional pathways and integration value of optimization models, probabilistic models, and graph models in intelligent algorithms, highlighting the fundamental role of mathematical modeling in enhancing representational capacity, decision-making stability, and structural generalization. The study further clarifies the potential applications of mathematical models in improving model interpretability, supporting cross-modal fusion, and constructing self-evolving systems, indicating that the deep integration of mathematical modeling and intelligent algorithms is an important direction for promoting the structural evolution of AI systems.