Abstract: The in-depth application of artificial intelligence (AI) technology has propelled ideological and political education into a new stage of intelligent development, where the theoretical construction and practical application of large models for ideological and political education have become a significant research topic. The theoretical elucidation of the internal generative mechanisms of these large models, together with their theoretical construction and practical exploration, holds increasingly prominent academic value and practical significance. To this end, mathematical models can be employed to provide a formal representation of the operational logic of large models for ideological and political education, thereby clarifying their internal correlations and operational laws. On this basis, the theoretical foundation of such large models guided by Marxism is elucidated, revealing an internal logic that unifies value guidance, technological support, discourse adaptation, and data assurance. This promotes the shift of ideological and political education from the mere application of technological tools to the construction of internal mechanisms, further enriching the theoretical system of intelligent ideological and political education and providing theoretical support and practical pathways for the standardized construction and high-quality development of large models in ideological and political education.