Deep Integration of Generative AI and Mathematical Models

Abstract

The expressive power of generative AI can capture complex distribution and generate content; while mathematical models provide rigorous analysis regarding formal constraint, structure preservation, and deductive reasoning — deeply integrate these two aspects has become one of the ways to enhance the structural consistency and trustworthiness in generative systems. With regard to "Deep Integration of Generative AI and Mathematical Models", we construct three levels: formal foundations and representation mechanisms, collaborative architectures and reasoning paradigms, optimization regulation and trustworthiness assurance. At the formal level, analyze the structural coupling between generative probabilistic models and mathematical symbolic systems, establish the semantic alignment between continuous latent space and discrete mathematical structures, propose a unified representation framework embedding mathematical constraints into the generation process. At the collaborative level, discuss collaborative computation between neural generation module and mathematical solving module, interactive reasoning between symbolic deduction and probabilistic sampling, and generative modeling driven by multi-scale mathematical structures. At the assurance level, formulate joint optimization objectives oriented toward mathematical consistency, analyze error propagation and stability regulation, evaluate the integrated model and characterize its boundaries under interpretability constraints. We present an integrated framework of structural representation, computational reasoning, and trustworthy regulation for the deep integration of generative AI and mathematical models.