The expected outcomes of this research include: 1) A transfer learning framework based on hypersurface manifolds that enables efficient cross-domain knowledge transfer in high-dimensional data and complex scenarios. 2) Experimental validation demonstrating the framework's versatility and efficiency across multiple tasks, particularly in image classification and natural language processing. 3) A new theoretical framework and technical tool for the transfer learning field, advancing related technologies. 4) New application scenarios and optimization ideas for OpenAI’s models and systems, particularly in handling high-dimensional data and complex geometric structures. These outcomes will enhance OpenAI models' capabilities in cross-domain tasks and promote their applications in more fields.