The impact of generative AI on the field of education is becoming increasingly significant. However, existing research primarily focuses on technical and practical applications, often lacking a thorough analysis of theoretical foundation. To advance the theoretical development of generative AI in artificial intelligence system design, this study employs a literature review and theoretical analysis from the cross disciplinary perspectives of linguistics, cognitive psychology, and education to explore the design principles of generative AI-based writing feedback and adaptive learning system. The findings suggest that the linguistic theories, including Distributional Semantics and Construction Grammar, provide essential semantic and grammatical analysis tools, enabling AI systems to generate more precise writing feedback and task recommendations. Cognitive Load Theory, a cognitive psychology theory, informs system design by guiding information presentation and task structuring to reduce learners’ cognitive load and optimize knowledge acquisition. The educational theory of the Zone of Proximal Development offers a framework for dynamically adjusting learning tasks and feedback, thereby supporting personalized learning experiences and continuous improvement. These theoretical foundations collectively contribute to the intelligent design of the generative AI-based adaptive writing feedback and task learning system, and their interconnections significantly enhance system adaptability and efficiency. The study offers a new perspective for advancing AI-empowered education from a focus on merely technological applications to the construction of intelligent systems grounded in interdisciplinary theories.