CDGFD: Cross-Domain Generalization in Ethnic Fashion Design Using LLMs and GANs: A Symbolic and Geometric Approach

In this paper, we propose a novel framework that leverages Large Language Models (LLMs) and Generative Adversarial Networks (GANs) to address the challenges of cross-domain generalization in ethnic fashion design. By introducing the concept of “Digital Cousins,” our approach generates culturally rich fashion designs that maintain both the symbolic integrity and geometric consistency of traditional ethnic garments. Specifically, we explore how LLMs can effectively encode the complex semantic relationships in cultural symbols and how GANs can transform these embeddings into visually coherent and geometrically plausible designs. Unlike traditional digital twin models, which require exact replication, our method allows for symbolic and geometric variations while preserving core cultural values. Our contributions are threefold: First, we propose a mathematical framework for mapping cultural symbols to a multi-dimensional semantic space using LLMs, ensuring the symbolic accuracy of generated designs. Second, we present a method to generate “Digital Cousins” of ethnic garments by employing GANs to introduce geometric transformations, enabling cross-cultural and cross-contextual adaptation. Finally, we demonstrate the robustness of our method in a series of experiments, including real-to-sim and sim-to-real tests, where we evaluate the generalization capabilities of the generated designs across different cultural contexts. Our results show that the proposed approach achieves higher cross-domain performance compared to traditional methods, while maintaining cultural authenticity. Experimental results show that our approach achieves a 15% improvement in cultural fidelity and a 20% enhancement in geometric adaptability compared to traditional methods. These findings suggest significant potential for AI-driven innovation in ethnic fashion design, with applications in both cultural preservation and modern fashion industries.