We introduce a novel technique for designing color filter metasurfaces using a data-driven approach based on deep learning. Our innovative approach employs inverse design principles to identify highly efficient designs that outperform all the configurations in the training dataset, which consists of 810 distinct geometries solely. By combining Multi-Valued Artificial Neural Networks and back-propagation optimization, we overcome the limitations of previous approaches, such as poor performance due to extrapolation and undesired local minima. The numerical tool developed in this study enables the cost-effective fabrication of structural color filters by exploring a wide range of narrow line shapes that exhibit high-quality resonances, aligning with desired spectral reflection responses. Notably, our methodology expands the color gamut beyond the conventional RGB colors, offering unprecedented versatility in color generation. Furthermore, our Deep Learning approach successfully respects fabrication constraints, ensuring practical feasibility. The achievements of our research significantly contribute to the field of optical device design. By pushing the boundaries of metasurface optimization, we open up new possibilities for the development of advanced optical devices. The proposed methodology holds promise for various applications, such as display technologies, data encoding, and artistic expression. These notable advancements not only enhance the understanding of metasurface design principles but also provide valuable insights for future research endeavors.