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. Consequently, we successfully create reliable and highly efficient configurations for metasurface color filters capable of producing exceptionally vivid colors that go beyond the sRGB gamut. Furthermore, our deep learning technique can be extended to design various pixellated metasurface configurations with different functionalities.