Researchers have developed a unified framework for Riemannian deep learning, addressing the limitations of existing approaches that rely on Euclidean approximations or are tied to specific manifolds. This framework provides a comprehensive foundation for deep neural networks on manifold-valued representations, enabling the creation of reusable neural modules and manifold-specific networks. By incorporating geometric operations in a more efficient and numerically stable manner, this approach overcomes the drawbacks of previous methods. The framework is developed from three complementary perspectives, offering a more robust and flexible foundation for Riemannian deep learning1. This advancement has significant implications for the field of artificial intelligence, as it enables more accurate and efficient processing of complex data. The development of this framework is a crucial step forward in the field, and its impact will be felt beyond the technical realm, influencing policy, security, and workforce dynamics.