This paper provides a comprehensive overview of rotation representations in machine learning, focusing on their impact on learning functions with gradient-based optimization. It discusses various rotation representations, including Euler angles, exponential coordinates, quaternions, and high-dimensional representations like $ R^6 + GSO $ and $ R^9 + SVD $. The paper highlights that high-dimensional representations are generally preferred due to their continuity and ability to avoid discontinuities that arise from double cover properties. For rotation estimation, $ R^9 + SVD $ outperforms $ R^6 + GSO $ and quaternions, especially for small rotations. For feature prediction, $ R^9 + SVD $ is also recommended, while quaternions with a half-space map can be effective under memory constraints. The paper also addresses the challenges of discontinuities in low-dimensional representations and suggests using data augmentation and half-space maps to mitigate these issues. Experiments show that $ R^9 + SVD $ performs well in rotation estimation and feature prediction tasks, while quaternions with half-space maps are useful for small rotations. The study concludes that high-dimensional representations are superior for learning with rotations, and careful consideration of representation properties is essential for effective machine learning.This paper provides a comprehensive overview of rotation representations in machine learning, focusing on their impact on learning functions with gradient-based optimization. It discusses various rotation representations, including Euler angles, exponential coordinates, quaternions, and high-dimensional representations like $ R^6 + GSO $ and $ R^9 + SVD $. The paper highlights that high-dimensional representations are generally preferred due to their continuity and ability to avoid discontinuities that arise from double cover properties. For rotation estimation, $ R^9 + SVD $ outperforms $ R^6 + GSO $ and quaternions, especially for small rotations. For feature prediction, $ R^9 + SVD $ is also recommended, while quaternions with a half-space map can be effective under memory constraints. The paper also addresses the challenges of discontinuities in low-dimensional representations and suggests using data augmentation and half-space maps to mitigate these issues. Experiments show that $ R^9 + SVD $ performs well in rotation estimation and feature prediction tasks, while quaternions with half-space maps are useful for small rotations. The study concludes that high-dimensional representations are superior for learning with rotations, and careful consideration of representation properties is essential for effective machine learning.