This paper investigates the continuity of rotation representations in neural networks. The authors propose a definition of continuity for rotation representations, which is suitable for neural networks. They analyze the continuity of rotation representations for 2D, 3D, and n-dimensional rotations. They show that for 3D rotations, all representations are discontinuous in four or fewer dimensions. However, they present continuous representations for 3D rotations in 5D and 6D, which are more suitable for learning. They also present continuous representations for the general case of the n-dimensional rotation group SO(n). The authors demonstrate that their continuous rotation representations outperform discontinuous ones for several practical problems in graphics and vision, including a simple autoencoder sanity test, a rotation estimator for 3D point clouds, and an inverse kinematics solver for 3D human poses. They also show that their constructions apply to other groups such as the orthogonal group and similarity transforms. The authors conclude that continuous rotation representations are more suitable for learning than discontinuous ones.This paper investigates the continuity of rotation representations in neural networks. The authors propose a definition of continuity for rotation representations, which is suitable for neural networks. They analyze the continuity of rotation representations for 2D, 3D, and n-dimensional rotations. They show that for 3D rotations, all representations are discontinuous in four or fewer dimensions. However, they present continuous representations for 3D rotations in 5D and 6D, which are more suitable for learning. They also present continuous representations for the general case of the n-dimensional rotation group SO(n). The authors demonstrate that their continuous rotation representations outperform discontinuous ones for several practical problems in graphics and vision, including a simple autoencoder sanity test, a rotation estimator for 3D point clouds, and an inverse kinematics solver for 3D human poses. They also show that their constructions apply to other groups such as the orthogonal group and similarity transforms. The authors conclude that continuous rotation representations are more suitable for learning than discontinuous ones.