Derives the SVD backward-pass Jacobian spectrum for SO(3) projection as rank 3 with singular values 2/(s_i + s_j) and condition number (s1+s2)/(s2+s3), proving gradient distortion is worst early in training and that 6D Gram-Schmidt gives asymmetric signals.
Deep regression on manifolds: A 3D rotation case study
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Training Without Orthogonalization, Inference With SVD: A Gradient Analysis of Rotation Representations
Derives the SVD backward-pass Jacobian spectrum for SO(3) projection as rank 3 with singular values 2/(s_i + s_j) and condition number (s1+s2)/(s2+s3), proving gradient distortion is worst early in training and that 6D Gram-Schmidt gives asymmetric signals.