Training Without Orthogonalization, Inference With SVD: A Gradient Analysis of Rotation Representations
Recent work has shown that removing orthogonalization during training and applying it only at inference improves rotation estimation in deep learning, with empirical evidence favoring 9D representations with SVD projection. However, the theoretical understanding of why SVD orthogonalization specifically harms training, and why it should be preferred over Gram-Schmidt at inference, remains incomplete. We provide a detailed gradient analysis of SVD orthogonalization specialized to $3 \times 3$ matrices and $SO(3)$ projection. Our central result derives the exact spectrum of the SVD backward pass Jacobian: it has rank $3$ (matching the dimension of $SO(3)$) with nonzero singular values $2/(s...
| Authors | Chris Choy |
|---|---|
| Primary category | cs.LG |
| Published | 7 April 2026 |
| Last updated at source | 7 April 2026 |
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