GSVD for Geometry-Grounded Dataset Comparison: An Alignment Angle Is All You Need
Geometry-grounded learning asks models to respect structure in the problem domain rather than treating observations as arbitrary vectors. Motivated by this view, we revisit a classical but underused primitive for comparing datasets: linear relations between two data matrices, expressed via the co-span constraint $Ax = By = z$ in a shared ambient space. To operationalize this comparison, we use the generalized singular value decomposition (GSVD) as a joint coordinate system for two subspaces. In particular, we exploit the GSVD form $A = HCU$, $B = HSV$ with $C^{\top}C + S^{\top}S = I$, which separates shared versus dataset-specific directions through the diagonal structure of $(C, S)$. Fro...
| Authors | Eduarda de Souza Marques, Arthur Sobrinho Ferreira da Rocha, Joao Paixao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 10 March 2026 |
| Last updated at source | 10 March 2026 |
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