AI RESEARCH
GSVD for Geometry-Grounded Dataset Comparison: An Alignment Angle Is All You Need
arXiv CS.LG
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ArXi:2603.10283v1 Announce Type: new 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.