Spline-Pullback Metric parameterizes a universal family of strictly increasing C1 diffeomorphisms on SPD matrices via monotonically constrained B-splines, subsuming prior pullback metrics while avoiding rank-swapping discontinuities.
V .3.3] states that applying a C 1 smooth scalar function to a symmetric matrix creates a Primary Matrix Function that is continuously Fréchet differentiable
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Beyond Rigid Geometries: The Spline-Pullback Metric for Universal Diffeomorphic SPD Representation Learning
Spline-Pullback Metric parameterizes a universal family of strictly increasing C1 diffeomorphisms on SPD matrices via monotonically constrained B-splines, subsuming prior pullback metrics while avoiding rank-swapping discontinuities.