Beyond Rigid Geometries: The Spline-Pullback Metric for Universal Diffeomorphic SPD Representation Learning
The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features in classical machine learning, these static formulations impose rigid geometries limiting network expressivity and adaptability. Recent attempts to parameterize these geometries often violate the axioms of primary matrix functions through unconstrained powers or rank-dependent scaling, inviting spatial folding, loss of global surjectivity, and gradient collapse at spectral singularities. In this paper, we introduce the Spline-Pullback Metric (SPM), instantiated as Spectral-SPM and Cholesky-SPM, marking a paradigm...
| Authors | Tushar Das, Subrata Dutta, Sarmistha Neogy et al. |
|---|---|
| Primary category | cs.LG |
| Published | 6 May 2026 |
| Last updated at source | 6 May 2026 |
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