SPD Manifolds
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Related Articles from SNS
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
arXiv:2604.20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule. These second-order representations are naturally captured by points on the symmetric...
Routing on the Stiefel Manifold: When Does Adaptive Subspace Selection Help for Cross-Domain EEG Decoding?
arXiv:2605.31043v1 Announce Type: cross Abstract: Cross-domain EEG decoding remains challenging despite advances in Riemannian deep learning: covariance matrices from different subjects occupy systematically distinct regions of the SPD manifold, yet existing domain adaptation methods either require target-domain calibration data or learn subject-specific components that cannot generalise across domains. We propose dynamic Stiefel routing: a pool of $K$ expert projection filters on the...
Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networks
arXiv:2605.31106v1 Announce Type: new Abstract: Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a...
Learning Manifold and It\^o Dynamics with Branched Neural Rough Differential Equations
arXiv:2606.05272v1 Announce Type: new Abstract: Neural rough differential equations (NRDEs) stay accurate under irregular sampling while taking far fewer integration steps than standard neural differential equations, summarising a finely sampled driver by its log-signature and advancing the hidden state over coarse intervals using the log-ODE method. This efficiency rests on the shuffle algebra, the algebraic counterpart of Stratonovich calculus. This reliance means NRDEs cannot expose the...
Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
Announce Type: cross Abstract: Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps. In Euclidean space, barycentric projection converts a coupling into a map by taking conditional expectations, but on a Riemannian manifold curvature and cut loci make this operation nontrivial. We develop a framework for barycentric projections of transport couplings on Riemannian manifolds.