AI RESEARCH
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
arXiv CS.LG
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ArXi:2604.20308v1 Announce Type: new 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 positive definite matrices (SPD) manifold; (2) Standard message passing applies shared transformations across edges.