Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
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. Sheaf neural networks address this via edge-specific transformations, but existing formulations remain confined to vector spaces and therefore ...
| Authors | Yuhan Peng, Junwen Dong, Yuzhi Zeng et al. |
|---|---|
| Primary category | cs.LG |
| Published | 22 April 2026 |
| Last updated at source | 31 May 2026 |
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