Oversmoothing as Representation Degeneracy in Neural Sheaf Diffusion
Neural Sheaf Diffusion (NSD) generalizes diffusion-based Graph Neural Networks by replacing scalar graph Laplacians with sheaf Laplacians whose learned restriction maps define a task-adapted geometry. While the diffusion limit of NSD is known to be the space of global sections, the representation-theoretic structure of this harmonic space remains largely implicit. We develop a quiver-theoretic interpretation of NSD by identifying cellular sheaves on graphs with representations of the associated incidence quiver. Under this correspondence, learned sheaf geometries become points in a finite-dimensional representation space. We show that direct-sum decompositions of the underlying incidence-...
| Authors | Arif Dönmez, Axel Mosig, Ellen Fritsche et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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