Demystifying Oversmoothing in Sheaf Neural Networks: An Index-Theoretic Criterion
To combat oversmoothing in Graph Convolutional Networks, Sheaf Neural Networks (SNNs) were proposed as a generalization by equipping the graph with a sheaf structure and replacing the graph Laplacian with a sheaf Laplacian $\mathcal{L}$. Existing analyses connect sheaf diffusion to oversmoothing via the harmonic space ($\ker\mathcal{L}$), taking its absolute dimension as an indicator of anti-oversmoothing capacity. However, absolute dimension alone is not a reliable measure: certain sheaf configurations inflate $\dim \ker \mathcal{L}$ while their harmonic sections remain entirely constant, without enriching discriminative capacity. We instead introduce the first relative, geometric approa...
| Authors | Junwen Dong, Yuhan Peng, Hao Li et al. |
|---|---|
| Primary category | cs.LG |
| Published | 17 August 2026 |
| Last updated at source | 17 August 2026 |
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