Polynomial Neural Sheaf Diffusion: Spectral Filtering on Cellular Sheaves
A novel technique named Polynomial Neural Sheaf Diffusion (PolyNSD) has been developed to overcome the shortcomings of current Sheaf Neural Networks. Traditional methods depend on SVD-based sheaf normalization and complex per-edge restriction maps that scale with stalk dimension, necessitating frequent updates to the Laplacian and resulting in unstable gradients. In contrast, PolyNSD employs a degree-K polynomial within a normalized sheaf Laplacian, which is computed through a reliable three-term recurrence on a spectrally rescaled operator. This approach enables an explicit K-hop receptive field within a single layer, unaffected by stalk dimension, and incorporates trainable spectral filtering. The research is available on arXiv with the identifier 2512.00242.
Key facts
- PolyNSD is a new sheaf diffusion approach.
- It addresses limitations of SVD-based sheaf normalization and dense per-edge restriction maps.
- The propagation operator is a degree-K polynomial in a normalized sheaf Laplacian.
- It is evaluated via a stable three-term recurrence on a spectrally rescaled operator.
- Provides an explicit K-hop receptive field in a single layer.
- The receptive field is independent of stalk dimension.
- Includes trainable spectral filtering.
- Paper available on arXiv: 2512.00242.
Entities
Institutions
- arXiv