Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves

ArXi:2512.00242v3 Announce Type: replace-cross Sheaf Neural Networks equip graph structures with a cellular sheaf: a geometric structure which assigns local vector spaces (stalks) and a linear learnable restriction/transport maps to nodes and edges, yielding an edge-aware inductive bias that handles heterophily and limits oversmoothing. However, common Neural Sheaf Diffusion implementations rely on SVD-based sheaf normalization and dense per-edge restriction maps, which scale with stalk dimension, require frequent Laplacian rebuilds, and yield brittle gradients.