HiSP is a sheaf-aware pooling framework using local spectral coarsening to project fine stalk features onto low-frequency modes of cluster sheaf Laplacians for hierarchical SNN representations.
Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
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. To address these limitations, we introduce Polynomial Neural Sheaf Diffusion (PolyNSD), a new sheaf diffusion approach whose propagation operator is a degree-K polynomial in a normalised sheaf Laplacian, evaluated via a stable three-term recurrence on a spectrally rescaled operator. This provides an explicit K-hop receptive field in a single layer (independently of the stalk dimension), with a trainable spectral response obtained as a convex mixture of K+1 orthogonal polynomial basis responses. PolyNSD enforces stability via convex mixtures, spectral rescaling, and residual/gated paths, reaching new state-of-the-art results on both homophilic and heterophilic benchmarks, inverting the Neural Sheaf Diffusion trend by obtaining these results with just diagonal restriction maps, decoupling performance from large stalk dimension, while reducing runtime and memory requirements.
years
2026 4verdicts
UNVERDICTED 4representative citing papers
TSNN equips temporal graphs with per-node time-varying orthogonal frames, explicit transport, and a geometric-residual decoder, delivering competitive or superior link prediction on benchmarks plus theoretical guarantees on sheaf diffusion.
DNSD replaces the sheaf Laplacian with a sheaf adjacency operator, adds normalization and gating, and empirically outperforms GNN and NSD baselines by up to 30 percentage points on synthetic long-range graph tasks while also improving on real-world benchmarks.
A modified graph Laplacian incorporating subspace projections, spectral adjustments, and frequency-based filtering is proposed to improve fairness in diffusion-based graph neural networks while preserving competitive performance.
citing papers explorer
-
Hierarchical Pooling for Sheaf Neural Networks
HiSP is a sheaf-aware pooling framework using local spectral coarsening to project fine stalk features onto low-frequency modes of cluster sheaf Laplacians for hierarchical SNN representations.
-
Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport
TSNN equips temporal graphs with per-node time-varying orthogonal frames, explicit transport, and a geometric-residual decoder, delivering competitive or superior link prediction on benchmarks plus theoretical guarantees on sheaf diffusion.
-
Deep Neural Sheaf Diffusion
DNSD replaces the sheaf Laplacian with a sheaf adjacency operator, adds normalization and gating, and empirically outperforms GNN and NSD baselines by up to 30 percentage points on synthetic long-range graph tasks while also improving on real-world benchmarks.
-
Geometrical fairness in graph neural networks
A modified graph Laplacian incorporating subspace projections, spectral adjustments, and frequency-based filtering is proposed to improve fairness in diffusion-based graph neural networks while preserving competitive performance.