Gaussian Sheaf Neural Networks
Abstract
Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better represented by probability distributions than real vectors. Concretely, when node features are Gaussians, characterized by a mean and a covariance matrix, naively concatenating their parameters into a single vector and applying standard message passing discards the geometric and algebraic structure that governs means and covariances. We propose Gaussian Sheaf Neural Networks (GSNNs), a principled framework that incorporates these inductive biases into graph-based learning. Building on the theory of cellular sheaves, we derive a new Laplacian operator that generalizes the sheaf Laplacian to this setting and preserves its key properties. We complement our theoretical contributions with experiments on synthetic and real-world data that illustrate the practical relevance of GSNNs.
Cite
@article{arxiv.2605.21435,
title = {Gaussian Sheaf Neural Networks},
author = {André Ribeiro and Ana Luiza Tenório and Tiago da Silva and Diego Mesquita},
journal= {arXiv preprint arXiv:2605.21435},
year = {2026}
}