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.
| Subjects: | Machine Learning (cs.LG); Algebraic Topology (math.AT); Category Theory (math.CT) |
| Cite as: | arXiv:2605.21435 [cs.LG] |
| (or arXiv:2605.21435v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.21435 arXiv-issued DOI via DataCite (pending registration) |
From: Ana Luiza Tenorio Dr [view email]
[v1]
Wed, 20 May 2026 17:26:32 UTC (399 KB)
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