# Sheaf Neural Networks with Connection Laplacians

arXiv: https://arxiv.org/abs/2206.08702 · HTML: https://mlsanity.com/paper/2206.08702/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 14 of 14)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs](https://mlsanity.com/paper/2006.11468/) (2020)

## Built on by (most cited first, 30 of 65)

- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [Latent Graph Inference using Product Manifolds](https://mlsanity.com/paper/2211.16199/) (2022)
- [Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2303.11323/) (2023)
- [E(n) Equivariant Topological Neural Networks](https://mlsanity.com/paper/2405.15429/) (2024)
- [From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module](https://mlsanity.com/paper/2305.16174/) (2023)
- [Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimization](https://mlsanity.com/paper/2309.04810/) (2023)
- [Bundle Neural Networks for message diffusion on graphs](https://mlsanity.com/paper/2405.15540/) (2024)
- [Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework](https://mlsanity.com/paper/2505.21251/) (2025)
- [Cooperative Sheaf Neural Networks](https://mlsanity.com/paper/2507.00647/) (2025)
- [Attending to Topological Spaces: The Cellular Transformer](https://mlsanity.com/paper/2405.14094/) (2024)
- [Graph Neural Networks in Vision-Language Image Understanding: A Survey](https://mlsanity.com/paper/2303.03761/) (2023)
- [Heterogeneous Sheaf Neural Networks](https://mlsanity.com/paper/2409.08036/) (2024)
- [Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2210.15058/) (2022)
- [Projections of Model Spaces for Latent Graph Inference](https://mlsanity.com/paper/2303.11754/) (2023)
- [Joint Diffusion Processes as an Inductive Bias in Sheaf Neural Networks](https://mlsanity.com/paper/2407.20597/) (2024)
- [Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves](https://mlsanity.com/paper/2512.00242/) (2025)
- [Sheaf4Rec: Sheaf Neural Networks for Graph-based Recommender Systems](https://mlsanity.com/paper/2304.09097/) (2023)
- [State of the Art and Potentialities of Graph-level Learning](https://mlsanity.com/paper/2301.05860/) (2023)
- [Implicit Gaussian process representation of vector fields over arbitrary latent manifolds](https://mlsanity.com/paper/2309.16746/) (2023)
- [Sheaf HyperNetworks for Personalized Federated Learning](https://mlsanity.com/paper/2405.20882/) (2024)
- [Bayesian Sheaf Neural Networks](https://mlsanity.com/paper/2410.09590/) (2024)
- [On the Necessity of Learnable Sheaf Laplacians](https://mlsanity.com/paper/2603.05395/) (2026)
- [DeepSN: A Sheaf Neural Framework for Influence Maximization](https://mlsanity.com/paper/2412.12416/) (2024)
- [Learning the Structure of Connection Graphs](https://mlsanity.com/paper/2510.11245/) (2025)
- [Categorical Equivariant Deep Learning: Category-Equivariant Neural Networks and Universal Approximation Theorems](https://mlsanity.com/paper/2511.18417/) (2025)
- [Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learning](https://mlsanity.com/paper/2505.05702/) (2025)
- [Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning](https://mlsanity.com/paper/2604.20308/) (2026)
- [Kan Extension Transformers: A Categorical Unification of Attention, Diffusion, and Predict-Detach Self-Conditioning](https://mlsanity.com/paper/2605.27259/) (2026)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)

## Abstract (arXiv)

A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have useful theoretical properties that help tackle issues arising from heterophily and over-smoothing. One complication intrinsic to these models is finding a good sheaf for the task to be solved. Previous works proposed two diametrically opposed approaches: manually constructing the sheaf based on domain knowledge and learning the sheaf end-to-end using gradient-based methods. However, domain knowledge is often insufficient, while learning a sheaf could lead to overfitting and significant computational overhead. In this work, we propose a novel way of computing sheaves drawing inspiration from Riemannian geometry: we leverage the manifold assumption to compute manifold-and-graph-aware orthogonal maps, which optimally align the tangent spaces of neighbouring data points. We show that this approach achieves promising results with less computational overhead when compared to previous SNN models. Overall, this work provides an interesting connection between algebraic topology and differential geometry, and we hope that it will spark future research in this direction.