mlsanityData to 14 Oct 2026

Sheaves Reloaded: A Directional Awakening

arXiv 2506.02842 ↗First posted 3 Jun 2025cs.LG cs.AIcited by 4

Not on the map. Why?

Abstract (arXiv)

Sheaf Neural Networks (SNNs) represent a powerful generalization of Graph Neural Networks (GNNs) that significantly improve our ability to model complex relational data. While directionality has been shown to substantially boost performance in graph learning tasks and is key to many real-world applications, existing SNNs fall short in representing it. To address this limitation, we introduce the Directed Cellular Sheaf, a special type of cellular sheaf designed to explicitly account for edge orientation. Building on this structure, we define a new sheaf Laplacian, the Directed Sheaf Laplacian, which captures both the graph's topology and its directional information. This operator serves as the backbone of the Directed Sheaf Neural Network (DSNN), the first SNN model to embed a directional bias into its architecture. Extensive experiments on nine real-world benchmarks show that DSNN consistently outperforms baseline methods.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 20 of its 33 references that are in the map. First posted on arXiv 3 Jun 2025.

Builds on

20 of 33 references.

References · 20

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2017Inductive Representation Learning on Large Graphscited by 6,320
  4. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,919
  5. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,223
  6. 2020Simple and Deep Graph Convolutional Networkscited by 860
  7. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  8. 2015Gated Graph Sequence Neural Networkscited by 796
  9. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
  10. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 443
  11. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 362
  12. 2023A critical look at the evaluation of GNNs under heterophily: Are we really making progress?cited by 343
8 more
  1. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 214
  2. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  3. 2021MagNet: A Neural Network for Directed Graphscited by 107
  4. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 90
  5. 2020Sheaf Neural Networkscited by 84
  6. 2020Directed Graph Convolutional Networkcited by 73
  7. 2023Sheaf Hypergraph Networkscited by 34
  8. 2022SigMaNet: One Laplacian to Rule Them Allcited by 24

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheavescited by 1
  2. 2026Benchmarking Sheaf Neural Networks for Inductive Taskscited by 1
  3. 2026Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphscited by 0
  4. 2026Mitigating Over-squashing without Rewiring: A Sheaf Effective Resistance Perspectivecited by 0