mlsanityData to 14 Oct 2026

Nonlinear Sheaf Diffusion in Graph Neural Networks

arXiv 2403.00337 ↗First posted 1 Mar 2024cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

This work focuses on exploring the potential benefits of introducing a nonlinear Laplacian in Sheaf Neural Networks for graph-related tasks. The primary aim is to understand the impact of such nonlinearity on diffusion dynamics, signal propagation, and performance of neural network architectures in discrete-time settings. The study primarily emphasizes experimental analysis, using real-world and synthetic datasets to validate the practical effectiveness of different versions of the model. This approach shifts the focus from an initial theoretical exploration to demonstrating the practical utility of the proposed model.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 31 of its 79 references that are in the map. First posted on arXiv 1 Mar 2024.

Builds on

31 of 79 references.

References · 31

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  4. 2017Inductive Representation Learning on Large Graphscited by 6,320
  5. 2018How Powerful are Graph Neural Networks?cited by 4,393
  6. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
  7. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  8. 2019Simplifying Graph Convolutional Networkscited by 1,477
  9. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  10. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  11. 2015Gated Graph Sequence Neural Networkscited by 796
  12. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 680
19 more
  1. 2020Benchmarking Graph Neural Networkscited by 680
  2. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 652
  3. 2019GraphSAINT: Graph Sampling Based Inductive Learning Methodcited by 618
  4. 2018FastGCN: Fast Learning with Graph Convolutional Networks via Importance Samplingcited by 584
  5. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 520
  6. 2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 413
  7. 2018Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generationcited by 364
  8. 2017Residual Gated Graph ConvNetscited by 346
  9. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 214
  10. 2020The Surprising Power of Graph Neural Networks with Random Node Initializationcited by 198
  11. 2020Low-Dimensional Hyperbolic Knowledge Graph Embeddingscited by 195
  12. 2018NetGAN: Generating Graphs via Random Walkscited by 131
  13. 2019Fake News Detection on Social Media using Geometric Deep Learningcited by 118
  14. 2022Topological Deep Learning: Going Beyond Graph Datacited by 97
  15. 2020Sheaf Neural Networkscited by 84
  16. 2023Generative Diffusion Models on Graphs: Methods and Applicationscited by 81
  17. 2023Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunitiescited by 61
  18. 2020CaSPR: Learning Canonical Spatiotemporal Point Cloud Representationscited by 51
  19. 2020Characterizing the Latent Space of Molecular Deep Generative Models with Persistent Homology Metricscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 1; 2026: 1.

4 papers.

  1. 2024Joint Diffusion Processes as an Inductive Bias in Sheaf Neural Networkscited by 9
  2. 2025Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheavescited by 9
  3. 2026Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learningcited by 3
  4. 2024Towards a Categorical Foundation of Deep Learning: A Surveycited by 2