mlsanityData to 14 Oct 2026

Bayesian Sheaf Neural Networks

arXiv 2410.09590 ↗First posted 12 Oct 2024cs.LG cs.SIcited by 5

Not on the map. Why?

Abstract (arXiv)

Equipping graph neural networks with a convolution operation defined in terms of a cellular sheaf offers advantages for learning expressive representations of heterophilic graph data. The most flexible approach to constructing the sheaf is to learn it as part of the network as a function of the node features. However, this leaves the network potentially overly sensitive to the learned sheaf. As a counter-measure, we propose a variational approach to learning cellular sheaves within sheaf neural networks, yielding an architecture we refer to as a Bayesian sheaf neural network. As part of this work, we define a novel family of reparameterizable probability distributions on the rotation group SO(n) using the Cayley transform. We evaluate the Bayesian sheaf neural network on several graph datasets, and show that our Bayesian sheaf models achieve leading performance compared to baseline models and are less sensitive to the choice of hyperparameters under limited training data settings.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 42 of its 69 references that are in the map. First posted on arXiv 12 Oct 2024.

Builds on

42 of 69 references.

References · 42

  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. 2017On Calibration of Modern Neural Networkscited by 4,960
  5. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  6. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  7. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  8. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,352
  9. 2016Variational Inference: A Review for Statisticianscited by 1,472
  10. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  11. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,138
  12. 2017Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecastingcited by 1,136
30 more
  1. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  2. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 913
  3. 2020Simple and Deep Graph Convolutional Networkscited by 860
  4. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  5. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
  6. 2018Hypergraph Neural Networkscited by 488
  7. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 443
  8. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 362
  9. 2020Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Userscited by 338
  10. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  11. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 247
  12. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  13. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  14. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 214
  15. 2019Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishingcited by 191
  16. 2018Hyperspherical Variational Auto-Encoderscited by 189
  17. 2015A Theoretically Grounded Application of Dropout in Recurrent Neural Networkscited by 161
  18. 2015Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inferencecited by 159
  19. 2020Simplicial Neural Networkscited by 110
  20. 2018Bayesian graph convolutional neural networks for semi-supervised classificationcited by 89
  21. 2019Variational Graph Recurrent Neural Networkscited by 87
  22. 2020Sheaf Neural Networkscited by 84
  23. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  24. 2022Sheaf Neural Networks with Connection Laplacianscited by 65
  25. 2024Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AIcited by 62
  26. 2020Bayesian Attention Modulescited by 51
  27. 2023Sheaf Hypergraph Networkscited by 34
  28. 2022On the Robustness of Bayesian Neural Networks to Adversarial Attackscited by 12
  29. 2020Bayesian Topological Learning for Classifying the Structure of Biological Networkscited by 6
  30. 2022A Topological Deep Learning Framework for Neural Spike Decodingcited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Copresheaf Topological Neural Networks: A Generalized Deep Learning Frameworkcited by 12
  2. 2025On the Sheafification of Higher-Order Message Passingcited by 1
  3. 2026From Classical to Topological Neural Networks Under Uncertaintycited by 0
  4. 2026Gaussian Sheaf Neural Networkscited by 0
  5. 2026Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Predictioncited by 0