Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.09590 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909784181047296 |
|---|---|
| author | Gillespie, Patrick Hamdan, Layal Bou Schizas, Ioannis Boothe, David L. Maroulas, Vasileios |
| author_facet | Gillespie, Patrick Hamdan, Layal Bou Schizas, Ioannis Boothe, David L. Maroulas, Vasileios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09590 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bayesian Sheaf Neural Networks Gillespie, Patrick Hamdan, Layal Bou Schizas, Ioannis Boothe, David L. Maroulas, Vasileios Machine Learning Social and Information Networks 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. |
| title | Bayesian Sheaf Neural Networks |
| topic | Machine Learning Social and Information Networks |
| url | https://arxiv.org/abs/2410.09590 |