Bayesian Sheaf Neural Networks
This work addresses the challenge of improving robustness and performance in graph neural networks for heterophilic data, representing an incremental advancement in the field.
The paper tackles the problem of graph neural networks being overly sensitive to learned cellular sheaves in heterophilic graph data by proposing Bayesian sheaf neural networks, which achieve leading performance and reduced hyperparameter sensitivity on several datasets.
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.