用贝叶斯方法学习图神经网络中的胞腔叠层，提升模型稳定性与表现。
Bayesian Sheaf Neural Networks
- 基于变分推断学习旋转群上的概率分布，实现可微的胞腔叠层建模
- 在有限数据下性能优于基线模型，对超参数不敏感
- 适合处理异质性图数据，尤其适用于小样本场景
将卷积操作基于胞腔叠层定义的图神经网络，在学习异质性图数据的表达方面具有优势。最灵活的叠层构造方式是将其作为网络的一部分，根据节点特征进行学习。然而，这可能导致网络对学习到的叠层过于敏感。为此，我们提出一种在叠层神经网络中学习胞腔叠层的变分方法，构建出称为贝叶斯叠层神经网络的架构。本工作还通过Cayley变换定义了一类新的、可重参数化的SO(n)旋转群上的概率分布。我们在多个图数据集上评估该模型，结果表明贝叶斯叠层模型在性能上达到领先水平，并在训练数据有限的情况下对超参数选择更为鲁棒。
原文摘要 · Abstract (English)
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.
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