Improving Graph Neural Networks with Learnable Propagation Operators
Improving Graph Neural Networks with Learnable Propagation Operators
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发表时间：
2022-10
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通讯作者：
Moshe Eliasof;Lars Ruthotto;Eran Treister
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作者：
Moshe Eliasof;Lars Ruthotto;Eran Treister
图神经网络（gnn）的传播算子是有限的。在许多情况下，这些运算符通常只包含非负元素，并且跨通道共享，限制了gnn的表达性。此外，一些gnn遭受过度平滑，限制了它们的深度。另一方面，卷积神经网络（cnn）可以学习多种传播滤波器，过度平滑等现象在cnn中通常不明显。在本文中，我们通过结合可训练的通道加权因子$\omega$来弥合这些差距，以学习和混合每层的多个平滑和锐化传播算子。我们的通用方法叫做$\omega$GNN，它很容易实现。我们研究了两个变体：$\omega$GCN和$\omega$GAT。对于$\omega$GCN，我们从理论上分析了它的行为以及$\omega$对获得的节点特征的影响。我们的实验证实了这些发现，证明并解释了这两种变体如何不会过度平滑。此外，我们在节点和图分类任务上对15个真实世界的数据集进行了实验，其中我们的$\omega$GCN和$\omega$GAT的性能与最先进的方法相当。
Graph Neural Networks (GNNs) are limited in their propagation operators. In many cases, these operators often contain non-negative elements only and are shared across channels, limiting the expressiveness of GNNs. Moreover, some GNNs suffer from over-smoothing, limiting their depth. On the other hand, Convolutional Neural Networks (CNNs) can learn diverse propagation filters, and phenomena like over-smoothing are typically not apparent in CNNs. In this paper, we bridge these gaps by incorporating trainable channel-wise weighting factors $\omega$ to learn and mix multiple smoothing and sharpening propagation operators at each layer. Our generic method is called $\omega$GNN, and is easy to implement. We study two variants: $\omega$GCN and $\omega$GAT. For $\omega$GCN, we theoretically analyse its behaviour and the impact of $\omega$ on the obtained node features. Our experiments confirm these findings, demonstrating and explaining how both variants do not over-smooth. Additionally, we experiment with 15 real-world datasets on node- and graph-classification tasks, where our $\omega$GCN and $\omega$GAT perform on par with state-of-the-art methods.