Improving Graph Neural Networks with Learnable Propagation Operators

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 $ω$ to learn and mix multiple smoothing and sharpening propagation operators at each layer. Our generic method is called $ω$GNN, and is easy to implement. We study two variants: $ω$GCN and $ω$GAT. For $ω$GCN, we theoretically analyse its behaviour and the impact of $ω$ 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 $ω$GCN and $ω$GAT perform on par with state-of-the-art methods.