GEOMETRIC SCATTERING ATTENTION NETWORKS.

Geometric scattering has recently gained recognition in graph representation learning, and recent work has shown that integrating scattering features in graph convolution networks (GCNs) can alleviate the typical oversmoothing of features in node representation learning. However, scattering often relies on handcrafted design, requiring careful selection of frequency bands via a cascade of wavelet transforms, as well as an effective weight sharing scheme to combine low- and band-pass information. Here, we introduce a new attention-based architecture to produce adaptive task-driven node representations by implicitly learning node-wise weights for combining multiple scattering and GCN channels in the network. We show the resulting geometric scattering attention network (GSAN) outperforms previous networks in semi-supervised node classification, while also enabling a spectral study of extracted information by examining node-wise attention weights.

Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks.

Graph convolutional networks (GCNs) have shown promising results in processing graph data by extracting structure-aware features. This gave rise to extensive work in geometric deep learning, focusing on designing network architectures that ensure neuron activations conform to regularity patterns within the input graph. However, in most cases the graph structure is only accounted for by considering the similarity of activations between adjacent nodes, which limits the capabilities of such methods to discriminate between nodes in a graph. Here, we propose to augment conventional GCNs with geometric scattering transforms and residual convolutions. The former enables band-pass filtering of graph signals, thus alleviating the so-called oversmoothing often encountered in GCNs, while the latter is introduced to clear the resulting features of high-frequency noise. We establish the advantages of the presented Scattering GCN with both theoretical results establishing the complementary benefits of scattering and GCN features, as well as experimental results showing the benefits of our method compared to leading graph neural networks for semi-supervised node classification, including the recently proposed GAT network that typically alleviates oversmoothing using graph attention mechanisms.