Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks
This work addresses limitations in graph neural networks for domains like social networks and biochemistry, offering an incremental improvement over existing methods.
The paper tackled the problem of oversmoothing and underreaching in Graph Convolutional Networks (GCNs) by proposing a hybrid GNN framework that combines GCN filters with geometric scattering band-pass filters and an attention mechanism, resulting in improved performance on various learning tasks as shown in experiments.
Geometric deep learning has made great strides towards generalizing the design of structure-aware neural networks from traditional domains to non-Euclidean ones, giving rise to graph neural networks (GNN) that can be applied to graph-structured data arising in, e.g., social networks, biochemistry, and material science. Graph convolutional networks (GCNs) in particular, inspired by their Euclidean counterparts, have been successful in processing graph data by extracting structure-aware features. However, current GNN models are often constrained by various phenomena that limit their expressive power and ability to generalize to more complex graph datasets. Most models essentially rely on low-pass filtering of graph signals via local averaging operations, leading to oversmoothing. Moreover, to avoid severe oversmoothing, most popular GCN-style networks tend to be shallow, with narrow receptive fields, leading to underreaching. Here, we propose a hybrid GNN framework that combines traditional GCN filters with band-pass filters defined via geometric scattering. We further introduce an attention framework that allows the model to locally attend over combined information from different filters at the node level. Our theoretical results establish the complementary benefits of the scattering filters to leverage structural information from the graph, while our experiments show the benefits of our method on various learning tasks.