Understanding Virtual Nodes: Oversquashing and Node Heterogeneity

Joshua Southern, Francesco Di Giovanni, Michael M. Bronstein, Johannes F. Lutzeyer

Keywords: Graph Neural Networks, Message Passing, Virtual Nodes, Oversquashing, Graph Transformers

TL;DR: We study the benefits of adding Virtual Nodes to Message Passing Neural Networks through the lenses of oversquashing and learning heterogeneous node importance.

Abstract: While message passing neural networks (MPNNs) have convincing success in a range of applications, they exhibit limitations such as the oversquashing problem and their inability to capture long-range interactions. Augmenting MPNNs with a virtual node (VN) removes the locality constraint of the layer aggregation and has been found to improve performance on a range of benchmarks. We provide a comprehensive theoretical analysis of the role of VNs and benefits thereof, through the lenses of oversquashing and sensitivity analysis. First, we characterize, precisely, how the improvement afforded by VNs on the mixing abilities of the network and hence in mitigating oversquashing, depends on the underlying topology. We then highlight that, unlike Graph-Transformers (GTs), classical instantiations of the VN are often constrained to assign uniform importance to different nodes. Consequently, we propose a variant of VN with the same computational complexity, which can have different sensitivity to nodes based on the graph structure. We show that this is an extremely effective and computationally efficient baseline for graph-level tasks.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 7076