PANDA: Expanded Width-Aware Message Passing Beyond Rewiring

TL;DR

PANDA introduces a width-aware message passing method that selectively expands high-centrality nodes to mitigate over-squashing in GNNs, outperforming traditional rewiring techniques without altering the original graph topology.

Contribution

The paper proposes a novel width-aware message passing paradigm that expands high-centrality nodes, providing an effective alternative to graph rewiring for overcoming over-squashing in GNNs.

Findings

Outperforms existing rewiring methods in experiments.

Effectively mitigates over-squashing without changing graph topology.

Enhances long-range information propagation in GNNs.

Abstract

Recent research in the field of graph neural network (GNN) has identified a critical issue known as "over-squashing," resulting from the bottleneck phenomenon in graph structures, which impedes the propagation of long-range information. Prior works have proposed a variety of graph rewiring concepts that aim at optimizing the spatial or spectral properties of graphs to promote the signal propagation. However, such approaches inevitably deteriorate the original graph topology, which may lead to a distortion of information flow. To address this, we introduce an expanded width-aware (PANDA) message passing, a new message passing paradigm where nodes with high centrality, a potential source of over-squashing, are selectively expanded in width to encapsulate the growing influx of signals from distant nodes. Experimental results show that our method outperforms existing rewiring methods, suggesting that selectively expanding the hidden state of nodes can be a compelling alternative to graph rewiring for addressing the over-squashing.