Graph Coarsening with Message-Passing Guarantees

Antonin Joly, Nicolas Keriven

Keywords: graph coarsening, message passing, graph neural network

TL;DR: We propose a new message-passing paradigm specific to coarsened graphs, with theoretical guarantees from the original graph.

Abstract:

Graph coarsening reduces the size of a large graph to decrease computational load and memory footprint, while preserving some of its key properties. For instance, training Graph Neural Networks (GNNs) on coarsened graphs leads to drastic savings in time and memory. However, GNNs rely on the Message-Passing (MP) paradigm, and classical spectral preservation guarantees for graph coarsening do not directly lead to theoretical guarantees when performing naive message-passing on the coarsened graph. In this work, we propose a new message-passing operation specific to coarsened graphs, which exhibit theoretical guarantees on the preservation of the propagated signal. We conduct node classification tasks on synthetic and real data and observe improved results compared to performing naive message-passing on the coarsened graph.

Submission Type: Extended abstract (max 4 main pages).

Submission Number: 48