DiffWire: Inductive Graph Rewiring via the Lovász BoundDownload PDF

Published: 24 Nov 2022, Last Modified: 12 Mar 2024LoG 2022 PosterReaders: Everyone
Keywords: GNN, graph neural networks, Geometric deep learning, MPNNs, graph rewiring, over-smoothing, over-squashing, Lovász bound, spectral gap, graph diffusion, commute times
TL;DR: We propose DiffWire, a unifying GNN rewiring method that is parameter-free and differentiable.
Abstract: Graph Neural Networks (GNNs) have been shown to achieve competitive results to tackle graph-related tasks, such as node and graph classification, link prediction and node and graph clustering in a variety of domains. Most GNNs use a message passing framework and hence are called MPNNs. Despite their promising results, MPNNs have been reported to suffer from over-smoothing, over-squashing and under-reaching. Graph rewiring and graph pooling have been proposed in the literature as solutions to address these limitations. However, most state-of-the-art graph rewiring methods fail to preserve the global topology of the graph, are neither differentiable nor inductive, and require the tuning of hyper-parameters. In this paper, we propose DiffWire, a novel framework for graph rewiring in MPNNs that is principled, fully differentiable and parameter-free by leveraging the Lovász bound. The proposed approach provides a unified theory for graph rewiring by proposing two new, complementary layers in MPNNs: CT-Layer, a layer that learns the commute times and uses them as a relevance function for edge re-weighting; and GAP-Layer, a layer to optimize the spectral gap, depending on the nature of the network and the task at hand. We empirically validate the value of each of these layers separately with benchmark datasets for graph classification. We also perform preliminary studies on the use of CT-Layer for homophilic and heterophilic node classification tasks. DiffWire brings together the learnability of commute times to related definitions of curvature, opening the door to creating more expressive MPNNs.
PDF File: pdf
Type Of Submission: Full paper proceedings track submission (max 9 main pages).
Agreement: Check this if you are okay with being contacted to participate in an anonymous survey.
Type Of Submission: Full paper proceedings track submission.
Software: https://github.com/AdrianArnaiz/DiffWire
Poster: png
Poster Preview: png
Community Implementations: [![CatalyzeX](/images/catalyzex_icon.svg) 2 code implementations](https://www.catalyzex.com/paper/arxiv:2206.07369/code)
6 Replies

Loading