Probabilistic Graph Rewiring via Virtual Nodes

Fuente: arXiv
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Hauptverfasser: Qian, Chendi, Manolache, Andrei, Morris, Christopher, Niepert, Mathias
Format: Preprint
Veröffentlicht: 2024
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author Qian, Chendi
Manolache, Andrei
Morris, Christopher
Niepert, Mathias
author_facet Qian, Chendi
Manolache, Andrei
Morris, Christopher
Niepert, Mathias
contents Message-passing graph neural networks (MPNNs) have emerged as a powerful paradigm for graph-based machine learning. Despite their effectiveness, MPNNs face challenges such as under-reaching and over-squashing, where limited receptive fields and structural bottlenecks hinder information flow in the graph. While graph transformers hold promise in addressing these issues, their scalability is limited due to quadratic complexity regarding the number of nodes, rendering them impractical for larger graphs. Here, we propose implicitly rewired message-passing neural networks (IPR-MPNNs), a novel approach that integrates implicit probabilistic graph rewiring into MPNNs. By introducing a small number of virtual nodes, i.e., adding additional nodes to a given graph and connecting them to existing nodes, in a differentiable, end-to-end manner, IPR-MPNNs enable long-distance message propagation, circumventing quadratic complexity. Theoretically, we demonstrate that IPR-MPNNs surpass the expressiveness of traditional MPNNs. Empirically, we validate our approach by showcasing its ability to mitigate under-reaching and over-squashing effects, achieving state-of-the-art performance across multiple graph datasets. Notably, IPR-MPNNs outperform graph transformers while maintaining significantly faster computational efficiency.
format Preprint
id arxiv_https___arxiv_org_abs_2405_17311
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Probabilistic Graph Rewiring via Virtual Nodes
Qian, Chendi
Manolache, Andrei
Morris, Christopher
Niepert, Mathias
Machine Learning
Message-passing graph neural networks (MPNNs) have emerged as a powerful paradigm for graph-based machine learning. Despite their effectiveness, MPNNs face challenges such as under-reaching and over-squashing, where limited receptive fields and structural bottlenecks hinder information flow in the graph. While graph transformers hold promise in addressing these issues, their scalability is limited due to quadratic complexity regarding the number of nodes, rendering them impractical for larger graphs. Here, we propose implicitly rewired message-passing neural networks (IPR-MPNNs), a novel approach that integrates implicit probabilistic graph rewiring into MPNNs. By introducing a small number of virtual nodes, i.e., adding additional nodes to a given graph and connecting them to existing nodes, in a differentiable, end-to-end manner, IPR-MPNNs enable long-distance message propagation, circumventing quadratic complexity. Theoretically, we demonstrate that IPR-MPNNs surpass the expressiveness of traditional MPNNs. Empirically, we validate our approach by showcasing its ability to mitigate under-reaching and over-squashing effects, achieving state-of-the-art performance across multiple graph datasets. Notably, IPR-MPNNs outperform graph transformers while maintaining significantly faster computational efficiency.
title Probabilistic Graph Rewiring via Virtual Nodes
topic Machine Learning
url https://arxiv.org/abs/2405.17311