Effects of Random Edge-Dropping on Over-Squashing in Graph Neural Networks

• URL: http://arxiv.org/abs/2502.07364v1
• Date: Tue, 11 Feb 2025 08:36:38 GMT
• Title: Effects of Random Edge-Dropping on Over-Squashing in Graph Neural Networks
• Authors: Jasraj Singh, Keyue Jiang, Brooks Paige, Laura Toni,
• Abstract summary: We present theoretical results that characterize the negative effects of DropEdge on sensitivity between distant nodes. Our findings are easily extended to its variants, allowing us to build a comprehensive understanding of how they affect over-squashing. Our conclusions highlight the need to re-evaluate various methods designed for training deep GNNs.
• Score: 8.524684315458243
• License:
• Abstract: Message Passing Neural Networks (MPNNs) are a class of Graph Neural Networks (GNNs) that leverage the graph topology to propagate messages across increasingly larger neighborhoods. The message-passing scheme leads to two distinct challenges: over-smoothing and over-squashing. While several algorithms, e.g. DropEdge and its variants -- DropNode, DropAgg and DropGNN -- have successfully addressed the over-smoothing problem, their impact on over-squashing remains largely unexplored. This represents a critical gap in the literature as failure to mitigate over-squashing would make these methods unsuitable for long-range tasks. In this work, we take the first step towards closing this gap by studying the aforementioned algorithms in the context of over-squashing. We present novel theoretical results that characterize the negative effects of DropEdge on sensitivity between distant nodes, suggesting its unsuitability for long-range tasks. Our findings are easily extended to its variants, allowing us to build a comprehensive understanding of how they affect over-squashing. We evaluate these methods using real-world datasets, demonstrating their detrimental effects. Specifically, we show that while DropEdge-variants improve test-time performance in short range tasks, they deteriorate performance in long-range ones. Our theory explains these results as follows: random edge-dropping lowers the effective receptive field of GNNs, which although beneficial for short-range tasks, misaligns the models on long-range ones. This forces the models to overfit to short-range artefacts in the training set, resulting in poor generalization. Our conclusions highlight the need to re-evaluate various methods designed for training deep GNNs, with a renewed focus on modelling long-range interactions.

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