Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks

• URL: http://arxiv.org/abs/2308.16800v3
• Date: Tue, 17 Sep 2024 19:19:17 GMT
• Title: Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks
• Authors: Andreas Roth, Thomas Liebig,
• Abstract summary: We show that with increased depth, node representations become dominated by a low-dimensional subspace that depends on the aggregation function but not on the feature transformations. For all aggregation functions, the rank of the node representations collapses, resulting in over-smoothing for particular aggregation functions.
• Score: 3.566568169425391
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Our study reveals new theoretical insights into over-smoothing and feature over-correlation in graph neural networks. Specifically, we demonstrate that with increased depth, node representations become dominated by a low-dimensional subspace that depends on the aggregation function but not on the feature transformations. For all aggregation functions, the rank of the node representations collapses, resulting in over-smoothing for particular aggregation functions. Our study emphasizes the importance for future research to focus on rank collapse rather than over-smoothing. Guided by our theory, we propose a sum of Kronecker products as a beneficial property that provably prevents over-smoothing, over-correlation, and rank collapse. We empirically demonstrate the shortcomings of existing models in fitting target functions of node classification tasks.

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