Demystifying MPNNs: Message Passing as Merely Efficient Matrix Multiplication

• URL: http://arxiv.org/abs/2502.00140v1
• Date: Fri, 31 Jan 2025 19:48:03 GMT
• Title: Demystifying MPNNs: Message Passing as Merely Efficient Matrix Multiplication
• Authors: Qin Jiang, Chengjia Wang, Michael Lones, Wei Pang,
• Abstract summary: Graph Neural Networks (GNNs) have achieved remarkable success, their design largely relies on empirical intuition rather than theoretical understanding. We present a comprehensive analysis of GNN behavior through three fundamental aspects. We demonstrate that gradient-related issues, rather than just over-smoothing, can significantly impact performance in sparse graphs. We also analyze how different normalization schemes affect model performance and how GNNs make predictions with uniform node features.
• Score: 4.002604752467421
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• Abstract: While Graph Neural Networks (GNNs) have achieved remarkable success, their design largely relies on empirical intuition rather than theoretical understanding. In this paper, we present a comprehensive analysis of GNN behavior through three fundamental aspects: (1) we establish that \textbf{$k$-layer} Message Passing Neural Networks efficiently aggregate \textbf{$k$-hop} neighborhood information through iterative computation, (2) analyze how different loop structures influence neighborhood computation, and (3) examine behavior across structure-feature hybrid and structure-only tasks. For deeper GNNs, we demonstrate that gradient-related issues, rather than just over-smoothing, can significantly impact performance in sparse graphs. We also analyze how different normalization schemes affect model performance and how GNNs make predictions with uniform node features, providing a theoretical framework that bridges the gap between empirical success and theoretical understanding.

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