<p>Graph Neural Networks (GNNs) are powerful tools for processing structured graph data but often suffer from over-smoothing, where nodes become indistinguishable as the network depth increases. To address this challenge, we present TRAIL (Trajectory-based Representation And Integration for Limiting over-smoothing), a novel framework that tracks how local embeddings change across layers and combines them to preserve informative node features. Extensive evaluations demonstrates that TRAIL significantly increases Dirichlet Energy, a key metric for quantifying over-smoothing, ensuring that feature differences between nodes remain distinguishable even in deep networks. These improvements translate into superior performance across diverse datasets, particularly excelling in heterophily graphs such as Cornell, Chameleon, and Wisconsin, with accuracy improvements of up to 15% over baseline models. Furthermore, TRAIL consistently outperforms existing spectral and spatial GNNs on high-homophily datasets like Cora, Citeseer, and Pubmed. Overall, TRAIL offers an effective and generalizable solution for improving GNN performance across a wide range of graph types.</p>

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TRAIL: Trajectory-Based Representation and Integration for Limiting Over-Smoothing

  • Seung Hyun Ham,
  • Jay Hoon Jung

摘要

Graph Neural Networks (GNNs) are powerful tools for processing structured graph data but often suffer from over-smoothing, where nodes become indistinguishable as the network depth increases. To address this challenge, we present TRAIL (Trajectory-based Representation And Integration for Limiting over-smoothing), a novel framework that tracks how local embeddings change across layers and combines them to preserve informative node features. Extensive evaluations demonstrates that TRAIL significantly increases Dirichlet Energy, a key metric for quantifying over-smoothing, ensuring that feature differences between nodes remain distinguishable even in deep networks. These improvements translate into superior performance across diverse datasets, particularly excelling in heterophily graphs such as Cornell, Chameleon, and Wisconsin, with accuracy improvements of up to 15% over baseline models. Furthermore, TRAIL consistently outperforms existing spectral and spatial GNNs on high-homophily datasets like Cora, Citeseer, and Pubmed. Overall, TRAIL offers an effective and generalizable solution for improving GNN performance across a wide range of graph types.