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Simplifying the Theory on Over-Smoothing

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arxiv 2407.11876 v2 pith:WSZYXVKQ submitted 2024-07-16 cs.LG

Andreas Roth This is my paper · ORCID
classification cs.LG
keywords over-smoothingtheoryconvolutionsdirectionsgraphhoweverabilityaccessible
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Graph convolutions have gained popularity due to their ability to efficiently operate on data with an irregular geometric structure. However, graph convolutions cause over-smoothing, which refers to representations becoming more similar with increased depth. However, many different definitions and intuitions currently coexist, leading to research efforts focusing on incompatible directions. This paper attempts to align these directions by showing that over-smoothing is merely a special case of power iteration. This greatly simplifies the existing theory on over-smoothing, making it more accessible. Based on the theory, we provide a novel comprehensive definition of rank collapse as a generalized form of over-smoothing and introduce the rank-one distance as a corresponding metric. Our empirical evaluation of 14 commonly used methods shows that more models than were previously known suffer from this issue.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exploring and Improving Initialization for Deep Graph Neural Networks: A Signal Propagation Perspective

    cs.LG 2025-06 conditional novelty 6.0 of 10

    SPoGInit stabilizes forward, backward, and embedding-variation signal propagation in deep graph convolutional networks, mitigating the performance degradation that normally comes with depth.

  2. What Can We Learn From MIMO Graph Convolutions?

    cs.LG 2025-05 conditional novelty 6.0 of 10

    Localized MIMO graph convolutions (LMGCs) generalize many linear message-passing GNNs and are provably injective and produce linearly independent representations for almost every edge weight choice.

  3. A Dynamical Systems-Inspired Pruning Strategy for Addressing Oversmoothing in Graph Neural Networks

    cs.LG 2024-12 reject novelty 4.0 of 10

    DYNAMO-GAT prunes GNN attention edges between highly correlated nodes to prevent oversmoothing, but its main theoretical lemma contradicts its goal and its accuracy claims exceed its own table.

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