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A Note on Over-Smoothing for Graph Neural Networks

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arxiv 2006.13318 v1 pith:MRV7KWVJ submitted 2020-06-23 cs.LG stat.ML

Chen Cai , Yusu Wang This is my paper
classification cs.LGstat.ML
keywords graphneuralnetworksover-smoothingcitedirichleteffectenergy
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Graph Neural Networks (GNNs) have achieved a lot of success on graph-structured data. However, it is observed that the performance of graph neural networks does not improve as the number of layers increases. This effect, known as over-smoothing, has been analyzed mostly in linear cases. In this paper, we build upon previous results \cite{oono2019graph} to further analyze the over-smoothing effect in the general graph neural network architecture. We show when the weight matrix satisfies the conditions determined by the spectrum of augmented normalized Laplacian, the Dirichlet energy of embeddings will converge to zero, resulting in the loss of discriminative power. Using Dirichlet energy to measure "expressiveness" of embedding is conceptually clean; it leads to simpler proofs than \cite{oono2019graph} and can handle more non-linearities.

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Cited by 9 Pith papers

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

  1. Bridging Theory and Practice in Link Representation with Graph Neural Networks

    cs.LG 2025-06 reject novelty 7.0 of 10

    A new framework classifies message-passing link representation models by neighborhood radius and base expressiveness, yielding a hierarchy in which SEAL is most expressive, plus a synthetic benchmark and symmetry-base...

  2. Remedying Coarsening-Based GNN Training under Heterophily via Adaptive Complementary Enhancement

    cs.LG 2026-07 conditional novelty 6.0 of 10

    ACE adds a heterophily-aware auxiliary loss to coarsening-based GNN training, recovering discarded node-level information and improving accuracy on heterophilic graphs by up to ~15 points.

  3. Beyond ReLU: Bifurcation, Oversmoothing, and Topological Priors

    cs.LG 2026-02 conditional novelty 6.0 of 10

    Replacing ReLU with odd activations that have a stabilizing cubic term (sin, tanh) provably destabilizes the oversmooth fixed point of message passing and creates stable non-homogeneous solutions with square-root ampl...

  4. TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows

    cs.LG 2025-08 conditional novelty 6.0 of 10

    TANGO adds a learnable energy gradient and an orthogonal tangential flow to GNN layers, improving long-range and heterophilic graph benchmarks.

  5. From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks

    cs.LG 2026-07 conditional novelty 5.0 of 10

    Hypergraph diffusion provably collapses node representations, and a reaction term that exactly cancels diffusion dissipation keeps a designed transverse energy level nonzero in Hypergraph Neural Reaction–Diffusion (HNRD).

  6. Geometric GNNs for Charged Particle Tracking at GlueX

    cs.LG 2025-05 conditional novelty 5.0 of 10

    On simulated GlueX Forward Drift Chamber data, a GNN edge classifier reaches 0.9806 segment efficiency at 0.9462 purity versus 0.9119 for the traditional method, with batched GPU inference at 44 microseconds per event...

  7. Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature

    cs.LG 2026-07 reject novelty 4.0 of 10

    A graph curvature proxy, κw, is claimed to bound oversmoothing and generalization and to guide rewiring/gating, but the central proofs rest on gaps and an invalid monotonicity argument.

  8. How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?

    stat.ML 2025-06 conditional novelty 4.0 of 10

    SBM-style probabilistic models outperform graph neural networks on link prediction when node features are low-dimensional, noisy, or the graph is heterophilic.

  9. Comment on "A Note on Over-Smoothing for Graph Neural Networks"

    cs.LG 2025-09 conditional novelty 3.0 of 10

    The authors show exponential decay of Dirichlet energy for GNNs with Leaky-ReLU and polynomial filters, but the proof relies on unverified spectral inequalities.

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