mlsanityData to 14 Oct 2026

Exploring Oversmoothing with Householder Matrices

arXiv 2608.12514 ↗First posted 12 Aug 2026cs.LGcited by 0

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Abstract (arXiv)

Deep graph neural networks(GNNs) suffer from oversmoothing- a progressive collapse of node representation towards a low information subspace as network depth increases because the normalized graph propagation operator is repeatedly applied directly to the hidden representations. In this work we study Householder Graph Neural Network (HouseGNN). Rather than updating the hidden state like standard GCN, HouseGNN uses the aggregated neighbourhood message solely to estimate a reflection direction; the node embedding is then updated by a Householder reflector followed by GroupSort, yielding a piecewise orthogonal layer that preserves Euclidean norm at every node and at every depth. We prove three core properties: (i) every internal layer preserves the node-wise Euclidean norm; (ii) the Householder reflector is scale scale and sign-invariant in the message; and (iii) pairwise distance between nodes can change through mismatch between node-wise orthogonal operators.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 28 of its 33 references that are in the map. First posted on arXiv 12 Aug 2026.

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References · 28

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16 more
  1. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 680
  2. 2023A critical look at the evaluation of GNNs under heterophily: Are we really making progress?cited by 343
  3. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
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  5. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 247
  6. 2018Sorting out Lipschitz function approximationcited by 213
  7. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  8. 2016Efficient Orthogonal Parametrisation of Recurrent Neural Networks Using Householder Reflectionscited by 57
  9. 2022A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networkscited by 49
  10. 2023Demystifying Oversmoothing in Attention-Based Graph Neural Networkscited by 49
  11. 2024Residual Connections and Normalization Can Provably Prevent Oversmoothing in GNNscited by 34
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  13. 2017Dynamics over Signed Networkscited by 8
  14. 2024Unitary convolutions for learning on graphs and groupscited by 8
  15. 2024Graph Unitary Message Passingcited by 5
  16. 2025A Signed Graph Approach to Understanding and Mitigating Oversmoothing in GNNscited by 2

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