mlsanityData to 7 Oct 2026

Graph Unitary Message Passing

arXiv 2403.11199 ↗First posted 17 Mar 2024cs.LG cs.AIcited by 5

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Abstract (arXiv)

Unitarity is a useful principle for stabilizing deep neural networks, but in graph neural networks (GNNs) instability is induced not only by learnable parameters but also by the graph propagation operator. Motivated by this distinction, we propose Graph Unitary Message Passing (GUMP), a message-passing framework that uses a unitary propagation operator on a transformed graph to avoid graph-induced exponential decay under repeated propagation. GUMP combines (i) a graph transformation that maps an input graph to an Eulerian line-graph construction admitting unitary adjacency matrices, and (ii) a practical unitary projection procedure based on Newton-Schulz iteration. Theoretical analysis clarifies that, under standard analysis assumptions, unitary propagation keeps the graph-propagation term depth-stable, while vanilla normalized propagation exhibits exponential decay in its non-trivial spectral components. Across synthetic long-range tasks, TUDataset benchmarks, and LRGB datasets, GUMP improves over vanilla message passing and achieves competitive or superior performance against strong baselines. Code is available at https://github.com/ucker/gump_code.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 61 of its 79 references that are in the map. First posted on arXiv 17 Mar 2024.

Builds on

61 of 79 references.

References · 61

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,616
  3. 2018How Powerful are Graph Neural Networks?cited by 4,355
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  5. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  6. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  7. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  8. 2017Modeling Relational Data with Graph Convolutional Networkscited by 1,684
  9. 2016Variational Graph Auto-Encoderscited by 1,373
  10. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  11. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  12. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
38 more
  1. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  2. 2020Simple and Deep Graph Convolutional Networkscited by 857
  3. 2018Link Prediction Based on Graph Neural Networkscited by 829
  4. 2021How Attentive are Graph Attention Networks?cited by 818
  5. 2023RWKV: Reinventing RNNs for the Transformer Eracited by 814
  6. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 786
  7. 2013Exact solutions to the nonlinear dynamics of learning in deep linear neural networkscited by 748
  8. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 718
  9. 2019Graph Neural Networks for Social Recommendationcited by 711
  10. 2022Recipe for a General, Powerful, Scalable Graph Transformercited by 702
  11. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  12. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 624
  13. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  14. 2019DeepGCNs: Can GCNs Go as Deep as CNNs?cited by 527
  15. 2019Graph U-Netscited by 489
  16. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  17. 2019Diffusion Improves Graph Learningcited by 414
  18. 2023Resurrecting Recurrent Neural Networks for Long Sequencescited by 397
  19. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  20. 2015Unitary Evolution Recurrent Neural Networkscited by 291
  21. 2021GRAND: Graph Neural Diffusioncited by 258
  22. 2022Long Range Graph Benchmarkcited by 258
  23. 2024Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Modelscited by 232
  24. 2023Exphormer: Sparse Transformers for Graphscited by 166
  25. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
  26. 2017The Shattered Gradients Problem: If resnets are the answer, then what is the question?cited by 156
  27. 2019Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Groupcited by 133
  28. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  29. 2022FoSR: First-order spectral rewiring for addressing oversquashing in GNNscited by 104
  30. 2018The Singular Values of Convolutional Layerscited by 95
  31. 2023Understanding Oversquashing in GNNs through the Lens of Effective Resistancecited by 94
  32. 2022A Generalization of ViT/MLP-Mixer to Graphscited by 93
  33. 2020Line Graph Neural Networks for Link Predictioncited by 89
  34. 2019Preventing Gradient Attenuation in Lipschitz Constrained Convolutional Networkscited by 86
  35. 2023Where Did the Gap Go? Reassessing the Long-Range Graph Benchmarkcited by 83
  36. 2017Orthogonal Recurrent Neural Networks with Scaled Cayley Transformcited by 82
  37. 2022Graph Neural Networks for Link Prediction with Subgraph Sketchingcited by 81
  38. 2023DRew: Dynamically Rewired Message Passing with Delaycited by 81

50 most cited of 61 All 61 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 3.

5 papers.

  1. 2024PANDA: Expanded Width-Aware Message Passing Beyond Rewiringcited by 10
  2. 2024Unitary convolutions for learning on graphs and groupscited by 8
  3. 2026Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observablescited by 0
  4. 2026Exploring Oversmoothing with Householder Matricescited by 0
  5. 2026LiftGCN: Efficient Energy-Preserving Graph Learning via Joukowski Spectral Lifting for Finite Element Stress Predictioncited by 0