mlsanityData to 7 Oct 2026

Principal Neighbourhood Aggregation for Graph Nets

arXiv 2004.05718 ↗First posted 12 Apr 2020cs.LG cs.CV stat.MLcited by 477

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Abstract (arXiv)

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.

Key facts. Cited by 477 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Apr 2020.

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Citing papers per year: 2021: 62; 2022: 89; 2023: 112; 2024: 96; 2025: 66; 2026: 52.

477 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2022Recipe for a General, Powerful, Scalable Graph Transformercited by 702
  3. 2021Rethinking Graph Transformers with Spectral Attentioncited by 468
  4. 2021Graph Neural Networks with Learnable Structural and Positional Representationscited by 326
  5. 2021Do Transformers Really Perform Bad for Graph Representation?cited by 318
  6. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  7. 2021Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Predictioncited by 273
  8. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  9. 2021Pre-training Molecular Graph Representation with 3D Geometrycited by 248
  10. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  11. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  12. 2022Representing Long-Range Context for Graph Neural Networks with Global Attentioncited by 193
38 more
  1. 2022Structure-Aware Transformer for Graph Representation Learningcited by 191
  2. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  3. 2022Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanismcited by 171
  4. 2023Exphormer: Sparse Transformers for Graphscited by 166
  5. 2021Equivariant Subgraph Aggregation Networkscited by 154
  6. 2021From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awarenesscited by 154
  7. 2023Graph Inductive Biases in Transformers without Message Passingcited by 150
  8. 20213D Infomax improves GNNs for Molecular Property Predictioncited by 146
  9. 2021Nested Graph Neural Networkscited by 136
  10. 2021ETA Prediction with Graph Neural Networks in Google Mapscited by 130
  11. 2022Graph-Coupled Oscillator Networkscited by 123
  12. 2023Rethinking the Expressive Power of GNNs via Graph Biconnectivitycited by 119
  13. 2021Global Self-Attention as a Replacement for Graph Convolutioncited by 113
  14. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  15. 2022The CLRS Algorithmic Reasoning Benchmarkcited by 103
  16. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
  17. 2021GNNAutoScale: Scalable and Expressive Graph Neural Networks via Historical Embeddingscited by 90
  18. 2022How Powerful are K-hop Message Passing Graph Neural Networkscited by 90
  19. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  20. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 88
  21. 2023Where Did the Gap Go? Reassessing the Long-Range Graph Benchmarkcited by 83
  22. 2024Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classificationcited by 83
  23. 2021Size-Invariant Graph Representations for Graph Classification Extrapolationscited by 82
  24. 2021OOD-GNN: Out-of-Distribution Generalized Graph Neural Networkcited by 78
  25. 2024Discrete-state Continuous-time Diffusion for Graph Generationcited by 73
  26. 2023A Comprehensive Survey on Deep Graph Representation Learningcited by 72
  27. 2021Learning to Extend Molecular Scaffolds with Structural Motifscited by 70
  28. 2022GRPE: Relative Positional Encoding for Graph Transformercited by 67
  29. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  30. 2021Reconstruction for Powerful Graph Representationscited by 65
  31. 2023A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Testscited by 64
  32. 2022Expressiveness and Approximation Properties of Graph Neural Networkscited by 63
  33. 2022Neural-Symbolic Models for Logical Queries on Knowledge Graphscited by 60
  34. 2024Graph Neural Networks for Learning Equivariant Representations of Neural Networkscited by 59
  35. 2021Hierarchical Graph Representations in Digital Pathologycited by 58
  36. 2022Interpretable Graph Neural Networks for Connectome-Based Brain Disorder Analysiscited by 58
  37. 2022Anti-Symmetric DGN: a stable architecture for Deep Graph Networkscited by 58
  38. 2022Ordered Subgraph Aggregation Networkscited by 57

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