mlsanityData to 14 Oct 2026

Understanding Pooling in Graph Neural Networks

arXiv 2110.05292 ↗First posted 11 Oct 2021cs.LG cs.AIcited by 69

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Abstract (arXiv)

Inspired by the conventional pooling layers in convolutional neural networks, many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. The great variety in the literature stems from the many possible strategies for coarsening a graph, which may depend on different assumptions on the graph structure or the specific downstream task. In this paper we propose a formal characterization of graph pooling based on three main operations, called selection, reduction, and connection, with the goal of unifying the literature under a common framework. Following this formalization, we introduce a taxonomy of pooling operators and categorize more than thirty pooling methods proposed in recent literature. We propose criteria to evaluate the performance of a pooling operator and use them to investigate and contrast the behavior of different classes of the taxonomy on a variety of tasks.

Key facts. Cited by 69 papers in the map (data through 14 Oct 2026). Builds on 41 of its 70 references that are in the map. First posted on arXiv 11 Oct 2021.

Builds on

41 of 70 references.

References · 41

  1. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  2. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,401
  3. 2018How Powerful are Graph Neural Networks?cited by 4,393
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  5. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,434
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  7. 2018Relational inductive biases, deep learning, and graph networkscited by 1,360
  8. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,102
  9. 2015Gated Graph Sequence Neural Networkscited by 796
  10. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 787
  11. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 728
  12. 2016TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systemscited by 664
29 more
  1. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  2. 2019Self-Attention Graph Poolingcited by 421
  3. 2016OctNet: Learning Deep 3D Representations at High Resolutionscited by 342
  4. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 310
  5. 2015Diffusion-Convolutional Neural Networkscited by 268
  6. 2015Order Matters: Sequence to sequence for setscited by 237
  7. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  8. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 183
  9. 2020Design Space for Graph Neural Networkscited by 182
  10. 2019Understanding Attention and Generalization in Graph Neural Networkscited by 169
  11. 2017SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernelscited by 161
  12. 2019ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representationscited by 156
  13. 2019On the Universality of Invariant Networkscited by 152
  14. 2020A Survey on The Expressive Power of Graph Neural Networkscited by 111
  15. 2018Towards Sparse Hierarchical Graph Classifierscited by 100
  16. 2019Graph Convolutional Networks with EigenPoolingcited by 94
  17. 2020Rethinking pooling in graph neural networkscited by 73
  18. 2020Graph Neural Networks in TensorFlow and Keras with Spektralcited by 60
  19. 2019DEMO-Net: Degree-specific Graph Neural Networks for Node and Graph Classificationcited by 59
  20. 2021Graph Coarsening with Neural Networkscited by 55
  21. 2019Edge Contraction Pooling for Graph Neural Networkscited by 53
  22. 2019Octree guided CNN with Spherical Kernels for 3D Point Cloudscited by 50
  23. 2019A Unifying Framework for Spectrum-Preserving Graph Sparsification and Coarseningcited by 31
  24. 2019Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Poolingcited by 30
  25. 2020Deep Graph Mapper: Seeing Graphs through the Neural Lenscited by 22
  26. 2019Towards Interpretable Sparse Graph Representation Learning with Laplacian Poolingcited by 20
  27. 2019A Non-Negative Factorization approach to node pooling in Graph Convolutional Neural Networkscited by 14
  28. 2019Clique pooling for graph classificationcited by 13
  29. 2019Function Space Pooling For Graph Convolutional Networkscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 12; 2023: 16; 2024: 19; 2025: 12; 2026: 10.

69 papers.

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  1. 2022BrainGB: A Benchmark for Brain Network Analysis with Graph Neural Networkscited by 75
  2. 2022Ordered Subgraph Aggregation Networkscited by 57
  3. 2022Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunitiescited by 52
  4. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  5. 2023The expressive power of pooling in Graph Neural Networkscited by 35
  6. 2023Graph Deep Learning for Time Series Forecastingcited by 26
  7. 2025LLM as GNN: Graph Vocabulary Learning for Text-Attributed Graph Foundation Modelscited by 22
  8. 2023Graph-based Time Series Clustering for End-to-End Hierarchical Forecastingcited by 17
  9. 2024Graph-based Forecasting with Missing Data through Spatiotemporal Downsamplingcited by 17
  10. 2023A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarseningcited by 15
  11. 2024Understanding Virtual Nodes: Oversquashing and Node Heterogeneitycited by 14
  12. 2023Search to Fine-tune Pre-trained Graph Neural Networks for Graph-level Taskscited by 13
38 more
  1. 2023Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networkscited by 13
  2. 2025Exact Computation of Any-Order Shapley Interactions for Graph Neural Networkscited by 13
  3. 2024Graph Pooling via Ricci Flowcited by 10
  4. 2024Heterogeneous Sheaf Neural Networkscited by 10
  5. 2024A Survey on Graph Condensationcited by 9
  6. 2024Boosting Graph Pooling with Persistent Homologycited by 9
  7. 2024Graph Coarsening with Message-Passing Guaranteescited by 9
  8. 2022Simplifying Clustering with Graph Neural Networkscited by 8
  9. 2022PatchGT: Transformer over Non-trainable Clusters for Learning Graph Representationscited by 8
  10. 2024Cluster-wise Graph Transformer with Dual-granularity Kernelized Attentioncited by 8
  11. 2022SS-GNN: A Simple-Structured Graph Neural Network for Affinity Predictioncited by 7
  12. 2022Total Variation Graph Neural Networkscited by 7
  13. 2024A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizabilitycited by 7
  14. 2022Pooling Strategies for Simplicial Convolutional Networkscited by 5
  15. 2023Adaptive Hierarchical SpatioTemporal Network for Traffic Forecastingcited by 5
  16. 2024MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networkscited by 5
  17. 2025Geometry-Aware Edge Pooling for Graph Neural Networkscited by 5
  18. 2023Graph State-Space Models and Latent Relational Inferencecited by 4
  19. 2023Feudal Graph Reinforcement Learningcited by 4
  20. 2023On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Poolingcited by 4
  21. 2023Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decomposecited by 3
  22. 2024GraphCNNpred: A stock market indices prediction using a Graph based deep learning systemcited by 3
  23. 2024Beyond Grid Data: Exploring Graph Neural Networks for Earth Observationcited by 3
  24. 2022DOTIN: Dropping Task-Irrelevant Nodes for GNNscited by 2
  25. 2022Graph Property Prediction on Open Graph Benchmark: A Winning Solution by Graph Neural Architecture Searchcited by 2
  26. 2022Deep learning and multi-level featurization of graph representations of microstructural datacited by 2
  27. 2022On the Effectiveness of Hybrid Pooling in Mixup-Based Graph Learning for Language Processingcited by 2
  28. 2024A Hybrid Graph Neural Network for Enhanced EEG-Based Depression Detectioncited by 2
  29. 2025BN-Pool: Bayesian Nonparametric Pooling for Graphscited by 2
  30. 2025Hierarchical Message-Passing Policies for Multi-Agent Reinforcement Learningcited by 2
  31. 2025Torch Geometric Pool: the PyTorch library for pooling in Graph Neural Networkscited by 2
  32. 2026Hierarchical Discrete Flow Matching for Graph Generationcited by 2
  33. 2023Imputing Brain Measurements Across Data Sets via Graph Neural Networkscited by 1
  34. 2023Careful Selection and Thoughtful Discarding: Graph Explicit Pooling Utilizing Discarded Nodescited by 1
  35. 2024Multi-Hierarchical Surrogate Learning for Structural Dynamical Crash Simulations Using Graph Convolutional Neural Networkscited by 1
  36. 2024Implicit Neural Representation For Accurate CFD Flow Field Predictioncited by 1
  37. 2024MDL-Pool: Adaptive Multilevel Graph Pooling Based on Minimum Description Lengthcited by 1
  38. 2024DLGNet: Hyperedge Classification through Directed Line Graphs for Chemical Reactionscited by 1

50 most cited of 69 All 69 (JSON)