# Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities

arXiv: https://arxiv.org/abs/2204.07321 · HTML: https://mlsanity.com/paper/2204.07321/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Builds on 75 of its 111 references that are in the map.
- First posted on arXiv 15 Apr 2022.

## Builds on (most cited first, 30 of 75)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Understanding Attention and Generalization in Graph Neural Networks](https://mlsanity.com/paper/1905.02850/) (2019)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Relational Pooling for Graph Representations](https://mlsanity.com/paper/1903.02541/) (2019)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [DropGNN: Random Dropouts Increase the Expressiveness of Graph Neural Networks](https://mlsanity.com/paper/2111.06283/) (2021)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Decoupling the Depth and Scope of Graph Neural Networks](https://mlsanity.com/paper/2201.07858/) (2022)
- [Sequential Recommendation with Graph Neural Networks](https://mlsanity.com/paper/2106.14226/) (2021)
- [Learning Dynamic Graph Representation of Brain Connectome with Spatio-Temporal Attention](https://mlsanity.com/paper/2105.13495/) (2021)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Rethinking pooling in graph neural networks](https://mlsanity.com/paper/2010.11418/) (2020)
- [End-to-End Spectro-Temporal Graph Attention Networks for Speaker Verification Anti-Spoofing and Speech Deepfake Detection](https://mlsanity.com/paper/2107.12710/) (2021)

## Built on by (most cited first, 30 of 52)

- [A graph convolutional autoencoder approach to model order reduction for parametrized PDEs](https://mlsanity.com/paper/2305.08573/) (2023)
- [MAGIC: Detecting Advanced Persistent Threats via Masked Graph Representation Learning](https://mlsanity.com/paper/2310.09831/) (2023)
- [Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detection](https://mlsanity.com/paper/2310.02861/) (2023)
- [Comprehensive Graph Gradual Pruning for Sparse Training in Graph Neural Networks](https://mlsanity.com/paper/2207.08629/) (2022)
- [Graph Sparsification via Mixture of Graphs](https://mlsanity.com/paper/2405.14260/) (2024)
- [Graph Neural Networks for Text Classification: A Survey](https://mlsanity.com/paper/2304.11534/) (2023)
- [GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications](https://mlsanity.com/paper/2406.03569/) (2024)
- [A Survey on Graph Condensation](https://mlsanity.com/paper/2402.02000/) (2024)
- [Cluster-wise Graph Transformer with Dual-granularity Kernelized Attention](https://mlsanity.com/paper/2410.06746/) (2024)
- [GDeR: Safeguarding Efficiency, Balancing, and Robustness via Prototypical Graph Pruning](https://mlsanity.com/paper/2410.13761/) (2024)
- [SGOOD: Substructure-enhanced Graph-Level Out-of-Distribution Detection](https://mlsanity.com/paper/2310.10237/) (2023)
- [PGODE: Towards High-quality System Dynamics Modeling](https://mlsanity.com/paper/2311.06554/) (2023)
- [A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizability](https://mlsanity.com/paper/2406.09031/) (2024)
- [QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression](https://mlsanity.com/paper/2211.05151/) (2022)
- [Clustering for Protein Representation Learning](https://mlsanity.com/paper/2404.00254/) (2024)
- [Pool Me Wisely: On the Effect of Pooling in Transformer-Based Models](https://mlsanity.com/paper/2510.03339/) (2025)
- [GEFL: Extended Filtration Learning for Graph Classification](https://mlsanity.com/paper/2406.02732/) (2024)
- [Geometry-Aware Edge Pooling for Graph Neural Networks](https://mlsanity.com/paper/2506.11700/) (2025)
- [Graph Parsing Networks](https://mlsanity.com/paper/2402.14393/) (2024)
- [Towards Efficient Training of Graph Neural Networks: A Multiscale Approach](https://mlsanity.com/paper/2503.19666/) (2025)
- [Compressed Heterogeneous Graph for Abstractive Multi-Document Summarization](https://mlsanity.com/paper/2303.06565/) (2023)
- [Domain independent post-processing with graph U-nets: Applications to Electrical Impedance Tomographic Imaging](https://mlsanity.com/paper/2305.05020/) (2023)
- [SurfGNN: A robust surface-based prediction model with interpretability for coactivation maps of spatial and cortical features](https://mlsanity.com/paper/2411.05825/) (2024)
- [A Theory for Compressibility of Graph Transformers for Transductive Learning](https://mlsanity.com/paper/2411.13028/) (2024)
- [Tackling Provably Hard Representative Selection via Graph Neural Networks](https://mlsanity.com/paper/2205.10403/) (2022)
- [Multi-object event graph representation learning for Video Question Answering](https://mlsanity.com/paper/2409.07747/) (2024)
- [Hierarchical Discrete Flow Matching for Graph Generation](https://mlsanity.com/paper/2604.00236/) (2026)
- [Careful Selection and Thoughtful Discarding: Graph Explicit Pooling Utilizing Discarded Nodes](https://mlsanity.com/paper/2311.12644/) (2023)
- [Forward Learning of Graph Neural Networks](https://mlsanity.com/paper/2403.11004/) (2024)
- [Discovering robust biomarkers of psychiatric disorders from resting-state functional MRI via graph neural networks: A systematic review](https://mlsanity.com/paper/2405.00577/) (2024)

## Abstract (arXiv)

Graph neural networks have emerged as a leading architecture for many graph-level tasks, such as graph classification and graph generation. As an essential component of the architecture, graph pooling is indispensable for obtaining a holistic graph-level representation of the whole graph. Although a great variety of methods have been proposed in this promising and fast-developing research field, to the best of our knowledge, little effort has been made to systematically summarize these works. To set the stage for the development of future works, in this paper, we attempt to fill this gap by providing a broad review of recent methods for graph pooling. Specifically, 1) we first propose a taxonomy of existing graph pooling methods with a mathematical summary for each category; 2) then, we provide an overview of the libraries related to graph pooling, including the commonly used datasets, model architectures for downstream tasks, and open-source implementations; 3) next, we further outline the applications that incorporate the idea of graph pooling in a variety of domains; 4) finally, we discuss certain critical challenges facing current studies and share our insights on future potential directions for research on the improvement of graph pooling.