# BN-Pool: Bayesian Nonparametric Pooling for Graphs

arXiv: https://arxiv.org/abs/2501.09821 · HTML: https://mlsanity.com/paper/2501.09821/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 70 references that are in the map.
- First posted on arXiv 16 Jan 2025.

## Builds on (most cited first, 30 of 47)

- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [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)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Understanding Attention and Generalization in Graph Neural Networks](https://mlsanity.com/paper/1905.02850/) (2019)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Structural Entropy Guided Graph Hierarchical Pooling](https://mlsanity.com/paper/2206.13510/) (2022)
- [Memory-Based Graph Networks](https://mlsanity.com/paper/2002.09518/) (2020)
- [Edge Contraction Pooling for Graph Neural Networks](https://mlsanity.com/paper/1905.10990/) (2019)
- [Stick-Breaking Variational Autoencoders](https://mlsanity.com/paper/1605.06197/) (2016)
- [Topology-Aware Graph Pooling Networks](https://mlsanity.com/paper/2010.09834/) (2020)
- [Dirichlet Variational Autoencoder](https://mlsanity.com/paper/1901.02739/) (2019)

## Built on by (most cited first, 2 of 2)

- [Torch Geometric Pool: the PyTorch library for pooling in Graph Neural Networks](https://mlsanity.com/paper/2512.12642/) (2025)
- [Deep Graph Learning will stall without Network Science](https://mlsanity.com/paper/2502.01177/) (2025)

## Abstract (arXiv)

We introduce BN-Pool, the first clustering-based pooling method for Graph Neural Networks that adaptively determines the number of supernodes in a coarsened graph. BN-Pool leverages a generative model based on a Bayesian nonparametric framework for partitioning graph nodes into an unbounded number of clusters. During training, the node-to-cluster assignments are learned by combining the supervised loss of the downstream task with an unsupervised auxiliary term, which encourages the reconstruction of the original graph topology while penalizing unnecessary proliferation of clusters. By automatically discovering the optimal coarsening level for each graph, BN-Pool preserves the performance of soft-clustering pooling methods while avoiding their typical redundancy by learning compact pooled graphs. The code is available at https://github.com/NGMLGroup/Bayesian-Nonparametric-Graph-Pooling.