# iPool -- Information-based Pooling in Hierarchical Graph Neural Networks

arXiv: https://arxiv.org/abs/1907.00832 · HTML: https://mlsanity.com/paper/1907.00832/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 21 of 21)

- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [Graph Neural Network-based EEG Classification: A Survey](https://mlsanity.com/paper/2310.02152/) (2023)
- [Comprehensive Graph Gradual Pruning for Sparse Training in Graph Neural Networks](https://mlsanity.com/paper/2207.08629/) (2022)
- [Hierarchical Adaptive Pooling by Capturing High-order Dependency for Graph Representation Learning](https://mlsanity.com/paper/2104.05960/) (2021)
- [Maximum Entropy Weighted Independent Set Pooling for Graph Neural Networks](https://mlsanity.com/paper/2107.01410/) (2021)
- [Generalizing Downsampling from Regular Data to Graphs](https://mlsanity.com/paper/2208.03523/) (2022)
- [Clustering for Protein Representation Learning](https://mlsanity.com/paper/2404.00254/) (2024)
- [MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks](https://mlsanity.com/paper/2409.05100/) (2024)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)
- [Implementing graph neural networks with TensorFlow-Keras](https://mlsanity.com/paper/2103.04318/) (2021)
- [Edge but not Least: Cross-View Graph Pooling](https://mlsanity.com/paper/2109.11796/) (2021)
- [MPool: Motif-Based Graph Pooling](https://mlsanity.com/paper/2303.03654/) (2023)
- [Tackling Provably Hard Representative Selection via Graph Neural Networks](https://mlsanity.com/paper/2205.10403/) (2022)
- [BN-Pool: Bayesian Nonparametric Pooling for Graphs](https://mlsanity.com/paper/2501.09821/) (2025)
- [Efficient Curvature-aware Graph Network](https://mlsanity.com/paper/2511.01443/) (2025)
- [Seeing All From a Few: Nodes Selection Using Graph Pooling for Graph Clustering](https://mlsanity.com/paper/2105.05320/) (2021)
- [SPGP: Structure Prototype Guided Graph Pooling](https://mlsanity.com/paper/2209.07817/) (2022)
- [Careful Selection and Thoughtful Discarding: Graph Explicit Pooling Utilizing Discarded Nodes](https://mlsanity.com/paper/2311.12644/) (2023)
- [Context Pooling: Query-specific Graph Pooling for Generic Inductive Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/2507.07595/) (2025)
- [S2-UniSeg: Fast Universal Agglomerative Pooling for Scalable Segment Anything without Supervision](https://mlsanity.com/paper/2508.06995/) (2025)

## Abstract (arXiv)

With the advent of data science, the analysis of network or graph data has become a very timely research problem. A variety of recent works have been proposed to generalize neural networks to graphs, either from a spectral graph theory or a spatial perspective. The majority of these works however focus on adapting the convolution operator to graph representation. At the same time, the pooling operator also plays an important role in distilling multiscale and hierarchical representations but it has been mostly overlooked so far. In this paper, we propose a parameter-free pooling operator, called iPool, that permits to retain the most informative features in arbitrary graphs. With the argument that informative nodes dominantly characterize graph signals, we propose a criterion to evaluate the amount of information of each node given its neighbors, and theoretically demonstrate its relationship to neighborhood conditional entropy. This new criterion determines how nodes are selected and coarsened graphs are constructed in the pooling layer. The resulting hierarchical structure yields an effective isomorphism-invariant representation of networked data in arbitrary topologies. The proposed strategy is evaluated in terms of graph classification on a collection of public graph datasets, including bioinformatics and social networks, and achieves state-of-the-art performance on most of the datasets.