# Topological Pooling on Graphs

arXiv: https://arxiv.org/abs/2303.14543 · HTML: https://mlsanity.com/paper/2303.14543/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 25 Mar 2023.

## Builds on (most cited first, 23 of 23)

- [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)
- [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)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Attentional Pooling for Action Recognition](https://mlsanity.com/paper/1711.01467/) (2017)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [Faster Kernels for Graphs with Continuous Attributes via Hashing](https://mlsanity.com/paper/1610.00064/) (2016)
- [Deep Graph Mapper: Seeing Graphs through the Neural Lens](https://mlsanity.com/paper/2002.03864/) (2020)
- [Hierarchical Graph Capsule Network](https://mlsanity.com/paper/2012.08734/) (2020)
- [GeomCA: Geometric Evaluation of Data Representations](https://mlsanity.com/paper/2105.12486/) (2021)

## Built on by (most cited first, 9 of 9)

- [Graph Classification via Reference Distribution Learning: Theory and Practice](https://mlsanity.com/paper/2408.11370/) (2024)
- [Conditional Uncertainty Quantification for Tensorized Topological Neural Networks](https://mlsanity.com/paper/2410.15241/) (2024)
- [Careful Selection and Thoughtful Discarding: Graph Explicit Pooling Utilizing Discarded Nodes](https://mlsanity.com/paper/2311.12644/) (2023)
- [Rhomboid Tiling for Geometric Graph Deep Learning](https://mlsanity.com/paper/2505.09586/) (2025)
- [Multi-Scale Harmonic Encoding for Feature-Wise Graph Message Passing](https://mlsanity.com/paper/2505.15015/) (2025)
- [Revealing Combinatorial Reasoning of GNNs via Graph Concept Bottleneck Layer](https://mlsanity.com/paper/2603.02025/) (2026)
- [Global to Local: Topology-Preserving Adaptive Graph Pooling via Granular-Ball](https://mlsanity.com/paper/2609.04978/) (2026)
- [Repurposing Unified Topological Signatures for Graph Representation Learning](https://mlsanity.com/paper/2609.17061/) (2026)
- [Signed Graph Pre-Training and Prompt Learning](https://mlsanity.com/paper/2609.25722/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from graph classification to anomaly detection. There recently has emerged a number of approaches adopting a graph pooling operation within GNNs, with a goal to preserve graph attributive and structural features during the graph representation learning. However, most existing graph pooling operations suffer from the limitations of relying on node-wise neighbor weighting and embedding, which leads to insufficient encoding of rich topological structures and node attributes exhibited by real-world networks. By invoking the machinery of persistent homology and the concept of landmarks, we propose a novel topological pooling layer and witness complex-based topological embedding mechanism that allow us to systematically integrate hidden topological information at both local and global levels. Specifically, we design new learnable local and global topological representations Wit-TopoPool which allow us to simultaneously extract rich discriminative topological information from graphs. Experiments on 11 diverse benchmark datasets against 18 baseline models in conjunction with graph classification tasks indicate that Wit-TopoPool significantly outperforms all competitors across all datasets.