mlsanityData to 7 Oct 2026

Boosting Graph Pooling with Persistent Homology

arXiv 2402.16346 ↗First posted 26 Feb 2024cs.LG math.ATcited by 9

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Abstract (arXiv)

Recently, there has been an emerging trend to integrate persistent homology (PH) into graph neural networks (GNNs) to enrich expressive power. However, naively plugging PH features into GNN layers always results in marginal improvement with low interpretability. In this paper, we investigate a novel mechanism for injecting global topological invariance into pooling layers using PH, motivated by the observation that filtration operation in PH naturally aligns graph pooling in a cut-off manner. In this fashion, message passing in the coarsened graph acts along persistent pooled topology, leading to improved performance. Experimentally, we apply our mechanism to a collection of graph pooling methods and observe consistent and substantial performance gain over several popular datasets, demonstrating its wide applicability and flexibility.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 36 of its 53 references that are in the map. First posted on arXiv 26 Feb 2024.

Builds on

36 of 53 references.

References · 36

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24 more
  1. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 312
  2. 2021Identity-aware Graph Neural Networkscited by 197
  3. 2020Graph Clustering with Graph Neural Networkscited by 163
  4. 2019ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representationscited by 156
  5. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
  6. 2019Topological Autoencoderscited by 124
  7. 2017Deep Learning with Topological Signaturescited by 113
  8. 2018Attentive Statistics Pooling for Deep Speaker Embeddingcited by 108
  9. 2018Towards Sparse Hierarchical Graph Classifierscited by 100
  10. 2019Graph Convolutional Networks with EigenPoolingcited by 94
  11. 2021Topological Graph Neural Networkscited by 86
  12. 2020Rethinking pooling in graph neural networkscited by 73
  13. 2021Understanding Pooling in Graph Neural Networkscited by 69
  14. 2019Graph Filtration Learningcited by 68
  15. 2022Structural Entropy Guided Graph Hierarchical Poolingcited by 62
  16. 2022Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNscited by 55
  17. 2019Connectivity-Optimized Representation Learning via Persistent Homologycited by 43
  18. 2023The expressive power of pooling in Graph Neural Networkscited by 35
  19. 2023Curvature Filtrations for Graph Generative Model Evaluationcited by 18
  20. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 18
  21. 2022Neural Approximation of Graph Topological Featurescited by 16
  22. 2019A Non-Negative Factorization approach to node pooling in Graph Convolutional Neural Networkscited by 14
  23. 2020PersGNN: Applying Topological Data Analysis and Geometric Deep Learning to Structure-Based Protein Function Predictioncited by 7
  24. 2023DeSCo: Towards Generalizable and Scalable Deep Subgraph Countingcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 4; 2026: 3.

9 papers.

  1. 2025Geometry-Aware Edge Pooling for Graph Neural Networkscited by 5
  2. 2025Persistent Homology-induced Graph Ensembles for Time Series Regressionscited by 3
  3. 2025Neural Graduated Assignment for Maximum Common Edge Subgraphscited by 3
  4. 2024PHLP: Sole Persistent Homology for Link Prediction - Interpretable Feature Extractioncited by 2
  5. 2024ReMAP: Neural Reparameterization for Scalable MAP Inference in Arbitrary-Order Markov Random Fieldscited by 0
  6. 2025UM3: Unsupervised Map to Map Matchingcited by 0
  7. 2026Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cellscited by 0
  8. 2026AbstainGNN: Teaching Graph Neural Networks to Abstain for Graph Classificationcited by 0
  9. 2026Global to Local: Topology-Preserving Adaptive Graph Pooling via Granular-Ballcited by 0