mlsanityData to 14 Oct 2026

On the Expressivity of Persistent Homology in Graph Learning

arXiv 2302.09826 ↗First posted 20 Feb 2023cs.LG math.AT stat.MLcited by 19

Not on the map. Why?

Abstract (arXiv)

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 36 of its 91 references that are in the map. First posted on arXiv 20 Feb 2023.

Builds on

36 of 91 references.

References · 36

  1. 2018How Powerful are Graph Neural Networks?cited by 4,393
  2. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  3. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,163
  4. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  5. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  6. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 881
  7. 2020Improving Graph Neural Network Expressivity via Subgraph Isomorphism Countingcited by 313
  8. 2019A Fair Comparison of Graph Neural Networks for Graph Classificationcited by 244
  9. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 236
  10. 2020Can Graph Neural Networks Count Substructures?cited by 236
  11. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  12. 2015A roadmap for the computation of persistent homologycited by 127
24 more
  1. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 126
  2. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 122
  3. 2019Ripser: efficient computation of Vietoris-Rips persistence barcodescited by 117
  4. 2017Deep Learning with Topological Signaturescited by 114
  5. 2020A Survey on The Expressive Power of Graph Neural Networkscited by 111
  6. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 90
  7. 2021Topological Graph Neural Networkscited by 87
  8. 2021The Logic of Graph Neural Networkscited by 85
  9. 2014A Stable Multi-Scale Kernel for Topological Machine Learningcited by 75
  10. 2019Graph Filtration Learningcited by 69
  11. 2019Learning metrics for persistence-based summaries and applications for graph classificationcited by 57
  12. 2022GraphWorld: Fake Graphs Bring Real Insights for GNNscited by 56
  13. 2022A Theoretical Comparison of Graph Neural Network Extensionscited by 48
  14. 2021Topological Relational Learning on Graphscited by 27
  15. 2019Persistent homology detects curvaturecited by 26
  16. 2022On the effectiveness of persistent homologycited by 20
  17. 2023Curvature Filtrations for Graph Generative Model Evaluationcited by 19
  18. 2022Neural Approximation of Graph Topological Featurescited by 17
  19. 2022Ollivier-Ricci Curvature for Hypergraphs: A Unified Frameworkcited by 12
  20. 2019Topological Machine Learning with Persistence Indicator Functionscited by 11
  21. 2022Keeping it sparse: Computing Persistent Homology revisitedcited by 6
  22. 2020Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radiuscited by 4
  23. 2021Computing Zigzag Persistence on Graphs in Near-Linear Timecited by 4
  24. 2021Geometric Approaches on Persistent Homologycited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 4; 2025: 9; 2026: 3.

19 papers.

Sort:

  1. 2023Going beyond persistent homology using persistent homologycited by 22
  2. 2024Topological Neural Networks go Persistent, Equivariant, and Continuouscited by 17
  3. 2024MANTRA: The Manifold Triangulations Assemblagecited by 12
  4. 2023Topological Data Analysis for Neural Network Analysis: A Comprehensive Surveycited by 9
  5. 2024Boosting Graph Pooling with Persistent Homologycited by 9
  6. 2024CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphscited by 3
  7. 2025On topological descriptors for graph productscited by 3
  8. 2025Graph Persistence goes Spectralcited by 2
  9. 2023Addressing caveats of neural persistence with deep graph persistencecited by 1
  10. 2025Towards Scalable Topological Regularizerscited by 1
  11. 2025CellCLAT: Preserving Topology and Trimming Redundancy in Self-Supervised Cellular Contrastive Learningcited by 1
  12. 2025Positional Encoding meets Persistent Homology on Graphscited by 1
7 more
  1. 2025Heat Kernel Goes Topologicalcited by 1
  2. 2025Topological Data Analysis for Unsupervised Anomaly Detection and Customer Segmentation on Banking Datacited by 1
  3. 2025Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysiscited by 1
  4. 2025Graph Homomorphism Distortion: A structural (pseudo)-metric for attributed graphscited by 1
  5. 2026Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cellscited by 1
  6. 2026Diversity Curves for Graph Representation Learningcited by 0
  7. 2026Exact Topological Compliance: Generating Persistence-Equivalent Graphscited by 0