mlsanityData to 7 Oct 2026

Neural Approximation of Graph Topological Features

arXiv 2201.12032 ↗First posted 28 Jan 2022cs.LGcited by 16

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Abstract (arXiv)

Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and can be a serious bottleneck for the learning pipeline. Inspired by recent success in neural algorithmic reasoning, we propose a novel graph neural network to estimate extended persistence diagrams (EPDs) on graphs efficiently. Our model is built on algorithmic insights, and benefits from better supervision and closer alignment with the EPD computation algorithm. We validate our method with convincing empirical results on approximating EPDs and downstream graph representation learning tasks. Our method is also efficient; on large and dense graphs, we accelerate the computation by nearly 100 times.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 44 of its 84 references that are in the map. First posted on arXiv 28 Jan 2022.

Builds on

44 of 84 references.

References · 44

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2018How Powerful are Graph Neural Networks?cited by 4,355
  4. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  5. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  6. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  7. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  8. 2018Link Prediction Based on Graph Neural Networkscited by 829
  9. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 718
  10. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  11. 2020Benchmarking Graph Neural Networkscited by 672
  12. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
32 more
  1. 2019Provably Powerful Graph Networkscited by 385
  2. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 235
  3. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  4. 2019Position-aware Graph Neural Networkscited by 203
  5. 2019Topology-Preserving Deep Image Segmentationcited by 198
  6. 2019What Can Neural Networks Reason About?cited by 155
  7. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
  8. 2015Neural GPUs Learn Algorithmscited by 118
  9. 2019Neural Execution of Graph Algorithmscited by 118
  10. 2017Deep Learning with Topological Signaturescited by 113
  11. 2014Learning to Executecited by 105
  12. 2015Neural Programmer-Interpreterscited by 96
  13. 2017Sliced Wasserstein Kernel for Persistence Diagramscited by 77
  14. 2014A Stable Multi-Scale Kernel for Topological Machine Learningcited by 74
  15. 2019Graph Filtration Learningcited by 68
  16. 2018Relational recurrent neural networkscited by 65
  17. 2018A Topological Regularizer for Classifiers via Persistent Homologycited by 62
  18. 2019Learning metrics for persistence-based summaries and applications for graph classificationcited by 57
  19. 2020Pointer Graph Networkscited by 52
  20. 2019Connectivity-Optimized Representation Learning via Persistent Homologycited by 43
  21. 2021Link Prediction with Persistent Homology: An Interactive Viewcited by 37
  22. 2020Neural Execution Engines: Learning to Execute Subroutinescited by 36
  23. 2021Topological Detection of Trojaned Neural Networkscited by 34
  24. 2015Neural Random-Access Machinescited by 32
  25. 2021Topological Relational Learning on Graphscited by 27
  26. 2021Cycle Representation Learning for Inductive Relation Predictioncited by 23
  27. 2021How to transfer algorithmic reasoning knowledge to learn new algorithms?cited by 22
  28. 2018Network Alignment by Discrete Ollivier-Ricci Flowcited by 14
  29. 2021Topological Attention for Time Series Forecastingcited by 14
  30. 2019PI-Net: A Deep Learning Approach to Extract Topological Persistence Imagescited by 12
  31. 2020Can neural networks learn persistent homology features?cited by 11
  32. 2021Learning Hyperbolic Representations of Topological Featurescited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 3; 2025: 4; 2026: 4.

16 papers.

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  1. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 18
  2. 2023An Efficient Subgraph GNN with Provable Substructure Counting Powercited by 13
  3. 2024TopoGCL: Topological Graph Contrastive Learningcited by 13
  4. 2024Boosting Graph Pooling with Persistent Homologycited by 9
  5. 2023Cycle Invariant Positional Encoding for Graph Representation Learningcited by 8
  6. 2023Improving Self-supervised Molecular Representation Learning using Persistent Homologycited by 6
  7. 2025Enhancing Graph Representation Learning with Localized Topological Featurescited by 6
  8. 2023DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveformscited by 3
  9. 2024Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphscited by 2
  10. 2025Graph Persistence goes Spectralcited by 1
  11. 2025TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtrationcited by 1
  12. 2025Cross-View Topology-Aware Graph Representation Learningcited by 1
4 more
  1. 2026TopoFormer: Topology Meets Attention for Graph Learningcited by 1
  2. 2026Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithmscited by 0
  3. 2026Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cellscited by 0
  4. 2026FILTR: Extracting Topological Features from Pretrained 3D Modelscited by 0