# Neural Approximation of Graph Topological Features

arXiv: https://arxiv.org/abs/2201.12032 · HTML: https://mlsanity.com/paper/2201.12032/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 84 references that are in the map.
- First posted on arXiv 28 Jan 2022.

## Builds on (most cited first, 30 of 44)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (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)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Neural GPUs Learn Algorithms](https://mlsanity.com/paper/1511.08228/) (2015)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Learning to Execute](https://mlsanity.com/paper/1410.4615/) (2014)
- [Neural Programmer-Interpreters](https://mlsanity.com/paper/1511.06279/) (2015)
- [Sliced Wasserstein Kernel for Persistence Diagrams](https://mlsanity.com/paper/1706.03358/) (2017)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Relational recurrent neural networks](https://mlsanity.com/paper/1806.01822/) (2018)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)

## Built on by (most cited first, 17 of 17)

- [On the Expressivity of Persistent Homology in Graph Learning](https://mlsanity.com/paper/2302.09826/) (2023)
- [TopoGCL: Topological Graph Contrastive Learning](https://mlsanity.com/paper/2406.17251/) (2024)
- [An Efficient Subgraph GNN with Provable Substructure Counting Power](https://mlsanity.com/paper/2303.10576/) (2023)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)
- [Cycle Invariant Positional Encoding for Graph Representation Learning](https://mlsanity.com/paper/2311.14333/) (2023)
- [Improving Self-supervised Molecular Representation Learning using Persistent Homology](https://mlsanity.com/paper/2311.17327/) (2023)
- [Enhancing Graph Representation Learning with Localized Topological Features](https://mlsanity.com/paper/2501.09178/) (2025)
- [DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms](https://mlsanity.com/paper/2309.09924/) (2023)
- [Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphs](https://mlsanity.com/paper/2408.09123/) (2024)
- [Graph Persistence goes Spectral](https://mlsanity.com/paper/2506.06571/) (2025)
- [TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtration](https://mlsanity.com/paper/2510.05102/) (2025)
- [Cross-View Topology-Aware Graph Representation Learning](https://mlsanity.com/paper/2512.02130/) (2025)
- [Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cells](https://mlsanity.com/paper/2604.17548/) (2026)
- [TopoFormer: Topology Meets Attention for Graph Learning](https://mlsanity.com/paper/2607.28259/) (2026)
- [Scalable Topology-Preserving Graph Coarsening: Concepts and Algorithms](https://mlsanity.com/paper/2601.22943/) (2026)
- [FILTR: Extracting Topological Features from Pretrained 3D Models](https://mlsanity.com/paper/2604.22334/) (2026)
- [Exact Topological Compliance: Generating Persistence-Equivalent Graphs](https://mlsanity.com/paper/2610.18856/) (2026)

## 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.