# Graph Filtration Learning

arXiv: https://arxiv.org/abs/1905.10996 · HTML: https://mlsanity.com/paper/1905.10996/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2019.

## Built on by (most cited first, 30 of 69)

- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [Trigger Hunting with a Topological Prior for Trojan Detection](https://mlsanity.com/paper/2110.08335/) (2021)
- [Link Prediction with Persistent Homology: An Interactive View](https://mlsanity.com/paper/2102.10255/) (2021)
- [Topological Detection of Trojaned Neural Networks](https://mlsanity.com/paper/2106.06469/) (2021)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [Cycle Representation Learning for Inductive Relation Prediction](https://mlsanity.com/paper/2110.02510/) (2021)
- [Going beyond persistent homology using persistent homology](https://mlsanity.com/paper/2311.06152/) (2023)
- [Curvature Filtrations for Graph Generative Model Evaluation](https://mlsanity.com/paper/2301.12906/) (2023)
- [On the Expressivity of Persistent Homology in Graph Learning](https://mlsanity.com/paper/2302.09826/) (2023)
- [Differentiable Euler Characteristic Transforms for Shape Classification](https://mlsanity.com/paper/2310.07630/) (2023)
- [Neural Approximation of Graph Topological Features](https://mlsanity.com/paper/2201.12032/) (2022)
- [Exploring the Geometry and Topology of Neural Network Loss Landscapes](https://mlsanity.com/paper/2102.00485/) (2021)
- [Topological Attention for Time Series Forecasting](https://mlsanity.com/paper/2107.09031/) (2021)
- [Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction](https://mlsanity.com/paper/2203.01703/) (2022)
- [ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discovery](https://mlsanity.com/paper/2211.03808/) (2022)
- [GRIL: A 2-parameter Persistence Based Vectorization for Machine Learning](https://mlsanity.com/paper/2304.04970/) (2023)
- [CLDG: Contrastive Learning on Dynamic Graphs](https://mlsanity.com/paper/2412.14451/) (2024)
- [Topological Pooling on Graphs](https://mlsanity.com/paper/2303.14543/) (2023)
- [PHG-Net: Persistent Homology Guided Medical Image Classification](https://mlsanity.com/paper/2311.17243/) (2023)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)
- [Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds](https://mlsanity.com/paper/2307.09259/) (2023)
- [Learning Hyperbolic Representations of Topological Features](https://mlsanity.com/paper/2103.09273/) (2021)
- [Diffeomorphic interpolation for efficient persistence-based topological optimization](https://mlsanity.com/paper/2405.18820/) (2024)
- [Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms](https://mlsanity.com/paper/2410.02622/) (2024)
- [Enhancing Graph Representation Learning with Localized Topological Features](https://mlsanity.com/paper/2501.09178/) (2025)
- [The Flood Complex: Large-Scale Persistent Homology on Millions of Points](https://mlsanity.com/paper/2509.22432/) (2025)
- [A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis](https://mlsanity.com/paper/2109.00530/) (2021)

## Abstract (arXiv)

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.