# RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds

arXiv: https://arxiv.org/abs/2202.01725 · HTML: https://mlsanity.com/paper/2202.01725/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [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)
- [Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks](https://mlsanity.com/paper/2111.13171/) (2021)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [On Characterizing the Capacity of Neural Networks using Algebraic Topology](https://mlsanity.com/paper/1802.04443/) (2018)
- [Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams](https://mlsanity.com/paper/1802.03569/) (2018)
- [When OT meets MoM: Robust estimation of Wasserstein Distance](https://mlsanity.com/paper/2006.10325/) (2020)
- [DTM-based Filtrations](https://mlsanity.com/paper/1811.04757/) (2018)
- [PI-Net: A Deep Learning Approach to Extract Topological Persistence Images](https://mlsanity.com/paper/1906.01769/) (2019)
- [Embeddings of Persistence Diagrams into Hilbert Spaces](https://mlsanity.com/paper/1905.05604/) (2019)
- [Can neural networks learn persistent homology features?](https://mlsanity.com/paper/2011.14688/) (2020)
- [On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces](https://mlsanity.com/paper/1806.06924/) (2018)

## Built on by (most cited first, 20 of 20)

- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds](https://mlsanity.com/paper/2307.09259/) (2023)
- [Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity](https://mlsanity.com/paper/2412.16619/) (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)
- [GEFL: Extended Filtration Learning for Graph Classification](https://mlsanity.com/paper/2406.02732/) (2024)
- [Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data](https://mlsanity.com/paper/2309.16968/) (2023)
- [Learning Significant Persistent Homology Features for 3D Shape Understanding](https://mlsanity.com/paper/2602.14228/) (2026)
- [Explaining the Power of Topological Data Analysis in Graph Machine Learning](https://mlsanity.com/paper/2401.04250/) (2024)
- [Noise-Robust Topology Estimation of 2D Image Data via Neural Networks and Persistent Homology](https://mlsanity.com/paper/2509.09140/) (2025)
- [CuMPerLay: Learning Cubical Multiparameter Persistence Vectorizations](https://mlsanity.com/paper/2510.12795/) (2025)
- [The Density of Cross-Persistence Diagrams and Its Applications](https://mlsanity.com/paper/2603.11623/) (2026)
- [A Persistent Homology Design Space for 3D Point Cloud Deep Learning](https://mlsanity.com/paper/2604.04299/) (2026)
- [TopoFormer: Topology Meets Attention for Graph Learning](https://mlsanity.com/paper/2607.28259/) (2026)
- [Challenges in 3D Data Synthesis for Training Neural Networks on Topological Features](https://mlsanity.com/paper/2511.04972/) (2025)
- [FILTR: Extracting Topological Features from Pretrained 3D Models](https://mlsanity.com/paper/2604.22334/) (2026)
- [Persistent Cross Entropy](https://mlsanity.com/paper/2608.24549/) (2026)
- [Signed Graph Pre-Training and Prompt Learning](https://mlsanity.com/paper/2609.25722/) (2026)

## Abstract (arXiv)

The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains. However, their practical use in applications is often hindered by two major limitations: the computational complexity required to compute such descriptors exactly, and their sensitivity to even low-level proportions of outliers. In this work, we propose to bypass these two burdens in a data-driven setting by entrusting the estimation of (vectorization of) PDs built on top of point clouds to a neural network architecture that we call RipsNet. Once trained on a given data set, RipsNet can estimate topological descriptors on test data very efficiently with generalization capacity. Furthermore, we prove that RipsNet is robust to input perturbations in terms of the 1-Wasserstein distance, a major improvement over the standard computation of PDs that only enjoys Hausdorff stability, yielding RipsNet to substantially outperform exactly-computed PDs in noisy settings. We showcase the use of RipsNet on both synthetic and real-world data. Our open-source implementation is publicly available at https://github.com/hensel-f/ripsnet and will be included in the Gudhi library.