# Cover Learning for Large-Scale Topology Representation

arXiv: https://arxiv.org/abs/2503.09767 · HTML: https://mlsanity.com/paper/2503.09767/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 89 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 27 of 27)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [Connectivity-Optimized Representation Learning via Persistent Homology](https://mlsanity.com/paper/1906.09003/) (2019)
- [A Framework for Differential Calculus on Persistence Barcodes](https://mlsanity.com/paper/1910.00960/) (2019)
- [BScNets: Block Simplicial Complex Neural Networks](https://mlsanity.com/paper/2112.06826/) (2021)
- [Statistical Analysis and Parameter Selection for Mapper](https://mlsanity.com/paper/1706.00204/) (2017)
- [Simplicial Representation Learning with Neural k-Forms](https://mlsanity.com/paper/2312.08515/) (2023)
- [Topological Optimization with Big Steps](https://mlsanity.com/paper/2203.16748/) (2022)
- [Coarse Graining of Data via Inhomogeneous Diffusion Condensation](https://mlsanity.com/paper/1907.04463/) (2019)
- [Topological Methods in Machine Learning: A Tutorial for Practitioners](https://mlsanity.com/paper/2409.02901/) (2024)
- [Network visualizations with Pyvis and VisJS](https://mlsanity.com/paper/2006.04951/) (2020)
- [Diffeomorphic interpolation for efficient persistence-based topological optimization](https://mlsanity.com/paper/2405.18820/) (2024)
- [Differentiability and Optimization of Multiparameter Persistent Homology](https://mlsanity.com/paper/2406.07224/) (2024)
- [A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis](https://mlsanity.com/paper/2109.00530/) (2021)
- [Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction](https://mlsanity.com/paper/2212.07201/) (2022)
- [Differentiable Mapper For Topological Optimization Of Data Representation](https://mlsanity.com/paper/2402.12854/) (2024)
- [Homotopy Reconstruction via the Cech Complex and the Vietoris-Rips Complex](https://mlsanity.com/paper/1903.06955/) (2019)
- [Stable and consistent density-based clustering via multiparameter persistence](https://mlsanity.com/paper/2005.09048/) (2020)
- [Time-inhomogeneous diffusion geometry and topology](https://mlsanity.com/paper/2203.14860/) (2022)
- [Improving Mapper's Robustness by Varying Resolution According to Lens-Space Density](https://mlsanity.com/paper/2410.03862/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning Tangent Bundles and Characteristic Classes with Autoencoder Atlases](https://mlsanity.com/paper/2602.22873/) (2026)

## Abstract (arXiv)

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation or infer local geometry by constructing a graph on the input data. More recently, topological data analysis popularized the use of simplicial complexes to represent data topology with two main methodologies: topological inference with geometric complexes and large-scale topology visualization with Mapper graphs -- central to these is the nerve construction from topology, which builds a simplicial complex given a cover of a space by subsets. While successful, these have limitations: geometric complexes scale poorly with data size, and Mapper graphs can be hard to tune and only contain low dimensional information. In this paper, we propose to study the problem of learning covers in its own right, and from the perspective of optimization. We describe a method for learning topologically-faithful covers of geometric datasets, and show that the simplicial complexes thus obtained can outperform standard topological inference approaches in terms of size, and Mapper-type algorithms in terms of representation of large-scale topology.