# TopoX: A Suite of Python Packages for Machine Learning on Topological Domains

arXiv: https://arxiv.org/abs/2402.02441 · HTML: https://mlsanity.com/paper/2402.02441/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 25 references that are in the map.
- First posted on arXiv 4 Feb 2024.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Cell Attention Networks](https://mlsanity.com/paper/2209.08179/) (2022)
- [Convolutional Learning on Simplicial Complexes](https://mlsanity.com/paper/2301.11163/) (2023)
- [ICML 2023 Topological Deep Learning Challenge : Design and Results](https://mlsanity.com/paper/2309.15188/) (2023)

## Built on by (most cited first, 22 of 22)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [E(n) Equivariant Topological Neural Networks](https://mlsanity.com/paper/2405.15429/) (2024)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks](https://mlsanity.com/paper/2410.06530/) (2024)
- [MANTRA: The Manifold Triangulations Assemblage](https://mlsanity.com/paper/2410.02392/) (2024)
- [Attending to Topological Spaces: The Cellular Transformer](https://mlsanity.com/paper/2405.14094/) (2024)
- [DHG-Bench: A Comprehensive Benchmark for Deep Hypergraph Learning](https://mlsanity.com/paper/2508.12244/) (2025)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain](https://mlsanity.com/paper/2409.05211/) (2024)
- [CosmoBench: A Multiscale, Multiview, Multitask Cosmology Benchmark for Geometric Deep Learning](https://mlsanity.com/paper/2507.03707/) (2025)
- [Topology-Preserving Neural Operator Learning via Hodge Decomposition](https://mlsanity.com/paper/2605.13834/) (2026)
- [Continuous Simplicial Neural Networks](https://mlsanity.com/paper/2503.12919/) (2025)
- [HLSAD: Hodge Laplacian-based Simplicial Anomaly Detection](https://mlsanity.com/paper/2505.24534/) (2025)
- [Topotein: Topological Deep Learning for Protein Representation Learning](https://mlsanity.com/paper/2509.03885/) (2025)
- [Learning From Simplicial Data Based on Random Walks and 1D Convolutions](https://mlsanity.com/paper/2404.03434/) (2024)
- [Enhancing the Utility of Higher-Order Information in Relational Learning](https://mlsanity.com/paper/2502.09570/) (2025)
- [Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding](https://mlsanity.com/paper/2505.17939/) (2025)
- [TopoU-Net: a U-Net architecture for topological domains](https://mlsanity.com/paper/2605.10091/) (2026)
- [Scaling Higher-Order Graph Learning with Maximal Clique Complexes](https://mlsanity.com/paper/2605.31373/) (2026)
- [Differentiable Lifting for Topological Neural Networks](https://mlsanity.com/paper/2608.01160/) (2026)
- [TopoEmbedX: A General Framework for Representation Learning on Topological Domains](https://mlsanity.com/paper/2609.37884/) (2026)

## Abstract (arXiv)

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelX is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/}{https://pyt-team.github.io/.