# Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform

arXiv: https://arxiv.org/abs/2410.17760 · HTML: https://mlsanity.com/paper/2410.17760/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 23 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Everything is Connected: Graph Neural Networks](https://mlsanity.com/paper/2301.08210/) (2023)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Annotated History of Modern AI and Deep Learning](https://mlsanity.com/paper/2212.11279/) (2022)
- [Differentiable Euler Characteristic Transforms for Shape Classification](https://mlsanity.com/paper/2310.07630/) (2023)
- [Simplicial Representation Learning with Neural k-Forms](https://mlsanity.com/paper/2312.08515/) (2023)
- [Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction](https://mlsanity.com/paper/2203.01703/) (2022)
- [An Invitation to the Euler Characteristic Transform](https://mlsanity.com/paper/2310.10395/) (2023)

## Built on by (most cited first, 4 of 4)

- [On topological descriptors for graph products](https://mlsanity.com/paper/2511.08846/) (2025)
- [LEAP: Local ECT-Based Learnable Positional Encodings for Graphs](https://mlsanity.com/paper/2510.00757/) (2025)
- [Molecular Machine Learning Using Euler Characteristic Transforms](https://mlsanity.com/paper/2507.03474/) (2025)
- [Geometry-Aware Simplicial Message Passing](https://mlsanity.com/paper/2605.06061/) (2026)

## Abstract (arXiv)

This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use cases that result in more efficient models for analyzing point clouds, graphs, and meshes. Moreover, I outline a vision for how topological concepts could be used in the future, comprising (1) the learning of functions on topological spaces, (2) the building of hybrid models that imbue neural networks with knowledge about the topological information in data, and (3) the analysis of qualitative properties of neural networks. With current research already addressing some of these aspects, this article thus serves as an introduction and invitation to this nascent area of research.