# Tensor Computation of Euler Characteristic Functions and Transforms

arXiv: https://arxiv.org/abs/2511.03909 · HTML: https://mlsanity.com/paper/2511.03909/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 29 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Builds on (most cited first, 9 of 9)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Differentiable Euler Characteristic Transforms for Shape Classification](https://mlsanity.com/paper/2310.07630/) (2023)
- [The Weighted Euler Curve Transform for Shape and Image Analysis](https://mlsanity.com/paper/2004.11128/) (2020)
- [An Invitation to the Euler Characteristic Transform](https://mlsanity.com/paper/2310.10395/) (2023)
- [A Fast and Scalable Computational Topology Framework for the Euler Characteristic](https://mlsanity.com/paper/2311.11740/) (2023)
- [GPU Computation of the Euler Characteristic Curve for Imaging Data](https://mlsanity.com/paper/2203.09087/) (2022)
- [The Weighted Euler Characteristic Transform for Image Shape Classification](https://mlsanity.com/paper/2307.13940/) (2023)
- [Efficient computation of topological integral transforms](https://mlsanity.com/paper/2405.02256/) (2024)
- [Scalable GPU-Accelerated Euler Characteristic Curves: Optimization and Differentiable Learning for PyTorch](https://mlsanity.com/paper/2510.20271/) (2025)

## Abstract (arXiv)

The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are either not optimized for GPU computation or do not scale to higher-dimensional settings. In this work, we present a tensor-based framework for computing such topological descriptors which is highly optimized for GPU architectures and works in full generality across simplicial and cubical complexes of arbitrary dimension. Experimentally, the framework demonstrates significant speedups over existing methods when computing the WECT and ECF across a variety of two- and three-dimensional datasets. Computation of these transforms is implemented in a publicly available Python package called pyECT.