[2511.03909] Tensor Computation of Euler Characteristic Functions and Transforms

Computer Science > Computational Geometry arXiv:2511.03909 (cs) [Submitted on 5 Nov 2025 (v1), last revised 2 Apr 2026 (this version, v3)] Title:Tensor Computation of Euler Characteristic Functions and Transforms Authors:Jessi Cisewski-Kehe, Brittany Terese Fasy, Alexander McCleary, Eli Quist View a PDF of the paper titled Tensor Computation of Euler Characteristic Functions and Transforms, by Jessi Cisewski-Kehe and 3 other authors View PDF HTML (experimental) Abstract: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. Subjects: Computational Geometry (cs.CG); Machine Learning (cs.LG); Algebraic Topology (math.AT) MSC classes: 55N31, 55-08 Cite as: arXiv:2511.03909 [cs.CG]   (or arXiv:2511.03909v3 [cs.CG] for this version)   htt...