Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms
Julius von Rohrscheidt, Bastian Rieck
Abstract
The Euler Characteristic Transform (ECT) is an efficiently computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the local Euler Characteristic Transform ($\ell$-ECT), a novel extension of the ECT designed to enhance expressivity and interpretability in graph representation learning. Unlike traditional Graph Neural Networks (GNNs), which may lose critical local details through aggregation, the $\ell$-ECT provides a lossless representation of local neighborhoods. This approach addresses key limitations in GNNs by preserving nuanced local structures while maintaining global interpretability. Moreover, we construct a rotation-invariant metric based on $\ell$-ECTs for spatial alignment of data spaces. Our method demonstrates superior performance compared to standard GNNs on various benchmarking node classification tasks, while also offering theoretical guarantees of its effectiveness.
BibTeX
@inproceedings{
rohrscheidt2025disslect,
title={Diss-l-{ECT}: Dissecting Graph Data with Local Euler Characteristic Transforms},
author={Julius von Rohrscheidt and Bastian Rieck},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=GAmmzu6GYS}
}