Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms

Julius von Rohrscheidt, Bastian Rieck
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:61790-61809, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-von-rohrscheidt25a, title = {Diss-l-{ECT}: Dissecting Graph Data with Local {E}uler Characteristic Transforms}, author = {von Rohrscheidt, Julius and Rieck, Bastian}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {61790--61809}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/von-rohrscheidt25a/von-rohrscheidt25a.pdf}, url = {https://proceedings.mlr.press/v267/von-rohrscheidt25a.html}, 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.} }
Endnote
%0 Conference Paper %T Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms %A Julius von Rohrscheidt %A Bastian Rieck %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-von-rohrscheidt25a %I PMLR %P 61790--61809 %U https://proceedings.mlr.press/v267/von-rohrscheidt25a.html %V 267 %X 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.
APA
von Rohrscheidt, J. & Rieck, B.. (2025). Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:61790-61809 Available from https://proceedings.mlr.press/v267/von-rohrscheidt25a.html.

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