von Rohrscheidt, Julius Rieck, Bastian 2025 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 (ℓ-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 ℓ-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 ℓ-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. application/pdf https://folia.unifr.ch/global/documents/334092 https://folia.unifr.ch/documents/334092/files/von-rohrscheidt25a.pdf eng https://proceedings.mlr.press/v267/von-rohrscheidt25a.html info:eu-repo/semantics/openAccess License undefined Proceedings of the 42nd International Conference on Machine Learning. - Vancouver Convention Center, Vancouver, Canada. - 2025, vol. PMLR 267, p. 61790-61809 topological data analysis topological deep learning geometric deep learning euler characteristic transform euler characteristic info:eu-repo/classification/udc/root_1 Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms http://purl.org/coar/resource_type/c_6501