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

=3em =10000 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 ($ $), a novel extension of the ECT particularly 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 $ $ provides a lossless representation of local neighborhoods. This approach addresses key limitations in GNNs by preserving local structures while maintaining global interpretability. Moreover, we construct a rotation-invariant metric based on $ $s for spatial alignment of data spaces. Our method exhibits superior performance compared to standard GNNs on a variety of benchmark node-classification tasks, while also offering theoretical guarantees that demonstrate its effectiveness.