Abstract:Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural networks (MPNNs) face well-documented theoretical and practical limitations. Graph positional encoding (PE) has emerged as a promising direction to address these limitations. The Euler Characteristic Transform (ECT) is an efficiently computable geometric-topological invariant that characterizes shapes and graphs. In this work, we combine the differentiable approximation of the ECT (DECT) and its local variant ($\ell$-ECT) to propose LEAP, a new end-to-end trainable local structural PE for graphs. We evaluate our approach on multiple real-world datasets as well as on a synthetic task designed to test its ability to extract topological features. Our results underline the potential of LEAP-based encodings as a powerful component for graph representation learning pipelines.
| Comments: | Accepted at the International Conference on Learning Representations (ICLR) 2026. Our code is available this https URL |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2510.00757 [cs.LG] |
| (or arXiv:2510.00757v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2510.00757 arXiv-issued DOI via DataCite |
Submission history
From: Ernst Roell [view email]
[v1]
Wed, 1 Oct 2025 10:44:01 UTC (955 KB)
[v2]
Fri, 27 Feb 2026 19:17:12 UTC (958 KB)
[v3]
Thu, 14 May 2026 07:11:49 UTC (958 KB)