{"ID":2862013,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.00757","arxiv_id":"2510.00757","title":"LEAP: Local ECT-Based Learnable Positional Encodings for Graphs","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.","short_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 direc...","url_abs":"https://arxiv.org/abs/2510.00757","url_pdf":"https://arxiv.org/pdf/2510.00757v3","authors":"[\"Juan Amboage\",\"Ernst Röell\",\"Patrick Schnider\",\"Bastian Rieck\"]","published":"2025-10-01T10:44:01Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Graph Neural Network\"]","has_code":false}