LEAP: Local ECT-Based Learnable Positional Encodings for Graphs

• URL: http://arxiv.org/abs/2510.00757v1
• Date: Wed, 01 Oct 2025 10:44:01 GMT
• Title: LEAP: Local ECT-Based Learnable Positional Encodings for Graphs
• Authors: Juan Amboage, Ernst Röell, Patrick Schnider, Bastian Rieck,
• Abstract summary: Graph positional encoding (PE) has emerged as a promising direction to address these limitations.<n>We propose LEAP, a new end-to-end trainable local structural PE for graphs.<n>Our results underline the potential of LEAP-based encodings as a powerful component for graph representation learning pipelines.
• Score: 15.740515132423205
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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