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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.00757 |
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| _version_ | 1866918500436541440 |
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| author | Amboage, Juan Röell, Ernst Schnider, Patrick Rieck, Bastian |
| author_facet | Amboage, Juan Röell, Ernst Schnider, Patrick Rieck, Bastian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | LEAP: Local ECT-Based Learnable Positional Encodings for Graphs Amboage, Juan Röell, Ernst Schnider, Patrick Rieck, Bastian Machine Learning 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. |
| title | LEAP: Local ECT-Based Learnable Positional Encodings for Graphs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.00757 |