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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.18141 |
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| _version_ | 1866916034614657024 |
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| author | Zosso, Mia Hariri, Ali Kawasaki-Borruat, Victor Berlureau, Pierre-Gabriel Vandergheynst, Pierre |
| author_facet | Zosso, Mia Hariri, Ali Kawasaki-Borruat, Victor Berlureau, Pierre-Gabriel Vandergheynst, Pierre |
| contents | Long-range graph tasks are challenging for Graph Neural Networks (GNNs): global mechanisms such as attention or rewiring schemes can be computationally expensive, while deep local propagation is prone to vanishing gradients, oversmoothing, and oversquashing. The introduced mu-ChebNet architecture is a simple spectral GNN that learns a node-wise weight function mu before applying ChebNet-style filters. The learned weighting mu induces a modified graph Laplacian which effectively changes the propagation geometry without altering the graph topology. This task-dependent geometry promotes preferred routes for information propagation, thereby helping long-range signals avoid highly contractive bottlenecks, and obviating the need for repeated layer stacking. In practice, we replace the fixed graph Laplacian L by a learned operator L_mu, keeping the proposed mu-ChebNet architecture lightweight while making propagation task-adaptive. Furthermore, we provide a spectral analysis demonstrating how mu modulates propagation dynamics, and empirically observe improved performance on both synthetic long-range reasoning tasks and real-world graph benchmarks. The learned weight function is not only interpretable, but also offers a lightweight alternative to attention and rewiring for adaptive graph propagation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18141 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry-Induced Diffusion on Graphs: A Learnable Weighted Laplacian for Spectral GNNs Zosso, Mia Hariri, Ali Kawasaki-Borruat, Victor Berlureau, Pierre-Gabriel Vandergheynst, Pierre Machine Learning Long-range graph tasks are challenging for Graph Neural Networks (GNNs): global mechanisms such as attention or rewiring schemes can be computationally expensive, while deep local propagation is prone to vanishing gradients, oversmoothing, and oversquashing. The introduced mu-ChebNet architecture is a simple spectral GNN that learns a node-wise weight function mu before applying ChebNet-style filters. The learned weighting mu induces a modified graph Laplacian which effectively changes the propagation geometry without altering the graph topology. This task-dependent geometry promotes preferred routes for information propagation, thereby helping long-range signals avoid highly contractive bottlenecks, and obviating the need for repeated layer stacking. In practice, we replace the fixed graph Laplacian L by a learned operator L_mu, keeping the proposed mu-ChebNet architecture lightweight while making propagation task-adaptive. Furthermore, we provide a spectral analysis demonstrating how mu modulates propagation dynamics, and empirically observe improved performance on both synthetic long-range reasoning tasks and real-world graph benchmarks. The learned weight function is not only interpretable, but also offers a lightweight alternative to attention and rewiring for adaptive graph propagation. |
| title | Geometry-Induced Diffusion on Graphs: A Learnable Weighted Laplacian for Spectral GNNs |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.18141 |