Abstract: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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2602.18141 [cs.LG] |
| (or arXiv:2602.18141v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2602.18141 arXiv-issued DOI via DataCite |
From: Ali Hariri [view email]
[v1]
Fri, 20 Feb 2026 11:01:12 UTC (287 KB)
[v2]
Thu, 21 May 2026 15:21:25 UTC (1,412 KB)
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