Long-Range Graph Wavelet Networks

• URL: http://arxiv.org/abs/2509.06743v3
• Date: Mon, 13 Oct 2025 08:56:32 GMT
• Title: Long-Range Graph Wavelet Networks
• Authors: Filippo Guerranti, Fabrizio Forte, Simon Geisler, Stephan Günnemann,
• Abstract summary: Long-range interactions are a central challenge in graph machine learning.<n>Existing wavelet-based graph neural networks rely on finite-order approximations.<n>We propose Long-Range Graphlet Networks (LR-GWN), which decompose wavelet into complementary local and global components.
• Score: 48.591533900586626
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Modeling long-range interactions, the propagation of information across distant parts of a graph, is a central challenge in graph machine learning. Graph wavelets, inspired by multi-resolution signal processing, provide a principled way to capture both local and global structures. However, existing wavelet-based graph neural networks rely on finite-order polynomial approximations, which limit their receptive fields and hinder long-range propagation. We propose Long-Range Graph Wavelet Networks (LR-GWN), which decompose wavelet filters into complementary local and global components. Local aggregation is handled with efficient low-order polynomials, while long-range interactions are captured through a flexible spectral-domain parameterization. This hybrid design unifies short- and long-distance information flow within a principled wavelet framework. Experiments show that LR-GWN achieves state-of-the-art performance among wavelet-based methods on long-range benchmarks, while remaining competitive on short-range datasets.

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