Title: Long-Range Graph Wavelet Networks
Primary area: learning on graphs and other geometries & topologies
Keywords: Long-Range Interactions, Graph Wavelets, Graph Neural Networks, Spectral Parametrization, Polynomial Approximation

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.

TL;DR: We propose LR-GWN, a principled wavelet-based model that overcomes limitations of polynomial filters by combining low-order polynomials with spectral filters, achieving SOTA results across wavelet-based methods on long-range benchmarks.