This paper proposes Long-Range Graph Wavelet Networks (LR-GWNs) to address the challenges of modeling long-range interactions in graph machine learning, namely the difficulty of information propagation between distant parts of a graph. Existing wavelet-based graph neural networks rely on finite-order polynomial approximations, resulting in limited receptive fields and difficulties with long-range propagation. LR-GWNs address these challenges by decomposing wavelet filters into complementary local and global components. Local aggregation is handled by efficient low-order polynomials, while long-range interactions are captured through flexible spectral-domain parameterization. This hybrid design integrates short-range and long-range information flow within a principled wavelet framework. Experimental results demonstrate that LR-GWNs achieve state-of-the-art performance among wavelet-based methods on long-range benchmarks, while also demonstrating competitive performance on short-range datasets.
