Spatial Message Passing Graph Neural Networks (MPGNNs) are widely used for learning on graph-structured data. However, key limitations of ℓ -step MPGNNs are that their "receptive field" is typically limited to the ℓ-hop neighborhood of a node and that information exchange between distant nodes is limited by over-squashing.

Graph neural networks (GNNs) have received extensive attention from researchers due to their excellent performance on various graph learning tasks such as social analysis [24, 17, 29], drug discovery [12, 25], traffic forecasting [18, 3, 6], recommendation system [38, 32] and computer vision[39,4].

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.

Designing spectral convolutional networks is a challenging problem in graph learning.

We approach this question by focusing on individual neurons, analyzing the behavior of their activations at different timescales.

We approach this question by focusing on individual neurons, analyzing the behavior of their activations at different timescales.