05 December 2025
ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness in capturing local graph structure. Despite their success, MPNNs are limited in their ability to capture long-range dependencies between nodes. This has led researchers to adapt MPNNs through rewiring or make use of Graph Transformers, which compromise the computational efficiency that characterized early spatial message passing architectures, and typically disregard the graph structure.
Almost a decade after its original introduction, EMERGE partners from the University of Pisa revisit ChebNet to shed light on its ability to model distant node interactions. The authors find that out-of-box, ChebNet already shows competitive advantages relative to classical MPNNs and GTs on long-range benchmarks, while maintaining good scalability properties for high-order polynomials. However, they uncover that this polynomial expansion leads ChebNet to an unstable regime during training. To address this limitation, they cast ChebNet as a stable and non-dissipative dynamical system, coined Stable-ChebNet.
Read the paper in the link below.
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