Advances in Spectral Graph Neural Networks

Introduction

The field of graph neural networks (GNNs) is rapidly advancing, with a focus on addressing the challenges of heterophily and over-smoothing. Recent research has led to the development of innovative solutions, including adaptive polynomial filters and hybrid-domain architectures.

General Direction

The field is moving towards the development of more robust and adaptive GNNs that can effectively handle heterophilic graphs and mitigate the effects of over-smoothing. This is being achieved through the design of new filter architectures and the exploration of different spectral domains.

Noteworthy Papers

  • KrawtchoukNet and LaguerreNet propose adaptive polynomial filters that achieve state-of-the-art results on challenging heterophilic benchmarks and demonstrate exceptional robustness to over-smoothing.
  • HybSpecNet introduces a hybrid-domain architecture that combines the stability of ChebyNet with the adaptivity of KrawtchoukNet, achieving strong results on both homophilic and heterophilic benchmarks while addressing the critical issue of instability poisoning.

Sources

KrawtchoukNet: A Unified GNN Solution for Heterophily and Over-smoothing with Adaptive Bounded Polynomials

LaguerreNet: Advancing a Unified Solution for Heterophily and Over-smoothing with Adaptive Continuous Polynomials

Gauge-Equivariant Graph Networks via Self-Interference Cancellation

L-JacobiNet and S-JacobiNet: An Analysis of Adaptive Generalization, Stabilization, and Spectral Domain Trade-offs in GNNs

HybSpecNet: A Critical Analysis of Architectural Instability in Hybrid-Domain Spectral GNNs

Built with on top of