Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs
A new paper proposes a unified theoretical framework for graph learning, arguing that the field should move beyond restrictive views of spectral and message-passing Graph Neural Networks (GNNs). The authors introduce a precise definition for spectral GNNs based on eigenbasis symmetries, contrasting it with the neighborhood permutation symmetries used for Message Passing Neural Networks (MPNNs). They suggest that while both approaches have largely equivalent expressive power under current definitions, the spectral perspective offers unique tools for understanding smoothing and stability, complementing the discrete structure analysis provided by MPNNs. AI