MORGAN: To Bridge Mixture of Experts and Spectral Graph Neural Network

Graph Neural Networks (GNNs) have demonstrated strong performance across a wide range of tasks by leveraging the structural properties of graph-structured data. To tackle the challenge of edge heterophily-where connected nodes may possess dissimilar labels or features-two primary families of GNNs have emerged: Mixture-of-Experts (MoE)-based spatial GNNs and frequency filtering-based spectral GNNs. MoE-based spatial GNNs intuitively assign specialized experts to different hops in the graph but often lack a solid theoretical foundation. In contrast, spectral GNNs are grounded in graph signal processing theory, yet they typically rely on handcrafted filters and ad-hoc global operators, which limits their scalability and adaptability. In this work, we uncover an inherent connection between these two paradigms by showing that eigengraph components in spectral methods can be interpreted as experts within the MoE framework. Building on this insight, we propose MORGAN, a novel spectral GNN that combines frequency filtering from spectral GNNs with the expert assignment strategy from MoE-based spatial GNNs. MORGAN performs eigen-decomposition of the graph Laplacian, partitions the spectrum into multiple frequency bands, and assigns a dedicated expert network to each band. A learnable gating mechanism dynamically combines the outputs of these experts based on their spectral characteristics. To support scalable and inductive learning, we further introduce MORGAN(L), a localized variant that incorporates subgraph sampling to perform spectral filtering without requiring access to the full graph Laplacian. Extensive experiments on real-world benchmark datasets demonstrate that MORGAN consistently achieves competitive or superior performance compared to state-of-theart baselines, particularly in inductive node classification tasks under heterophilic settings.