# SS-AdaMoE: Spatio-Spectral Adaptive Mixture of Experts with Global Structural Priors for Graph Node Classification

## TL;DR

This paper introduces SS-AdaMoE, a new graph node classification framework that improves performance on both homophilic and heterophilic graphs by combining spatial and spectral methods with global structural awareness.

## Contribution

SS-AdaMoE introduces a Dual-Domain Expert System and a Hierarchical Global-Prior Gating Network to better capture high-frequency signals and global structure in graph data.

## Key findings

- SS-AdaMoE outperforms existing MoE baselines by up to 2.65% on Chameleon and 1.41% on Roman-empire.
- The model surpasses traditional GCN architectures by over 28% on heterophilic datasets like Texas.
- The integration of spectral filters and global topological awareness improves generalization across diverse graph patterns.

## Abstract

Graph Neural Networks (GNNs) have emerged as the standard for learning representations from graph-structured data. While traditional architectures relying on message-passing mechanisms excel in homophilic settings, they essentially function as fixed low-pass filters. However, this smoothing operation limits their ability to generalize to heterophilic graphs, where connected nodes often exhibit dissimilar labels and high-frequency signals are crucial for discrimination. Furthermore, existing Mixture-of-Experts (MoE) methods for graphs often suffer from local-view routing, failing to capture global structural context during expert selection. To address these challenges, this paper proposes SS-AdaMoE, a novel Spatio-Spectral Adaptive Mixture of Experts framework designed for robust node classification across diverse graph patterns. Specifically, a Dual-Domain Expert System is constructed, integrating heterogeneous spatial aggregators with learnable spectral filters based on Bernstein polynomials. This allows the model to adaptively capture arbitrary frequency responses—including high-pass and band-pass signals—which are overlooked by standard GNNs. To resolve the locality bias, a Hierarchical Global-Prior Gating Network augmented by a Linear Graph Transformer is introduced, ensuring that expert selection is guided by both local node features and global topological awareness. Extensive experiments are conducted on five benchmark datasets spanning both homophilic and heterophilic networks. The results demonstrate that SS-AdaMoE consistently outperforms baselines, achieving accuracy improvements of up to 2.65% on Chameleon and 1.41% on Roman-empire over the strongest MoE baseline, while surpassing traditional GCN architectures by margins exceeding 28% on heterophilic datasets such as Texas. These findings validate that the synergy of learnable spectral priors and global gating effectively bridges the gap between spatial aggregation and spectral filtering.