Graph Mediator Networks Bridging Local and Global Semantics via Serial Message Passing

Jiangfeng Sun, SiHao He, Yanlong Lin, Zhonghong Ou, Meina Song

Abstract: Graph Neural Networks (GNNs) have achieved remarkable success in modeling structured data through local message passing. However, their effectiveness diminishes on graphs with low homophily or irregular structures, where long-range dependencies are hard to capture and features tend to suffer from over-smoothing and noise amplification. To address these limitations, we propose GMN, a novel dual-path Graph Mediator Network that explicitly enhances both global information propagation and spectral stability. In the spatial path, GMN introduces a lightweight Mediator node connected to all graph nodes, allowing long-range communication to occur in a single hop without increasing network depth. In parallel, the spectral path leverages multi-scale Chebyshev filtering along with a spectral energy regularization term that suppresses high-frequency noise, leading to smoother and more stable node embeddings. These two complementary pathways are adaptively integrated via a gated fusion mechanism, which dynamically balances their contributions based on structural context. Final graph-level representations are obtained through task-specific pooling strategies, enabling GMN to generalize effectively across different tasks. Extensive experiments on benchmark datasets with varying homophily levels and structural perturbations demonstrate that GMN consistently achieves state-of-the-art performance in terms of accuracy, robustness, and generalization. Code is available at: https://github.com/sun2017bupt/GMN.

Submission Number: 121