Making Classic GNNs Strong Baselines Across Varying Homophily: A Smoothness-Generalization Perspective
Ming Gu, Zhuonan Zheng, Sheng Zhou, Meihan Liu, Jiawei Chen, Tanyu Qiao, Liangcheng Li, Jiajun Bu
TL;DR
This work tackles the challenge of making classic GNNs robust across graphs with varying homophily. By theoretically identifying a smoothness-generalization dilemma in multi-hop message passing, the authors show that increasing hops boosts smoothness but can degrade generalization, hindering universality. They propose IGNN, a minimal, three-principle framework—separative neighborhood transformation, inceptive neighborhood aggregation, and neighborhood relationship learning—that enables hop-wise generalization and adaptive smoothness, while preserving low-order representations. Theoretical results demonstrate that IGNN can approximate arbitrary graph filters and mitigate the dilemma, and extensive experiments against 30 baselines on 13 datasets reveal superior performance and notable universality in several homoGNN variants. Overall, IGNN provides a practical, universal baseline for GNNs across homophily regimes, with strong empirical and theoretical support.
Abstract
Graph Neural Networks (GNNs) have achieved great success but are often considered to be challenged by varying levels of homophily in graphs. Recent \textit{empirical} studies have surprisingly shown that homophilic GNNs can perform well across datasets of different homophily levels with proper hyperparameter tuning, but the underlying theory and effective architectures remain unclear. To advance GNN universality across varying homophily, we theoretically revisit GNN message passing and uncover a novel \textit{smoothness-generalization dilemma}, where increasing hops inevitably enhances smoothness at the cost of generalization. This dilemma hinders learning in high-order homophilic neighborhoods and all heterophilic ones, where generalization is critical due to complex neighborhood class distributions that are sensitive to shifts induced by noise or sparsity. To address this, we introduce the Inceptive Graph Neural Network (IGNN) built on three simple yet effective design principles, which alleviate the dilemma by enabling distinct hop-wise generalization alongside improved overall generalization with adaptive smoothness. Benchmarking against 30 baselines demonstrates IGNN's superiority and reveals notable universality in certain homophilic GNN variants. Our code and datasets are available at \href{https://github.com/galogm/IGNN}{https://github.com/galogm/IGNN}.