Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily

2025-11-10

AI Summary

Traditional graph neural networks (GNNs) suffer from limited performance on heterophilous graphs with low homophily and typically employ fixed-layer message passing, ignoring node-level structural heterogeneity; existing approaches also struggle to generalize across both homophilous and heterophilous scenarios. To address this, we establish, for the first time, a theoretical connection between node-wise optimal propagation depth and local homophily. We propose a theoretically grounded dynamic depth selection mechanism that adaptively determines the number of aggregation steps per node based on a principled local homophily metric. This mechanism is architecture-agnostic and can be seamlessly integrated into mainstream GNN frameworks to enable node-level adaptive message passing. Extensive experiments on multiple benchmark datasets demonstrate significant improvements in node classification accuracy. Moreover, our method exhibits strong robustness and generalization across graphs with varying degrees of homophily.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Local Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Graph Neural Networks (GNNs) have achieved significant success in addressing node classification tasks. However, the effectiveness of traditional GNNs degrades on heterophilic graphs, where connected nodes often belong to different labels or properties. While recent work has introduced mechanisms to improve GNN performance under heterophily, certain key limitations still exist. Most existing models apply a fixed aggregation depth across all nodes, overlooking the fact that nodes may require different propagation depths based on their local homophily levels and neighborhood structures. Moreover, many methods are tailored to either homophilic or heterophilic settings, lacking the flexibility to generalize across both regimes. To address these challenges, we develop a theoretical framework that links local structural and label characteristics to information propagation dynamics at the node level. Our analysis shows that optimal aggregation depth varies across nodes and is critical for preserving class-discriminative information. Guided by this insight, we propose a novel adaptive-depth GNN architecture that dynamically selects node-specific aggregation depths using theoretically grounded metrics. Our method seamlessly adapts to both homophilic and heterophilic patterns within a unified model. Extensive experiments demonstrate that our approach consistently enhances the performance of standard GNN backbones across diverse benchmarks.

Problem

• Addressing performance degradation of GNNs on heterophilic graphs
• Overcoming fixed aggregation depth limitations across all nodes
• Developing flexible models for both homophilic and heterophilic settings

Innovation

• Adaptive-depth GNN architecture for node classification
• Dynamic node-specific aggregation depth selection
• Unified model for homophilic and heterophilic graphs