GRAIN: Multi-Granular and Implicit Information Aggregation Graph Neural Network for Heterophilous Graphs

TL;DR

This work tackles the challenge of heterophilous graphs where traditional GNNs falter due to the breakdown of the homophily assumption. It introduces GRAIN, a Graph Neural Network that aggregates information across multiple granularity levels and incorporates implicit relationships from distant nodes, formulated as a Markov Decision Process solved with TD3-based actor-critic reinforcement learning. The framework comprises an Intelligent Granularity Perceiver that learns per-node granularity policies and a Multi-view Aggregator that fuses multi-granularity and implicit signals into node embeddings, with an Efficient GNN Aggregation scheme to reduce parameters and speed training. Extensive experiments on 13 datasets show GRAIN outperforms 12 state-of-the-art methods on both homophilous and heterophilous graphs, supported by sensitivity analyses and visualizations that highlight improved representation quality. This approach advances robust, context-aware graph representations suitable for complex networks with diverse homophily properties, while acknowledging scalability considerations for large-scale deployment.

Abstract

Graph neural networks (GNNs) have shown significant success in learning graph representations. However, recent studies reveal that GNNs often fail to outperform simple MLPs on heterophilous graph tasks, where connected nodes may differ in features or labels, challenging the homophily assumption. Existing methods addressing this issue often overlook the importance of information granularity and rarely consider implicit relationships between distant nodes. To overcome these limitations, we propose the Granular and Implicit Graph Network (GRAIN), a novel GNN model specifically designed for heterophilous graphs. GRAIN enhances node embeddings by aggregating multi-view information at various granularity levels and incorporating implicit data from distant, non-neighboring nodes. This approach effectively integrates local and global information, resulting in smoother, more accurate node representations. We also introduce an adaptive graph information aggregator that efficiently combines multi-granularity and implicit data, significantly improving node representation quality, as shown by experiments on 13 datasets covering varying homophily and heterophily. GRAIN consistently outperforms 12 state-of-the-art models, excelling on both homophilous and heterophilous graphs.

Figures (4)

• Figure 1: An illustration of our proposed framework. The key idea of the model is to explore different levels of granularity information and implicit information of the target nodes in the graph through the intelligent granularity perceiver. We aim to smooth the representation by aggregating the different information into embedding the nodes through the multi-view aggregator.
• Figure 2: Analysis of balancing parameters ($\alpha$) for different datasets, where $\alpha$ influences the proportion of aggregation chosen for coarse- and fine-grained information.
• Figure 3: The visualization of classification results of the proposed model for different datasets.
• Figure 4: Performance of the proposed method based on different reinforcement learning on a graph representation learning task.