Heterophilous Distribution Propagation for Graph Neural Networks

TL;DR

This work tackles the challenge of heterophily in graph neural networks by introducing Heterophilous Distribution Propagation (HDP), which adaptively partitions neighborhood signals into homophilous and heterophilous components using pseudo-labels and learns heterophilous distributions under an orthogonality constraint via a Trusted Prototype Contrastive (TPC) loss. It combines a semantic-aware neighborhood partition with mean-operator-based heterophilous modeling and a semantic-aware message passing framework to propagate both patterns, achieving strong performance on heterophilous graphs across nine datasets. The approach is supported by extensive ablations and analyses showing the contributions of assignment initialization, semantic structural encoding, SMP, and TPC, as well as insights into the discriminability of the learned representations. Overall, HDP advances robust, discriminative graph representation learning in heterophilous settings with practical implications for real-world networks.

Abstract

Graph Neural Networks (GNNs) have achieved remarkable success in various graph mining tasks by aggregating information from neighborhoods for representation learning. The success relies on the homophily assumption that nearby nodes exhibit similar behaviors, while it may be violated in many real-world graphs. Recently, heterophilous graph neural networks (HeterGNNs) have attracted increasing attention by modifying the neural message passing schema for heterophilous neighborhoods. However, they suffer from insufficient neighborhood partition and heterophily modeling, both of which are critical but challenging to break through. To tackle these challenges, in this paper, we propose heterophilous distribution propagation (HDP) for graph neural networks. Instead of aggregating information from all neighborhoods, HDP adaptively separates the neighbors into homophilous and heterphilous parts based on the pseudo assignments during training. The heterophilous neighborhood distribution is learned with orthogonality-oriented constraint via a trusted prototype contrastive learning paradigm. Both the homophilous and heterophilous patterns are propagated with a novel semantic-aware message passing mechanism. We conduct extensive experiments on 9 benchmark datasets with different levels of homophily. Experimental results show that our method outperforms representative baselines on heterophilous datasets.

Figures (8)

• Figure 1: The illustration of neighborhood partition and heterophily modeling. (a) A and B are two nodes that belong to different classes but have extremely similar neighborhoods, where colors denote classes. Without neighborhood partition, message passing neural networks(MPNN) produce confused node representations due to the similar neighborhood. On the contrary, partitioning neighborhoods explicitly and handling them separately can increase the discriminability of representations. (b) We count the average connection preference for each class in Cornell. In the whole neighborhood, the connection preferences of different classes are similar, which is probably caused by the imbalanced numbers of nodes in each class. After neighborhood partition, the connection preferences in heterophilous neighborhood shows the discriminability. Thus, heterophily modeling can bring additional information for discriminative representation learning.
• Figure 2: Overall framework of HDP, which contains three main parts including semantic-aware neighborhood partition, heterophilous neighbor distribution modeling and semantic-aware message passing.
• Figure 3: The illustration of semantic structural encoding. Nodes with a red circle denote the target nodes. After initialization, the structural embedding is calculated through the random walk with self-loop.
• Figure 4: Detailed statistics of datasets and classification performance on 6 datasets with various levels of heterophily and 3 homophilous datasets.
• Figure 5: The visualization of neighborhood partition results on representative datasets. The 3 columns of each dataset denote the whole neighborhood, the homophilous and heterophilous neighborhoods partitioned by HDP respectively.

Theorems & Definitions (2)

• Theorem 1
• Lemma 1