GCN-MPPR: Enhancing the Propagation of Message Passing Neural Networks via Motif-Based Personalized PageRank

TL;DR

The paper addresses the limited propagation depth and over-smoothing of MPNNs by introducing Motif-Based Personalized PageRank (MPPR), which leverages higher-order motif relationships to guide diffusion. MPPR is integrated into Graph Convolutional Networks as GCN-MPPR, decoupling feature transformation from propagation and enabling deeper effective diffusion without adding layers. The authors define motif-based adjacency, derive a closed-form MPPR diffusion operator, and demonstrate improvements in node classification and link prediction, along with a plug-in demonstration in DGCRL. The approach offers gains in accuracy, stability, and efficiency, and is shown to be broadly compatible with existing GCN frameworks, making it a practical enhancement for real-world graph learning tasks.

Abstract

The algorithms based on message passing neural networks (MPNNs) on graphs have recently achieved great success for various graph applications. However, studies find that these methods always propagate the information to very limited neighborhoods with shallow depth, particularly due to over-smoothing. That means most of the existing MPNNs fail to be so `deep'. Although some previous work tended to handle this challenge via optimization- or structure-level remedies, the overall performance of GCNs still suffers from limited accuracy, poor stability, and unaffordable computational cost. Moreover, neglect of higher-order relationships during the propagation of MPNNs has further limited the performance of them. To overcome these challenges, a novel variant of PageRank named motif-based personalized PageRank (MPPR) is proposed to measure the influence of one node to another on the basis of considering higher-order motif relationships. Secondly, the MPPR is utilized to the message passing process of GCNs, thereby guiding the message passing process at a relatively `high' level. The experimental results show that the proposed method outperforms almost all of the baselines on accuracy, stability, and time consumption. Additionally, the proposed method can be considered as a component that can underpin almost all GCN tasks, with DGCRL being demonstrated in the experiment. The anonymous code repository is available at: https://anonymous.4open.science/r/GCN-MPPR-AFD6/.

Figures (4)

• Figure 1: Visualization of the contributions of GCN-MPPR upon existing works, whereas $\Delta$ = (a) message passing; (b) message passing with PPR and (c) message passing with MPPR (spreading information further considering higher-order motifs).
• Figure 2: Visualization of Seven Types of Motifs Considered and the Example for the Calculation of Motif-Based Adjacency Matrix.
• Figure 3: Accuracy when varying parameters.
• Figure 4: The Box Figures of a Hundred Runs on Various Datasets.

Theorems & Definitions (2)

• definition 1
• definition 2