Adaptive Universal Generalized PageRank Graph Neural Network

TL;DR

This paper introduces an adaptive Generalized PageRank GNN that automatically learns optimal weights to effectively utilize node features and topology, excelling across homophilic and heterophilic graph patterns.

Contribution

It proposes a universal GNN architecture with adaptive GPR weights that optimize information extraction regardless of graph label homophily or heterophily.

Findings

Significant performance improvements over state-of-the-art GNNs.

Effective handling of both synthetic and real-world datasets.

Avoids feature over-smoothing without shallow networks.

Abstract

In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not optimally trade-off their utility and integrate them in a manner that is also universal. Here, universality refers to independence on homophily or heterophily graph assumptions. We address these issues by introducing a new Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR weights so as to jointly optimize node feature and topological information extraction, regardless of the extent to which the node labels are homophilic or heterophilic. Learned GPR weights automatically adjust to the node label pattern, irrelevant on the type of initialization, and thereby guarantee excellent learning performance for label patterns that are usually hard to handle. Furthermore, they allow one to avoid feature over-smoothing, a process which renders feature information nondiscriminative, without requiring the network to be shallow. Our accompanying theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the so-called contextual stochastic block model. We also compare the performance of our GNN architecture with that of several state-of-the-art GNNs on the problem of node-classification, using well-known benchmark homophilic and heterophilic datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data.