Adaptive Universal Generalized PageRank Graph Neural Network (2006.07988v6)

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.

• The paper introduces adaptive GPR weights to effectively extract node features and topology, mitigating feature over-smoothing in deeper networks.
• It validates the approach through rigorous empirical and theoretical analysis using synthetic benchmarks and diverse real-world datasets.
• The framework establishes a theoretical link to polynomial graph filters, outperforming state-of-the-art models in handling varied graph signal frequencies.

Adaptive Universal Generalized PageRank Graph Neural Network

The paper presents a novel Graph Neural Network (GNN) architecture called the Adaptive Universal Generalized PageRank Graph Neural Network (GPR-GNN). The authors address two primary challenges in existing GNN frameworks: non-universality regarding graph homophily/heterophily and the issue of feature over-smoothing in deeper networks.

Key Contributions

GPR-GNN introduces a Generalized PageRank (GPR) approach that adapts the weights of GPR to optimize the extraction of both node features and topological information. This adaptability allows for effective application across graphs with varying homophily and heterophily levels, thereby enhancing universality.

1. Adaptive GPR Weights: The architecture learns GPR weights to cope with different node label patterns, mitigating the need for tailored graph assumptions. This is essential for preventing feature over-smoothing without constraining the network depth.
2. Empirical and Theoretical Validation: The paper combines robust empirical analysis with theoretical insights. The authors use a contextual Stochastic Block Model (cSBM) for synthetic benchmark generation and perform comprehensive comparisons using homophilic and heterophilic datasets for node classification tasks.
3. Theoretical Link to Graph Filtering: The authors establish connections between GPR and polynomial graph filters, highlighting the flexibility of GPR-GNN in handling varied graph signal frequencies—a limitation in some existing GNN models like APPNP and SGC, which tend to act as low-pass filters.

Numerical Results

Empirical evaluations indicate substantial performance improvements by GPR-GNN across synthetic and real-world datasets, particularly on heterophilic graphs. The architecture consistently outperforms state-of-the-art GNN models such as GCN, GAT, and APPNP in terms of accuracy.

Implications and Future Directions

• Theoretical Implications: GPR-GNN’s adaptive filtering can be seen as a pathway towards more generalizable GNN architectures, capable of learning effectively across diverse graph structures.
• Practical Applications: The demonstrated robustness on heterophilic datasets suggests potential for deployment in real-world scenarios, such as social networks or recommendation systems, where graph structures do not adhere strictly to homophily.
• Future Research: Investigations into scaling GPR-GNN for large graphs could amplify its applicability. Moreover, exploring connections with other filtering techniques may yield richer insights into addressing the over-smoothing challenge.

In summary, GPR-GNN provides a compelling framework for tackling two critical limitations in existing GNN architectures, enhancing both theoretical insights and practical utility. Its foundation in adaptive learning marks a significant step towards universality in graph-based machine learning models.