Adaptive Universal Generalized PageRank Graph Neural Network

TL;DR

This work tackles universal graph learning by introducing GPR-GNN, which jointly exploits node features and graph topology through adaptive Generalized PageRank weights. By learning the propagation coefficients $\gamma_k$, the model can reshape the graph filter from low-pass to high-pass to suit homophilic or heterophilic structures, thereby addressing over-smoothing and depth limitations. Theoretical results link GPR to polynomial graph filtering and show conditions under which the method preserves discriminative information, while empirical evaluations on synthetic (cSBM) and real-world datasets demonstrate robust, state-of-the-art performance across graph regimes and provide interpretability of the learned propagation patterns. Overall, the approach yields a practical universal GNN that auto-tunes its reliance on topology versus features and remains effective in diverse graph settings.

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.

Figures (10)

• Figure 1: (a) Hidden state feature extraction is performed by a neural networks using individual node features propagated via GPR. Note that both the GPR weights $\gamma_k$ and parameter set $\{{\theta\}}$ of the neural network are learned simultaneously in an end-to-end fashion (as indicated in red). (b)-(c) The learnt GPR weights of the GPR-GNN on real world datasets. Cora is homophilic while Texas is heterophilic (Here, $\mathcal{H}$ stands for the level of homophily defined below). An interesting trend may be observed: For the heterophilic case the weights alternate from positive to negative with dampening amplitudes (more examples are provided in Section \ref{['sec:cSBM_intro']}). The shaded region corresponds to a $95\%$ confidence interval.
• Figure 2: Accuracy of tested models on cSBM. Error bars indicate $95\%$ confidence interval.
• Figure 3: Figure (a)-(d) shows the learnt GPR weights by GPR-GNN with random initialization on cSBM, dense split. The shaded region indicates $95\%$ confidence interval.
• Figure 4: Figures (a)-(d) show the learned GPR weights of our GPR-GNN method with random initialization on various datasets, for dense splitting. Figures (e)-(f) show the learned weights of our GPR-GNN method with initialization $\delta_{kK}$ on cSBM$(\phi=-1)$, for dense splitting. The shaded region indicates a $95\%$ confidence interval.
• Figure 5: A simple example demonstrating how GPR-GNN escapes over-smoothing.

Theorems & Definitions (11)

• Theorem 4.1: Informal
• Theorem 4.2: Informal
• Theorem A.1: Formal version of Theorem \ref{['thm:LPF']}
• proof
• Lemma A.2
• Definition A.3: The over-smoothing phenomenon
• Lemma A.4
• Lemma A.5
• Theorem A.6: Formal version of Theorem \ref{['thm:OS']}
• proof