Principal Neighbourhood Aggregation for Graph Nets

TL;DR

This paper introduces Principal Neighbourhood Aggregation (PNA), a new GNN architecture that combines multiple aggregation functions and degree-scalers to enhance expressive power for continuous features, supported by a comprehensive benchmark.

Contribution

The paper extends the theoretical understanding of GNNs to continuous features and proposes PNA, a novel architecture with multiple aggregators and degree-scalers, demonstrating improved capacity.

Findings

PNA outperforms existing models on classical graph theory tasks.

Multiple aggregators and degree-scalers improve GNN expressive power.

Benchmark results show PNA's robustness across diverse tasks.

Abstract

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.