Principal Neighbourhood Aggregation for Graph Nets (2004.05718v5)

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.

• The paper introduces the PNA model to enhance GNN expressive power by integrating diverse aggregators and degree-scalers.
• It mathematically demonstrates injectivity through degree-scalers, surpassing traditional single-method aggregation techniques.
• Empirical results on both synthetic and real-world datasets show that PNA outperforms models like GCN, GAT, GIN, and MPNN in capturing complex graph structures.

Principal Neighbourhood Aggregation for Graph Nets

The paper introduces a novel approach to enhance the expressive power of Graph Neural Networks (GNNs) through a new architecture called Principal Neighbourhood Aggregation (PNA). The research addresses the limitations of existing GNNs in effectively capturing structural information from graph-structured data, particularly when dealing with continuous features commonly found in real-world applications.

Theoretical Framework

The authors extend the theoretical framework to include continuous feature spaces and demonstrate the necessity of multiple aggregation functions for enhancing GNN performance. Unlike traditional methods that rely on singular aggregation techniques such as mean or sum, PNA utilizes a combination of multiple aggregators and degree-scalers. This approach generalizes the sum aggregation by introducing degree-scalers, which adjust based on node degree, to balance signal amplification within the network.

Principal Neighbourhood Aggregation (PNA)

PNA combines the use of diverse aggregators — including mean, maximum, minimum, and standard deviation — with degree-scalers to better capture the structural nuances of graphs. This combination ensures that GNNs can distinguish between different node neighborhoods more effectively, a requirement proven mathematically by the authors through injectivity arguments.

The PNA model is integrated within a message passing neural network, where multiple towers are employed to enhance computational efficiency and performance. This design enables PNA to consistently outperform established models such as GCN, GAT, GIN, and MPNN across various tasks.

Empirical Evaluation

The paper presents a multi-task synthetic benchmark as well as real-world datasets from domains like molecular chemistry and computer vision. The results indicate that PNA significantly improves upon state-of-the-art models, particularly in tasks requiring a deep understanding of graph structures.

The benchmarks encompass both synthetic graph theory problems and real-world datasets, highlighting PNA's practical applicability. The synthetic benchmarks affirm PNA's superiority in capturing complex graph properties across varied graph types, while the real-world datasets demonstrate its competitive edge in practical applications.

Implications and Future Directions

The research has important implications for the development of more robust and expressive GNN architectures. By showcasing the need for multiple complementary aggregation strategies, the paper encourages further exploration into aggregation methods beyond the traditional single-function approach.

Future developments may focus on expanding PNA's architecture to other types of neural networks and exploring its application in under-explored domains. Moreover, advancements in adaptive aggregation strategies could address scalability issues, facilitating better generalization across diverse graph structures.

In conclusion, the introduction of PNA offers a significant enhancement in the expressive capacity of GNNs, paving the way for future research and development in graph-based machine learning models. As the field progresses, such comprehensive approaches towards aggregation and scalability will likely play a central role in advancing the efficacy of GNNs in both theoretical and applied settings.