Towards characterizing the value of edge embeddings in Graph Neural Networks

TL;DR

This paper investigates the role of edge embeddings in Graph Neural Networks, demonstrating both theoretically and empirically that architectures utilizing edge embeddings can be more efficient and often outperform node-only models, especially in complex graph topologies.

Contribution

It provides the first theoretical analysis of edge embeddings in GNNs and empirically shows their benefits over node-only architectures across various graph structures.

Findings

Edge embeddings enable shallower architectures for certain tasks.

Empirical results show edge-based GNNs outperform node-only models.

Performance gains are significant in graphs with hub nodes.

Abstract

Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design for GNNs remains impoverished. In this paper, we consider the benefits of architectures that maintain and update edge embeddings. On the theoretical front, under a suitable computational abstraction for a layer in the model, as well as memory constraints on the embeddings, we show that there are natural tasks on graphical models for which architectures leveraging edge embeddings can be much shallower. Our techniques are inspired by results on time-space tradeoffs in theoretical computer science. Empirically, we show architectures that maintain edge embeddings almost always improve on their node-based counterparts -- frequently significantly so in topologies that have ``hub'' nodes.