Towards characterizing the value of edge embeddings in Graph Neural Networks
This work addresses a finer-grained architectural design problem in GNNs for researchers and practitioners, offering incremental improvements in efficiency and performance.
The paper investigates the benefits of using edge embeddings in Graph Neural Networks (GNNs), showing theoretically that such architectures can be much shallower for certain tasks and empirically that they often outperform node-based counterparts, with significant gains in topologies with hub nodes.
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.