Towards characterizing the value of edge embeddings in graph neural networks

Dhruv Rohatgi, Tanya Marwah, Zachary Chase Lipton, Jianfeng Lu, Ankur Moitra, Andrej Risteski

Keywords: graph neural networks, theory, representational power, communication complexity, memory tradeoffs, edge embeddings

TL;DR: We characterize the added representational power conferred to by edge embeddings, considering additional constraints like memory and symmetry.

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.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 8936