Neural Execution of Graph Algorithms

Petar Veličković, Rex Ying, Matilde Padovano, Raia Hadsell, Charles Blundell

TL;DR: We supervise graph neural networks to imitate intermediate and step-wise outputs of classical graph algorithms, recovering highly favourable insights.

Abstract: Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without explicit guidance on how to structure their problem-solving. Here, instead, we focus on learning in the space of algorithms: we train several state-of-the-art GNN architectures to imitate individual steps of classical graph algorithms, parallel (breadth-first search, Bellman-Ford) as well as sequential (Prim's algorithm). As graph algorithms usually rely on making discrete decisions within neighbourhoods, we hypothesise that maximisation-based message passing neural networks are best-suited for such objectives, and validate this claim empirically. We also demonstrate how learning in the space of algorithms can yield new opportunities for positive transfer between tasks---showing how learning a shortest-path algorithm can be substantially improved when simultaneously learning a reachability algorithm.

Keywords: Graph Neural Networks, Graph Algorithms, Learning to Execute, Program Synthesis, Message Passing Neural Networks, Deep Learning