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.

中文翻译：

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图算法的神经执行

图神经网络 (GNN) 是解决图结构输入问题的强大表征工具。然而，到目前为止，在几乎所有情况下，它们都被应用于直接从原始输入中恢复最终解决方案，而没有明确指导如何构建他们的问题解决方案。在这里，我们专注于算法空间的学习：我们训练了几种最先进的 GNN 架构来模仿经典图算法、并行（广度优先搜索，Bellman-Ford）以及顺序图算法的各个步骤（Prim 算法）。由于图算法通常依赖于在邻域内做出离散决策，我们假设基于最大化的消息传递神经网络最适合此类目标，并根据经验验证这一主张。