Graph Neural Networks are a natural fit for learning algorithms. They can directly represent tasks through an abstract but versatile graph structure and handle inputs of different sizes. This opens up the possibility for scaling and extrapolation to larger graphs, one of the most important advantages of an algorithm. However, this raises two core questions i) How can we enable nodes to gather the required information in a given graph ($\textit{information exchange}$), even if is far away and ii) How can we design an execution framework which enables this information exchange for extrapolation to larger graph sizes ($\textit{algorithmic alignment for extrapolation}$). We propose a new execution framework that is inspired by the design principles of distributed algorithms: Flood and Echo Net. It propagates messages through the entire graph in a wave like activation pattern, which naturally generalizes to larger instances. Through its sparse but parallel activations it is provably more efficient in terms of message complexity. We study the proposed model and provide both empirical evidence and theoretical insights in terms of its expressiveness, efficiency, information exchange and ability to extrapolate.

翻译：图神经网络天然适用于学习算法。它们可以通过抽象而通用的图结构直接表达任务，并处理不同规模的输入。这为扩展和推演至更大图结构开辟了可能性——这是算法最重要的优势之一。然而，这引发了两个核心问题：i) 如何使节点能够在给定图中收集所需信息（即使该信息位于远处）——即信息交换；ii) 如何设计一个执行框架，使其能够实现这种信息交换并支持向更大图结构的推演——即用于推演的算法对齐。我们提出了一种受分布式算法设计原则启发的新执行框架：洪水与回声网络。它通过波状激活模式在整个图中传播消息，这种模式自然地泛化到更大规模的实例。凭借其稀疏但并行的激活机制，该框架在消息复杂度方面被证明更为高效。我们研究了所提出的模型，并从表达能力、效率、信息交换和推演能力等方面提供了实证证据与理论洞见。