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.

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