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Graph neural networks (GNNs) are one of the most popular approaches to usingdeep learning on graph-structured data, and they have shown state-of-the-artperformances on a variety of tasks. However, according to a recent study, acareful choice of pooling functions, which are used for the aggregation andreadout operations in GNNs, is crucial for enabling GNNs to extrapolate.Without proper choices of pooling functions, which varies across tasks, GNNscompletely fail to generalize to out-of-distribution data, while the number ofpossible choices grows exponentially with the number of layers. In this paper,we present GNP, a $L^p$ norm-like pooling function that is trainable end-to-endfor any given task. Notably, GNP generalizes most of the widely-used poolingfunctions. We verify experimentally that simply using GNP for every aggregationand readout operation enables GNNs to extrapolate well on many node-level,graph-level, and set-related tasks; and GNP sometimes performs even better thanthe best-performing choices among existing pooling functions.

Learning to Pool in Graph Neural Networks for Extrapolation