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This work provides the first theoretical study on the ability of graphMessage Passing Neural Networks (gMPNNs) -- such as Graph Neural Networks(GNNs) -- to perform inductive out-of-distribution (OOD) link prediction tasks,where deployment (test) graph sizes are larger than training graphs. We firstprove non-asymptotic bounds showing that link predictors based onpermutation-equivariant (structural) node embeddings obtained by gMPNNs canconverge to a random guess as test graphs get larger. We then propose atheoretically-sound gMPNN that outputs structural pairwise (2-node) embeddingsand prove non-asymptotic bounds showing that, as test graphs grow, theseembeddings converge to embeddings of a continuous function that retains itsability to predict links OOD. Empirical results on random graphs show agreementwith our theoretical results.

OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs