Learning representations of sets of nodes in a graph is crucial for applications ranging from noderole discovery to link prediction and molecule classification. Graph Neural Networks (GNNs) have achieved great success in graph representation learning. However, expressive power of GNNs is limited by the 1WeisfeilerLehman (WL) test and thus GNNs generate identical representations for graph substructures that may in fact be very different. More powerful GNNs, proposed recently by mimicking higherorderWL tests, only focus on representing entire graphs and they are computationally inefficient as they cannot utilize sparsity of the underlying graph. Here we propose and mathematically analyze a general class of structure related features, termed Distance Encoding (DE). DE assists GNNs in representing any set of nodes, while providing strictly more expressive power than the 1WL test. DE captures the distance between the node set whose representation is to be learned and each node in the graph. To capture the distance DE can apply various graphdistance measures such as shortest path distance or generalized PageRank scores. We propose two ways for GNNs to use DEs (1) as extra node features, and (2) as controllers of message aggregation in GNNs. Both approaches can utilize the sparse structure of the underlying graph, which leads to computational efficiency and scalability. We also prove that DE can distinguish node sets embedded in almost all regular graphs where traditional GNNs always fail. We evaluate DE on three tasks over six real networks: structural role prediction, link prediction, and triangle prediction. Results show that our models outperform GNNs without DE by upto 15% in accuracy and AUROC. Furthermore, our models also significantly outperform other stateoftheart methods especially designed for the above tasks.
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This content will become publicly available on December 14, 2023
OOD Link Prediction Generalization Capabilities of MessagePassing GNNs in Larger Test Graphs
This work provides the first theoretical study on the ability of graph Message Passing Neural Networks (gMPNNs)  such as Graph Neural Networks (GNNs)  to perform inductive outofdistribution (OOD) link prediction tasks, where deployment (test) graph sizes are larger than training graphs. We first prove nonasymptotic bounds showing that link predictors based on permutationequivariant (structural) node embeddings obtained by gMPNNs can converge to a random guess as test graphs get larger. We then propose a theoreticallysound gMPNN that outputs structural pairwise (2node) embeddings and prove nonasymptotic bounds showing that, as test graphs grow, these embeddings converge to embeddings of a continuous function that retains its ability to predict links OOD. Empirical results on random graphs show agreement with our theoretical results.
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 NSFPAR ID:
 10404652
 Date Published:
 Journal Name:
 Advances in neural information processing systems
 ISSN:
 10495258
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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