Title: Exchangeability of GNN Representations  with Applications to Graph Retrieval
Primary area: learning on graphs and other geometries & topologies
Keywords: GNN, Locality sensitive hashing

Abstract: In this work, we discover a probabilistic symmetry, called as exchangeability in graph neural networks (GNNs). Specifically, we show that the trained node embedding computed using a large family of graph neural networks, learned under standard optimization tools,  are exchangeable random variables. This implies that the probability density of the node embeddings remains invariant with respect to a permutation applied on their dimension axis. This results in identical distribution across the elements of the graph representations.  Such a property enables approximation of transportation-based graph similarities by Euclidean similarities between order statistics. Leveraging this reduction, we propose a unified locality-sensitive hashing (LSH) framework that supports diverse relevance measures, including subgraph matching and graph edit distance. Experiments show that our method helps to do LSH more effectively than baselines.

TL;DR: It shows that graph representations are exchangeable random variables which can help in LSH in graphs