Exchangeability of GNN Representations with Applications to Graph Retrieval

ICLR 2026 Conference Submission24538 Authors

Keywords: GNN, Locality sensitive hashing

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

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.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 24538