Title: TREEGEAR: Learning Graph Edit Distance with Zero Ground-truth Labels
Primary area: learning on graphs and other geometries & topologies
Keywords: graph edit distance, Graph neural networks

Abstract: Graph Edit Distance (GED) is a fundamental measure for assessing similarity between graphs, with broad applications across domains such as bioinformatics, cheminformatics, and social network analysis. Unfortunately, computing exact
GED is NP-hard. Besides a number of approximation algorithms, neural methods have emerged as a promising solution to this challenge. However, the training of these neural models requires a large number of ground-truth labels, which
is computationally expensive to obtain due to the NP-hardness, thereby hindering their scalability. In this work, we introduce a novel framework, TREEGEAR for learning GED without the need of ground-truth GED labels. Our approach
uses structural supervision from tree edit distances (TED), which can be computed in polynomial time, enabling the model to learn meaningful representations from approximate signals. Unlike existing approaches that directly regress to
GED, TREEGEAR learns pairwise node mappability scores through node embeddings, on which, we apply a neighbor-biased mapper to derive the best possible edit paths between two graphs. This novel reformulation enables strong out-of-distribution generalization, interpretability, and better alignment with the properties of the true GED. Extensive experiments across GED benchmarks demonstrate
that TREEGEAR achieves state-of-the-art results, beating both non-neural and neural baselines that are trained on 100% ground-truth GED. Moreover, TREEGEAR is architecture-agnostic and generalizes effectively to unseen graphs, making it suitable for real-world deployment across diverse graph domains.