GRAIL: Graph Edit Distance and Node Alignment Using LLM-Generated Code
This addresses a fundamental graph similarity problem for researchers and practitioners in graph analysis, offering a novel paradigm shift from prediction to program generation.
The paper tackles the problem of computing Graph Edit Distance (GED), which is NP-hard and challenging for neural methods due to data requirements and lack of interpretability, by introducing GRAIL, a method that uses LLMs to generate programs for GED computation, achieving superior prediction quality and cross-domain generalization on seven datasets.
Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved improved approximation quality compared to non-neural approaches, they face significant challenges: (1) They require large amounts of ground truth data, which is itself NP-hard to compute. (2) They operate as black boxes, offering limited interpretability. (3) They lack cross-domain generalization, necessitating expensive retraining for each new dataset. We address these limitations with GRAIL, introducing a paradigm shift in this domain. Instead of training a neural model to predict GED, GRAIL employs a novel combination of large language models (LLMs) and automated prompt tuning to generate a program that is used to compute GED. This shift from predicting GED to generating programs imparts various advantages, including end-to-end interpretability and an autonomous self-evolutionary learning mechanism without ground-truth supervision. Extensive experiments on seven datasets confirm that GRAIL not only surpasses state-of-the-art GED approximation methods in prediction quality but also achieves robust cross-domain generalization across diverse graph distributions.