GRAIL: Graph Edit Distance and Node Alignment Using LLM-Generated Code

2025-05-04

AI Summary

Addressing three key challenges in graph edit distance (GED) computation—scarcity of ground-truth annotations, poor interpretability of neural approaches, and weak cross-domain generalization—this paper proposes GRAIL, the first LLM-driven program synthesis framework for GED solving. GRAIL abandons end-to-end neural fitting, instead leveraging automated prompt tuning and code generation to produce executable programs that compute GED and output node alignments—enabling zero-shot supervised training, full interpretability, and out-of-the-box cross-domain generalization without fine-tuning. Methodologically, it integrates LLM-based reasoning with classical graph matching and edit path search algorithms. Evaluated on seven benchmark datasets, GRAIL consistently surpasses state-of-the-art approximate methods in accuracy while natively supporting heterogeneous graph distributions.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Computing optimal Graph Edit Distance is NP-hard
• Neural methods lack interpretability and cross-domain generalization
• GRAIL generates programs for GED without ground-truth data

Innovation

• Uses LLMs to generate GED computation code
• Automated prompt tuning for program generation
• Self-evolutionary learning without ground-truth data