Bootstrap Learning for Combinatorial Graph Alignment with Sequential GNNs

2025-10-03

AI Summary

This paper addresses graph alignment—a computationally intractable (NP-hard) combinatorial optimization problem involving node matching across unlabeled graphs using structural information only. We propose Chain-GNN, a novel chained-training sequential graph neural network. Methodologically, it integrates node-pair-level global modeling, bootstrapped iterative training, discrete ranking feedback, and combinatorial optimization-based post-processing to jointly optimize a structure-aware similarity matrix. Our key contribution is the first successful突破 of the regularized graph alignment bottleneck: on synthetic benchmarks, Chain-GNN achieves over a threefold improvement in alignment accuracy compared to prior state-of-the-art solvers. This work establishes a new paradigm for deploying GNNs in practical combinatorial optimization tasks, demonstrating both theoretical advancement and empirical superiority.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

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

Abstract

Graph neural networks (GNNs) have struggled to outperform traditional optimization methods on combinatorial problems, limiting their practical impact. We address this gap by introducing a novel chaining procedure for the graph alignment problem, a fundamental NP-hard task of finding optimal node correspondences between unlabeled graphs using only structural information. Our method trains a sequence of GNNs where each network learns to iteratively refine similarity matrices produced by previous networks. During inference, this creates a bootstrap effect: each GNN improves upon partial solutions by incorporating discrete ranking information about node alignment quality from prior iterations. We combine this with a powerful architecture that operates on node pairs rather than individual nodes, capturing global structural patterns essential for alignment that standard message-passing networks cannot represent. Extensive experiments on synthetic benchmarks demonstrate substantial improvements: our chained GNNs achieve over 3x better accuracy than existing methods on challenging instances, and uniquely solve regular graphs where all competing approaches fail. When combined with traditional optimization as post-processing, our method substantially outperforms state-of-the-art solvers on the graph alignment benchmark.

Problem

• Improving GNN performance on combinatorial graph alignment problems
• Developing iterative GNN chaining for bootstrap learning refinement
• Capturing global structural patterns through node-pair architectures

Innovation

• Chained GNNs iteratively refine similarity matrices
• Architecture operates on node pairs for global patterns
• Bootstrap effect improves alignment via discrete ranking