Bootstrap Learning for Combinatorial Graph Alignment with Sequential GNNs

ICLR 2026 Conference Submission12989 Authors

Keywords: Graph Neural Networks, Graph Alignment, Combinatorial Optimization, Sequential Learning, Graph Matching, Bootstrap Learning, Quadratic Assignment Problem

TL;DR: We train multiple GNNs in sequence where each one learns to improve upon the previous network's solution, creating the first learning-based method to outperform traditional optimization algorithms on the graph alignment problem.

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 3× better accuracy than existing methods on challenging instances, and uniquely solve regular graphs where all competing approaches fail completely. When combined with traditional optimization as post-processing, our method substantially outperforms state-of-the-art solvers on the graph alignment benchmark.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 12989