Chaining 2-FWL GNNs for Combinatorial Graph Alignment
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916072962129920 |
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| author | Lelarge, Marc |
| author_facet | Lelarge, Marc |
| contents | For the combinatorial graph alignment problem (GAP) -- finding the node correspondence that maximizes the number of common edges (nce) between two unlabeled graphs -- properly initialized FAQ remains a strong classical baseline, while existing GNN approaches struggle in the purely structural setting. We introduce a chaining procedure: a sequence of Folklore-type (2-FWL) GNNs in which each network is trained with cross-entropy after decoding the previous network's similarity matrix and ranking nodes by their current alignment quality. This non-differentiable ranking step injects discrete combinatorial feedback at every link; at inference, we iterate the final network and keep the candidate with highest observed nce. On sparse Erdos-Renyi graphs at noise level 0.25, chained FGNNs with FAQ post-processing reach 85% accuracy versus 13% for FAQ initialized from the convex relaxation, and essentially 0% for prior GNN methods. On correlated regular graphs, where MPNNs with constant features produce identical node embeddings (1-WL fails to refine) and FAQ's convex initialization is degenerate, chaining is the only method we know that recovers a non-trivial alignment. On three real-world benchmarks (yeast PPI, coauthorship, and road networks), we show that recent comparisons underestimate FAQ by initializing it from a uniform doubly stochastic matrix; once FAQ is initialized from the convex relaxation it already surpasses prior reported numbers, and dataset-specific chained FGNNs further improve on this strengthened baseline. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_03086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chaining 2-FWL GNNs for Combinatorial Graph Alignment Lelarge, Marc Machine Learning For the combinatorial graph alignment problem (GAP) -- finding the node correspondence that maximizes the number of common edges (nce) between two unlabeled graphs -- properly initialized FAQ remains a strong classical baseline, while existing GNN approaches struggle in the purely structural setting. We introduce a chaining procedure: a sequence of Folklore-type (2-FWL) GNNs in which each network is trained with cross-entropy after decoding the previous network's similarity matrix and ranking nodes by their current alignment quality. This non-differentiable ranking step injects discrete combinatorial feedback at every link; at inference, we iterate the final network and keep the candidate with highest observed nce. On sparse Erdos-Renyi graphs at noise level 0.25, chained FGNNs with FAQ post-processing reach 85% accuracy versus 13% for FAQ initialized from the convex relaxation, and essentially 0% for prior GNN methods. On correlated regular graphs, where MPNNs with constant features produce identical node embeddings (1-WL fails to refine) and FAQ's convex initialization is degenerate, chaining is the only method we know that recovers a non-trivial alignment. On three real-world benchmarks (yeast PPI, coauthorship, and road networks), we show that recent comparisons underestimate FAQ by initializing it from a uniform doubly stochastic matrix; once FAQ is initialized from the convex relaxation it already surpasses prior reported numbers, and dataset-specific chained FGNNs further improve on this strengthened baseline. |
| title | Chaining 2-FWL GNNs for Combinatorial Graph Alignment |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.03086 |