Towards Metric-Faithful Neural Graph Matching

2026-05-07

AI Summary

This work addresses the unclear role of encoder geometry in neural graph matching for estimating graph edit distance (GED). It establishes, for the first time, a theoretical connection between the bi-Lipschitz geometric properties of graph neural network encoders and the fidelity of GED estimation, proposing bi-Lipschitz constraints as a guiding design principle for neural graph matching. Building upon an FSW-GNN encoder that simultaneously satisfies Weisfeiler–Lehman expressiveness and bi-Lipschitz continuity, the authors integrate this encoder into mainstream GED frameworks and demonstrate significant improvements in both prediction accuracy and ranking performance across multiple benchmark datasets. Ablation and transfer experiments confirm that these gains stem from enhanced geometric structure in the learned representations.

Abstract

Graph Edit Distance (GED) is a fundamental, albeit NP-hard, metric for structural graph similarity. Recent neural graph matching architectures approximate GED by first encoding graphs with a Graph Neural Network (GNN) and then applying either a graph-level regression head or a matching-based alignment module. Despite substantial architectural progress, the role of encoder geometry in neural GED estimation remains poorly understood. In this paper, we develop a theoretical framework that connects encoder geometry to GED estimation quality for two broad classes of neural GED estimators: graph similarity predictors and alignment-based methods. On fixed graph collections, where the doubly-stochastic metric $d_{\mathrm{DS}}$ is comparable to GED, we show that graph-level bi-Lipschitz encoders yield controlled GED surrogates and improved ranking stability; for matching-based estimators, node-level bi-Lipschitz geometry propagates to encoder-induced alignment costs and the resulting optimized alignment objective. We instantiate this perspective using FSW-GNN, a bi-Lipschitz WL-equivalent encoder, as a drop-in replacement in representative neural GED architectures. Across representative baselines and benchmark datasets, the resulting geometry-aware variants significantly improve GED prediction and ranking metrics. A faithfulness case study of untrained encoders, together with ablations and transfer experiments, supports the view that these gains arise from improved representation geometry, positioning encoder geometry as a useful design principle for neural graph matching.

Problem

• Graph Edit Distance
• Neural Graph Matching
• Encoder Geometry
• Bi-Lipschitz
• Graph Similarity

Innovation

• bi-Lipschitz encoder
• Graph Edit Distance
• neural graph matching
• representation geometry
• metric faithfulness