Graph Matching Relaxations and Amortization for Supervised Graph Prediction

2026-09-14

AI Summary

研究解决了监督图预测中的图匹配问题，采用Gromov-Wasserstein目标函数，并通过参数化匹配器实现图匹配的摊销，以提高效率。

Abstract

End-to-end Supervised Graph Prediction (SGP) requires a permutation-invariant loss to compare predicted and target graphs with arbitrary node orderings. Such losses typically involve a costly graph-matching problem. We first study three Optimal Transport relaxations of this problem and show, theoretically and empirically, that the Gromov-Wasserstein (GW) objective is the most suitable for SGP. Then, to avoid solving the resulting inner optimization for every training example, we propose to amortize the graph matching (node alignment) problem. For each training sample, the loss function leverages a transport plan provided by a parametric matcher based on the differentiable Sinkhorn algorithm applied on empirical node distributions. The graph prediction module and the matcher are jointly learned. We showcase the efficiency of this approach on toy and real world SGP problems of increasing complexity including a novel Mass-spectra to Scaffold task that we introduce.

Problem

• Supervised Graph Prediction
• permutation-invariant loss
• graph-matching problem
• Optimal Transport relaxations

Innovation

• Optimal Transport Relaxations
• Gromov-Wasserstein
• Amortization
• Differentiable Sinkhorn Algorithm