发表机构
Institut Polytechnique de Paris; École Polytechnique; Télécom Paris（巴黎理工学院; 巴黎综合理工学院; 巴黎电信学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对监督图预测中的置换不变损失，研究最优传输松弛并证明GW最优，提出用可微Sinkhorn匹配器摊销图匹配，联合学习预测与匹配，在含新任务的多个问题上验证效率。
AI 中文摘要
端到端监督图预测（SGP）需要一个置换不变损失函数来比较具有任意节点顺序的预测图与目标图。此类损失通常涉及代价高昂的图匹配问题。我们首先研究了该问题的三种最优传输松弛，并从理论和实验上证明，Gromov-Wasserstein（GW）目标最适合SGP。然后，为避免对每个训练样本求解由此产生的内部优化，我们提出对图匹配（节点对齐）问题进行摊销。对于每个训练样本，损失函数利用由参数化匹配器提供的传输计划，该匹配器基于可微的Sinkhorn算法应用于经验节点分布。图预测模块和匹配器被联合学习。我们在日益复杂的玩具和真实世界SGP问题上展示了该方法的效率，包括我们引入的一个新颖的质谱到支架（Mass-spectra to Scaffold）任务。
英文摘要
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.
