用于等变图生成的格罗莫夫-蒙日流匹配
Alignment Matters Inside and Out in Equivariant Graph Flow Matching
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中文总结 AI 辅助
该研究提出格罗莫夫-蒙日流匹配方法，通过构造感知结构的商耦合，在小积分预算下提升图与分子生成质量，且兼容标准置换等变架构。
中文摘要 AI 辅助
图在节点置换下具有不变性，这促使生成模型中使用置换等变架构。然而在流匹配中，对称性也可能进入源-目标耦合：当图对按节点重标记进行比较时，其自然的瓦瑟斯坦几何是图商空间的几何。该空间的欧氏商度量与格罗莫夫-蒙日距离一致，该距离通过对节点进行最优重标记得到。我们从理论上发展了这一视角，表明商耦合可以无额外代价地提升为对齐的代表，且对称化会产生等变流匹配极小化器，包括针对分类端点预测的情况。在实践中，精确的格罗莫夫-蒙日对齐难以处理，因此我们使用高效的格罗莫夫-瓦瑟斯坦型松弛方法和内部节点对齐的下界来构造小批量耦合，还可选择性结合图之间的外部分配。所得过程仅改变训练耦合，且与标准置换等变架构兼容。在连续图和分类分子生成任务中，这些感知结构的耦合在小积分预算下显著提升了样本质量，而我们的放大分子模型在传统多步采样下仍保持竞争力。
英文摘要
Graphs are invariant under node permutations, motivating permutation-equivariant architectures in generative models. In flow matching, however, symmetry also affects the source-target coupling: one must choose both which graphs to pair and which node representatives to align. We study these two forms of alignment, termed outer and inner alignment, and their effect on equivariant graph flow matching. We connect inner alignment to transport on the graph quotient space, whose Euclidean quotient metric coincides with Gromov-Monge distance, and show that quotient couplings admit aligned representative lifts while symmetrization yields equivariant flow-matching minimizers, including for categorical endpoints. In practice, we compare random augmentation, permutation-blind minibatch optimal transport, approximate Gromov-Wasserstein alignment, and combinations of inner and outer alignment. Across continuous graph and molecular generation, alignment can substantially simplify trajectories and improve few-step generation, while its benefits depend on the alignment and computational budget. Our results highlight that effective graph flow matching benefits from alignment both inside and across graph pairs.
发表机构
- Institute of Mathematics, Technische Universität Berlin（柏林工业大学数学研究所）
- Institut Camille Jordan, INSA Lyon（里昂国立应用科学学院卡米尔·乔丹研究所）
机构由 AI 辅助整理，请以论文原文为准。
