等变神经原始-对偶分配用于最大公共边子图
Equivariant Neural Primal-Dual Assignment for Maximum Common Edge Subgraphs
浏览论文内容
中文总结 AI 辅助
针对最大公共边子图匹配，提出等变神经原始-对偶分配（ENPDA），学习共享策略以快速处理新图对，无需重训练，速度提升约三个数量级，并在多个基准上显著提高准确率。
中文摘要 AI 辅助
最大公共边子图（MCES）匹配在两个带标签图之间寻找部分顶点对应关系，该对应关系尽可能保留带标签的边。分子相似性搜索需要匹配许多图对，因此重复查询的成本至关重要。最强的基线方法能够获得准确的MCES解，但需要为每一对图训练一个独立的网络。我们提出了等变神经原始-对偶分配（ENPDA），该方法学习一个共享的匹配策略，并将其应用于新的图对而无需进一步训练，使得查询速度大约快三个数量级，并在几十次查询后即可收回训练成本。该策略为候选匹配重新计算精确的目标边际值，并学习更新其分数的修正量和步长。当多个源顶点偏好同一个目标时，目标价格会对竞争做出响应。四轮更新和一次匈牙利投影产生一个部分的一对一匹配。我们证明了对于任何网络参数都成立的逐对保证。在精确算术下，对任一图进行重排会置换分配和价格状态，投影后的匹配是一对一的，修复后的价格给出有效的MCES上界。减去保留边数可界定最优性差距；结合结构上限，这些证书证明了291个原生测试对中的60对具有全局最优性。在三个具有不相交训练/验证/测试划分的分子基准上，ENPDA在相同的更新和投影预算下比解析对应方法提高了7.4-8.6个准确率点；经过一秒的细化搜索后，仍有2.5-3个点的增益保留。无需微调即可迁移到来自社交图和蛋白质图的边删除任务，该策略比解析对应方法提高了9.1-17.6个点。当输出匹配必须保持芳香环完整时，ENPDA在所有三个数据集上比基线恢复了更多的参考键。
英文摘要
Maximum common edge subgraph (MCES) matching finds a partial vertex correspondence between two labeled graphs that preserves as many labeled edges as possible. Molecular similarity search requires matching many graph pairs, making the cost of repeated queries important. The strongest baseline attains accurate MCES solutions but trains a separate network for each pair. We introduce Equivariant Neural Primal-Dual Assignment (ENPDA), which learns a shared matching policy and applies it to new pairs without further training, answering queries roughly three orders of magnitude faster and recovering its training cost after a few dozen queries. The policy recomputes exact objective marginals for candidate matches and learns corrections and step sizes that update their scores. Target prices respond to competition when several source vertices favor the same target. Four update rounds and a Hungarian projection produce a partial one-to-one matching. We prove per-pair guarantees that hold for any network parameters. In exact arithmetic, reordering either graph permutes the assignment and price states, the projected matching is one-to-one, and repaired prices give a valid MCES upper bound. Subtracting the preserved-edge count bounds the optimality gap; combined with structural caps, these certificates prove global optimality for 60 of 291 native test pairs. On three molecular benchmarks with disjoint train/validation/test splits, ENPDA improves over an analytic counterpart with the same update and projection budget by 7.4-8.6 accuracy points; after one second of refinement search, 2.5-3 points of the gain remain. Transferred without fine-tuning to edge-deletion tasks from social and protein graphs, the policy gains 9.1-17.6 points over the analytic counterpart. When output matchings must keep aromatic rings intact, ENPDA recovers more reference bonds than the baselines on all three datasets.
