Wasserstein-Fisher-Rao嵌入：具有局部比较与全局传输的逻辑查询嵌入
Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport
AI总结：
本文提出Wasserstein-Fisher-Rao嵌入（WFRE），利用非平衡最优传输理论平衡局部比较与全局传输，实现知识图谱复杂查询的高效嵌入，并在标准及层次数据集上超越现有方法。
摘要：
在知识图谱上回答复杂查询非常重要，但由于数据不完整性而特别具有挑战性。查询嵌入方法通过基于学习的模型和集合运算符模拟逻辑推理来解决这一问题。以往的工作侧重于特定形式的嵌入，但嵌入之间的评分函数尚未得到充分探索。与现有受局部比较或全局传输启发的评分函数不同，本研究利用非平衡最优传输理论探讨局部与全局的权衡。具体而言，我们将集合嵌入为实数空间中的有界测度，并采用由Wasserstein-Fisher-Rao度量启发的评分函数。这种设计还促进了嵌入空间中闭合形式的集合运算符。此外，我们引入了一种基于卷积的算法以实现线性时间计算，以及一个块对角核来强制实现权衡。结果表明，WFRE在标准数据集、具有组合复杂查询的评估集以及层次知识图谱上能够优于现有的查询嵌入方法。消融研究表明，找到更好的局部与全局权衡对于性能提升至关重要。
英文摘要：
Answering complex queries on knowledge graphs is important but particularly challenging because of the data incompleteness. Query embedding methods address this issue by learning-based models and simulating logical reasoning with set operators. Previous works focus on specific forms of embeddings, but scoring functions between embeddings are underexplored. In contrast to existing scoring functions motivated by local comparison or global transport, this work investigates the local and global trade-off with unbalanced optimal transport theory. Specifically, we embed sets as bounded measures in $\real$ endowed with a scoring function motivated by the Wasserstein-Fisher-Rao metric. Such a design also facilitates closed-form set operators in the embedding space. Moreover, we introduce a convolution-based algorithm for linear time computation and a block-diagonal kernel to enforce the trade-off. Results show that WFRE can outperform existing query embedding methods on standard datasets, evaluation sets with combinatorially complex queries, and hierarchical knowledge graphs. Ablation study shows that finding a better local and global trade-off is essential for performance improvement.
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