Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport

TL;DR

This paper introduces a novel embedding method for knowledge graph queries using Wasserstein-Fisher-Rao metrics, balancing local comparison and global transport to improve reasoning over incomplete data.

Contribution

It proposes a new embedding framework leveraging unbalanced optimal transport theory, with closed-form operators and efficient computation, outperforming existing methods.

Findings

Outperforms existing query embedding methods on standard datasets

Effective in handling combinatorially complex queries

Ablation shows importance of local-global trade-off

Abstract

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.