Logical Message Passing Networks with One-hop Inference on Atomic Formulas

Complex Query Answering (CQA) over Knowledge Graphs (KGs) has attracted a lot of attention to potentially support many applications. Given that KGs are usually incomplete, neural models are proposed to answer logical queries by parameterizing set operators with complex neural networks. However, such methods usually train neural set operators with a large number of entity and relation embeddings from zero, where whether and how the embeddings or the neural set operators contribute to the performance remains not clear. In this paper, we propose a simple framework for complex query answering that decomposes the KG embeddings from neural set operators. We propose to represent the complex queries in the query graph. On top of the query graph, we propose the Logical Message Passing Neural Network (LMPNN) that connects the \textit{local} one-hop inferences on atomic formulas to the \textit{global} logical reasoning for complex query answering. We leverage existing effective KG embeddings to conduct one-hop inferences on atomic formulas, the results of which are regarded as the messages passed in LMPNN. The reasoning process over the overall logical formulas is turned into the forward pass of LMPNN that incrementally aggregates local information to predict the answers' embeddings finally. The complex logical inference across different types of queries will then be learned from training examples based on the LMPNN architecture. Theoretically, our query-graph representation is more general than the prevailing operator-tree formulation, so our approach applies to a broader range of complex KG queries. Empirically, our approach yields a new state-of-the-art neural CQA model. Our research bridges the gap between complex KG query answering tasks and the long-standing achievements of knowledge graph representation learning.