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Answering complex logical queries on incomplete knowledge graphs is achallenging task, and has been widely studied. Embedding-based methods requiretraining on complex queries, and cannot generalize well to out-of-distributionquery structures. Recent work frames this task as an end-to-end optimizationproblem, and it only requires a pretrained link predictor. However, due to theexponentially large combinatorial search space, the optimal solution can onlybe approximated, limiting the final accuracy. In this work, we propose QTO(Query Computation Tree Optimization) that can efficiently find the exactoptimal solution. QTO finds the optimal solution by a forward-backwardpropagation on the tree-like computation graph, i.e., query computation tree.In particular, QTO utilizes the independence encoded in the query computationtree to reduce the search space, where only local computations are involvedduring the optimization procedure. Experiments on 3 datasets show that QTOobtains state-of-the-art performance on complex query answering, outperformingprevious best results by an average of 22%. Moreover, QTO can interpret theintermediate solutions for each of the one-hop atoms in the query with over 90%accuracy. The code of our paper is at https://github.com/bys0318/QTO.

Answering Complex Logical Queries on Knowledge Graphs via Query Computation Tree Optimization