Answering Complex Logical Queries on Knowledge Graphs via Query Computation Tree Optimization (2212.09567v3)

Abstract: Answering complex logical queries on incomplete knowledge graphs is a challenging task, and has been widely studied. Embedding-based methods require training on complex queries, and cannot generalize well to out-of-distribution query structures. Recent work frames this task as an end-to-end optimization problem, and it only requires a pretrained link predictor. However, due to the exponentially large combinatorial search space, the optimal solution can only be approximated, limiting the final accuracy. In this work, we propose QTO (Query Computation Tree Optimization) that can efficiently find the exact optimal solution. QTO finds the optimal solution by a forward-backward propagation on the tree-like computation graph, i.e., query computation tree. In particular, QTO utilizes the independence encoded in the query computation tree to reduce the search space, where only local computations are involved during the optimization procedure. Experiments on 3 datasets show that QTO obtains state-of-the-art performance on complex query answering, outperforming previous best results by an average of 22%. Moreover, QTO can interpret the intermediate 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.

• The paper introduces Query Computation Tree Optimization (QTO) to compute optimal answers for complex queries without training on them.
• It utilizes a forward-backward propagation algorithm on a tree-like structure to reduce search space and enhance interpretability.
• Experiments across three datasets show a 22% average improvement, demonstrating QTO's superior performance in KG-based reasoning.

Advanced Logical Query Answering on Knowledge Graphs with Query Computation Tree Optimization

Introduction

Research into answering complex logical queries on Knowledge Graphs (KG) has gained substantial momentum due to its significance in enhancing the interpretability and performance of graph-based reasoning tasks. Knowledge Graphs represent entities and their interrelations in a structured form, facilitating various downstream applications in AI, including recommendation systems, question answering, and information retrieval. However, despite advancements, accurately answering complex queries on incomplete KGs remains a challenging endeavor.

Query Computation Tree Optimization (QTO)

The introduction of Query Computation Tree Optimization (QTO) marks a pivotal evolution in the field of KG query answering. This novel approach efficiently identifies the exact optimal solution for complex query answering without necessitating training on complex queries, thereby overcoming the generalization issues associated with out-of-distribution (OOD) query structures. At its core, QTO leverages a tree-like computation graph, termed as the query computation tree, which serves as the backbone for reducing the search space through the independence encoded in its structure.

QTO's methodology is rooted in the forward-backward propagation algorithm on the query computation tree. The forward propagation efficiently computes the maximal truth value for query subcomponents, while the backward propagation reveals the most probable entity assignments for each query atom, thereby enhancing interpretability. Experiments across three datasets have demonstrated QTO's superior performance, with a notable average improvement of 22% over existing methods.

Methodological Insights

The implementation of QTO entails a series of meticulous steps:

• Neural Adjacency Matrix Calculation: A pre-trained Knowledge Graph Embedding (KGE) model is utilized to score the likelihood of atomic formulas, which are then calibrated to probabilities between [0,1] to form the neural adjacency matrix.
• Optimization Formalization: The complex logical query is transformed into a query computation tree, allowing for an end-to-end optimization framework that efficiently infers the optimal solution through forward and backward propagation. This process utilizes tailored operations to handle the intersection, union, and (anti-)relational projections encapsulated within the query structure.

Theoretical and Practical Implications

QTO introduces a robust framework for KG-based query answering, embodying both theoretical innovation and practical utility. Theoretically, it guarantees an exact optimal solution to complex query answering, circumventing the challenges posed by KG incompleteness. Practically, QTO can be leveraged in various applications that demand rigorous logical reasoning over KGs, potentially improving the accuracy and interpretability of knowledge-driven systems. Moreover, through rigorous experimentation, QTO has shown promising generalization capabilities, outperforming state-of-the-art alternatives across multiple benchmarks.

Future Directions

While QTO exhibits exceptional prowess in handling complex queries on KGs, potential avenues for enhancement and adaptation remain. Key among these is the exploration of scalability solutions for accommodating larger KGs, and extending the framework to support cyclic query structures and queries with multiple answer variables. Furthermore, investigating the optimization of the neural adjacency matrix parameters could unveil new dimensions in the calibration of KGE models for complex query answering.

Conclusion

Query Computation Tree Optimization stands as a significant advancement in the field of KG-based reasoning, introducing a methodologically sound and theoretically robust approach to answering complex logical queries. By harnessing the structure encoded within query computation trees and efficiently finding optimal solutions, QTO paves the way for enhanced interpretability and accuracy in knowledge graph reasoning tasks. It beckons a fertile ground for future research, aiming to bridge the gap between theoretical query answering frameworks and their practical applications in AI systems.