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arXiv:2502.17973 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Quantum Negative Sampling Strategy for Knowledge Graph Embedding with Variational Circuit

Pulak Ranjan Giri, Mori Kurokawa, Kazuhiro Saito

Published Sep 17, 2023• 4 citations
arXivHTMLPDF

Abstract

Knowledge graph is a collection of facts, known as triples(head, relation, tail), which are represented in form of a network, where nodes are entities and edges are relations among the respective head and tail entities. Embedding of knowledge graph for facilitating downstream tasks such as knowledge graph completion, link prediction, recommendation, has been a major area of research recently in classical machine learning. Because the size of knowledge graphs are becoming larger, one of the natural choices is to exploit quantum computing for knowledge graph embedding. Recently, a hybrid quantum classical model for knowledge graph embedding has been studied in which a variational quantum circuit is trained. One of the important aspects in knowledge graph embedding is the sampling of negative triples, which plays a crucial role in efficient training of the model. In classical machine learning various negative sampling strategies have been studied. In quantum knowledge graph embedding model, although we can use these strategies in principle, it is natural to ask if we can exploit quantum advantage in negative sampling. In this article we study such a negative sampling strategy, which exploits quantum superposition, and evaluate the model's performance with a knowledge graph database.

DOI
10.1109/qce57702.2023.10242

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Knowledge graph is a collection of facts, known as triples(head, relation, tail), which are represented in form of a network, where nodes are entities and edges are relations among the respective head and tail entities. Embedding of knowledge graph for facilitating downstream tasks such as knowledge graph completion, link prediction, recommendation, has been a major area of research recently in classical machine learning. Because the size of knowledge graphs are becoming larger, one of the natural choices is to exploit quantum computing for knowledge graph embedding. Recently, a hybrid quantum classical model for knowledge graph embedding has been studied in which a variational quantum circuit is trained. One of the important aspects in knowledge graph embedding is the sampling of negative triples, which plays a crucial role in efficient training of the model. In classical machine learning various negative sampling strategies have been studied. In quantum knowledge graph embedding model, although we can use these strategies in principle, it is natural to ask if we can exploit quantum advantage in negative sampling. In this article we study such a negative sampling strategy, which exploits quantum superposition, and evaluate the model's performance with a knowledge graph database.
Embedding of a knowledge graph(KG) entities and relations in the form of vectors is an important aspect for the manipulation of the KG database for several downstream tasks, such as link prediction, knowledge graph completion, and recommendation. Because of the growing size of the knowledge graph databases, it has become a daunting task for the classical computer to train a model efficiently. Quantum computer can help speedup the embedding process of the KGs by encoding the entities into a variational quantum circuit of polynomial depth. Usually, the time complexity for such variational circuit-dependent quantum classical algorithms for each epoch is O(Npoly(logM)), whereNNNis number of elements in the knowledge graph andMMMis the number of features of each entities of the knowledge graph. In this article we exploit additional quantum advantage by training multiple elements of KG in superpositions, thereby reducing the computing time further for the knowledge graph embedding model.
In this work, we propose the first quantum Ansätze for the statistical relational learning on knowledge graphs using parametric quantum circuits. We introduce two types of variational quantum circuits for knowledge graph embedding. Inspired by the classical representation learning, we first consider latent features for entities as coefficients of quantum states, while predicates are characterized by parametric gates acting on the quantum states. For the first model, the quantum advantages disappear when it comes to the optimization of this model. Therefore, we introduce a second quantum circuit model where embeddings of entities are generated from parameterized quantum gates acting on the pure quantum state. The benefit of the second method is that the quantum embeddings can be trained efficiently meanwhile preserving the quantum advantages. We show the proposed methods can achieve comparable results to the state-of-the-art classical models, e.g., RESCAL, DistMult. Furthermore, after optimizing the models, the complexity of inductive inference on the knowledge graphs might be reduced with respect to the number of entities.
Abstract In this work, the first quantum Ansätze for the statistical relational learning on knowledge graphs using parametric quantum circuits are proposed. Two types of variational quantum circuits for knowledge graph embedding are introduced. Inspired by the classical representation learning, latent features for entities are first considered as coefficients of quantum states, while predicates are characterized by parametric gates acting on the quantum states. For the first model, the quantum advantages disappear when it comes to the optimization of this model. Therefore, a second quantum circuit model is introduced where embeddings of entities are generated from parameterized quantum gates acting on the pure quantum state. The benefit of the second method is that the quantum embeddings can be trained efficiently meanwhile preserving the quantum advantages. It is shown that the proposed methods can achieve comparable results to the state‐of‐the‐art classical models, for example, RESCAL , DistMult . Furthermore, after optimizing the models, the complexity of inductive inference on the knowledge graphs might be reduced with respect to the number of entities.
Knowledge reasoning is a critical task in information fusion systems, and its core step is reasoning missing information from existing facts to improve the knowledge graphs. Embedding-based reasoning methods and path-based reasoning methods are two mainstream knowledge reasoning methods. Embedding-based reasoning methods enable fast and direct reasoning but are limited to simple relationships between entities and exhibit poor performance in reasoning complex logical relationships. Path-based reasoning methods perform better in complex reasoning tasks, but suffer from high computational complexity, a large number of model parameters, and low reasoning efficiency. To address the aforementioned issues, this paper introduces a knowledge reasoning model called Quantum-Inspired Reinforcement Learning (QIRL). QIRL leverages quantum reinforcement learning to train a strategy network via a quantum circuit, aiming to generate and optimize reasoning paths. Quantum circuit achieves complex nonlinear operations through limited quantum reasoning paths gate operations, reducing computational complexity. In addition, this article utilizes the quantum entanglement property to encode high-dimensional data, reducing the number of model training parameters. This article evaluates the QIRL method on entity prediction task and proves that the QIRL method can effectively reduce the number of model training parameters.
Semantic knowledge graphs are large-scale triple-oriented databases for knowledge representation and reasoning. Implicit knowledge can be inferred by modeling the tensor representations generated from knowledge graphs. However, as the sizes of knowledge graphs continue to grow, classical modeling becomes increasingly computationally resource intensive. This article investigates how to capitalize on quantum resources to accelerate the modeling of knowledge graphs. In particular, we propose the first quantum machine learning algorithm for inference on tensorized data, i.e., on knowledge graphs. Since most tensor problems are NP-hard [18], it is challenging to devise quantum algorithms to support the inference task. We simplify the modeling task by making the plausible assumption that the tensor representation of a knowledge graph can be approximated by its low-rank tensor singular value decomposition, which is verified by our experiments. The proposed sampling-based quantum algorithm achieves speedup with a polylogarithmic runtime in the dimension of knowledge graph tensor.
Knowledge graphs (KGs) are informative knowledge bases for various applications such as semantic web search or question answering. Since KGs often have missing facts mainly due to large construction costs, KG completion is a fundamental problem. Nowadays, as KGs have become large-scale, KG completion has become gradually intractable for classical computers. One promising direction is to utilize quantum circuits to capture complex structural information that entities and relations in KGs have. By encoding entities into quantum states and representing relations between entities as quantum circuits running on the quantum states, it becomes able to score and predict plausible missing entities or relations. However, it is still unclear how to design the quantum circuits to enhance KG completion accuracy. In this paper, we evaluate variations of quantum circuits in terms of KG completion accuracy, and investigate the relationship between the accuracy and the quality of the circuits (e.g., expressibility and entangling capacity). The experiments using a real KG show some correlation between the completion accuracy and the goodness of the circuits.