Knowledge Graph Completion via Complex Tensor Factorization

By Théo Trouillon, Christopher R. Dance, Éric Gaussier, Johannes Welbl, Sebastian Riedel, Guillaume Bouchard. Journal of machine learning research, 2017

331 citations recorded by the source corpus.

In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices---thus all possible relation/adjacency matrices---are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.

Subfields: Artificial Intelligence, Computational Mathematics, Information Systems

View Paper: https://www.semanticscholar.org/paper/a4dfb121275a6408d290b803baf8c9caeb23dc5b

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Citations in the corpus

TuckER: Tensor Factorization for Knowledge Graph Completion (2019, background): “As shown in (Trouillon et al., 2017), ComplEx is fully expressive with the bound on entity and relation embedding dimensionality of de = dr = ne · nr for achieving full expressiveness.”
Facts as Experts: Adaptable and Interpretable Neural Memory over Symbolic Knowledge (2020, background): “More recently, the past decade has seen huge amount of work on knowledge base embeddings (Bordes et al., 2013; Lin et al., 2015; Trouillon et al., 2017; Dettmers et al., 2018) which enable generalization through similarities between learned embeddings.”
Representation Learning for Dynamic Graphs: A Survey (2019, background): “Kazemi and Poole (2018c), Trouillon et al. (2017), Fatemi et al. (2019a), Balažević et al. (2019) and several other works provide expressivity results for models operating on KGs (see Section 3.2.2).”
Relational Representation Learning for Dynamic (Knowledge) Graphs: A Survey (2019, background): “While a few recent works study the expressiveness of some models for (knowledge) graphs [219, 115, 238, 164], a more detailed and in-depth study of the expressiveness and its empirical impact may be a promising direction for future research.”
Revisiting Evaluation of Knowledge Base Completion Models (2020, methodology): “By using different scoring functions that capture the uncertainty in each fact [Trouillon et al., 2017, Dettmers et al., 2018, Sun et al., 2019a], such knowledge graph completion models have achieved tremendous success on existing benchmarks.”
Diachronic Embedding for Temporal Knowledge Graph Completion (2019, background): “Expressivity is an important property and has been the subject of study in several recent works on static (knowledge) graphs (Trouillon et al. 2017; Kazemi and Poole 2018b; Xu et al. 2019; Fatemi, Ravanbakhsh, and Poole 2019).”
Inductive Relation Prediction by Subgraph Reasoning (2019, methodology): “We ensemble GraIL with each of TransE (Bordes et al., 2013), DistMult (Yang et al., 2014), ComplEx (Trouillon et al., 2017), and RotatE (Sun et al., 2019) which constitute a representative set of KGE methods.”
SimplE Embedding for Link Prediction in Knowledge Graphs (2018, methodology): “We also show that the function used in ComplEx [39, 40], a state-of-the-art approach for link prediction, involves redundant computations.”
Deep learning for noise-tolerant RDFS reasoning (2019, methodology): “This category includes RESCAL [59], DistMul [60] where Mr is simplified to a diagonal matrix, ComplEx [61] which extends DistMul by using complex valued embedding in order to support asymmetric relations.”