mlsanityData to 7 Oct 2026

Canonical Tensor Decomposition for Knowledge Base Completion

arXiv 1806.07297 ↗First posted 19 Jun 2018stat.ML cs.AI cs.LGcited by 150

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Abstract (arXiv)

The problem of Knowledge Base Completion can be framed as a 3rd-order binary tensor completion problem. In this light, the Canonical Tensor Decomposition (CP) (Hitchcock, 1927) seems like a natural solution; however, current implementations of CP on standard Knowledge Base Completion benchmarks are lagging behind their competitors. In this work, we attempt to understand the limits of CP for knowledge base completion. First, we motivate and test a novel regularizer, based on tensor nuclear p-norms. Then, we present a reformulation of the problem that makes it invariant to arbitrary choices in the inclusion of predicates or their reciprocals in the dataset. These two methods combined allow us to beat the current state of the art on several datasets with a CP decomposition, and obtain even better results using the more advanced ComplEx model.

Key facts. Cited by 150 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 38; 2022: 35; 2023: 26; 2024: 22; 2025: 18; 2026: 11.

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  1. 2021Question Answering Over Temporal Knowledge Graphscited by 99
  2. 2021Knowledge Graph Reasoning with Relational Digraphcited by 91
  3. 2021ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphscited by 78
  4. 2022When Do Flat Minima Optimizers Work?cited by 78
  5. 2021NodePiece: Compositional and Parameter-Efficient Representations of Large Knowledge Graphscited by 71
  6. 2022Knowledge Graph Embedding: A Survey from the Perspective of Representation Spacescited by 41
  7. 2021Relation Prediction as an Auxiliary Training Objective for Improving Multi-Relational Graph Representationscited by 37
  8. 2023Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databasescited by 35
  9. 2021ChronoR: Rotation Based Temporal Knowledge Graph Embeddingcited by 34
  10. 2021Role-Aware Modeling for N-ary Relational Knowledge Basescited by 29
  11. 2022Answering Complex Logical Queries on Knowledge Graphs via Query Computation Tree Optimizationcited by 28
  12. 2023Logical Message Passing Networks with One-hop Inference on Atomic Formulascited by 28
38 more
  1. 2024A Prompt-Based Knowledge Graph Foundation Model for Universal In-Context Reasoningcited by 25
  2. 2023A Multi-Task Perspective for Link Prediction with New Relation Types and Nodescited by 23
  3. 2021Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matricescited by 22
  4. 2022Rethinking Graph Convolutional Networks in Knowledge Graph Completioncited by 20
  5. 2022Ultrahyperbolic Knowledge Graph Embeddingscited by 20
  6. 2023How to Turn Your Knowledge Graph Embeddings into Generative Modelscited by 20
  7. 2023UUKG: Unified Urban Knowledge Graph Dataset for Urban Spatiotemporal Predictioncited by 20
  8. 2021DisenKGAT: Knowledge Graph Embedding with Disentangled Graph Attention Networkcited by 19
  9. 2021BiQUE: Biquaternionic Embeddings of Knowledge Graphscited by 19
  10. 2022Geometry Interaction Knowledge Graph Embeddingscited by 18
  11. 2023Data Scarcity in Recommendation Systems: A Surveycited by 17
  12. 2021Adversarial Attacks on Knowledge Graph Embeddings via Instance Attribution Methodscited by 16
  13. 2021Convolutional Hypercomplex Embeddings for Link Predictioncited by 15
  14. 2023Link Prediction with Attention Applied on Multiple Knowledge Graph Embedding Modelscited by 15
  15. 2021EventNarrative: A large-scale Event-centric Dataset for Knowledge Graph-to-Text Generationcited by 14
  16. 2022MoSE: Modality Split and Ensemble for Multimodal Knowledge Graph Completioncited by 14
  17. 2023A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospectscited by 14
  18. 2021Searching to Sparsify Tensor Decomposition for N-ary Relational Datacited by 13
  19. 2021Trans4E: Link Prediction on Scholarly Knowledge Graphscited by 13
  20. 2023Adapting Neural Link Predictors for Data-Efficient Complex Query Answeringcited by 13
  21. 2021Context-aware Entity Typing in Knowledge Graphscited by 12
  22. 2022ReFactor GNNs: Revisiting Factorisation-based Models from a Message-Passing Perspectivecited by 12
  23. 2022SMiLE: Schema-augmented Multi-level Contrastive Learning for Knowledge Graph Link Predictioncited by 12
  24. 2023Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictorscited by 12
  25. 2021Bilinear Scoring Function Search for Knowledge Graph Learningcited by 11
  26. 2021Knowledge Hypergraph Embedding Meets Relational Algebracited by 10
  27. 2023Knowledge Graph Embeddings in the Biomedical Domain: Are They Useful? A Look at Link Prediction, Rule Learning, and Downstream Polypharmacy Taskscited by 9
  28. 2024A Unified Temporal Knowledge Graph Reasoning Model Towards Interpolation and Extrapolationcited by 9
  29. 2021Multiple Run Ensemble Learning with Low-Dimensional Knowledge Graph Embeddingscited by 8
  30. 2021Efficient Relation-aware Scoring Function Search for Knowledge Graph Embeddingcited by 8
  31. 2021Self-attention Presents Low-dimensional Knowledge Graph Embeddings for Link Predictioncited by 8
  32. 2023Toward Practical Entity Alignment Method Design: Insights from New Highly Heterogeneous Knowledge Graph Datasetscited by 8
  33. 2021Combining Rules and Embeddings via Neuro-Symbolic AI for Knowledge Base Completioncited by 7
  34. 2022On the Convergence of mSGD and AdaGrad for Stochastic Optimizationcited by 7
  35. 2022Duality-Induced Regularizer for Semantic Matching Knowledge Graph Embeddingscited by 7
  36. 2022KGTuner: Efficient Hyper-parameter Search for Knowledge Graph Learningcited by 7
  37. 2024Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterizationcited by 7
  38. 2021Switch Spaces: Learning Product Spaces with Sparse Gatingcited by 6

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