# Canonical Tensor Decomposition for Knowledge Base Completion

arXiv: https://arxiv.org/abs/1806.07297 · HTML: https://mlsanity.com/paper/1806.07297/

## Key facts

- Cited by 150 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2018.

## Built on by (most cited first, 30 of 150)

- [Question Answering Over Temporal Knowledge Graphs](https://mlsanity.com/paper/2106.01515/) (2021)
- [Knowledge Graph Reasoning with Relational Digraph](https://mlsanity.com/paper/2108.06040/) (2021)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [When Do Flat Minima Optimizers Work?](https://mlsanity.com/paper/2202.00661/) (2022)
- [NodePiece: Compositional and Parameter-Efficient Representations of Large Knowledge Graphs](https://mlsanity.com/paper/2106.12144/) (2021)
- [Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces](https://mlsanity.com/paper/2211.03536/) (2022)
- [Relation Prediction as an Auxiliary Training Objective for Improving Multi-Relational Graph Representations](https://mlsanity.com/paper/2110.02834/) (2021)
- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [ChronoR: Rotation Based Temporal Knowledge Graph Embedding](https://mlsanity.com/paper/2103.10379/) (2021)
- [Role-Aware Modeling for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2104.09780/) (2021)
- [Answering Complex Logical Queries on Knowledge Graphs via Query Computation Tree Optimization](https://mlsanity.com/paper/2212.09567/) (2022)
- [Logical Message Passing Networks with One-hop Inference on Atomic Formulas](https://mlsanity.com/paper/2301.08859/) (2023)
- [A Prompt-Based Knowledge Graph Foundation Model for Universal In-Context Reasoning](https://mlsanity.com/paper/2410.12288/) (2024)
- [A Multi-Task Perspective for Link Prediction with New Relation Types and Nodes](https://mlsanity.com/paper/2307.06046/) (2023)
- [Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/2110.13475/) (2021)
- [Rethinking Graph Convolutional Networks in Knowledge Graph Completion](https://mlsanity.com/paper/2202.05679/) (2022)
- [Ultrahyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.00449/) (2022)
- [How to Turn Your Knowledge Graph Embeddings into Generative Models](https://mlsanity.com/paper/2305.15944/) (2023)
- [UUKG: Unified Urban Knowledge Graph Dataset for Urban Spatiotemporal Prediction](https://mlsanity.com/paper/2306.11443/) (2023)
- [DisenKGAT: Knowledge Graph Embedding with Disentangled Graph Attention Network](https://mlsanity.com/paper/2108.09628/) (2021)
- [BiQUE: Biquaternionic Embeddings of Knowledge Graphs](https://mlsanity.com/paper/2109.14401/) (2021)
- [Geometry Interaction Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.12418/) (2022)
- [Data Scarcity in Recommendation Systems: A Survey](https://mlsanity.com/paper/2312.10073/) (2023)
- [Adversarial Attacks on Knowledge Graph Embeddings via Instance Attribution Methods](https://mlsanity.com/paper/2111.03120/) (2021)
- [Convolutional Hypercomplex Embeddings for Link Prediction](https://mlsanity.com/paper/2106.15230/) (2021)
- [Link Prediction with Attention Applied on Multiple Knowledge Graph Embedding Models](https://mlsanity.com/paper/2302.06229/) (2023)
- [EventNarrative: A large-scale Event-centric Dataset for Knowledge Graph-to-Text Generation](https://mlsanity.com/paper/2111.00276/) (2021)
- [MoSE: Modality Split and Ensemble for Multimodal Knowledge Graph Completion](https://mlsanity.com/paper/2210.08821/) (2022)
- [A Survey on Temporal Knowledge Graph Completion: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2308.02457/) (2023)
- [Searching to Sparsify Tensor Decomposition for N-ary Relational Data](https://mlsanity.com/paper/2104.10625/) (2021)

## 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.