Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is the task of inferring missing facts based on existing ones. We propose TuckER, a relatively simple yet powerful linear model based on Tucker decomposition of the binary tensor representation of knowledge graph triples. By using this particular decomposition, parameters are shared between relations, enabling multi-task learning. TuckER outperforms previous state-of-the-art models across several standard link prediction datasets. Vast amounts of information available in the world can be represented succinctly as entities and relations between them. Knowledge graphs are large, graph-structured databases which store facts in triple form (e s , r, e o ), with e s and e o representing subject and object entities and r a relation. However, far from all available information is stored in existing knowledge graphs, which creates the need for algorithms that automatically infer missing facts. Knowledge graphs can be represented by a third-order binary tensor, where each element corresponds to a triple, 1 indicating a true fact and 0 indicating the unknown (either a false or a missing fact). The task of link prediction is to infer which of the 0 entries in the tensor are indeed false, and which are missing but actually true.A large number of approaches to link prediction so far have been linear, based on various methods of factorizing the third-order binary tensor BID12 BID22 BID19 BID7 . Recently, state-of-the-art results have been achieved using non-linear convolutional models BID3 BID0 . Despite achieving very good per- formance, the fundamental problem with deep, non-linear models is that they are non-transparent and poorly understood, as opposed to more mathematically principled and widely studied tensor decomposition models.In this paper, we introduce TuckER (E stands for entities, R for relations), a simple linear model for link prediction in knowledge graphs, based on Tucker decomposition BID21 of the binary tensor of triples. Tucker decomposition factorizes a tensor into a core tensor multiplied by a matrix along each mode. In our case, rows of the matrices contain entity and relation embeddings, while entries of the core tensor determine the level of interaction between them. Due to having the core tensor, unlike simpler models, such as RESCAL, DistMult and ComplEx, where parameters for each relation are often learned separately, TuckER makes use of multi-task learning between different relations BID24 . Subject and object entity embedding matrices are assumed equivalent, i.e. we make no distinction between the embeddings of an entity depending on whether it appears as a subject or as an object in a particular triple. Our experiments show that TuckER achieves state-of-the-art results across all standard link prediction datasets. In this work, we introduce TuckER, a relatively simple yet highly flexible linear model for link prediction in knowledge graphs based on the Tucker decomposition of a binary tensor of training set triples, which achieves state-of-the-art results on several standard link prediction datasets. TuckER's number of parameters grows linearly with respect to embedding dimension as the number of entities or relations in a knowledge graph increases, which makes it easily scalable to large knowledge graphs. Future work might include exploring how to incorporate background knowledge on individual relation properties into the existing model.
 We propose TuckER, a relatively simple but powerful linear model for link prediction in knowledge graphs, based on Tucker decomposition of the binary tensor representation of knowledge graph triples. 
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