  Knowledge graph embedding research has mainly focused on learning continuous
representations of entities and relations tailored towards the link prediction
problem. Recent results indicate an ever increasing predictive ability of
current approaches on benchmark datasets. However, this effectiveness often
comes with the cost of over-parameterization and increased computationally
complexity. The former induces extensive hyperparameter optimization to
mitigate malicious overfitting. The latter magnifies the importance of winning
the hardware lottery. Here, we investigate a remedy for the first problem. We
propose a technique based on Kronecker decomposition to reduce the number of
parameters in a knowledge graph embedding model, while retaining its
expressiveness. Through Kronecker decomposition, large embedding matrices are
split into smaller embedding matrices during the training process. Hence,
embeddings of knowledge graphs are not plainly retrieved but reconstructed on
the fly. The decomposition ensures that elementwise interactions between three
embedding vectors are extended with interactions within each embedding vector.
This implicitly reduces redundancy in embedding vectors and encourages feature
reuse. To quantify the impact of applying Kronecker decomposition on embedding
matrices, we conduct a series of experiments on benchmark datasets. Our
experiments suggest that applying Kronecker decomposition on embedding matrices
leads to an improved parameter efficiency on all benchmark datasets. Moreover,
empirical evidence suggests that reconstructed embeddings entail robustness
against noise in the input knowledge graph. To foster reproducible research, we
provide an open-source implementation of our approach, including training and
evaluation scripts as well as pre-trained models in our knowledge graph
embedding framework (https://github.com/dice-group/dice-embeddings).
