Knowledge Graph Embedding

RotatE is a method for generating graph embeddings which is able to model and infer various relation patterns including: symmetry/antisymmetry, inversion, and composition. Specifically, the RotatE model defines each relation as a rotation from the source entity to the target entity in the complex vector space. The RotatE model is trained using a self-adversarial negative sampling technique.

MEI introduces the multi-partition embedding interaction technique with block term tensor format to systematically address the efficiency--expressiveness trade-off in knowledge graph embedding. It divides the embedding vector into multiple partitions and learns the local interaction patterns from data instead of using fixed special patterns as in ComplEx or SimplE models. This enables MEI to achieve optimal efficiency--expressiveness trade-off, not just being fully expressive. Previous methods such as TuckER, RESCAL, DistMult, ComplEx, and SimplE are suboptimal restricted special cases of MEI.

To avoid the problem caused by low-frequent entity-relation pairs, our MBS uses the estimated probabilities from a trained model $\mathbf{\theta}'$ to calculate frequencies for each triplet and query. By using $\mathbf{\theta}'$, the NS loss in KGE with MBS is represented as follows: \begin{align} &\ell_{mbs}(\mathbf{\theta};\mathbf{\theta}') \nonumber \ =&-\frac{1}{|D|}\sum_{(x,y) \in D} \Bigl[A_{mbs}(\mathbf{\theta}')\log(\sigma(s_{\mathbf{\theta}}(x,y)+\gamma))\nonumber\ &+\frac{1}{\nu}sum_{y_{i}\sim p_n(y_{i}|x)}^{\nu}B_{mbs}(\mathbf{\theta}')\log(\sigma(-s_{\mathbf{\theta}}(x,y_i)-\gamma))\Bigr], \end{align}

CP with N3 Regularizer and Relation Prediction

ComplEx model trained with a nuclear norm regularizer; A relation prediction objective is added on top of the commonly used 1vsAll objective.

RESCAL model trained with a relation prediction objective on top of the 1vsAll loss

TuckER model trained with a relation prediction objective on top of the 1vsAll loss