Semiring parsing is an elegant framework for describing parsers by using semiring weighted logic programs. In this paper we present a generalization of this concept: latent-variable semiring parsing. With our framework, any semiring weighted logic program can be latentified by transforming weights from scalar values of a semiring to rank-n arrays, or tensors, of semiring values, allowing the modelling of latent-variable models within the semiring parsing framework. Semiring is too strong a notion when dealing with tensors, and we have to resort to a weaker structure: a partial semiring. We prove that this generalization preserves all the desired properties of the original semiring framework while strictly increasing its expressiveness.

Bilinear models such as DistMult and ComplEx are effective methods for knowledge graph (KG) completion. However, they require large batch sizes, which becomes a performance bottleneck when training on large scale datasets due to memory constraints. In this paper we use occurrences of entity-relation pairs in the dataset to construct a joint learning model and to increase the quality of sampled negatives during training. We show on three standard datasets that when these two techniques are combined, they give a significant improvement in performance, especially when the batch size and the number of generated negative examples are low relative to the size of the dataset. We then apply our techniques to a dataset containing 2 million entities and demonstrate that our model outperforms the baseline by 2.8% absolute on hits@1.