Tensors over Semirings for Latent-Variable Weighted Logic Programs
This is an incremental extension of the semiring parsing framework for natural language processing.
The paper tackles the problem of incorporating latent variables into semiring parsing by generalizing weights from scalars to tensors, proving that this preserves original properties while increasing expressiveness.
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 variables 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.