Tensors over Semirings for Latent-Variable Weighted Logic Programs

TL;DR

This paper extends semiring parsing by introducing tensor-based weights to model latent variables, preserving core properties while increasing expressiveness in logic programming.

Contribution

It generalizes semiring parsing to tensor weights, enabling latent variable modeling while maintaining the framework's fundamental properties.

Findings

Preserves properties of semiring parsing with tensor weights.

Introduces partial semirings for tensor-based weights.

Enhances expressiveness of logic programs with latent variables.

Abstract

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.