On the Correspondence between Compositional Matrix-Space Models of Language and Weighted Automata

摘要

Compositional matrix-space models of language were recently proposed for the task of meaning representation of complex text structures in natural language processing. These models have been shown to be a theoretically elegant way to model com-positionality in natural language. However, in practical cases, appropriate methods are required to learn such models by automatically acquiring the necessary token-to-matrix assignments. In this paper, we introduce graded matrix grammars of natural language, a variant of the matrix grammars proposed by Rudolph and Giesbrecht (2010), and show a close correspondence between this matrix-space model and weighted finite automata. We conclude that the problem of learning compositional matrix-space models can be mapped to the problem of learning weighted finite automata over the real numbers.