Composing distributions: mathematical structures and their linguistic interpretation

The goal of this paper is to consider the mathematical operations proposed in the literature for composing distributional vectors using mixture models, and assess their linguistic plausibility by looking at various aspects of their behaviour. We explore representational issues related to the space in which distributional vectors live, and to the ways composition operations affect that space. Having generally argued in favour of pointwise operations, we investigate which of those allow for full recursivity and conclude with an extensive discussion of additive and multiplicative models. Our claims are supported both by experimental results from the literature on distributional compositionality and linguistic considerations on the representation of lexical meaning.