  Words can have multiple senses. Compositional distributional models of
meaning have been argued to deal well with finer shades of meaning variation
known as polysemy, but are not so well equipped to handle word senses that are
etymologically unrelated, or homonymy. Moving from vectors to density matrices
allows us to encode a probability distribution over different senses of a word,
and can also be accommodated within a compositional distributional model of
meaning. In this paper we present three new neural models for learning density
matrices from a corpus, and test their ability to discriminate between word
senses on a range of compositional datasets. When paired with a particular
composition method, our best model outperforms existing vector-based
compositional models as well as strong sentence encoders.
