  The Linguistic Matrix Theory programme introduced by Kartsaklis, Ramgoolam
and Sadrzadeh is an approach to the statistics of matrices that are generated
in type-driven distributional semantics, based on permutation invariant
polynomial functions which are regarded as the key observables encoding the
significant statistics. In this paper we generalize the previous results on the
approximate Gaussianity of matrix distributions arising from compositional
distributional semantics. We also introduce a geometry of observable vectors
for words, defined by exploiting the graph-theoretic basis for the permutation
invariants and the statistical characteristics of the ensemble of matrices
associated with the words. We describe successful applications of this unified
framework to a number of tasks in computational linguistics, associated with
the distinctions between synonyms, antonyms, hypernyms and hyponyms.
