Permutation invariant matrix statistics and computational language tasks
This work addresses the problem of improving semantic distinctions in computational linguistics, but it appears incremental as it builds on prior Linguistic Matrix Theory results.
The paper generalizes previous results on the approximate Gaussianity of matrix distributions in compositional distributional semantics and introduces a geometry of observable vectors for words based on permutation invariants and matrix statistics. It applies this framework to computational linguistics tasks, successfully distinguishing synonyms, antonyms, hypernyms, and hyponyms.
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.