Permutation invariant matrix statistics and computational language tasks
Abstract
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.
Cite
@article{arxiv.2202.06829,
title = {Permutation invariant matrix statistics and computational language tasks},
author = {Manuel Accettulli Huber and Adriana Correia and Sanjaye Ramgoolam and Mehrnoosh Sadrzadeh},
journal= {arXiv preprint arXiv:2202.06829},
year = {2023}
}
Comments
34 pages, 4 figures, GitHub link available in the paper ; Revised version - improved discussion of statistical uncertainties