Permutation invariant matrix statistics and computational language tasks

Huber, Manuel Accettulli; Correia, Adriana; Ramgoolam, Sanjaye; Sadrzadeh, Mehrnoosh

Permutation invariant matrix statistics and computational language tasks

Feb 14, 2022

34 pages

e-Print:

2202.06829 [cs.CL]

Report number:

QMUL-PH-22-02,
SAGEX-22-21-E

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Abstract: (arXiv)

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.

Note:

34 pages, 4 figures, GitHub link available in the paper ; Revised version - improved discussion of statistical uncertainties

statistics
matrix model
statistical
information theory
graph theory
programming

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Figures(5)

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