Linguistic Matrix Theory
This work addresses the challenge of understanding universality in statistical properties of word matrices for computational linguistics, though it appears incremental as it builds on existing compositional distributional semantics.
The authors tackled the problem of modeling word matrices in computational linguistics by proposing a Matrix Theory approach based on permutation symmetry and Gaussian perturbations, which they tested on a large text corpus to characterize departures from the model as signatures for comparing linguistic corpora.
Recent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a vector space of context words. They are used to construct the meaning of composite expressions from that of the elementary constituents, forming part of a compositional distributional approach to semantics. We propose a Matrix Theory approach to this data, based on permutation symmetry along with Gaussian weights and their perturbations. A simple Gaussian model is tested against word matrices created from a large corpus of text. We characterize the cubic and quartic departures from the model, which we propose, alongside the Gaussian parameters, as signatures for comparison of linguistic corpora. We propose that perturbed Gaussian models with permutation symmetry provide a promising framework for characterizing the nature of universality in the statistical properties of word matrices. The matrix theory framework developed here exploits the view of statistics as zero dimensional perturbative quantum field theory. It perceives language as a physical system realizing a universality class of matrix statistics characterized by permutation symmetry.