Permutation invariant matrix statistics and computational language tasks

The Linguistic Matrix Theory (LMT) programme [1, 2] proposes to use permutation invariant random matrix theories to model the statistical properties of ensembles of matrices arising from machine learning algorithms that learn natural language semantics in the subfields of Computational Linguistics and Natural Language Processing in Artificial 1 Intelligence. The use of vectors to represent word meanings has a well-established history in Computational Linguistics (see for example [3]). This usage was initiated in the field of distributional semantics, the ideas behind which are succinctly captured by J. R. Firth's famous quote "You shall know the meaning of a word by the company it keeps" [38]. Advances in neural network machine learning in Natural Language Processing have led to algorithms that learn meaning vectors from large corpora of text. One such algorithm applied to mining the semantic relation of similarity between words is word2vec [12]. Word2vec has been successfully experimented with in a variety of tasks and datasets (see e.g.