# Permutation invariant matrix statistics and computational language tasks

arXiv: https://arxiv.org/abs/2202.06829 · HTML: https://mlsanity.com/paper/2202.06829/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 69 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [SimLex-999: Evaluating Semantic Models with (Genuine) Similarity Estimation](https://mlsanity.com/paper/1408.3456/) (2014)
- [SimVerb-3500: A Large-Scale Evaluation Set of Verb Similarity](https://mlsanity.com/paper/1608.00869/) (2016)
- [Specialising Word Vectors for Lexical Entailment](https://mlsanity.com/paper/1710.06371/) (2017)
- [Integrating Distributional Lexical Contrast into Word Embeddings for Antonym-Synonym Distinction](https://mlsanity.com/paper/1605.07766/) (2016)
- [Computing Lexical Contrast](https://mlsanity.com/paper/1308.6300/) (2013)
- [Multi-Step Regression Learning for Compositional Distributional Semantics](https://mlsanity.com/paper/1301.6939/) (2013)
- [The Lifted Matrix-Space Model for Semantic Composition](https://mlsanity.com/paper/1711.03602/) (2017)
- [Permutation Invariant Gaussian Matrix Models](https://mlsanity.com/paper/1809.07559/) (2018)
- [Gaussianity and typicality in matrix distributional semantics](https://mlsanity.com/paper/1912.10839/) (2019)

## 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.