A Random Matrix Approach to Language Acquisition

TL;DR

This paper models language acquisition using a random matrix approach, revealing how innate ability and lexicon size are exponentially related, which explains biological language differences and potential for rapid vocabulary growth.

Contribution

It introduces a novel physics-inspired random matrix model for protolanguage, linking innate ability and lexicon size with analytical and simulation methods.

Findings

Lexicon size grows exponentially with innate language ability

Small increases in innate ability can lead to large vocabulary expansions

Model explains biological language diversity and acquisition dynamics

Abstract

Since language is tied to cognition, we expect the linguistic structures to reflect patterns we encounter in nature and analyzed by physics. Within this realm we investigate the process of protolanguage acquisition, using analytical and tractable methods developed within physics. A protolanguage is a mapping between sounds and objects (or concepts) of the perceived world. This mapping is represented by a matrix and the linguistic interaction among individuals is described by a random matrix model. There are two essential parameters in our approach. The strength of the linguistic interaction $\beta$, which following Chomsky's tradition, we consider as a genetically determined ability, and the number $N$ of employed sounds (the lexicon size). Our model of linguistic interaction is analytically studied using methods of statistical physics and simulated by Monte Carlo techniques. The analysis reveals an intricate relationship between the innate propensity for language acquisition $\beta$ and the lexicon size $N$, $N \sim \exp(\beta)$. Thus a small increase of the genetically determined $\beta$ may lead to an incredible lexical explosion. Our approximate scheme offers an explanation for the biological affinity of different species and their simultaneous linguistic disparity.