Correlation Dimension of Natural Language in a Statistical Manifold

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Hauptverfasser: Du, Xin, Tanaka-Ishii, Kumiko
Format: Preprint
Veröffentlicht: 2024
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author Du, Xin
Tanaka-Ishii, Kumiko
author_facet Du, Xin
Tanaka-Ishii, Kumiko
contents The correlation dimension of natural language is measured by applying the Grassberger-Procaccia algorithm to high-dimensional sequences produced by a large-scale language model. This method, previously studied only in a Euclidean space, is reformulated in a statistical manifold via the Fisher-Rao distance. Language exhibits a multifractal, with global self-similarity and a universal dimension around 6.5, which is smaller than those of simple discrete random sequences and larger than that of a Barabási-Albert process. Long memory is the key to producing self-similarity. Our method is applicable to any probabilistic model of real-world discrete sequences, and we show an application to music data.
format Preprint
id arxiv_https___arxiv_org_abs_2405_06321
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Correlation Dimension of Natural Language in a Statistical Manifold
Du, Xin
Tanaka-Ishii, Kumiko
Computation and Language
Statistical Mechanics
Artificial Intelligence
The correlation dimension of natural language is measured by applying the Grassberger-Procaccia algorithm to high-dimensional sequences produced by a large-scale language model. This method, previously studied only in a Euclidean space, is reformulated in a statistical manifold via the Fisher-Rao distance. Language exhibits a multifractal, with global self-similarity and a universal dimension around 6.5, which is smaller than those of simple discrete random sequences and larger than that of a Barabási-Albert process. Long memory is the key to producing self-similarity. Our method is applicable to any probabilistic model of real-world discrete sequences, and we show an application to music data.
title Correlation Dimension of Natural Language in a Statistical Manifold
topic Computation and Language
Statistical Mechanics
Artificial Intelligence
url https://arxiv.org/abs/2405.06321