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Statistical regularities in human language have fascinated researchers for decades, suggesting deep underlying principles governing its evolution and information structuring for efficient communication. While Zipf's Law describes the…

Physics and Society · Physics 2025-04-29 Alessandro Bellina , Vito D. P. Servedio

In this study, we investigate whether speech symbols, learned through deep learning, follow Zipf's law, akin to natural language symbols. Zipf's law is an empirical law that delineates the frequency distribution of words, forming…

Computation and Language · Computer Science 2023-09-19 Shinnosuke Takamichi , Hiroki Maeda , Joonyong Park , Daisuke Saito , Hiroshi Saruwatari

Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern…

Physics and Society · Physics 2016-05-27 Eduardo G. Altmann , Martin Gerlach

Zipf's law in language lacks a definitive origin, debated across fields. This study explains Zipf-like behavior using geometric mechanisms without linguistic elements. The Full Combinatorial Word Model (FCWM) forms words from a finite…

Methodology · Statistics 2025-11-27 Vladimir Berman

Tokenization is a fundamental step in natural language processing (NLP) and other sequence modeling domains, where the choice of vocabulary size significantly impacts model performance. Despite its importance, selecting an optimal…

Machine Learning · Computer Science 2025-07-31 Yanjin He , Qingkai Zeng , Meng Jiang

Despite being a paradigm of quantitative linguistics, Zipf's law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been…

Applications · Statistics 2016-02-17 Isabel Moreno-Sánchez , Francesc Font-Clos , Álvaro Corral

We investigate the origin of Zipf's law for words in written texts by means of a stochastic dynamical model for text generation. The model incorporates both features related to the general structure of languages and memory effects inherent…

Statistical Mechanics · Physics 2007-05-23 Damián H. Zanette , Marcelo A. Montemurro

Zipf's law has been found in many human-related fields, including language, where the frequency of a word is persistently found as a power law function of its frequency rank, known as Zipf's law. However, there is much dispute whether it is…

Computation and Language · Computer Science 2018-07-06 Shuiyuan Yu , Chunshan Xu , Haitao Liu

According to Zipf's meaning-frequency law, words that are more frequent tend to have more meanings. Here it is shown that a linear dependency between the frequency of a form and its number of meanings is found in a family of models of…

Computation and Language · Computer Science 2016-10-14 Ramon Ferrer-i-Cancho

Recent studies have investigated siamese network architectures for learning invariant speech representations using same-different side information at the word level. Here we investigate systematically an often ignored component of siamese…

Computation and Language · Computer Science 2018-08-24 Rachid Riad , Corentin Dancette , Julien Karadayi , Neil Zeghidour , Thomas Schatz , Emmanuel Dupoux

We study a deliberately simple, fully non-linguistic model of text: a sequence of independent draws from a finite alphabet of letters plus a single space symbol. A word is defined as a maximal block of non-space symbols. Within this…

Computation and Language · Computer Science 2025-11-25 Vladimir Berman

Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes…

Data Analysis, Statistics and Probability · Physics 2013-05-03 Linyuan Lu , Zi-Ke Zhang , Tao Zhou

The dependence with text length of the statistical properties of word occurrences has long been considered a severe limitation quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies…

Physics and Society · Physics 2015-06-15 Francesc Font-Clos , Gemma Boleda , Álvaro Corral

The Zipf's law is the major regularity of statistical linguistics that served as a prototype for rank-frequency relations and scaling laws in natural sciences. Here we show that the Zipf's law -- together with its applicability for a single…

Data Analysis, Statistics and Probability · Physics 2015-06-15 Armen E. Allahverdyan , Weibing Deng , Q. A. Wang

We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…

Physics and Society · Physics 2025-04-16 Kim Chol-jun

The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word-usage earlier in that sentence. We study a simple…

Physics and Society · Physics 2015-05-28 Stefan Thurner , Rudolf Hanel , Bo Liu , Bernat Corominas-Murtra

Zipf's law is the main regularity of quantitative linguistics. Despite of many works devoted to foundations of this law, it is still unclear whether it is only a statistical regularity, or it has deeper relations with information-carrying…

Computation and Language · Computer Science 2018-09-25 Weibing Deng , Armen E. Allahverdyan

Zipf's law is a fundamental paradigm in the statistics of written and spoken natural language as well as in other communication systems. We raise the question of the elementary units for which Zipf's law should hold in the most natural way,…

Physics and Society · Physics 2015-07-14 Alvaro Corral , Gemma Boleda , Ramon Ferrer-i-Cancho

The task of text segmentation may be undertaken at many levels in text analysis---paragraphs, sentences, words, or even letters. Here, we focus on a relatively fine scale of segmentation, hypothesizing it to be in accord with a stochastic…

Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component…

Statistical Mechanics · Physics 2018-12-05 Andrea Mazzolini , Alberto Colliva , Michele Caselle , Matteo Osella
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