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Background: Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication.…

Computation and Language · Computer Science 2009-11-11 Eduardo G. Altmann , Janet B. Pierrehumbert , Adilson E. Motter

Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed…

Physics and Society · Physics 2020-02-17 Juan Ignacio Perotti , Orlando Vito Billoni

It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes…

Physics and Society · Physics 2017-10-02 Bernat Corominas-Murtra , Rudolf Hanel , Stefan Thurner

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

Emergent communication (EmCom) with deep neural network-based agents promises to yield insights into the nature of human language, but remains focused primarily on a few subfield-specific goals and metrics that prioritize communication…

Computation and Language · Computer Science 2025-10-22 Miles Gilberti , Shane Storks , Huteng Dai

Recently, there has been a great deal of research in emergent communication on artificial agents interacting in simulated environments. Recent studies have revealed that, in general, emergent languages do not follow the compositionality…

Computation and Language · Computer Science 2023-01-30 Rishi Hazra , Sonu Dixit , Sayambhu Sen

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

We have translated fractional Brownian motion (FBM) signals into a text based on two ''letters'', as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the $\zeta '$ exponent…

Condensed Matter · Physics 2009-11-07 Ph. Bronlet , M. Ausloos

We use large language models (LLMs) to uncover long-ranged structure in English texts from a variety of sources. The conditional entropy or code length in many cases continues to decrease with context length at least to $N\sim 10^4$…

Statistical Mechanics · Physics 2026-01-01 Colin Scheibner , Lindsay M. Smith , William Bialek

The design of safety-critical agents based on large language models (LLMs) requires more than simple prompt engineering. This paper presents a comprehensive information-theoretic analysis of how rule encodings in system prompts influence…

Artificial Intelligence · Computer Science 2025-10-10 Joachim Diederich

Deep learning has been successfully applied to various tasks, but its underlying mechanism remains unclear. Neural networks associate similar inputs in the visible layer to the same state of hidden variables in deep layers. The fraction of…

Machine Learning · Computer Science 2018-03-21 Juyong Song , Matteo Marsili , Junghyo Jo

Languages are shaped by the inductive biases of their users. Using a classical referential game, we investigate how artificial languages evolve when optimised for inductive biases in humans and large language models (LLMs) via Human-Human,…

Computation and Language · Computer Science 2025-05-29 Tom Kouwenhoven , Max Peeperkorn , Roy de Kleijn , Tessa Verhoef

The choice of tokenizer can profoundly impact language model performance, yet accessible and reliable evaluations of tokenizer quality remain an open challenge. Inspired by scaling consistency, we show that smaller models can accurately…

Computation and Language · Computer Science 2025-06-04 Jonas F. Lotz , António V. Lopes , Stephan Peitz , Hendra Setiawan , Leonardo Emili

Compositionality is a hallmark of human language that not only enables linguistic generalization, but also potentially facilitates acquisition. When simulating language emergence with neural networks, compositionality has been shown to…

Computation and Language · Computer Science 2023-05-23 Emily Cheng , Mathieu Rita , Thierry Poibeau

It is widely accepted that the brain operates near a critical state, characterized by neural avalanches that follow power-law distributions. However, the functional rationale for why neural systems attain criticality remains unclear. Here,…

Neurons and Cognition · Quantitative Biology 2026-05-22 He Xiao , Xinyue Zhao , Weikang Wang

We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…

Information Theory · Computer Science 2022-11-03 Łukasz Dębowski

We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with…

Probability · Mathematics 2013-12-23 Michael J. Fox , Behrouz Touri , Jeff S. Shamma

Large language models (LLMs) exhibit failures on elementary symbolic tasks such as character counting in a word, despite excelling on complex benchmarks. Although this limitation has been noted, the internal reasons remain unclear. We use…

Computation and Language · Computer Science 2026-04-02 Ayan Datta , Mounika Marreddy , Alexander Mehler , Zhixue Zhao , Radhika Mamidi

Natural languages display a trade-off among different strategies to convey syntactic structure, such as word order or inflection. This trade-off, however, has not appeared in recent simulations of iterated language learning with neural…

Computation and Language · Computer Science 2021-09-13 Yuchen Lian , Arianna Bisazza , Tessa Verhoef

Despite the recent successes of deep learning in natural language processing (NLP), there remains widespread usage of and demand for techniques that do not rely on machine learning. The advantage of these techniques is their…

Computation and Language · Computer Science 2020-12-04 Adam Hare , Yu Chen , Yinan Liu , Zhenming Liu , Christopher G. Brinton