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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

Tokenization is a fundamental component of large language models (LLMs), yet its influence on model scaling and performance is not fully explored. In this paper, we introduce Over-Tokenized Transformers, a novel framework that decouples…

Computation and Language · Computer Science 2025-05-26 Hongzhi Huang , Defa Zhu , Banggu Wu , Yutao Zeng , Ya Wang , Qiyang Min , Xun Zhou

We cast neural machine translation (NMT) as a classification task in an autoregressive setting and analyze the limitations of both classification and autoregression components. Classifiers are known to perform better with balanced class…

Computation and Language · Computer Science 2021-04-06 Thamme Gowda , Jonathan May

Large language models (LLMs) sometimes fail to respond appropriately to deterministic tasks -- such as counting or forming acronyms -- because the implicit prior distribution they have learned over sequences of tokens influences their…

Computation and Language · Computer Science 2025-04-18 Liyi Zhang , Veniamin Veselovsky , R. Thomas McCoy , Thomas L. Griffiths

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…

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…

Machine Learning · Computer Science 2022-11-01 Alexander Maloney , Daniel A. Roberts , James Sully

Scaling properties of language are a useful tool for understanding generative processes in texts. We investigate the scaling relations in citywise Twitter corpora coming from the Metropolitan and Micropolitan Statistical Areas of the United…

Physics and Society · Physics 2019-03-12 Eszter Bokányi , Dániel Kondor , Gábor Vattay

Tokenization is an understudied and often neglected component of modern LLMs. Most published works use a single tokenizer for all experiments, often borrowed from another model, without performing ablations or analysis to optimize…

Computation and Language · Computer Science 2024-02-08 Gautier Dagan , Gabriel Synnaeve , Baptiste Rozière

Large language models (LLMs) have been widely employed across various application domains, yet their black-box nature poses significant challenges to understanding how these models process input data internally to make predictions. In this…

Machine Learning · Computer Science 2025-09-03 Hangfeng He , Weijie J. Su

Recent work has shown that larger language models have better predictive power for eye movement and reading time data. While even the best models under-allocate probability mass to human responses, larger models assign higher-quality…

Computation and Language · Computer Science 2026-02-23 Cassandra L. Jacobs , Morgan Grobol

Scaling laws aim to accurately predict model performance across different scales. Existing scaling-law studies almost exclusively rely on cross-entropy as the evaluation metric. However, cross-entropy provides only a partial view of…

Machine Learning · Computer Science 2025-10-24 Baoqing Yue , Jinyuan Zhou , Zixi Wei , Jingtao Zhan , Qingyao Ai , Yiqun Liu

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

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

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

While scaling laws for Large Language Models (LLMs) traditionally focus on proxy metrics like pretraining loss, predicting downstream task performance has been considered unreliable. This paper challenges that view by proposing a direct…

Machine Learning · Computer Science 2025-12-10 Jakub Krajewski , Amitis Shidani , Dan Busbridge , Sam Wiseman , Jason Ramapuram

Neural language models typically tokenise input text into sub-word units to achieve an open vocabulary. The standard approach is to use a single canonical tokenisation at both train and test time. We suggest that this approach is…

Computation and Language · Computer Science 2021-09-22 Kris Cao , Laura Rimell

The frequency distributions of DNA k-mers are shaped by fundamental biological processes and offer a window into genome structure and evolution. Inspired by analogies to natural language, prior studies have attempted to model genomic k-mer…

While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper presents a systematic empirical…

This paper investigates the classification capability of small-scale spiking neural networks based on the Leaky Integrate-and-Fire (LIF) neuron model. We analyze the relationship between classification accuracy and three factors: the number…

Neurons and Cognition · Quantitative Biology 2026-01-22 Zhengdi Zhang , Cong Han , Wenjun Xia

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