相关论文: Corrections of Zipf's and Heaps' Laws Derived from…

We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution p(k) of the elements k of a population can be approximated by the…

Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language…

A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law. The same pow-like behavior is exhibited by some simple random citation models. The observed regularity indicates not so…

For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…

We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two…

We study some features of learning models based on "delayed" and undifferentiated reinforcement and realized by simple algorithms which may be considered of a very elementary nature. We show that a modification of the Hebb-rule works well…

An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is…

Current evaluation metrics for language modeling and generation rely heavily on the accuracy of predicted (or generated) words as compared to a reference ground truth. While important, token-level accuracy only captures one aspect of a…

Zipf's law appears in many application areas but does not have a closed form expression, which may make its use cumbersome. Since it coincides with the truncated version of the Zeta distribution, in this paper we propose three approximate…

It is shown that the distribution of low variability periods in the activity of human heart rate typically follows a multi-scaling Zipf's law. The presence or failure of a power law, as well as the values of the scaling exponents, are…

Existing training criteria in automatic speech recognition(ASR) permit the model to freely explore more than one time alignments between the feature and label sequences. In this paper, we use entropy to measure a model's uncertainty, i.e.…

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…

Unprecedented events intertwine with the repetition of the past in natural phenomena and human activities. Key statistical patterns, such as Heaps' and Taylor's laws and Zipf's law, have been identified as characterizing the dynamical…

When an i.i.d.\ sequence of letters is cut into words according to i.i.d.\ renewal times, an i.i.d.\ sequence of words is obtained. In the \emph{annealed} LDP (large deviation principle) for the empirical process of words, the rate function…

We consider a random generalisation of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping $\mathtt{a}\mapsto \mathtt{baa}$ and $\mathtt{b} \mapsto \mathtt{ab}$ with probability $p$ and…

This paper introduces a statistical and other analysis of peer reviewers in order to approach their "quality" through some quantification measure, thereby leading to some quality metrics. Peer reviewer reports for the Journal of the Serbian…

Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…

Heaps' law is an empirical relation in text analysis that predicts vocabulary growth as a function of corpus size. While this law has been validated in diverse human-authored text corpora, its applicability to large language model generated…

Construct recursively a long string of words w1. .. wn, such that at each step k, w k+1 is a new word with a fixed probability p $\in$ (0, 1), and repeats some preceding word with complementary probability 1 -- p. More precisely, given a…

The inverse relationship between the length of a word and the frequency of its use, first identified by G.K. Zipf in 1935, is a classic empirical law that holds across a wide range of human languages. We demonstrate that length is one…