Cover Image

From Zipf's Law to Neural Scaling through Heaps' Law and Hilberg's Hypothesis

Fuente: arXiv

Saved in:

Bibliographic Details
Main Author:	Dębowski, Łukasz
Format:	Preprint
Published:	2025
Subjects:	Information Theory Machine Learning Statistics Theory 94A17 (Primary) 60G10, 91F20, 68T07 (Secondary)
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Multiperiodic Processes: Ergodic Sources with a Sublinear Entropy
by: Dębowski, Łukasz
Published: (2023)

Repetition and recurrence times: Dual statements and summable mixing rates
by: Dębowski, Łukasz
Published: (2023)

From Letters to Words and Back: Invertible Coding of Stationary Measures
by: Dębowski, Łukasz
Published: (2024)

Wide stable neural networks: Sample regularity, functional convergence and Bayesian inverse problems
by: Soto, Tomás
Published: (2024)

High-dimensional learning dynamics of multi-pass Stochastic Gradient Descent in multi-index models
by: Fan, Zhou, et al.
Published: (2026)

Simple and Sharp Generalization Bounds via Lifting
by: Liu, Jingbo
Published: (2025)

Generalized Fisher-Darmois-Koopman-Pitman Theorem and Rao-Blackwell Type Estimators for Power-Law Distributions
by: Gayen, Atin, et al.
Published: (2022)

Paths of Stochastic Processes: a Sudden Turnaround
by: Schaback, Robert, et al.
Published: (2024)

American Options Pricing under Heston Model via Curriculum Learning in Coupled PINNs
by: Rohan, et al.
Published: (2026)

Bankruptcy analysis using images and convolutional neural networks (CNN)
by: Tavares, Luiz, et al.
Published: (2025)

Normalized Fractional Order Entropy-Based Decision-Making Models under Risk
by: Paul, Poulami, et al.
Published: (2026)

On the Asymptotics of Importance Weighted Variational Inference
by: Cherief-Abdellatif, Badr-Eddine, et al.
Published: (2025)

On Finite Time Span Estimators of Parameters for Ornstein-Uhlenbeck Processes
by: Han, Jun S., et al.
Published: (2025)

Laws of Large Numbers for Information Resolution
by: Raban, Daniel
Published: (2025)

Functional Large Deviations for Wide Deep Neural Networks with Gaussian Initialization and Lipschitz Activations
by: Macci, Claudio, et al.
Published: (2026)

Predictive Inference via Kernel Density Estimates
by: Hilbert, Torey
Published: (2026)

Multiple rational normal forms in Lie theory
by: Voloshyn, Dmitriy
Published: (2025)

Approximating $f$-Divergences with Rank Statistics
by: Stein, Viktor, et al.
Published: (2026)

Ties, Tails and Spectra: On Rank-Based Dependency Measures in High Dimensions
by: Dörnemann, Nina, et al.
Published: (2025)

Feature Learning in Wide Neural Networks under $μ$P: Identifiability and Sparse-Dictionary Decomposition of the Mean-Field Limit
by: Xodarev, Akmal
Published: (2026)

Asymptotic e-processes
by: Massiani, Pierre-François, et al.
Published: (2026)

An Exponential Averaging Process with Strong Convergence Properties
by: Köhne, Frederik, et al.
Published: (2025)

The Theorems of Dr. David Blackwell and Their Contributions to Artificial Intelligence
by: Paxton, Napoleon
Published: (2026)

A Characterization of Complexity in Public Goods Games
by: Gilboa, Matan
Published: (2023)

Nonparametric estimation of a factorizable density using diffusion models
by: Kwon, Hyeok Kyu, et al.
Published: (2025)

BrainIB++: Leveraging Graph Neural Networks and Information Bottleneck for Functional Brain Biomarkers in Schizophrenia
by: Hu, Tianzheng, et al.
Published: (2025)

A mathematical study of the excess growth rate
by: Campbell, Steven, et al.
Published: (2025)

Convergence rates of non-stationary and deep Gaussian process regression
by: Osborne, Conor, et al.
Published: (2023)

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences
by: Gorsky, Mikhail, et al.
Published: (2025)

Quantitative Error Bounds for Scaling Limits of Stochastic Iterative Algorithms
by: Wang, Xiaoyu, et al.
Published: (2025)

Fractional order entropy-based decision-making models under risk
by: Paul, Poulami, et al.
Published: (2025)

Bivariate change point detection in movement direction and speed
by: Plomer, Solveig, et al.
Published: (2024)

On Naive Mean-Field Approximation for high-dimensional canonical GLMs
by: Mukherjee, Sumit, et al.
Published: (2024)

The Gaussian central limit theorem for a stationary time series with infinite variance
by: Matsui, Muneya, et al.
Published: (2025)

The limit joint distributions of some statistics used in testing the quality of random number generators
by: Savelov, M. P.
Published: (2025)

The insider problem in the trinomial model: a discrete-time jump process approach
by: Halconruy, Hélène
Published: (2021)

On the convergence rate in the central limit theorem for linearly extended negative quadrant dependent random variables and its applications
by: Alem, Mohamed Kaber El, et al.
Published: (2025)

A Bootstrap Test for Independence of Time Series Based on the Distance Covariance
by: Betken, Annika, et al.
Published: (2021)

Testing Independence of Infinite Dimensional Random Elements: A Sup-norm Approach
by: Bhar, Suprio, et al.
Published: (2023)

Covariate-Adaptive Randomization in Clinical Trials without Inflated Variances
by: Li-Xin, Zhang
Published: (2026)