arxiv_cl 75% Match Research Paper Linguists,Computational Linguists,NLP Researchers,Cognitive Scientists 20 hours ago

Rethinking the Relationship between the Power Law and Hierarchical Structures

large-language-models › reasoning

📄 Abstract

Abstract: Statistical analysis of corpora provides an approach to quantitatively investigate natural languages. This approach has revealed that several power laws consistently emerge across different corpora and languages, suggesting universal mechanisms underlying languages. Particularly, the power-law decay of correlation has been interpreted as evidence for underlying hierarchical structures in syntax, semantics, and discourse. This perspective has also been extended to child speeches and animal signals. However, the argument supporting this interpretation has not been empirically tested in natural languages. To address this problem, the present study examines the validity of the argument for syntactic structures. Specifically, we test whether the statistical properties of parse trees align with the assumptions in the argument. Using English and Japanese corpora, we analyze the mutual information, deviations from probabilistic context-free grammars (PCFGs), and other properties in natural language parse trees, as well as in the PCFG that approximates these parse trees. Our results indicate that the assumptions do not hold for syntactic structures and that it is difficult to apply the proposed argument to child speeches and animal signals, highlighting the need to reconsider the relationship between the power law and hierarchical structures.

Key Contributions

This paper empirically tests the long-standing argument that power-law decay in correlation implies hierarchical structures in natural language. By analyzing syntactic structures in English and Japanese corpora, it investigates the alignment of statistical properties of parse trees with the assumptions of this argument, providing a quantitative assessment of a core linguistic hypothesis.

Business Value

Understanding fundamental linguistic structures can inform the development of more sophisticated NLP models, leading to better language understanding and generation capabilities in applications like translation and text analysis.

Paper Metadata

Innovation Type

Theoretical validation

Deployment Feasibility

High, as it focuses on theoretical analysis and statistical methods applicable to existing linguistic data.

Limitations Addressed

Lack of empirical testing for the interpretation of power-law decay as evidence for hierarchical structures in natural languages.

Technical Tags

power lawhierarchical structuresstatistical analysisnatural language processingsyntactic structuresprobabilistic context-free grammarscorpora analysislinguistic universals

Research Topics

LinguisticsComputational LinguisticsStatistical Language ModelingCognitive ScienceInformation Theory

Methods & Architectures

Statistical analysisParse tree analysisMutual information calculationDeviation analysis from PCFGs

Applications & Tasks

Natural Language Processing Linguistics Research Understanding language structureValidating linguistic theoriesAnalyzing syntactic properties Syntactic parsing analysisCorrelation decay analysisHierarchical structure validation

Datasets & Benchmarks

Datasets

English corpora, Japanese corpora

Mutual informationDeviations from PCFGs

Related Fields

Computational LinguisticsTheoretical LinguisticsStatistical ModelingCognitive Science

Keywords

power lawhierarchical structurenatural languagesyntaxsemanticsdiscoursecorporastatistical analysisprobabilistic context-free grammarlinguistic universalsparse treesmutual informationcorrelation decay

Academic Context

#Linguistics#Computational Linguistics#Statistical Language Modeling#Cognitive Science#Information Theory

Technology Stack

Frameworks & Libraries

Probabilistic Context-Free Grammars (PCFGs)

Commercial Potential

Competitive Edge

This work provides a rigorous empirical test for a theoretical interpretation that has been widely assumed in linguistics and NLP, offering a more grounded understanding compared to purely theoretical arguments.

Resource Requirements

Compute Needs

Low to moderate, primarily for statistical analysis of corpora.

Data Requirements

Large, diverse corpora of natural language (e.g., English, Japanese) with associated syntactic parse trees.

Scalability

The statistical methods are generally scalable to larger corpora, but the availability and quality of parse trees can be a bottleneck.

Production Readiness

Maturity Level

Theoretical Research

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