Rethinking the Relationship between the Power Law and Hierarchical Structures

TL;DR

This study critically examines the assumption that power-law distributions in language corpora directly indicate hierarchical syntactic structures, finding that the assumptions do not hold for natural language parse trees.

Contribution

It empirically tests the relationship between power laws and hierarchical syntax, challenging previous interpretations and suggesting the need for a revised understanding.

Findings

Power-law decay of correlations does not align with syntactic structures.

Assumptions linking power laws to hierarchical syntax are not supported by data.

Reconsideration of the relationship between power laws and language structure is necessary.

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. In particular, the power-law decay of correlations has been interpreted as evidence of underlying hierarchical structures in syntax, semantics, and discourse. This perspective has also been extended beyond corpora produced by human adults, including child speech, birdsong, and chimpanzee action sequences. However, the argument supporting this interpretation has not been empirically tested in natural languages. To address this gap, 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 not only to sentences by human adults but also to other domains, highlighting the need to reconsider the relationship between the power law and hierarchical structures.