Rethinking the Relationship between the Power Law and Hierarchical Structures

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 the universal principles 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 languages and animal signals. However, the argument supporting this interpretation has not been empirically tested. To address this problem, this study examines the validity of the argument for syntactic structures. Specifically, we test whether the statistical properties of parse trees align with the implicit assumptions in the argument. Using English corpora, we analyze the mutual information, deviations from probabilistic context-free grammars (PCFGs), and other properties in parse trees, as well as in the PCFG that approximates these 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 languages and animal signals, highlighting the need to reconsider the relationship between the power law and hierarchical structures.

Critical Phase Transition in a Large Language Model

The performance of large language models (LLMs) strongly depends on the \textit{temperature} parameter. Empirically, at very low temperatures, LLMs generate sentences with clear repetitive structures, while at very high temperatures, generated sentences are often incomprehensible. In this study, using GPT-2, we numerically demonstrate that the difference between the two regimes is not just a smooth change but a phase transition with singular, divergent statistical quantities. Our extensive analysis shows that critical behaviors, such as a power-law decay of correlation in a text, emerge in the LLM at the transition temperature as well as in a natural language dataset. We also discuss that several statistical quantities characterizing the criticality should be useful to evaluate the performance of LLMs.