arXiv subjects

Kai Nakaishi

Publications and source records attributed to Kai Nakaishi.

4 recordsLinked to original sources

arXiv2026

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 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.

cs.CL↗

arXiv2026

Phase transition in large language models and the criticality of natural languages

Generation of text and speech in natural languages can be modeled as a stochastic process. This idea dates back to the seminal work of Markov and, later, to that of Shannon and also underlies the recent development of large language models (LLMs). The stochastic processes corresponding to natural languages should be distinct from those that generate nonlinguistic sequences. One of the features that discriminate linguistic and nonlinguistic sequences is power-law behavior, which is universally observed across different languages. In statistical physics, such behavior suggests that natural languages are critical: They lie near a phase transition point in a parametrized space of stochastic processes. However, testing this conjecture is not straightforward. A phase transition, even if it exists, cannot be directly observed in real-world natural languages because they do not have any controllable parameters. Here, we use LLMs as controllable effective models of natural languages. Through statistical analyses of texts generated by LLMs, we find that, when a parameter analogous to physical temperature is varied, LLMs undergo a phase transition. The transition separates a low-temperature phase with complex repetitive structures in generated texts from a high-temperature phase in which LLMs generate incomprehensible texts. At the critical point between these phases, generated texts display the power-law behavior similar to that of natural languages and most closely resemble natural languages as measured by a standard metric in natural language processing. These findings strongly suggest that natural languages are indeed critical.

cond-mat.dis-nn↗

arXiv2024

Statistical properties of probabilistic context-sensitive grammars

Probabilistic context-free grammars (PCFGs), which are commonly used to generate trees randomly, have been well analyzed theoretically, leading to applications in various domains. Despite their utility, the distributions that the grammar can express are limited to those in which the distribution of a subtree depends only on its root and not on its context. This limitation presents a challenge for modeling various real-world phenomena, such as natural languages. To overcome this limitation, a probabilistic context-sensitive grammar (PCSG) is introduced, where the distribution of a subtree depends on its context. Numerical analysis of a PCSG reveals that the distribution of a symbol does not constitute a qualitative difference from that in the context-free case, but mutual information does. Furthermore, a novel metric introduced to directly quantify the breaking of this limitation detects a distinct difference between PCFGs and PCSGs. This metric, applicable to an arbitrary distribution of a tree, allows for further investigation and characterization of various tree structures that PCFGs cannot express.

cond-mat.dis-nn↗

arXiv2022

Absence of Phase Transition in Random Language Model

The Random Language Model, proposed as a simple model of human languages, is defined by the averaged model of a probabilistic context-free grammar. This grammar expresses the process of sentence generation as a tree graph with nodes having symbols as variables. Previous studies proposed that a phase transition, which can be considered to represent the emergence of order in language, occurs in the random language model. We discuss theoretically that the analysis of the "order parameter" introduced in previous studies can be reduced to solving the maximum eigenvector of the transition probability matrix determined by a grammar. This helps analyze the distribution of a quantity determining the behavior of the "order parameter" and reveals that no phase transition occurs. Our results suggest the need to study a more complex model such as a probabilistic context-sensitive grammar, in order for phase transitions to occur.

cond-mat.dis-nn↗