Kumiko Tanaka-Ishii

Kumiko Tanaka-Ishii

Evaluating whether large language models (LLMs) capture the structure of natural language beyond local fluency remains an open challenge. Existing evaluation methods, largely based on task performance or short-context behavior, provide limited insight into the long-range statistical organization of generated text. We propose a complementary evaluation framework based on repeated subsequences. By analyzing their distribution across scales and relating it to higher-order Rényi entropies, we probe how texts reuse previously established structure under finite-length conditions. Experiments on human-written texts and length-matched GPT-generated texts show that, while power-law models can describe restricted ranges of block length, the observed entropy growth is often equally or better characterized by logarithmic--power forms. Across datasets, natural language exhibits stable entropy-growth patterns over accessible ranges, with consistent average behavior despite variability across individual texts. In contrast, GPT-generated texts show systematic and statistically significant shifts in estimated exponents with model size. These results demonstrate that repeated-subsequence entropy provides a quantitative structural diagnostic that reveals systematic differences in long-range organization, distinguishing natural language from state-of-the-art LLM outputs beyond surface-level fluency.

Kumiko Tanaka-Ishii, Akira Tanaka

The Strahler number was originally proposed to characterize the complexity of river bifurcation and has found various applications. This article proposes computation of the Strahler number's upper and lower limits for natural language sentence tree structures. Through empirical measurements across grammatically annotated data, the Strahler number of natural language sentences is shown to be almost 3 or 4, similarly to the case of river bifurcation as reported by Strahler (1957). From the theory behind the number, we show that it is one kind of lower limit on the amount of memory required to process sentences. We consider the Strahler number to provide reasoning that explains reports showing that the number of required memory areas to process sentences is 3 to 4 for parsing (Schuler et al., 2010), and reports indicating a psychological "magical number" of 3 to 5 (Cowan, 2001). An analytical and empirical analysis shows that the Strahler number is not constant but grows logarithmically; therefore, the Strahler number of sentences derives from the range of sentence lengths. Furthermore, the Strahler number is not different for random trees, which could suggest that its origin is not specific to natural language.

Giulia Occhini, Kumiko Tanaka-Ishii, Anna Barford et al.

Artificial intelligence (AI) has the potential to transform healthcare, education, governance and socioeconomic equity, but its benefits remain concentrated in a small number of languages (Bender, 2019; Blasi et al., 2022; Joshi et al., 2020; Ranathunga and de Silva, 2022; Young, 2015). Language AI - the technologies that underpin widely-used conversational systems such as ChatGPT - could provide major benefits if available in people's native languages, yet most of the world's 7,000+ linguistic communities currently lack access and face persistent digital marginalization. Here we present a global longitudinal analysis of social, economic and infrastructural conditions across languages to assess systemic inequalities in language AI. We first analyze the existence of AI resources for 6003 languages. We find that despite efforts of the community to broaden the reach of language technologies (Bapna et al., 2022; Costa-Jussà et al., 2022), the dominance of a handful of languages is exacerbating disparities on an unprecedented scale, with divides widening exponentially rather than narrowing. Further, we contrast the longitudinal diffusion of AI with that of earlier IT technologies, revealing a distinctive hype-driven pattern of spread. To translate our findings into practical insights and guide prioritization efforts, we introduce the Language AI Readiness Index (EQUATE), which maps the state of technological, socio-economic, and infrastructural prerequisites for AI deployment across languages. The index highlights communities where capacity exists but remains underutilized, and provides a framework for accelerating more equitable diffusion of language AI. Our work contributes to setting the baseline for a transition towards more sustainable and equitable language technologies.

Xin Du, Kumiko Tanaka-Ishii

Mode collapse is a persistent challenge in generative modeling and appears in autoregressive text generation as behaviors ranging from explicit looping to gradual loss of diversity and premature trajectory convergence. We take a dynamical-systems view and reinterpret mode collapse as reduced state-space accessibility caused by *geometric collapse*: during generation, the model's internal trajectory becomes confined to a low-dimensional region of its representation space. This implies mode collapse is not purely a token-level phenomenon and cannot be reliably solved by symbolic constraints or probability-only decoding heuristics. Guided by this perspective, we propose *Reinforced Mode Regulation* (RMR), a lightweight, online state-space intervention that regulates dominant self-reinforcing directions in the Transformer value cache (implemented as low-rank damping). Across multiple large language models, RMR substantially reduces mode collapse and enables stable, high-quality generation at extremely low entropy rates (down to 0.8 nats/step), whereas standard decoding typically collapses near 2.0 nats/step.

Xin Du, Lixin Xiu, Kumiko Tanaka-Ishii

We apply an information-theoretic perspective to reconsider generative document retrieval (GDR), in which a document $x \in X$ is indexed by $t \in T$, and a neural autoregressive model is trained to map queries $Q$ to $T$. GDR can be considered to involve information transmission from documents $X$ to queries $Q$, with the requirement to transmit more bits via the indexes $T$. By applying Shannon's rate-distortion theory, the optimality of indexing can be analyzed in terms of the mutual information, and the design of the indexes $T$ can then be regarded as a {\em bottleneck} in GDR. After reformulating GDR from this perspective, we empirically quantify the bottleneck underlying GDR. Finally, using the NQ320K and MARCO datasets, we evaluate our proposed bottleneck-minimal indexing method in comparison with various previous indexing methods, and we show that it outperforms those methods.

Xin Du, Kumiko Tanaka-Ishii

The correlation dimension of natural language is measured by applying the Grassberger-Procaccia algorithm to high-dimensional sequences produced by a large-scale language model. This method, previously studied only in a Euclidean space, is reformulated in a statistical manifold via the Fisher-Rao distance. Language exhibits a multifractal, with global self-similarity and a universal dimension around 6.5, which is smaller than those of simple discrete random sequences and larger than that of a Barabási-Albert process. Long memory is the key to producing self-similarity. Our method is applicable to any probabilistic model of real-world discrete sequences, and we show an application to music data.

Xin Du, Kumiko Tanaka-Ishii

We present {\em generative clustering} (GC) for clustering a set of documents, $\mathrm{X}$, by using texts $\mathrm{Y}$ generated by large language models (LLMs) instead of by clustering the original documents $\mathrm{X}$. Because LLMs provide probability distributions, the similarity between two documents can be rigorously defined in an information-theoretic manner by the KL divergence. We also propose a natural, novel clustering algorithm by using importance sampling. We show that GC achieves the state-of-the-art performance, outperforming any previous clustering method often by a large margin. Furthermore, we show an application to generative document retrieval in which documents are indexed via hierarchical clustering and our method improves the retrieval accuracy.

Xin Du, Kumiko Tanaka-Ishii

Large language models (LLMs) have achieved remarkable progress in natural language generation, yet they continue to display puzzling behaviors -- such as repetition and incoherence -- even when exhibiting low perplexity. This highlights a key limitation of conventional evaluation metrics, which emphasize local prediction accuracy while overlooking long-range structural complexity. We introduce correlation dimension, a fractal-geometric measure of self-similarity, to quantify the epistemological complexity of text as perceived by a language model. This measure captures the hierarchical recurrence structure of language, bridging local and global properties in a unified framework. Through extensive experiments, we show that correlation dimension (1) reveals three distinct phases during pretraining, (2) reflects context-dependent complexity, (3) indicates a model's tendency toward hallucination, and (4) reliably detects multiple forms of degeneration in generated text. The method is computationally efficient, robust to model quantization (down to 4-bit precision), broadly applicable across autoregressive architectures (e.g., Transformer and Mamba), and provides fresh insight into the generative dynamics of LLMs.

Haoyang Chen, Kumiko Tanaka-Ishii

We explore the applicability of text-to-code to solve real-world problems that are typically solved in natural language, such as legal judgment and medical QA. Unlike previous works, our approach leverages the explicit reasoning provided by program generation. We present ICRAG, a framework that transforms natural language into executable programs through iterative refinement using external knowledge from domain resources and GitHub. Across 13 benchmarks, ICRAG achieves up to 161.1\% relative improvement. We provide a detailed analysis of the generated code and the impact of external knowledge, and we discuss the limitations of applying text-to-code approaches to real-world natural language tasks.

Haoyang Chen, Kumiko Tanaka-Ishii

We present a comparative analysis of text complexity across domains using scale-free metrics. We quantify linguistic complexity via Heaps' exponent $β$ (vocabulary growth), Taylor's exponent $α$ (word-frequency fluctuation scaling), compression rate $r$ (redundancy), and entropy. Our corpora span three domains: legal documents (statutes, cases, deeds) as a specialized domain, general natural language texts (literature, Wikipedia), and AI-generated (GPT) text. We find that legal texts exhibit slower vocabulary growth (lower $β$) and higher term consistency (higher $α$) than general texts. Within legal domain, statutory codes have the lowest $β$ and highest $α$, reflecting strict drafting conventions, while cases and deeds show higher $β$ and lower $α$. In contrast, GPT-generated text shows the statistics more aligning with general language patterns. These results demonstrate that legal texts exhibit domain-specific structures and complexities, which current generative models do not fully replicate.

Kumiko Tanaka-Ishii, Shuntaro Takahashi

This article considers the fluctuation analysis methods of Taylor and Ebeling & Neiman. While both have been applied to various phenomena in the statistical mechanics domain, their similarities and differences have not been clarified. After considering their analytical aspects, this article presents a large-scale application of these methods to text. It is found that both methods can distinguish real text from independently and identically distributed (i.i.d.) sequences. Furthermore, it is found that the Taylor exponents acquired from words can roughly distinguish text categories; this is also the case for Ebeling and Neiman exponents, but to a lesser extent. Additionally, both methods show some possibility of capturing script kinds.

Daiki Hirano, Kumiko Tanaka-Ishii, Andrew Finch

The extraction of templates such as ``regard X as Y'' from a set of related phrases requires the identification of their internal structures. This paper presents an unsupervised approach for extracting templates on-the-fly from only tagged text by using a novel relaxed variant of the Sequence Binary Decision Diagram (SeqBDD). A SeqBDD can compress a set of sequences into a graphical structure equivalent to a minimal DFA, but more compact and better suited to the task of template extraction. The main contribution of this paper is a relaxed form of the SeqBDD construction algorithm that enables it to form general representations from a small amount of data. The process of compression of shared structures in the text during Relaxed SeqBDD construction, naturally induces the templates we wish to extract. Experiments show that the method is capable of high-quality extraction on tasks based on verb+preposition templates from corpora and phrasal templates from short messages from social media.

Shuntaro Takahashi, Kumiko Tanaka-Ishii

In this article, we evaluate computational models of natural language with respect to the universal statistical behaviors of natural language. Statistical mechanical analyses have revealed that natural language text is characterized by scaling properties, which quantify the global structure in the vocabulary population and the long memory of a text. We study whether five scaling properties (given by Zipf's law, Heaps' law, Ebeling's method, Taylor's law, and long-range correlation analysis) can serve for evaluation of computational models. Specifically, we test $n$-gram language models, a probabilistic context-free grammar (PCFG), language models based on Simon/Pitman-Yor processes, neural language models, and generative adversarial networks (GANs) for text generation. Our analysis reveals that language models based on recurrent neural networks (RNNs) with a gating mechanism (i.e., long short-term memory, LSTM; a gated recurrent unit, GRU; and quasi-recurrent neural networks, QRNNs) are the only computational models that can reproduce the long memory behavior of natural language. Furthermore, through comparison with recently proposed model-based evaluation methods, we find that the exponent of Taylor's law is a good indicator of model quality.

Kumiko Tanaka-Ishii, Hiroshi Terada

Word frequency is assumed to correlate with word familiarity, but the strength of this correlation has not been thoroughly investigated. In this paper, we report on our analysis of the correlation between a word familiarity rating list obtained through a psycholinguistic experiment and the log-frequency obtained from various corpora of different kinds and sizes (up to the terabyte scale) for English and Japanese. Major findings are threefold: First, for a given corpus, familiarity is necessary for a word to achieve high frequency, but familiar words are not necessarily frequent. Second, correlation increases with the corpus data size. Third, a corpus of spoken language correlates better than one of written language. These findings suggest that cognitive familiarity ratings are correlated to frequency, but more highly to that of spoken rather than written language.

Shuntaro Takahashi, Kumiko Tanaka-Ishii

Language models have primarily been evaluated with perplexity. While perplexity quantifies the most comprehensible prediction performance, it does not provide qualitative information on the success or failure of models. Another approach for evaluating language models is thus proposed, using the scaling properties of natural language. Five such tests are considered, with the first two accounting for the vocabulary population and the other three for the long memory of natural language. The following models were evaluated with these tests: n-grams, probabilistic context-free grammar (PCFG), Simon and Pitman-Yor (PY) processes, hierarchical PY, and neural language models. Only the neural language models exhibit the long memory properties of natural language, but to a limited degree. The effectiveness of every test of these models is also discussed.

Tatsuru Kobayashi, Kumiko Tanaka-Ishii

Taylor's law describes the fluctuation characteristics underlying a system in which the variance of an event within a time span grows by a power law with respect to the mean. Although Taylor's law has been applied in many natural and social systems, its application for language has been scarce. This article describes a new quantification of Taylor's law in natural language and reports an analysis of over 1100 texts across 14 languages. The Taylor exponents of written natural language texts were found to exhibit almost the same value. The exponent was also compared for other language-related data, such as the child-directed speech, music, and programming language code. The results show how the Taylor exponent serves to quantify the fundamental structural complexity underlying linguistic time series. The article also shows the applicability of these findings in evaluating language models.

Kumiko Tanaka-Ishii

Long-range correlation, a property of time series exhibiting long-term memory, is mainly studied in the statistical physics domain and has been reported to exist in natural language. Using a state-of-the-art method for such analysis, long-range correlation is first shown to occur in long CHILDES data sets. To understand why, Bayesian generative models of language, originally proposed in the cognitive scientific domain, are investigated. Among representative models, the Simon model was found to exhibit surprisingly good long-range correlation, but not the Pitman-Yor model. Since the Simon model is known not to correctly reflect the vocabulary growth of natural language, a simple new model is devised as a conjunct of the Simon and Pitman-Yor models, such that long-range correlation holds with a correct vocabulary growth rate. The investigation overall suggests that uniform sampling is one cause of long-range correlation and could thus have a relation with actual linguistic processes.

Shuntaro Takahashi, Kumiko Tanaka-Ishii

The performance of deep learning in natural language processing has been spectacular, but the reasons for this success remain unclear because of the inherent complexity of deep learning. This paper provides empirical evidence of its effectiveness and of a limitation of neural networks for language engineering. Precisely, we demonstrate that a neural language model based on long short-term memory (LSTM) effectively reproduces Zipf's law and Heaps' law, two representative statistical properties underlying natural language. We discuss the quality of reproducibility and the emergence of Zipf's law and Heaps' law as training progresses. We also point out that the neural language model has a limitation in reproducing long-range correlation, another statistical property of natural language. This understanding could provide a direction for improving the architectures of neural networks.