We present a comparative analysis of text complexity across domains using scale-free metrics. We quantify linguistic complexity via Heaps’ exponent \(\beta \) (vocabulary growth), Taylor’s exponent \(\alpha \) (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 \(\beta \) ) and higher term consistency (higher \(\alpha \) ) than general texts. Within legal domain, statutory codes have the lowest \(\beta \) and highest \(\alpha \) , reflecting strict drafting conventions, while cases and deeds show higher \(\beta \) and lower \(\alpha \) . 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.

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Scale-Free Characteristics of Multilingual Legal Texts and the Limitations of LLMs

  • Haoyang Chen,
  • Kumiko Tanaka-Ishii

摘要

We present a comparative analysis of text complexity across domains using scale-free metrics. We quantify linguistic complexity via Heaps’ exponent \(\beta \) (vocabulary growth), Taylor’s exponent \(\alpha \) (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 \(\beta \) ) and higher term consistency (higher \(\alpha \) ) than general texts. Within legal domain, statutory codes have the lowest \(\beta \) and highest \(\alpha \) , reflecting strict drafting conventions, while cases and deeds show higher \(\beta \) and lower \(\alpha \) . 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.