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arXiv · 2604.05536

Turbulence-like 5/3 spectral scaling in contextual representations of language as a complex system

Zhongxin Yang·Chun Bao·Yuanwei Bin·Xiang I. A. Yang·Shiyi Chen
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Abstract

Natural language is a complex system that exhibits robust statistical regularities. Here, we represent text as a trajectory in a high-dimensional embedding space generated by transformer-based language models, and quantify scale-dependent fluctuations along the token sequence using an embedding-step signal. Across multiple languages and corpora, the resulting power spectrum exhibits a robust power law with an exponent close to $5/3$ over an extended frequency range. This scaling is observed consistently in contextual embeddings from both human-written and AI-generated text, but is absent in static word embeddings and is disrupted by randomization of token order. These results show that the observed scaling reflects multiscale, context-dependent organization rather than lexical statistics alone. By analogy with the Kolmogorov spectrum in turbulence, our findings suggest that semantic information is integrated in a scale-free, self-similar manner across linguistic scales, and provide a quantitative, model-agnostic benchmark for studying complex structure in language representations.

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Zhongxin Yang, Chun Bao, Yuanwei Bin, Xiang I. A. Yang, Shiyi Chen. 2026-04-07. Turbulence-like 5/3 spectral scaling in contextual representations of language as a complex system. https://arxiv.org/abs/2604.05536

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