Scale-Dependent Semantic Dynamics Revealed by Allan Deviation

Debayan Dasgupta

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arXiv · 2601.21678

Scale-Dependent Semantic Dynamics Revealed by Allan Deviation

Debayan Dasgupta

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Abstract

While language progresses through a sequence of semantic states, the underlying dynamics of this progression remain elusive. Here, we treat the semantic progression of written text as a stochastic trajectory in a high-dimensional state space. We utilize Allan deviation, a tool from precision metrology, to analyze the stability of meaning by treating ordered sentence embeddings as a displacement signal. Our analysis reveals two distinct dynamical regimes: short-time power-law scaling, which differentiates creative literature from technical texts, and a long-time crossover to a stability-limited noise floor. We find that while large language models successfully mimic the local scaling statistics of human text, they exhibit a systematic reduction in their stability horizon. These results establish semantic coherence as a measurable physical property, offering a framework to differentiate the nuanced dynamics of human cognition from the patterns generated by algorithmic models.

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Debayan Dasgupta. 2026-01-29. Scale-Dependent Semantic Dynamics Revealed by Allan Deviation. https://arxiv.org/abs/2601.21678

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