Scale-Dependent Semantic Dynamics Revealed by Allan Deviation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915761140793344 |
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| author | Dasgupta, Debayan |
| author_facet | Dasgupta, Debayan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_21678 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scale-Dependent Semantic Dynamics Revealed by Allan Deviation Dasgupta, Debayan Computation and Language Data Analysis, Statistics and Probability 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. |
| title | Scale-Dependent Semantic Dynamics Revealed by Allan Deviation |
| topic | Computation and Language Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2601.21678 |