Scale-Dependent Semantic Dynamics Revealed by Allan Deviation

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.

The flow of ideas in word embeddings

The flow of ideas has been extensively studied by physicists, psychologists, and machine learning engineers. This paper adopts specific tools from microrheology to investigate the similarity-based flow of ideas. We introduce a random walker in word embeddings and study its behavior. Such similarity-mediated random walks through the embedding space show signatures of anomalous diffusion commonly observed in complex structured systems such as biological cells and complex fluids. The paper concludes by proposing the application of popular tools employed in the study of random walks and diffusion of particles under Brownian motion to assess quantitatively the incorporation of diverse ideas in a document. Overall, this paper presents a self-referenced method combining microrheology and machine learning concepts to explore the meandering tendencies of language models and their potential association with creativity.