The semantic power of text content as a flow of a vector field of embeddings
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The growing volume of textual data demands advanced methods for evaluating both content effectiveness and semantic structure. While current Natural Language Processing (NLP) techniques offer powerful tools, they often lack metrics for quantifying intrinsic semantic intensity or conceptual coherence. This paper introduces “semantic power” – a novel quantitative measure designed to analyze the conceptual structure and semantic richness of texts, grounded in principles of field theory. The proposed methodology draws on the Ostrogradsky–Gauss theorem and the divergence operator, establishing a theoretical link between local semantic properties of a text (derived from LaBSE vector embeddings) and their global influence. The approach involves computing a semantic centroid, representing the point of highest meaning concentration, and measuring semantic power using a model that assumes an inverse-square decay of vector influence. For further analysis, Gaussian Mixture Model (GMM) clustering id applied, and Principal Component Analysis (PCA) is used for dimensionality reduction and visualization. Experiments on philosophical texts by key Early Modern thinkers – G. W. Leibniz, R. Descartes, and I. Kant – reveal distinct and meaningful variations in semantic power (0.6010, 0.5633, and 0.5787, respectively) and in the resulting clustering patterns (2, 7, and 2 clusters). These findings suggest that semantic power is not merely a numerical descriptor but one that correlates with established intellectual styles and methodological orientations of the authors. As such, semantic power emerges as a powerful and objective metric for assessing the deep cognitive and semantic dimensions of textual content, with potential applications in philology, cognitive science, and computational linguistics and related disciplines.
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