New Geometric Framework Measures Semantic Content in Text Using Sentence Embeddings
Researchers developed a geometric framework that measures semantic content in text by analyzing the structure of sentence embeddings, moving beyond Shannon's information theory which ignores meaning. The framework characterizes three dimensions: novelty (how different from generic discourse), breadth (diversity of ideas), and integration (connectedness among ideas). This work matters because it provides a principled mathematical approach to quantifying meaning in text, with potential applications in natural language processing and text analysis.
A new arXiv paper presents a geometric approach to measuring semantic information in text that goes beyond traditional information theory. The researchers establish a frame-conditional uniqueness theorem showing that six natural axioms uniquely determine a scalar measure of semantic content (up to scale) within a fixed embedding framework. They propose a three-coordinate semantic profile capturing novelty, breadth, and integration, along with a discrete minimal unit called the semantic quantum. Critically, they prove a no-go theorem demonstrating that no single scalar summary can simultaneously satisfy three desirable properties: analytic stability under paraphrase and concatenation, ordinal robustness across text scales, and cross-representation comparability. The authors present two practical scalar measures occupying different corners of this trade-off triangle and validate their approach across synthetic categories, literary texts, and multiple embedding models, with the recommended configuration passing 25 of 28 ordinal checks.
What's missing
The study's limitations include: the trade-off triangle theorem indicates fundamental constraints on what any scalar summary can achieve simultaneously; validation relies on relatively small datasets (5 novels, 3 embedding models); the choice of clustering threshold τ for determining semantic quantum resolution is not fully explored; and generalization to non-English text or specialized domains remains unclear.
What different sources said
- arXiv cs.CLCenter
A Geometric Profile of Semantic Information in Text: Frame-Conditional Uniqueness and a Trade-Off Triangle for Scalar Summaries
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