New Geometric Framework Measures Semantic Content in Text Using Sentence Embeddings
A new mathematical framework uses sentence embedding geometry to quantify how much meaning a text carries, introducing a three-coordinate 'semantic profile' of novelty, breadth, and integration. The work addresses a longstanding gap between Shannon information theory, which ignores meaning, and pairwise text comparison metrics like BERTScore. It offers a principled, axiomatically grounded approach to semantic measurement with potential applications in NLP evaluation and text analysis.
Researchers have developed a geometric framework for measuring semantic content in text based on the structure of sentence embeddings, aiming to fill the gap left by Shannon entropy (which is meaning-agnostic) and pairwise metrics (which compare texts rather than characterizing them). The framework begins with a frame-conditional uniqueness theorem showing that six natural axioms uniquely determine a scalar semantic measure up to scale within a fixed embedding and baseline. Because this scalar is found to be too coarse in practice, the authors propose a richer three-coordinate semantic profile capturing novelty (displacement from generic discourse), breadth (diversity of distinct ideas), and integration (connectedness among ideas), along with a discrete minimal unit called the 'semantic quantum.' A no-go theorem is also proved, demonstrating that no single scalar summary can simultaneously satisfy analytic stability under paraphrase and concatenation, ordinal robustness across text scales, and cross-representation comparability — forming a 'trade-off triangle.' Two practical scalar measures, S_minmax and S_rank, are proposed, each occupying a distinct corner of this triangle, with the rank-normalized configuration passing 25 of 28 ordinal checks as point estimates. Validation was conducted across 23 synthetic categories, five Project Gutenberg novels, and three embedding models, with a variational result connecting the breadth coordinate to the log-determinant of a determinantal point process (Spearman ρ = 0.985 over 507 Gutenberg chapters).
What's missing
The framework's performance is conditioned on the choice of embedding model and clustering threshold τ, and generalization across languages, domains, or non-English text is not evaluated. The practical implications of choosing between S_minmax and S_rank in downstream NLP tasks remain unexplored. The robustness of results to different baseline corpora is not fully characterized.
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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