A Geometric Profile of Semantic Information in Text: Frame-Conditional Uniqueness and a Trade-Off Triangle for Scalar Summaries
How much meaning does a text carry? Shannon's theory measures uncertainty over symbols and is intentionally indifferent to meaning, while pairwise metrics such as BERTScore compare two texts rather than characterizing one. We develop a geometric framework that measures semantic content from the structure of a text's sentence embeddings. The framework has three parts. First, within a fixed embedding and baseline, six natural axioms uniquely determine a scalar measure up to scale, a frame-conditional uniqueness theorem. The resulting scalar is empirically too coarse, motivating a richer representation. Second, we propose a three-coordinate semantic profile capturing novelty (displacement fr...
| Authors | Dmitriy Kompaneets |
|---|---|
| Primary category | cs.CL |
| Published | 27 May 2026 |
| Last updated at source | 27 May 2026 |
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