A Geometric Profile of Semantic Information in Text: Frame-Conditional Uniqueness and a Trade-Off Triangle for Scalar Summaries
arXiv:2606.11222v1 Announce Type: new Abstract: 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 empi
This research provides a foundational theoretical framework for semantic information measurement, essential as AI models become more sophisticated and require nuanced understanding of meaning.
A rigorous method for quantifying semantic content could enable more precise evaluations of AI models, improved information retrieval, and smarter agentic systems.
The ability to geometrically measure semantic content provides a new, objective lens for analyzing text beyond symbolic or pairwise comparisons, pushing AI further towards understanding rather than just processing.
- · AI researchers
- · NLP developers
- · Information retrieval systems
- · AI agent developers
- · Systems relying solely on keyword matching
- · Less semantically advanced AI models
Improved methods for evaluating and comparing large language models based on semantic depth.
Development of more robust and reliable AI agents capable of understanding complex instructions and contexts.
New forms of knowledge representation and transfer that prioritize semantic essence over surface syntax.
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Read at arXiv cs.CL