Laguerre Geometry for Interpreting Large Language Models

Existing hypotheses represent a concept in an LLM as a single point, a linear direction, or a Gaussian cluster, yet it remains unclear how and why such structures emerge. Here, we show that concept geometry can be precisely characterized via Laguerre Geometry, in which a concept is defined as a region--a Laguerre-Voronoi cell or a union of cells--allowing us to strictly define, measure, and separate concepts. Building on this formulation, we show that finer-grained concept structures, such as in

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ethics.ai (12 July 2026), “Laguerre Geometry for Interpreting Large Language Models,” evidence record 38, https://ethics.ai/record/38 (originally published by arXiv).

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