park2025-polytope-convex-hull
IN premise — summaries/2026/08/24/park-2024-categorical-hierarchical-concepts-s1-we-show-how-to-move-from-representations-of-binary-concepts-.md
Created 2026-08-25T02:58:24+00:00
A categorical concept {c₁, …, cₖ} maps to the convex hull (polytope) of the member vectors {v₁, …, vₖ} in representation space.
Summary
When the system represents a category (like "reptile" made up of snake, lizard, turtle), it doesn't place a single point for the category; instead, the category occupies the entire geometric region enclosed by its members in the vector space. This means a category's meaning is fully determined by and bounded by its constituent examples, so adding or removing a member reshapes what the category "is" for the system's reasoning.