Non-Euclidean competency geometry through product-manifold embeddings and calibrated LLM scoring for aptitude diagnostics

Goal: embed taxonomies in a product of hyperbolic and Euclidean space, scale to 10,000 nodes, and calibrate LLM scoring against expert panels.

The research

Skill taxonomies are trees that grow exponentially; flat vector spaces cannot hold them. We embed competencies in hyperbolic and mixed-curvature spaces and bind LLM scoring to observable behaviour.

What it changes in practice

After the rebuild, who fills which role? Matching people and roles on evidence, not on keyword overlap, is part of the Adopt layer.