Psychometric Tests for AI Agents and Their Moduli Space
This work provides a theoretical foundation for assessing AI autonomy and general intelligence, though it appears incremental as it builds on prior AAI score concepts.
The paper formalizes psychometric test batteries for AI agents using a moduli-theoretic framework, connecting it to the existing AAI score and introducing concepts like AAI functionals and cognitive cores to analyze evaluation invariants.
We develop a moduli-theoretic view of psychometric test batteries for AI agents and connect it explicitly to the AAI score developed previously. First, we make precise the notion of an AAI functional on a battery and set out axioms that any reasonable autonomy/general intelligence score should satisfy. Second, we show that the composite index ('AAI-Index') defined previously is a special case of our AAI functional. Third, we introduce the notion of a cognitive core of an agent relative to a battery and define the associated AAI$_{\textrm{core}}$ score as the restriction of an AAI functional to that core. Finally, we use these notions to describe invariants of batteries under evaluation-preserving symmetries and outline how moduli of equivalent batteries are organized.