Psychometric Tests for AI Agents and Their Moduli Space

TL;DR

This paper introduces a moduli-theoretic framework for psychometric testing of AI agents, connecting it to existing AAI scores, and defining invariants and symmetries in agent evaluation.

Contribution

It formalizes psychometric test batteries using moduli theory, relates the AAI-Index to a broader class of AAI functionals, and introduces the concept of a cognitive core for AI agents.

Findings

AAI-Index is a special case of AAI functional.

Defined invariants of batteries under symmetries.

Organized moduli of equivalent batteries.

Abstract

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.