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arXiv · 2511.19262

Psychometric Tests for AI Agents and Their Moduli Space

Przemyslaw Chojecki
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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.

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Przemyslaw Chojecki. 2025-11-24. Psychometric Tests for AI Agents and Their Moduli Space. https://arxiv.org/abs/2511.19262

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