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Psychometric Tests for AI Agents and Their Moduli Space

Przemyslaw Chojecki

TL;DR

A moduli-theoretic view of psychometric test batteries for AI agents is developed and the notion of a cognitive core of an agent relative to a battery is introduced and the associated AAI score is defined as the restriction of an AAI functional to that core.

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.

Psychometric Tests for AI Agents and Their Moduli Space

TL;DR

A moduli-theoretic view of psychometric test batteries for AI agents is developed and the notion of a cognitive core of an agent relative to a battery is introduced and the associated AAI score is defined as the restriction of an AAI functional to that core.

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 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.

Paper Structure

This paper contains 25 sections, 20 theorems, 60 equations.

Table of Contents

  1. Introduction
  2. Batteries and Morphisms
  3. Symmetries and the Moduli Space
  4. PIT Normalization and Canonical Representation
  5. Topological Structure of the Moduli
  6. Discrete and continuous moduli.
  7. Stratification by combinatorial type.
  8. AAI as a Functional on Representations
  9. Determinacy from dense agreement on batteries and laws
  10. The AAI Score as an AAI Functional
  11. Regularity of the AAI score
  12. Cognitive Cores and the Score AAI$_{\textrm{core}}$
  13. Given Core Scores and Continuations
  14. Statistical Guarantees and Stability
  15. Operational Implementation
  16. ...and 10 more sections

Key Result

Proposition 2.4

Batteries and their morphisms form a category $\mathbf{Bat}$ under composition and identities.

Theorems & Definitions (66)

  • Definition 2.1: Battery
  • Definition 2.2: Agent representation on a battery
  • Proposition 2.4
  • proof
  • Definition 3.1: Symmetry group
  • Definition 3.2: Moduli space
  • Definition 4.1: Randomized PIT
  • Proposition 4.2: Uniformity and invariance
  • proof
  • proof
  • ...and 56 more