An Operational Kardashev-Style Scale for Autonomous AI - Towards AGI and Superintelligence

TL;DR

This paper introduces an operational, multi-axis scale for autonomous AI development inspired by the Kardashev scale, enabling measurable progress from automation to superintelligence, with formal criteria and benchmarks.

Contribution

It proposes a novel, testable AAI scale with capability axes, a composite index, and formal criteria for self-improvement and closure, advancing the measurement of AI progress.

Findings

Defines ten capability axes and a composite AAI-Index.

Introduces the Self-Improvement Coefficient $$ and closure properties.

Illustrates how current systems map onto the scale and formalizes progress towards superintelligence.

Abstract

We propose a Kardashev-inspired yet operational Autonomous AI (AAI) Scale that measures the progression from fixed robotic process automation (AAI-0) to full artificial general intelligence (AAI-4) and beyond. Unlike narrative ladders, our scale is multi-axis and testable. We define ten capability axes (Autonomy, Generality, Planning, Memory/Persistence, Tool Economy, Self-Revision, Sociality/Coordination, Embodiment, World-Model Fidelity, Economic Throughput) aggregated by a composite AAI-Index (a weighted geometric mean). We introduce a measurable Self-Improvement Coefficient $\kappa$ (capability growth per unit of agent-initiated resources) and two closure properties (maintenance and expansion) that convert ``self-improving AI'' into falsifiable criteria. We specify OWA-Bench, an open-world agency benchmark suite that evaluates long-horizon, tool-using, persistent agents. We define level gates for AAI-0\ldots AAI-4 using thresholds on the axes, $\kappa$, and closure proofs. Synthetic experiments illustrate how present-day systems map onto the scale and how the delegability frontier (quality vs.\ autonomy) advances with self-improvement. We also prove a theorem that AAI-3 agent becomes AAI-5 over time with sufficient conditions, formalizing "baby AGI" becomes Superintelligence intuition.