ARC-$\infty$: Automating the Design of Recursively Growing Intelligence Tests

Conceptual bootstrapping, using known concepts to acquire new ones, is a hallmark of human intelligence, yet existing intelligence tests cannot measure it: their tasks are independent or fixed, and once solved, leave nothing to measure. Measuring bootstrapping requires a test that grows recursively, with each environment building on the concepts of earlier ones, which is impractical to design by hand. We introduce the Abstraction and Reasoning Continuum (ARC-$\infty$), a framework that automates the design of recursively growing intelligence tests. From a seed world, a Designer agent repeatedly produces the next world, yielding an unbounded worldline whose depth and breadth are controlled by two hyperparameters. We show that these controls steer growth as intended and that concepts accumulate across worlds. Evaluating state-of-the-art agent harnesses along a generated worldline, we find that they bootstrap from earlier worlds but fail to sustain it, and that a simple library learning step that consolidates prior knowledge extends their bootstrapping.