Measuring Intelligence and Growth Rate: Variations on Hibbard's Intelligence Measure

TL;DR

This paper reinterprets Hibbard's intelligence measure as two separate ideas, explores alternative growth rate measurement methods, and introduces novel intelligence taxonomies based on Big-O and Big-Theta notations, challenging traditional views.

Contribution

It separates Hibbard's measure into two ideas, surveys alternative growth rate methods, and proposes new intelligence taxonomies using Big-O and Big-Theta, offering fresh perspectives.

Findings

Hibbard's measure can be split into two distinct ideas.

Alternative growth rate measurement methods are surveyed.

Novel intelligence taxonomies based on Big-O and Big-Theta are introduced.

Abstract

In 2011, Hibbard suggested an intelligence measure for agents who compete in an adversarial sequence prediction game. We argue that Hibbard's idea should actually be considered as two separate ideas: first, that the intelligence of such agents can be measured based on the growth rates of the runtimes of the competitors that they defeat; and second, one specific (somewhat arbitrary) method for measuring said growth rates. Whereas Hibbard's intelligence measure is based on the latter growth-rate-measuring method, we survey other methods for measuring function growth rates, and exhibit the resulting Hibbard-like intelligence measures and taxonomies. Of particular interest, we obtain intelligence taxonomies based on Big-O and Big-Theta notation systems, which taxonomies are novel in that they challenge conventional notions of what an intelligence measure should look like. We discuss how intelligence measurement of sequence predictors can indirectly serve as intelligence measurement for agents with Artificial General Intelligence (AGIs).