On the Measure of Intelligence

To make deliberate progress towards more intelligent and more human-like artificial systems, we need to be following an appropriate feedback signal: we need to be able to define and evaluate intelligence in a way that enables comparisons between two systems, as well as comparisons with humans. Over the past hundred years, there has been an abundance of attempts to define and measure intelligence, across both the fields of psychology and AI. We summarize and critically assess these definitions and evaluation approaches, while making apparent the two historical conceptions of intelligence that have implicitly guided them. We note that in practice, the contemporary AI community still gravitates towards benchmarking intelligence by comparing the skill exhibited by AIs and humans at specific tasks, such as board games and video games. We argue that solely measuring skill at any given task falls short of measuring intelligence, because skill is heavily modulated by prior knowledge and experience: unlimited priors or unlimited training data allow experimenters to “buy” arbitrary levels of skills for a system, in a way that masks the system’s own generalization power. We then articulate a new formal definition of intelligence based on Algorithmic Information Theory, describing intelligence as skill-acquisition efficiency and highlighting the concepts of scope, generalization difficulty, priors, and experience, as critical pieces to be accounted for in characterizing intelligent systems. Using this definition, we propose a set of guidelines for what a general AI benchmark should look like. Finally, we present a new benchmark closely following these guidelines, the Abstraction and Reasoning Corpus (ARC), built upon an explicit set of priors designed to be as close as possible to innate human priors. We argue that ARC can be used to measure a human-like form of general fluid intelligence and that it enables fair general intelligence comparisons between AI systems and humans.

Introduction. The promise of the field of AI, spelled out explicitly at its inception in the 1950s and repeated countless times since, is to develop machines that possess intelligence comparable to that of humans. But AI has since been falling short of its ideal: although we are able to engineer systems that perform extremely well on specific tasks, they have still stark limitations, being brittle, data-hungry, unable to make sense of situations that deviate slightly from their training data or the assumptions of their creators, and unable to repurpose themselves to deal with novel tasks without significant involvement from human researchers. If the only successes of AI have been in developing narrow, task-specific systems, it is perhaps because only within a very narrow and grounded context have we been able to define our goal sufficiently precisely, and to measure progress in an actionable way. Goal definitions and evaluation benchmarks are among the most potent drivers of scientific progress. To make progress towards the promise of our field, we need precise, quantitative definitions and measures of intelligence – in particular human-like general intelligence. These would not be merely definitions and measures meant to describe or characterize intelligence, but precise, explanatory definitions meant to serve as a North Star, an objective function showing the way towards a clear target, capable of acting as a reliable measure of our progress and as a way to identify and highlight worthwhile new approaches that may not be immediately applicable, and would otherwise be discounted. For instance, common-sense dictionary definitions of intelligence may be useful to make sure we are talking about the same concepts, but they are not useful for our purpose, as they are not actionable, explanatory, or measurable. Similarly, the Turing Test [91] and its many variants (e.g. Total Turing Test and Loebner Prize [75]) are not useful as a driver of progress (and have in fact served as a red herring 1), since such tests completely opt out of objectively defining and measuring intelligence, and instead outsource the task to unreliable human judges who themselves do not have clear definitions or evaluation protocols. It is a testimony to the immaturity of our field that the question of what we mean when we talk about intelligence still doesn’t have a satisfying answer. What’s worse, very little attention has been devoted to rigorously defining it or benchmarking our progress towards it. Legg and Hutter noted in a 2007 survey of intelligence definitions and evaluation methods [53]: “to the best of our knowledge, no general survey of tests and definitions has been published”. A decade later, in 2017, Hern ́andez-Orallo released an extensive survey of evaluation methods [36] as well as a comprehensive book on AI evaluation [37]. Results and recommendations from both of these efforts have since been largely ignored by the community. We believe this lack of attention is a mistake, as the absence of widely-accepted ex- Many formal and informal definitions of intelligence have been proposed over the past few decades, although there is no existing scientific consensus around any single definition. Sternberg & Detterman noted in 1986 [87] that when two dozen prominent psychologists were asked to define intelligence, they all gave somewhat divergent answers. In the context of AI research, Legg and Hutter [53] summarized in 2007 no fewer than 70 definitions from the literature into a single statement: “Intelligence measures an agent’s ability to achieve goals in a wide range of environments.” This summary points to two characterizations, which are nearly universally – but often separately – found in definitions of intelligence: one with an emphasis on task-specific skill (“achieving goals”), and one focused on generality and adaptation (“in a wide range of environments”). In this view, an intelligent agent would achieve high skill across many different tasks (for instance, achieving high scores across many different video games). Implicitly here, the tasks may not necessarily be known in advance: to truly achieve generality, the agent would have to be able to learn to handle new tasks (skill acquisition). These two characterizations map to Catell’s 1971 theory of fluid and crystallized intelligence (Gf-Gc) [13], which has become one of the pillars of the dominant theory of human cognitive abilities, the Cattell-Horn-Caroll theory (CHC) [62].

Related work. Besides efforts to broaden task-specific evaluation to batteries of multi-task tests, there have been more direct and explicit attempts to integrate AI evaluation and psychometrics. A first approach is to reuse existing psychometric intelligence tests, initially developed for humans, as a way to assess intelligence in AI systems – perhaps an obvious idea if we are to take the term “artificial intelligence” literally. This idea was first proposed by Green in 1964 [29], and was, around the same time, explored by Evans [24], who wrote a LISP program We deplore this discrepancy between a focus on surpassing humans at tests of skill on one hand (while entirely disregarding whether the methods through which skill is achieved are generalizable), and a manifest interest in developing broad abilities on the other hand – an endeavour entirely orthogonal to skill itself. We hypothesize that this discrepancy is due to a lack of a clear conceptualization of intelligence, skill, and generalization, as well as a lack of appropriate measures and benchmarks for broad cognitive abilities. In what follows, we expose in more detail the issue with using task-specific “moonshots” (e.g. achieving better-than-human performance in a video game or board game) as stepping stones towards more general forms of AI, and we propose a formal definition of intelligence meant to be actionable in the pursuit of flexible AI and general AI.

Method. In 1973, psychologist and computer science pioneer Allen Newell, worried that recent advances in cognitive psychology were not bringing the field any closer to a holistic theory of cognition, published his seminal paper You can’t play 20 questions with nature and win [66], which helped focus research efforts on cognitive architecture modelling, and provided new impetus to the longstanding quest to build a chess-playing AI that would outperform any human. Twenty-four years later, In 1997, IBM’s DeepBlue beat Gary Kasparov, the best chess player in the world, bringing this quest to an end [12]. When the dust settled, researchers were left with the realization that building an artificial chess champion had not actually taught them much, if anything, about human cognition. They had learned how to build a chess-playing AI, and neither this knowledge nor the AI they had built could generalize to anything other than similar board games. It may be obvious from a modern perspective that a static chess-playing program based on minimax and tree search would not be informative about human intelligence, nor competitive with humans in anything other than chess. But it was not obvious in the 1970s, when chess-playing was thought by many to capture, and require, the entire scope of rational human thought. Perhaps less obvious in 2019 is that efforts to “solve” complex video games using modern machine learning methods still follow the same pattern. Newell wrote [66]: “we know already from existing work [psychological studies on humans] that the task [chess] involves forms of reasoning and search and complex perceptual and memorial processes. For more general considerations we know that it also involves planning, evaluation, means-ends analysis and redefinition of the situation, as well as several varieties of learning – short-term, post-hoc analysis, preparatory analysis, study from books, etc.”. The assumption was that solving chess would require implementing these general abilities. Chess does indeed involve these abilities – in humans. But while possessing these general abilities makes it possible to solve chess (and many more problems), by going from the general to the specific, inversely, there is no clear path from the specific to the general. Chess does not require any of these abilities, and can be solved by taking radical shortcuts that run orthogonal to human cognition. Optimizing for single-purpose performance is useful and valid if one’s measure of success can capture exactly what one seeks (as we outlined in I.3.1), e.g. if one’s end goal is a chess-playing machine and nothing more. But from the moment the objective is settled, the process of developing a solution will be prone to taking all shortcuts available to satisfy the objective of choice – whether this process is gradient descent or human-driven research. These shortcuts often come with undesirable side-effects when it comes to considerations not incorporated the measure of performance. If the environment in which the system is to operate is too unpredictable for an all-encompassing objective function to be defined beforehand (e.g. most real-world applications of robotics, where systems face unknown In summary, the hallmark of broad abilities (including general intelligence, as per II.1.2) is the power to adapt to change, acquire skills, and solve previously unseen problems – not skill itself, which is merely the crystallized output of the process of intelligence. Testing for skill at a task that is known in advance to system developers (as is the current trend in general AI research) can be gamed without displaying intelligence, in two ways: 1) unlimited prior knowledge, 2) unlimited training data. To actually assess broad abilities, and thus make progress toward flexible AI and eventually general AI, it is imperative that we control for priors, experience, and generalization difficulty in our evaluation methods, in a rigorous and quantitative way.

Discussion. Consequences for research directions towards flexible or general AI:

• It clearly spells out that the process of creating an intelligent system can be approached as an optimization problem, where the objective function would be a computable approximation of our quantitative intelligence formula. As pointed out in II.2.2, this objective function could be further refined by incorporating regularization terms that would take into account alternative forms of efficiency.

• It encourages a focus on developing broad or general-purpose abilities rather than pursuing skill alone, by proposing a target metric that penalises excessive reliance on experience or priors, and discounting tasks that feature low generalization difficulty.

• By defining and quantifying generalization difficulty, it offers a way to formally reason about what it means to perform “local generalization”, “broad generalization”, and “extreme generalization” (cf. the spectrum of generalization introduced in I.3.2), and to weed out tests that feature zero generalization difficulty.

• It should set out to measure broad abilities and developer-aware generalization:

Conclusion. • Intelligence is the efficiency with which a learning system turns experience and priors into skill at previously unknown tasks.

• As such, a measure of intelligence must account for priors, experience, and generalization difficulty.

• All intelligence is relative to a scope of application. Two intelligent systems may only be meaningfully compared within a shared scope and if they share similar priors.

• ARC takes the position that intelligence testing should control for scope, priors, and experience: every test task should be novel (measuring the ability to understand a new task, rather than skill) and should assume an explicit set of priors shared by all test-takers.

• ARC explicitly assumes the same Core Knowledge priors innately possessed by humans.

• ARC can be fully solved by humans, but cannot be meaningfully approached by current machine learning techniques, including Deep Learning.

Limitations. • Generalization is not quantified. While ARC is explicitly designed to measure “broad generalization” as opposed to “local generalization” or “extreme generalization”, we do not offer a quantitative measure of the generalization of the evaluation • Test validity is not established. Validity represents the predictiveness of test performance with regard to performance on other non-test activities. The validity of ARC should be investigated via large-sample size statistical studies on humans, following the process established by psychometrics. Further, when AI ARC solvers become a reality, we will also be able to study how well ARC performance translates into real-world usefulness across a range of tasks.