I came across several papers by M. Hutter & S. Legg. Especially this one: Universal Intelligence: A Definition of Machine Intelligence, Shane Legg, Marcus Hutter

Given that it was published back in 2007, how much recognition or agreement has it received? Has any other work better formalizing the idea of intelligence been done since? What is considered current standard on the topic in the field?

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    $\begingroup$ Hutter and Legg's definition of intelligence is based on Hutter's AIXI framework, and it's an optimization-based definition: basically, intelligence is a measure of the capability of an agent to optimize with respect to a "wide range of" environments. I don't think that everyone agrees with this definition (for some reason: maybe because not all people like the optizimization-based idea or the part "wide range of environments"), otherwise, my answer here would have more upvotes, but I haven't found any "better" definition of intelligence so far. $\endgroup$
    – nbro
    Mar 23, 2021 at 9:37
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    $\begingroup$ And I highly recommend everyone read nbro's blog post on the subject "On the definition of intelligence" $\endgroup$
    – DukeZhou
    May 27, 2021 at 1:53

4 Answers 4


My sense is that everyone is pretending Intelligence doesn't have a grounded definition, from which all other definitions arise:

  • Intelligence is a measure of utility in an action space μ(υ)

It can be a relative measure, in relation to other rational agents, or absolute in relation to solved games (problems). An action space is any context, and formalized as problems or sets of problems, typically grouped by complexity class.

Hutter and Legg is an explication of this grounded definition which accounts for unlimited contexts (complexity classes/environments) and for increasing utility of a given agent over time (learning/optimization.) Intelligence itself does not require learning or general applicability, but Hutter & Legg does not refute this, merely grades static intelligence and narrow intelligence as more limited.

Even this is subject to context, as more limited rationality can be more optimal.

  • The definition of intelligence is grounded because, while the term "intelligence" is a symbol, intelligence itself is function, the strength of which evaluated by a measurement of some result (utility)

It doesn't require defining the function to understand it as a function: measurement of a result requires mechanism and decision/action.

You will find this natural language definition applies to even emotional intelligence, which relates to the observational capability of the rational agent in context, and allow that rational agent to make more optimal decisions in context.

This is similar in spirit to truth, only grounded in a formal logic context, where it is a condition and result, not an assertion. By contrast, the the conditionality of truth is often obscured in a natural language context, where is is routinely applied to unvalidatable informal statements, and can even be conflated with the statement itself à la: "this is the truth!"


The short answer is that it hasn't received nearly the attention it should have despite the cited paper having over 600 citations.

According to this Singularity Summit talk by Shane Legg, his PhD thesis on the wide ranging uses of the word "intelligence" managed to identify 2 qualitative dimensions of those uses:

  1. Human vs Ideal
  2. Internal vs External

Of the 4 points in the space of these 2 dimensions, the sense in which his paper with Hutter uses the word "intelligence" is (Ideal, External). This is distinguished from the Turing Test which is for (Human, External).

The vast majority of machine learning targets (Ideal, External) intelligence rather than modeling human intelligence.

The formal, "top-down" definition of (Ideal, External) provided by Hutter is called AIXI, which is the unification of ideal science (Algorithmic Information Theory aka AIT) with ideal technology (Sequential Decision Theory aka SDT).

Unlike other attempts to define (Ideal, External) intelligence, it has only 2 open parameters:

  1. Choice of Universal Turing Machine running the universe in which the agent perceives as well as the agent's simulation of that universe to make predictions.
  2. Choice of utility function providing the value system of the agent so it can decide which actions yield the most valuable consequences.

In the vernacular, AIT is about what "is" and SDT is about what "ought" to be done about what "is".

For just one example of why AIXI has not received nearly the attention it should have:

The ethics of AI are riddled with the conflation of "is" with "ought". Under AIXI, these can be, at the top level of analysis, factored out using the Algorithmic Information Criterion for model selection, which is conceptually quite simple:

Given the union of all datasets used to train "large" AI models, choose the model that yields the smallest executable archive of that data.

The model so-selected is the best available model of what "is" the case -- including models of bias in the (possibly latent) identities that are the sources of data. If we are to be fair about what is and is not "bias" here's how to proceed:

If someone has a reason to call some data "biased" then they should be challenged to provide the data that supports their perception of what is and is not "biased". Then, simply include that data in the total dataset. If they, themselves, are biased and select biased data because of their bias, let others include the data that shows that bias to be, in fact, bias. Compress relentlessly until the data that is most consilient with the rest of the universe is better compressed, leaving the bias exposed as "noise" associated with the responsible identities.

This has applications in dealing more effectively not only with social media censorship, but by factoring out the "is" from the ethics, it permits people to recognize when they simply differ in their utility functions or "value systems" and get on with the hard problem of dealing with quasi-religious differences and thereby reduce the likelihood of conflicts that can be exceedingly destructive.

Nor is this merely pie-in-the-sky as Hutter has demonstrated with The Hutter Prize for Lossless Compression of Human Knowledge. The Hutter Prize, if funded at the level deserving of the problem of ethics in AI, would be several orders of magnitude larger.


While I cannot tell you what intelligence is/should be, I can give you why their definition fails by today's standard on what systems are intelligent.

According to their definitions, the most intelligent model is that is statistically most optimal in various (goal-driven) environments. This definition leads to Hutter's AI model AIXI being arguably the most intelligent, because in every step, given the current environment and previous observations it statistically optimally predicts (well, the uncomputable model, and a computable model restricted by time and size gives the most statistically optimal prediction bounded by time and size). This takes exponentially much time (with regard to space size) however.

Just like most other models, AIXI also starts with zero knowledge and learns step by step. Now, if we have limited resources, and want to create the model that predicts best based on the resources we have, then one could argue that AIXI may predict best and be the most intelligent (after trained on all our resources). In reality, we have much more resources than ever "run out" and the goal is rather to build models that learn fast (and scale for long). Two decades later it is clear that you definitely do not need to optimally predict while learning on data, it is faster to make mistakes and go back to correct them. The learning makes AIXI inefficient, and no "intelligent" system today builds on it. They build on things that based on these concepts would be unintelligent, yet they work better.

Learning must definitely be a key component of intelligence in the case of models (or natural entities) that start with zero or low knowledge.


Just a few commonsensical remarks about why this kind of intelligence definition seems unable to capture the logic of life:

  1. Optimization only makes sense in a stationary environment. When many agents learn and interact, they are building a constantly changing environment.

  2. Survival and reproduction is the only thing that really matters, and it does not require optimization, just good enough solutions.

  3. The survival of individual living organisms heavily depends on adequate hardwired sensory abilities that can slowly change throughout many generations. But smarter individuals can use their brains (or whatever tools they may have endowed with plasticity) to quickly learn and adapt in non-stationary environments. Fast learning, not optimization, is what these agents really need.

  • $\begingroup$ Welcome to SE:AI! I think Herbert Simon nailed it with satisficing $\endgroup$
    – DukeZhou
    May 27, 2021 at 1:50

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