On the definition of intelligence


Introduction

There are many people that claim that we still do not agree on a definition of intelligence (and thus what constitutes an artificial intelligence), with the usual argument that intelligence means something different for different people or that we still do not understand everything about (human or animal) intelligence. In fact, in the article What is artificial intelligence? (2007), John McCarthy, one of the official founders of the AI field, states

The problem is that we cannot yet characterize in general what kinds of computational procedures we want to call intelligent. We understand some of the mechanisms of intelligence and not others.

To understand all mechanisms of intelligence, some people, such as Jeff Hawkins, have been studying the human brain (which is the main example of an information-processing system that is associated with intelligence). Definitely, we still do not fully understand how the human brain processes information, but this does not mean that we can’t come up with a general definition of intelligence that comprises all forms of intelligence (that people could possibly refer to). In other words, you do not need to fully understand all mechanisms of intelligence in order to attempt to provide a general and sound definition of intelligence. In fact, theoretical physicists (such as Albert Einstein) do not need to understand all the details of physics in order to come up with general laws of physics that are applicable in most cases and that explain many phenomena.

Universal Intelligence: A Definition of Machine Intelligence

There has been at least one quite serious attempt to formally define intelligence (and machine intelligence), so that it comprises all forms of intelligence that people could refer to.

In the paper Universal Intelligence: A Definition of Machine Intelligence (2007), Legg and Hutter, after having researched many previously given definitions of intelligence, informally define intelligence as follows

Intelligence measures an agent’s ability to achieve goals in a wide range of environments

This definition apparently favors systems that are able to solve more tasks (e.g. AGIs) than systems that are only able to solve a specific task (e.g. narrow AIs).

To understand if this is true, let’s look at their simple mathematical formalization of this definition (section 3.3 of the paper)

\[\Gamma(\pi) := \sum_{\mu \in E} \frac{1}{2^{K(\mu)}} V_{\mu}^{\pi}\]

where

  • \(\Gamma(\pi)\) is the universal intelligence of agent \(\pi\)
  • \(E\) is the space of all computable reward summable environmental measures with respect to the reference machine \(U\) (aka the space of all environments)
  • \(\mu\) is the environment (or task/problem)
  • \(V_{\mu}^{\pi}\) is the ability of the agent \(\pi\) to achieve goals in the environment \(\mu\)
  • \(K(\mu)\) is the Kolmogorov complexity of the environment \(\mu\)

We can immediately notice that the intelligence of an agent is a weighted combination of the ability to achieve goals in the environments (which represent the tasks/problems to be solved), where each weight is inversely proportional to the complexity of the environment (i.e. the difficulty of describing/solving the corresponding task).

So, the higher the complexity of an environment, the less the ability of the agent to achieve goals in this environment contributes to the intelligence of the agent. In other words, the ability to solve a very difficult task successfully is not enough to achieve high intelligence. You can actually achieve higher intelligence by solving many but simpler problems. Of course, an intelligent agent that solves all tasks optimally would be the optimal or perfect agent. AIXI, developed and formalized by Hutter, is actually an optimal agent (in some sense), but, unfortunately, it is incomputable (because it uses the Kolmogorov complexity)1.

Consequently, according to this definition, almost all animals are more intelligent than AlphaGo. I agree with this, but many people that believe that intelligence is mainly utility may not agree with this (so we are back to the same problem that we still do not agree on the definition of intelligence), although I think that a fundamental aspect of intelligence (almost a synonym) is adaptability to different environments or tasks, but systems like AlphaGo do not really have this property. In any case, note that, according to the definition of universal intelligence, AlphaGo is still intelligent, but just not as intelligent as many other animals 2!

In the paper, they also discuss issues like intelligence tests and their relation to the definition of intelligence: that is, is an intelligence test sufficient to define intelligence, or is an intelligence test and a definition of intelligence distinct concepts?

  1. \(\Gamma(\pi)\) is also a function of the Kolmogorov complexity, but this is just a definition, i.e. it does not directly give you the instructions to develop intelligent agents. 

  2. According to this definition, even a virus could be considered more intelligent than AlphaGo! Isn’t that true anyway? In fact, you can’t compete with most viruses (e.g. HIVs have been winning games against us for a long time)!