Shane Legg on Measuring Machine Intelligence

At the 2010 Singularity Summit, Shane Legg begins with the rapid historical growth of supercomputer calculations. A logarithmic chart makes exponential progress look almost ordinary, but he finds the scale startling.

Legg describes a contemporary projection of around 10²⁰ calculations per second within 15 years. He compares that number with estimates of beach sand grains and neurons across human brains; these analogies convey scale, not equivalence between a calculation and a neuron.

Computing speed alone does not answer the question he cares about. A machine may do spreadsheets faster or play a particular game better; he wants a graph showing whether general intelligence itself is improving.

To measure intelligence, one first needs a concept of it. Legg credits an introductory distinction in Russell and Norvig’s AI textbook: decide whether the target is human-like performance or some ideal such as rationality or optimality.

A second distinction concerns internal properties versus observable behavior. An account may care about thought, emotion, consciousness or biological substrate, or it may care principally about what the system does. Together the two distinctions form four broad quadrants.

Legg places the Turing test in the human-like behavior quadrant. Marcus Hutter’s AIXI model represents an idealized behavioral approach, while John Searle’s Chinese room argument questions whether outward performance establishes internal understanding.

He treats the quadrants as different questions, not simply competing answers. Someone seeking a machine to solve problems may care about outcomes, while someone interested in mind uploading may care deeply about consciousness. His own target is idealized behavior, without dismissing the other questions.

Legg collected nearly 80 definitions of intelligence and found recurring clusters. Across examples, an intelligent system acts successfully in many environments, adapts to uncertainty and pursues some notion of a goal. Generality matters: a system cannot just be a one-trick specialist.

He summarizes the shared idea as an agent interacting with an environment to achieve goals across a wide range of environments. Reinforcement learning offers mathematical tools for expressing agents, interactions and performance.

A formal overall score still needs a way to weight the potentially infinite environments. Legg illustrates the issue with a number sequence: more than one rule fits observed values, but an IQ test usually favors the simpler continuation.

He invokes Occam’s razor as a heuristic: simpler explanations are favored, although they can be wrong. In his formalization, environments with greater algorithmic complexity receive less weight.

The resulting equation combines an agent, an environment, a measure of success and a weighted range of computable environments. Legg describes the agent in probabilistic terms and evaluates its expected performance through interaction.

Legg argues that the definition is useful partly because it is explicit: researchers can dispute the definition or analyze its implications. It connects recurring informal definitions to a mathematical quantity, and theoretically distinguishes simple learning agents.

At the other end of the range is Hutter’s AIXI, an idealized model requiring unbounded computation. Legg describes the measure as spanning simple agents and this theoretical ideal; those mathematical properties do not make the ideal directly practical.

Unlike a binary pass-or-fail test, a continuous score could show whether an algorithm becomes a little more capable after a modification. Legg also values a definition that does not require human judges to decide whether behavior looks human.

The theoretical measure includes uncomputable components, so building a practical test requires approximations. Legg says he and collaborator Joel Veness have implemented an approach and stresses that the results are very preliminary.

Their first sanity check compares a random agent, a simple frequency-based learner and more sophisticated reinforcement-learning algorithms including Q-learning variants. The experimental score orders these examples as the researchers expected, though he says they will continue refining the test.

A second experiment tests Monte Carlo AIXI, a practical approximation that samples possible models. Legg says the agent can learn several simple games; the experiment varies the model’s context depth, an approximate measure of the complexity it can represent.

The preliminary score rises as the model becomes larger, and a separate variation in available computation shows a similar pattern. Legg reports confidence intervals and significance for the points available at the time, while noting that more computing would allow more data.

A measurable concept could support both theory and experiments: researchers could change an algorithm, run it on the test and observe whether performance shifts. Legg mentions possible work with Demis Hassabis on incorporating ideas from theoretical neuroscience.

He also suggests examining narrower kinds of intelligence by changing how the test is sliced. His closing argument is that explicit definitions and measurements help artificial intelligence research state and investigate its goals.

In questions, Legg explains that the practical test samples environments generated from a simple computational framework and estimates expected performance using Monte Carlo methods. He cautions that the full implementation is too involved to explain in a short answer.

For the early tests, the team needed more than a thousand sampled environments to obtain useful confidence intervals. As agents become more capable, differences may become subtler, so more samples or methods such as stratified sampling may be needed.

Asked where learning appears in the equation, Legg says adaptation is implicit in the task: the agent enters unfamiliar environments and must learn enough to perform well across them.

The team has not formally scored a human. Veness tried some generated environments: a few were easy, others required thought, and some remained hard to understand even after examining the program. A full score would have required many trials.

An audience member proposes making the Turing test more continuous by comparing systems with people at different developmental levels. Legg responds that toddlers already have sophisticated physical and interactive abilities that contemporary algorithms do not match.

Asked about connections to statistical learning theory and limitations of approximation, Legg says he has not analyzed the first question. For the second, he reiterates that the practical method uses a finite Monte Carlo sample instead of all possible weighted environments.

A final question raises the sensitivity of rankings to environment choice. Legg agrees that weighting is a major challenge: simple reference machines emphasize environments with simple computational structure, while a world-like reference could favor capabilities adapted to our world.

He proposes thinking of a family of tests along a spectrum of reference machines. The theoretical ideal offers a common point of comparison, but maintaining a stable practical scale as the environment distribution changes remains a challenge raised by the questioner.