A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.
Metadata: arXiv. Abstracts retain their original authors’ rights.
In the conversation
Original HN comments, with labels from simple text rules. A label describes the whole comment and may miss context or irony. Read the discussion to make up your own mind. About the labels
> Maybe it is human like intelligence already.
It objectively is not.
First, intelligence (human or otherwise) is typically defined as the sum of value functions of a given policy across all states, divided by an exponential of the complexity of the environment[0] (page 23). The GPT-4 technical report[1] specifically points out that it is unable to make money when given an initial amount and AWS access (appendix H § 2.9). A human can.
Second, let's look at it mechanically. It is very easy to anthropomorphize machines, but they are just built differently. Neurons fundamentally are not approximated by self-attention and it is highly unlikely that they improve through…
Read the full comment
backpropagation. In terms of behaviour, we can and do notice differences. They can, and do, make logical mistakes; when asked to immediately answer a complex question, they can only think through it for a fixed amount of time, and thus fail to give an accurate answer. More importantly, they just don't care about their (or your) own survival; they can give lethal advice. All it takes is to find a prompt for which the most common completion is lethal, and they will just complete that. Removing those completions is a whack-a-mole in RLHF: each that gets popular on Twitter will be fixed, but there are more, and GPT just won't take extra time to think just because a life is on the line.
[0]: https://arxiv.org/pdf/0712.3329.pdf
[1]: https://cdn.openai.com/papers/gpt-4.pdf
> It is a term gaining in popularity due to this difficult to define definition and allows for more a porn like definition
> Philosophers, psychologists, neuroscientists, and many others have been contemplating the definition of intelligence for centuries and we're still not -quite there
Given the decade-old, seminal, widely cited papers by Legg (co-founder of Deepmind) & Hutter (long-term professor of ANU with multiple awards, currently researcher at Deepmind) titled "Universal Intelligence: A Definition of Machine Intelligence"[1] and "A Collection of Definitions of Intelligence"[2] and the whole rigorous mathematical theory of universal bayesian reinforcement learning…
Read the full comment
aka "AIXI"[3] developed during the last decades which you fail to mention, this soft language of "not quite there" looks evasive, bordering on disingenious even.
Citing Chomsky, with his theorems which were interesting at their own time yet quickly faded into irrelevance once the modern assumptions of learning theory were developed, and Marcus whose simplistic prompts are a laughing stock among degreed and amateur practicing researchers alike brings little of value to the already biased discussion.
> Of course, there are others in the field that argue that the algorithms can learn this through enough data
Such as Rich Sutton, one of the fathers of Reinforcement Learning as an academic discipline, whose recent essay "Bitter Lesson"[4] took the field by word of mouth, if nothing else. It takes a certain amount of honesty and resolution to acknowledge that one's competitive pursuit of knowledge, status and fame via participating in academic "publish or perish" culture does not bring humanity forward along a chosen axis, compared to more mundane engineering-centric research, many people commend him for that.
> So another thing, is that machines haven't shown really good generalization, abstraction, or really inference.
To play a devil's advocate: "Scaling is all you need" and "Attention is all you need" are devilishly simple hypotheses which seem to work again and again when we reluctantly dole out more compute to push them further. With a combination of BIG-bench[5] and an assortment of RL environments as the latest measuring stick, why should we, as a society, avoid doling out enough compute to take it by storm in favor of a certain hypothesis implicit to your writing, which could as well be named "Diverse academic AI funding is all you need"? Especially when variations of this hypothesis have failed us for decades starting with the later part of the XX century, at least if we consider AI research.
> but let's recognize that this camp does exist (we have no facts, so there's opinions).
With all due respect, the continuing lavish (by global standards) funding of your career and careers of many other unlucky researchers should not be a priority when such massive boon to all of humanity as a practical near-HLI/AGI is at stake. "Think of the children", "think of the ill", think of everybody who is not yourself - I say as a taxpayer, hoping for AGI checkpoint to be produced by academics and not the megacorporations, and owned by the people, and not the select few.
Which - the proprietary nature of FAANG-developed AI - might be a real problem we are going to face this decade which is going to overshadow any career anxiety you may have experienced so far.
1. https://arxiv.org/abs/0712.3329
2. https://arxiv.org/abs/0706.3639
3. https://arxiv.org/abs/cs/0004001
4. http://www.incompleteideas.net/IncIdeas/BitterLesson.html
5. https://github.com/google/BIG-bench
> I will continue dismissing AGI until someone can tell me what GI is
Here's a rather famous recommendation for a definition of general intelligence: https://arxiv.org/pdf/0712.3329.pdf
Very loosely paraphrasing their paper, general intelligence is the ability to adapt to novel situations and predict the future better than any other algorithm could do.
Personally, I think of perfect AGI as this: given that our universe is capable of approximation to arbitrary precision using a universal Turing machine (and infinite time and memory), AGI is the best* computable approximation to Solomonoff induction.
*"best" being some mathematical notion of optimality.
> There is a body of thousands of scientific studies discussing what intelligence means
Which don't agree on a single definition. See for example:
https://arxiv.org/abs/0712.3329
>Practical intelligence is clearly multidimensional
I wouldn't call that clear at all! Of course no matter how intelligent a person is, there will be environments in which they do poorly. Feynman would do poorly in the environment called, "Everyone find Feynman and beat him up". But that environment is very contrived, or, more formally, has a high Kolmogorov complexity.
Legg and Hutter argue quite strongly for single-dimensional practical intelligence in this paper (I don't agree with their reasoning, but the point is that it's definitely not blatantly "clear" that practical intelligence is multidimensional): https://arxiv.org/pdf/0712.3329.pdf
Shane Legg (co-founder DeepMind) and Marcus Hutter (Schmidhuber pedigree) defined machine intelligence in this canonical paper from 2007: https://arxiv.org/abs/0712.3329
> Universal Intelligence: A Definition of Machine Intelligence
> A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we approach this problem in the following way: We take a number of well known informal definitions of human intelligence that have been given by experts, and extract their essential features. These are then…
Read the full comment
mathematically formalised to produce a general measure of intelligence for arbitrary machines. We believe that this equation formally captures the concept of machine intelligence in the broadest reasonable sense. We then show how this formal definition is related to the theory of universal optimal learning agents. Finally, we survey the many other tests and definitions of intelligence that have been proposed for machines.
General intelligence usually meant in relation to humans, but you are correct in noting that it is a spectrum, not a binary.
Well, this seems to be the definition Deepmind uses: https://arxiv.org/abs/0712.3329 . And there has been work to establish a quantitative measure of the extent to which an agents behavior is intelligent or mechanical: https://arxiv.org/abs/1805.12387 .
> the assumption that humans have it [general intelligence] is a conceit without convincing evidence
Why do you make this claim? Engineering, science, and mathematics are all convincing evidence that humans have general intelligence. Humans also score highly in measures of intelligence like https://arxiv.org/abs/0712.3329.
One of the co-founders of DeepMind (Shane Legg) has provided the following definition of intelligence: "Intelligence measures an agent’s ability to achieve goals in a wide range of environments" in [1]. This definition has been pretty influential, and in the sense of this definition, AlphaGo is not AI. But it is a great step towards AI.
[1] S. Legg, M. Hutter, Universal Intelligence: A Definition of Machine Intelligence. https://arxiv.org/abs/0712.3329
> consciousness and insight
Being unmeasurable and undefined, and therefore irrelevant to measures of intelligence, "consciousness" is typically not considered part of AGI [1]. Not sure what you mean by "insight".
[1] http://arxiv.org/abs/0712.3329
Cool paper! learned a lot about shared beliefs. But I was asking myself "why is 50k traders using similar trading patterns an example of collective intelligence"? I expected an example of a collective accomplishing a group goal as opposed to optimizing individual ability to accomplish goals.
Noted in first paragraph: "we still lack a coherent formal perspective on what human collective intelligence actually is". But, why not reference the closest definition or propose your own rigorous definition of collective intelligence to ground assumptions in the paper?
For instance, in 2007 Legg and Hutter presented a paper, "A Definition of Machine Intelligence"…
Read the full comment
(http://arxiv.org/pdf/0712.3329v1.pdf) which inventoried existing definitions of machine intelligence and suggested their own definition. Seems like these definitional papers would be the starting point for presenting research on any kind of intelligence. Do you see meaningful work in this direction regarding defining collection intelligence?
The No Free Lunch Theorems don't apply in reality anyway, as explained at https://en.wikipedia.org/wiki/No_free_lunch_in_search_and_op...
Essentially: NFL says the performance (1 / number of trials are required to find a solution), when averaged over all fitness functions, will be the same for all optimisation algorithms. However, most fitness functions require more computational power than the Universe to evaluate; making even a single trial impossible to perform.
Since those problems are already impossible, it doesn't matter how many trials our optimisation algorithm would require when tackling them. We can use this unobservable bad performance to offset some observable…
Read the full comment
good performance, to remain within the average dictated by NFL whilst still becoming objectively better.
In fact, one of this paper's authors (Shane Legg) has used this fact to define a general intelligence test which favours performance on simple functions http://arxiv.org/abs/0712.3329
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.
Artificial intelligence (AI) researchers have been developing and refining large language models (LLMs) that exhibit remarkable capabilities across a variety of domains and tasks, challenging our understanding of learning and cognition.