Some Notes on Intelligence


Responding to Benjamin Riley, Modeling Minds (Human and Artificial): What are we talking about when we talk about intelligence? See also the discussion here.

In the paper on Modelling Minds Riley writes, " improving one’s knowledge within a specific domain generally does not significantly improve one’s reasoning abilities."

To the extent that this is true (and it is probably not true) it is true only in strictly limited circumstances. I would treat with a lot of scepticism the De Bruyckere, Kirschner and Hulshof paper purporting to make the case.

In the strictly limited case, the principal amounts to this: if you only learn A, you only learn A, and learning A will not help you learn B, even if both A and B involve some higher level skill, C. So (for example) if you only learn physics, which also involves learning mathematics, it will not help you learn engineering, which also involves learning mathematics.

It's hard to believe not learning mathematics while learning physics would not also help you learn engineering. The only way to make the argument work is to argue that, if you only learn physics, you do not actually learn any mathematics at all. That is, in a nutshell, you cannot generalize from a single instance, because (in principle) you don't know what parts of physics generalize, and what parts of physics are specific to physics.

But it is, in my view, a bad argument (a terrible argument, actually) because as soon as you start to learn engineering, you begin to recognize patterns that you already saw in physics. You see that the exact same shapes and operations are used (specifically, numbers and math functions). You don't actually need some higher level principle in order to obtain this benefit, you just need to recognize the pattern.

That's just as well, because the high level 'knowledge' stipulated by De Bruyckere, Kirschner and Hulshof are effectively meaningless as descriptions of any sort of knowledge. Here's what they are, in the order presented in the paper:
- creativity (chess)
- problem solving (computer programming)
- executive functions (music)
- better thinking (languages)

The authors go so far as to assert that these higher level 'skills' are innate and not learned. For example, they write, "Creativity is not a skill, and it cannot be taught or learned. Creativity is a quality or characteristic that a person possesses."

The diagram presented in the Riley article has a more plausible set of higher order skills: inference, planning and abstraction in the first instance, and the larger set of test-specific skills (above and below, center, clean up, etc...) later on. But it's interesting to see that learning these higher level skills is not impossible for LLMs, just difficult. As you note, "On the other hand…the fact that LLMs can solve them at all is impressive! Further, some might argue that in time we should expect them to get better at this type of thing."

The more solved examples of this sort you present to an LLM, the more nuanced the pattern recognition becomes, and the more likely it will solve the problem. Critically, it does not need to infer some higher level principle at work in the examples (much less any of the completely specious 'skills' described by De Bruyckere, Kirschner and Hulshof), it just has to detect the pattern. And this is what LLMs, and neural nets in general, are very good at.

Indeed, what these examples will show in general is that the difference between human and LLM performance (if, ultimately, there is any) will come down not to some presupposed inability of LLMs to acquire some putative 'innate' skills, but rather, the body previous experience (in other domains) that a human will have that an LLM won't. A human that has taken other tests in other domains will recognize the conventions around test-taking that an LLM will have to figure out for itself.

So the proper test isn't when learning A also results in someone (or something) learning C. The possibility that there even is a C won't be recognized until attempting to learn B. And previous experience in other domains will suggest that there is a possibility of being able to recognize similarities between A and B. And that's why it's helpful to teach mathematics as a separate subject. Not because of the content knowledge acquired. But because it eases the learning of B after having learned A by identifying aspects of C that might be relevant.

So what is 'intelligence' on this alternative account? Well, it's not a shopping list of 'higher order skills' - certainly not 'creativity, problem solving, executive function and better thinking', not 'inference, planning and abstraction', and not even 'above and below, center, clean up, etc...'. No. On this view, knowledge is recognition, and intelligence is the capacity to recognize, and this is most certainly something that can be learned or developed in a person, and this represents a cultural difference, generally, and not an inherent or genetic difference.


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