I disagree. I routinely let LLMs speculate or generate hypotheses along the way of helping with technical research. Sometimes they can prove the correctness of a concrete math idea but other times even an unproven conjecture helps with the numerical algorithm implementation and the result is then simply supported by additional data. I guess that any autoresearch-adjacent application has LLMs intuiting and coming up with hypotheses/conjectures—as do the steps/lemmas along a complex proof. In my opinion the modern LLMs are powerful intuitive thinkers that generate lots of conjectures of varying quality or importance.
People keep saying this. Why?
Surely the AI can complete the prompt “Generate new research questions based on these observations”?
When I read the reasoning traces of coding models they are constantly asking themselves questions and attempting to answer them.
Humans can “intuit” based on a much larger, if not unlimited, context. Also I just want to say that human cognition is something so insanely complex and deep that we will not understand it at all in my lifetime. To attribute all, or really any, aspects of human cognition to a machine at this point is silly to me.
Most humans are dumber than a box of rocks. Here in Seattle we had one of many light rail-related fuckups where they had to replace part of the line with buses. People piled into the front of one when it was full. When people got out they never moved back. As the driver struggled to close the door and people struggled to get in the wad of people never moved back to fill the ample space.
Chatgpt was smarter than the average person a while ago
There are processes at work there that we don’t even have the language to describe.
(86 billion is the number ChatGPT, ironically enough, has given me a couple of times. I remember hearing for a long time that it was estimated to be somewhere in the ballpark of 100 billion. This is not my field of study.)
For now, caring about a topic (or having somebody you trust care for you) still gets you better information than asking an LLM.
This does not demonstrate a lack of intelligence. It demonstrates laziness and a lack of interest in spreading apart. Or just lack of consideration (or even malice) on the part of those at the back of the wad.
> Chatgpt was smarter than the average person a while ago
This is an absurd claim that fundamentally misunderstands what it means to be "smart". Reasoning that would get you to this conclusion would equally well apply to Google's search engine over a decade ago.
They can't exit the hull until the "intuition" starts spawning points outside the convex hull.
The extent to which they are able to do this is the more interesting question!
By the way, convex hull permits extrapolating past the training data. LLM won't invent a new word that could not be defined by a sequence of known words. Just if it's meaningless and fully random/hallucinated, the new knowledge won't work with other known information blocks (breaks convexity).
It's a convex hull of information that is reflective and spans outside of itself and combines in a new way, when you shine two known rays of light together from the inside.
Now it gets better. AI can be orders of magnitude more creative than any human could ever hope for, because his convex hull of information is orders of magnitude larger, and the possibilities for new combinations are equally larger.
Not completely. Novelty used to be a major thing, when Humans did it. Another important criteria used to be if that new thing makes sense at all. Here the language model has a problem, as it doesn't have the means to evaluate this criteria.
Maybe there's some sense of "remix" that covers all of that, but then that meaning is not the standard one, or maybe you would concede that this happened in the past, but isn't happening now, but then where's the cutoff, or maybe something else...?
In your analogy, I would love to see some elaboration on the "reflective and spans outside of itself" part -- geometry doesn't work that way, do you have a more intuitive metaphor, or ideally a mechanism, or even better, some examples?
For the same reason that you can't draw a 15 of Diamonds from a regular card deck.
You can't find things on a map that aren't there, but maybe you can draw a route nobody used before.
Since we're quoting Douglas Adams in this thread, I'll mention something I posted a while back, with his writings as example. After Douglas Adams passed away, somebody was tasked to "finish" The Hitchhiker's Guide to the Galaxy :
> And Another Thing... is the sixth and final novel in The Hitchhiker's Guide to the Galaxy series. Written by Eoin Colfer with the blessing of Douglas Adams' widow Jane Belson
Being a rather big fan, I immediately bought and read this novel and I have to say that Eoin Colfer did a really really great job, nailing the tone, humour and writing style of Douglas Adams.
IMVHO, he did about as good as anyone could reasonably expect someone to do, when given this task. It was big shoes to fill, and I was impressed.
But it just also wasn't good enough, in a weird way that I found hard to put my finger on at first.
The thing is that Colfer was doing the tone of voice, even came up with somewhat new jokes perfectly in the style of, etc etc. And for the sake of argument let's say he was able to get "arbitrarily close".
But there was always one thing he couldn't do: Actually make something new happen, make a new kind of joke, do a real plot twist, a big reveal, stuff like that. Because then it would deviate from Douglas Adams' work too much.
However, if Douglas Adams was still alive, this limitation would not apply to him: he could make a new kind of joke, do a plot twist, big reveal, and it would become canon.
This the best "good faith" argument I can present for how LLMs lack "intuition", in some sense. Now "intuition" is not a very exactly defined term, but I'm arguing that the thing I'm describing here, is at least a part of intuition, that an LLM fundamentally can't reach (until they start getting their own volition, which I would prefer they didn't).
To address your question:
> Surely the AI can complete the prompt “Generate new research questions based on these observations”?
Yes I imagine it could do that very well. But it would still need a human to decide if the research questions are "relevant" or "within scope" of what the human wants (a.k.a. their volition). Without that filter, the research would just bloom out exponentially, with more and more questions nobody was asking.
And yes, up to some point that "blooming" behaviour is a useful aspect of research, the exploratory aspect/phase, but at some point you need to get back to the "synthesis" aspect/phase, to distill all the explorations back to "stuff that matters". And just like Douglas Adams vs Eoin Colfer, only the human who wants to know something, can decide to widen or change the domain of that synthesis, but if the LLM were to decide this (outside of exploratory phase), it would actually be considered the wrong answer.
And this is not at all to say you can't do research with LLMs, obviously you can. But this is just a thing they can't do, on a real philosophical level. I'm also not saying you can't work around this limitation, you probably can, I'm just saying it exists.
That's how they are finding these solutions though, unless we are just going to label intuition as something only humans can do. Like a submarine being unable to swim or whatever that example is.
The two places were seeing lots of movement are:
* Updates to lower/upper bounds. In many cases, these kinds of problems are the deep-math equivalent of calculating more digits of pi. Yes, if you throw time at it you'll break the record, but it may not be terribly worthwhile.
* Finding counter examples which disprove conjectures. This is really useful, and helps offset some positivity bias on the human side, often bringing together known tools from distant silos.
If you read the list of ten results, almost all fall into one of these buckets.
As someone with a PhD in combinatorics, I believe that I'm qualified to say that, yes, there are problems as useless as calculating more digits of pi.
There's nowhere else to move the goalposts. You've already stashed them in the far corner of the parking garage down the street from the stadium. If you go any farther you'll leave the school grounds entirely.
Matrices are an implementation detail in reconstructing the surface of human knowledge. It's a complex surface, but it's a regurgitation.
Of course computers can grind in a way that humans can't. But now we have systems that convert the human-comprehensible ideas into a computer's plan of attack, in a way that greatly expands the frontier of ideas thus treatable.
"Excuse me, We demand rigidly defined areas of doubt and uncertainty!"
DT: Might I make an observation at this point?
MT: You keep out of this metal nose.
VF: We demand that that machine not be allowed to think about this problem!
DT: If I might make an observation…
MT: We’ll go on strike!
VF: That’s right. You’ll have a national philosopher’s strike on your hands.
DT: Who will that inconvenience?
MT: Never you mind who it’ll inconvenience you box of black legging binary bits! It’ll hurt, buster! It’ll hurt!
DT: [Booming] If I might make an observation …
“All I wanted to say,” bellowed the computer, “is that my circuits are now irrevocably committed to calculating the answer to the Ultimate Question of Life, the Universe, and Everything.” He paused and satisfied himself that he now had everyone’s attention, before continuing more quietly. “But the program will take me a little while to run.”
Fook glanced impatiently at his watch.
“How long?” he said.
“Seven and a half million years,” said Deep Thought.
Lunkwill and Fook blinked at each other.
“Seven and a half million years!” they cried in chorus.
“Yes,” declaimed Deep Thought, “I said I’d have to think about it, didn’t I? And it occurs to me that running a program like this is bound to create an enormous amount of popular publicity for the whole are of philosophy in general. Everyone’s going to have their own theories about what answer I’m eventually going to come up with, and who better, to capitalize on that media market than you yourselves? So long as you can keep disagreeing with each other violently enough and maligning each other in the popular press, and so long as you have clever agents, you can keep yourselves on the gravy train for life. How does that sound?”
The two philosophers gaped at him.
“Bloody hell,” said Majikthise, “now that is what I call thinking. Here, Vroomfondel, why do we never think of things like that?”
“Dunno,” said Vroomfondel in an awed whisper; “think our brains must be too highly trained, Majikthise.”
So saying, they turned on their heels and walked out of the door and into a life-style beyond their wildest dreams.”
>I don’t understand it yet. Maybe it’ll take me an afternoon to check all the calculations, but what would still be missing is why this was an approach that would’ve made sense in the first place. Is there some broader context or theory within which this would’ve been the obvious thing to do? What other results can be proven using these techniques? What is it telling us about quantum information or operator theory? I have no idea. I spent about an hour this morning asking ChatGPT these questions, but it’s somewhat frustrating because it speaks with a mishmash of physicist, operator algebraist, quantum information theorist-lingo, plus the usual LLM breezy lilt that annoys everybody.
They certainly seem to have "intuited", in a way that is not immediately obvious to experts in the field, the way to solve at least some of these problems. This was not just simply grinding away at a method that humans already knew would work and just hadn't gotten to yet.
[0] https://nitter.poast.org/henryquantum/status/208362369543662...
Quantum waveform collapse has been proposed as explanation for consciousness, allowing to explain how an entity can have free will and yet obey rigid physical laws: https://en.wikipedia.org/wiki/Consciousness_causes_collapse
I think OP is suggesting a similar thing happened in the LLM, implying it gained consciousness despite following a well-defined compute process.
https://github.com/mxgmn/WaveFunctionCollapse
It's one of the coolest things I've ever seen.
I guess I've been pronouncing it wrong though. It's wave function collapse, not waveform.
I haven't studied it properly yet but it kind of looks like how sudokus work. You have a bunch of plausible options, and the various possible worlds overlap with each other but not completely and then you eliminate the things that are not possible until the actual possibility remains.
I think thinking works similarly, and I wouldn't be surprised if artificial thinking also worked similarly.
The waveform collapse is natively "very high dimensional", not sure why the "but" part of the sentence belongs here.
Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this.
--
"Yes we are," insisted Majikthise. "We are quite definitely here as representatives of the Amalgamated Union of Philosophers, Sages, Luminaries and Other Thinking Persons, and we want this machine off, and we want it off now!"
"What's the problem?" said Lunkwill.
"I'll tell you what the problem is mate," said Majikthise, "demarcation, that's the problem!"
"We demand," yelled Vroomfondel, "that demarcation may or may not be the problem!"
"You just let the machines get on with the adding up," warned Majikthise, "and we'll take care of the eternal verities thank you very much. You want to check your legal position you do mate. Under law the Quest for Ultimate Truth is quite clearly the inalienable prerogative of your working thinkers. Any bloody machine goes and actually finds it and we're straight out of a job aren't we? I mean what's the use of our sitting up half the night arguing that there may or may not be a God if this machine only goes and gives us his bleeding phone number the next morning?"