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If your idea of an idea is "concept that I personally am not aware of but which has been conceived, elaborated on and documented by another human being"…
Then yes, totally!
And that alone is worth a lot
The AI can extrapolate, but even if it couldn't, ultimately I need an idea that works, not necessarily a completely original idea that works (and most humans don't come up with completely original ideas very often either).
Yeah, I was gonna say, most engineers are gonna be taking a lot of code from the internet anyway. Most problems modern companies face have already been solved in one way or another, its just figuring out what fits your specific product and needs. That being said, I'm pro "ai as a tool in non-creative fields", but it certainly doesn't replace engey level engineers. I see it closer to a calculator or like factory machine. It can cut out the grunt work and summarize things well, but it takes a looooot of steering to actually work. And the engineer can maybe learn some new concepts or techniques along the way
Sauce for the first sentence?
Well, I have my personal experience, but there are also all those math problems that AI has been solving recently... Here's one mathematician's discussion, with links to blog posts by other mathematicians who had spent years unsuccessfully working on some of those problems. He says:
That's what's gotta sting the most about this. Imagine you worked a problem for a long time… and then The Giant Pattern Matcher With Zero Fluid Intelligence actually finds something.
If it did find something, that implies the solution already existed in bits and pieces in the published literature. You would "just" have had to have read about it, and remember it, for successful application.
But suppose you had succeeded in that. You would have published a paper that enumerates a bunch of results some other people had reached, then plugs them together for a supposedly new theorem. Sort of like importing a dozen Python libraries, adding around fifty lines of glue code around them and then going, yeah, here's a "new" thing, Fields Medal plz!
How much remaining interestingness did your chosen problem really have if the new math you had to create for it fits on the placemat buttressing the campus cafeteria sandwich you had for lunch?
What I've seen appears to indicate some genuinely new approaches by the AI, rather than putting together existing information. That blog post, for example, quotes some running commentary from a mathematician studying the proof of the theorem that she had been working on for years:
Note that this particular proof is correct, according to that same mathematician.
The issue with longstanding problems such as these is that yes, they can be used to establish evidence of plagiarizing if your LLM is simply regurgitating stuff, but suppose you cannot come up with any… you don't really know if it's because this particular line of thought is new, or because you just hadn't read about it.
That's true even if you're an expert practitioner; LLMs have been trained on All Of The Text and have superhuman recall after all.
I think the blog says exactly the opposite, the AI is very bad at explaining its solution and core idea.
I think the interesting part is that explaining ideas is something that don't seem to have an obvious reward for RL to train on, unless mathematicians keeps handing them training data.
(OMG of course this guy is a rationalist 🫠
Both can be true at once - it is coming up with original ideas but explaining them poorly. I'm not a mathematician but I find that in my field (software development) the AI is much better at writing code than it is at writing documentation - it will write documentation if you ask it to, but the documentation will be unfocused and difficult to read, with explanations of things that don't matter and garden path sentences. I got this sentence from it recently:
That is actually not gibberish - it's technically correct, but it certainly isn't clear.
Maybe I miss understand what "extrapolate" means in your context. To me that means "extract the core idea and explain/apply them", as AI do not learn by producing output (unlike human), applying core idea requires it to be explained in clear language.
I was arguing that AI, at present, cannot effectively extract core idea which is what I would characterize as "extrapolate".
No, by "extrapolate" I mean to learn a pattern in the training data and then apply that pattern (in a useful way) to a problem outside the domain of the training data. An AI that cannot extrapolate would only be able to do the specific things that it had been taught to do, whereas an AI that can extrapolate is capable of solving new problems.
As for the language, I suspect that it is clear to the AI itself. During their training, programming AIs communicate with other programming AIs more than they do with humans, so they develop their own dialect of sorts which is good for exchanging information among themselves. This is just conjecture on my part, but my evidence is that if the AI really was internally confused about those math problems, it wouldn't have been able to solve them.
I think the ability to generalize is the very definition of "machine learning", without it, models would just be really slow databases. We observed these phenomena quite frequently, like the original Groking paper, where models remembers modular arithmetic and generalize it to produce an algroithm in its weight to solve all modular arithmetic.
It is kind of hard to say whether the model are "aware" of its weight and "understand" the algorithm it developed. We certainly don't have a good understanding of how our brain works.
"clearity" and "confusion" are really hard to assess for anything other than ourselves. It is certainly valid to say that if AI can solve math problem it must understand it. In other way, Dijkstra famously argued that the question of whether machine can "think" and "understand" is completely pointless.
But the end goal of code, math and many other subjects IMO is to "communicate", so that these knowledge can be maintained and transfered. Of course, unless we want to complete forefit our understanding to machine, which I feel can be a bit dangerous especially for foundational fields like mathematics, but we will see.
Sounds like a pretty smart mathematician
The blog post was written less than a day after the proofs were released, and apparently they're very hard for humans to follow. Now that a month has passed, there are human mathematicians' explanations of how the proofs work up on the internet.
"one mathematician" who happened to work at openAI, btw.
You can look at Terence Tao's blog instead if you'd like. Just from the last week or so, there are the following headlines:
I looked at Egoless Mathematics in the AI Era, and it was AI slop. BTW, his blog is full of guest posts now