Where I work, PR counts are a major metric come perf reviews. Surprise, surprise every team has a pointless migration going on. The number of promotions though...
This is a great question. I am not a mathematician but I've had similar questions about my own field (CS/Elec) as well.
I have always felt that a huge amount of brain power has to be expended in understanding the jargon and getting used to the machinery. Once we get past that, what people would think are highly challenging subjects become rather simple and logical. An analogy I like to use is old people struggling with simple tech tasks. I remember an uncle of mine who approached me to fix their laptop which wasn't connecting to the internet. Turns out the laptop had not been booted in a while and the public certs shipped with the machine had expired. Said person is a highly accomplished person in their field but was helpless when it came to this task. After I solved the issue, the uncle was eager to know what the problem was and I tried to ELI5 it but to no avail. It is possible I did a really bad job of explaining it but there was too much basic machinery to cover. Why is there a public and private key, what is symmetric/asymmetric, why do certs even expire etc. I couldn't even touch on the foundational math underpinning all of it so I left him in a confused daze.
To any SWE, all this is table stakes but for non-tech people it is way too much jargon. Today, I'm confident my uncle could prompt his way to a working understanding of PKI - heck maybe even some aspects of cryptography and prime number math that makes it work. This is where I see LLMs making a massive difference - they can crunch a massive amount of jargon and leave only the actual trick/idea for you to understand.
This is also what people like Szegedy and Tao have also said - LLMs will make math closer to what SWE is - a lot more people doing it in workmanlike fashion rather than a small community writing papers. At one point, dynamic programming was some research topic that Bellman worked on and now every 20 year old works on tens to hundreds of these problems in the hopes of cracking a job. But I'm sure the Math field will go through some turbulence and I wish them the best. There will always be a need for SMEs who deeply understand a subject and can come up with interesting problems.
Tbf OP said they have the tools to understand what was going on, not that they could build a model to compete with OpenAI tomorrow. EE (especifically DSP and communications) uses a lot of the same building blocks as ML so yes it does prepare you.
You are right in that the emergent abilities come from humongous amounts of training data and compute which only a handful of companies (and the people working in them) deal with today. I'm sure there's a lot of secret gotchas which only arise at a certain scale so one cannot self-study for them. Companies also guard these wherever possible because of economic incentives. But that applies to most other engineering disciplines. You can take a course in civil engineering and have enough knowledge to reason about why a skyscraper will not fall apart in the wind; doesn't mean you have the ability to build one.
Yeah, I think you can't just throw money randomly at problems and expect results unless you know a line of attack that can get you all the way. OpenAI chose the line of attack only after it became known to them via rumors. They "front-ran" the researchers.
Yes. What the headlines hailed as an AGI discovery the facts show more to be someone spending years mining for gold, rumor gets to OpenAI that there might be gold in this specific place, they mine there and instantly discover gold, then tell the world they’ve developed the worlds best gold finding/mining machine.
Separate from all the allegations of more nefarious actions and ethical issues, that’s the most charitable version of what happened here.
they threw it on all the millenial math problems (I think there are 6 at this point unsolved, well, 5 now).
And according to them at some point they saw that one was close to being solved, so they pointed all the agents at it.
The same thing happens to humans - at this time there are no simple problems left, so solving the hard ones requires using prior knowledge and attempts at solving things.
Yeah but the one they decided the AI was close to solving may have been so because the researchers' progress on this problem became part of the training data for that AI...
Almost but not quite I think. You can throw money at parts of problems. I think it's helpful to think it kind of like supercomputer MD/MC or electronic structure calculations. A tool that can get you valuable answers but not necessarily aid understanding. Simulations can be used to aid understanding also, and are integral to theory development. In the same way the approach to this result is.
Plausible deniability - The line of attack is in their sessions/prompts data. Just make the prompt pointed enough that the search space is tractable and use your ginormous compute.
> "Of course we don’t know whether that is true"
Yep. Who is verifying these claims? We all know how trustworthy Altman & Co are.
“relying on” is misleading here relative to what the researchers have said.
If I write a book and pass it through a spelling and polish checker, I still wrote the book and its core IP. I didn’t “rely on” the tool to create the IP.
it’s much more like you come up with the premise and someone else writes the book. the released prompts for other foundational problems (like unit distance) prove that.
The tools the researchers used though was much more than an spellchecker, because spellcheckers don't come up with chains of reasoning for the arguments in the book. The LLMs did in the case of the Navier-Stokes problem.
that's not how AI was used in this case. It's more like a professor with assistants.
Professor says the assistants - why don't you dig in this direction, I have a hunch it might produce something valuable. And AI assistant does just that, proving or disproving a hunch. This would take the professor a lot of time if doing by themselves.
Yes, and keyboards also save a lot of time over handwriting. Numerical methods and proof engines save even more time. LLMs are just another tool in the kit.
Keyboards don't suggest chains of reasoning or words to type. When I press the K key, I know exactly what will happen. It's just a translation layer that gives an output known ahead of time and thus does not impinge upon the creativity of putting words together.
A better example would be playing chess against a player slightly stronger than me and using a chess computer to suggest some good moves. I could win, but it certianly wouldn't be just my brain that wins. It would be an amalgamation of my brain with a machine that suggests good moves.
This is straight up misleading. When you press your K key on a touchscreen, your keyboard program may decide you meant to press the neighboring L key (by dynamically inflating the collision geometry on it) because it was statistically far more likely that you meant to press the L key next.
This likely doesn't happen exactly on an analog keyboard, but then many text-processing environments that do the same thing in post. My keyboard just edited 'yuor' to 'your' even though I successfully input the prior string.
The researchers were driving prompts and trying to actually do math.
The OpenAI effort was a pure brute force attempt. I'm not even sure an LLM was actually involved. I think they just used their hardware to run the matrix multiplies required by the search for a counter example. Perhaps some clever approach guided the search but that seems to be about it.
You can’t do anything novel with these models from scratch and let it fly. I’ve observed something over the past few months
Work on something novel -> llm is kinda useless and low value-add -> Keep at it and in the process feed it more information -> keep doing this periodically -> a few months go by and you realise the model outputs are almost like-for-like regurgitations of what was inputted in some prior period.
Once it’s accumulated new info can it produce something automated that is somewhat useful? Sure.
But by itself - absolutely not.
I clearly see humans will be needed - the best ones that is. For ‘rote work’ and stuff that is not IP sensitive firms will be ok with employees putting that as inputs into models.
But I’d wary about trusting the labs. They will push the letter of the law to the max.
Personally I’ve stopped doing anything novel with these models. If I do use a model on something adjacent but not totally novel I have to craft the inputs in a strategic way not to give much away.
I’d wager firms will soon realise this and that growth rate of revenues of the frontier labs will become questionable. The economic cost that firms have brought out thus far is only financial. There’s a whole bunch of other costs people aren’t talking about.
Agree all. And as the revenues become questionable, the frontier labs practices will necessarily become (more) questionable. Vicious cycle.
To avert that dynamic, the frontier labs must deflect and otherwise act to prevent this controversy from breaking through. Both to the general public, but also more specifically to the firms' decision-makers. All of whom are generally aware of the IP issues, and some of whom are aware of what happened with Cursor and Figma, but with few exceptions have not yet themselves acted to protect their property.
This doesn't follow for me. There are what, Dozens or Erdos tier problems that got solved with no progress for decades? How does that factor in to your view?
IIUC the argument is that while unsolved there was much work done on them that shows up in the training data. The idea being that the LLM is limited to a small amount of inference over externally supplied data.
OAI doesn't need to mention Buckmaster's name directly in a prompt. They just need to select a basket of sessions that is guaranteed to contain Buckmaster's and then direct the LLM to attack only a specific method/angle. This is trivial to do while maintaining plausible deniability about not using his work.
OAI started working on this only after they found out it was close to being solved. They threw a team of researchers who spent sleepless nights + a ton of compute. This is not exactly healthy academic competition - it's like if you spend a year hunting for oil fields and finally find a very promising area to be explored, only to find that Exxon tapped their entire exploration unit to go all in and and find it overnight just to stake claim to the discovery. Tao said it right - math should not be treated as a non-renewable resource to be mined.
but a very large part of the whole model was trained on work in a manner the authors didn't consent to, the "for research purposes only" datasets of the entire Internet, etc
and you can argue this is "fair use" or whatever, not the point now, the point is that it definitely makes those accusations no longer "baseless".
in addition, it is not given freely to the world, it is the knowledge of the Internet/WWW being sold back to you as a subscription service. it's not free. and it's not even "given", because they can (technically) turn off the tap at any moment and you don't have it any more.
Humans do this all the time. You watch a YouTube video and subconsciously choose the same colour palette. They hear a rumour that it's a solved problem, i.e. they were pointed in the right direction that is all.
I mean some companies glean insight into new products merely by asking other people what they do for a living.
People need to get over this ownership thing, it's being taken too far. Humans benefit from the efforts of others simple as that.
it seems like OAI tried to share, but didn't want to share with an Ant employee. a bit childish, but understandable to want to avoid a headline "Anthropic researcher solves Millennium problem"
it seems like Buckmaster got one-upped and is upset. understandable, but I find their reaction childish as well
> OAI tried to share, but didn't want to share with an Ant employee
Why does OpenAI get to dictate who Buckmaster can claim co-authorship with?
> I find their reaction childish
OpenAI may have, with full plausible deniability, taken Buckmaster’s work and passed it off—in substantial part—as their own. (Fitting into a fact pattern of them having tried to do the same with Apple.)
There is a material takeaway for anyone who does creative or otherwise unique work from this. (Which is unfortunate. Whatever happened here, AI clearly accelerated the discovery process.) For anyone else, I agree it’s just drama.
More like OAI needed someone like Buckmaster's stamp of approval. They know they can't get Tao's. Now they won't be able to get Zoroa's. You have to hope the rest of the guys they didn't know to cite will readily give up honour and dignity
It doesn't seem like there's anyone at OAI who knows much about the problem they are solving. Seems like CS theorists or algebraists* trying to own the pros by driving a car that's beyond their skill level. For one, they didn't cite the guys that B&A based their work on.
*It would be most fair to say there are no analysts on board, nor are they likely hire any soon; those are the least impressionable people in math. Applied math PDE elves who hadn't already left on the world-model boats would have jumped off around the time that eg Ilya did because they wouldnt have been able to stand the three Bs pretending to be experts in fields they imagine to be "adjacent".. like Public Relations
> OAI didn't try to claim Buckmaster's work as their own
We can't say this until we have more information on what the OpenAI researchers prompted their model with and to what degree Buckmaster's work was fed into its training data, either by Buckmaster himself or by his co-author.
Apparently Tristan was working on this problem for years, with AI providing help. Vs OpenAI spending a week with their new model, potentially having access to Tristan’s work.
I'd think nothing is "safe". Anything you say can and will be used by the LLM if it has enough statistical similarity to the prompt. Call it "Ma Random Rights"
I don't think OAI should be given the benefit of doubt. They are doing the research equivalent of front-running. Knowing where to look is one of the main challenges in research. Tristan's argument from his essay was that it is hard to brute force with a vanilla prompt (even for seasoned mathematicians) unless you knew very specifically what to mention i.e the search space would have been intractable even for OAI's compute budget.
"deidentified data" isn't much to go by. Say I prompted the internal model this way - "Hey there's a solution to a unsolved problem X. The solution uses a less known Method Y so don't bother wasting time with the usual methods. Take papers A, B and C as references. Oh btw, here's the last year's worth of data of all prompt sessions that mention this problem. Pay special attention to the ones that mention Method Y and sub-keywords Z,W".
This is obviously all speculation but the timing is very suspect. If OAI actually did this (and I suspect whatever they did is pretty much close to this), I think it is highly unethical.
> Tristan's argument from his essay was that it is hard to brute force with a vanilla prompt (even for seasoned mathematicians) unless you knew very specifically what to mention i.e the search space would have been intractable even for OAI's compute budget.
This is a bad argument. This is clearly not how it works. And unless Tristan is some truly alien-like savant (and maybe he is), what's necessary to initiate the AI's work already exists in countless published research papers and not exclusively in his head or notes. AIs can survey the sum total of all prior work on a problem and discern reasonable paths for inquiry.
Tristan is acting as if he's working off of an outdated model of AI, similar to primitive chess-playing models that winnowed the search space much more deterministically. If someone this intelligent truly doesn't get that this is not at all what AI is anymore, then maybe there's no hope that we ever understand it.
But I think he does realize this and he's flailing about for counterarguments from a place of bitterness and dejection, accepting even those that are too weak to be defensible. And that is very human and even forgivable.
Are you saying there is no search space intractable to LLMs? That wouldn't be possible. AIs are statistical pattern-matchers on steroids. The prompt is key to getting anything useful out of them. They are incredibly useful and major game changers but ultimately that does not alter this fact. People (including OAI) have already tried to solve Millenium Problems with it. That OAI woke up last week and suddenly decided that throwing their researchers armed with millions of compute on one particular idea to a problem is highly suspicious in itself.
Even if OAI had zero data from Buckmaster's sessions, this is in very poor taste and highly unethical. You are front running a researcher just to be able to say you did it first? Tao is right - OAI is treating math results like oil. This is the like Exxon getting a whiff of a massive oil field and racing to the punch by deploying their full crew.
> Even if OAI had zero data from Buckmaster's sessions, this is in very poor taste and highly unethical. You are front running a researcher just to be able to say you did it first? Tao is right - OAI is treating math results like oil. This is the like Exxon getting a whiff of a massive oil field and racing to the punch by deploying their full crew.
I want to be clear that I agree with this view and with Tao more generally. But we're all just yelling at the wind now.
Try to increase the complexity of the work you're doing. It's not that AIs don't makes mistakes but they are able to pattern match to larger and larger pieces of the problem as more people use it and more iterations of the model are released. So your challenge is now in steering it in a way that these errors are minimised while reducing bloat.
Try to think of yourself as a professor who's trying to come up with a problem statement worth solving. The AI is your "lab" that will help you run experiments.
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