space of problems is limited and has been fully explored.
So the claim of novelty here is just that we wrote them ourselves and didn't take them from a book.
Well, here, as I'll show you some research problem steps.
I'm gonna get to that. Um, okay, so this is how you can access it. We have a data sharing agreement, as I said.
Now I'm gonna show you 3 problems from the benchmark.
Um, and the, uh, um…
So, for the harder side, now there are easy problems on Baycast anymore. So this one here is called a hard radio problem, so this would be a run level below research.
And, uh, so the answer to that is not novel, actually it's written down here where the answer can be found. However,
The, uh, um, the way how the problem has been framed is different from how it's written in this paper.
And, uh, it would be, sort of, we tried, for example, using something like deep research to locate the answer to this problem.
And now… and it cannot, uh, sort of… so it cannot be found. So models that solve this here, we looked in the solution, we really actually did the calculation, but we're gonna show you… I'm gonna show you two research problems that… that are, um…
a bit more advanced. But anyway, so this is one example here. So calculate the entropy of the string in terms of these parameters, and this is the answer. That's what's 84.
84? I just as a reference, so it's a reference.
No, it's Ed as a paper, but yeah, but yeah, so I…
I actually… I looked at the past, that's a problem from Dan Chungler for me, but I looked at the paper, and I could not find this problem in this paper, so it's somehow…
content, but it was not, uh… I could not find these answers in the paper, so it is… it was sort of reformatted from, uh…
From, um, the right of. But, okay, I want to say, so you can attack, like, you can discuss our problems, how novel they are, but this is the same for industry problems. So if people…
If the problem isn't even public, what do you guys think people put into frontier math, right? If you're paid $1,000 to write a problem, will you sit down a year to write something entirely new, or will you draw on previous stuff and then sort of make some judgment calls?
Um, okay, so here is a problem from my research, so there I can answer the most questions on. And this is a level 5 problem, meaning it's a research problem, but it is one
That is, uh, that was unsolved by any model when the problem… when it came out, uh, when we wrote the thing, and now models can do it.
So the answer here is, it's about 2 pages off.
of integrals over by Gaussians, so I'm not a field theorist, those are cosmological calculation.
Um, but we do it ourselves, and to our knowledge, this expression is not contained in a paper. At least, I haven't found one, I've given the talk many times, nobody has told me where it is.
To my knowledge, stuff of a new result.
And uh… and the calculation now models can do this with very high accuracy, given the statement defined the right answer.
Um, here's an unsolved problem, um, this one here is unsolved.
Here again, uh, here, the, um, this is something both Bogolubov coefficients,
And, uh, so far, no model has ever succeeded on us, it's like 3 pages of algebra, and then Chang'e, our field theorist, worked this out.
He did those for a previous paper, but without giving away the calculation, and therefore, uh…
Um, yeah, so therefore the model could not memorize the previous calculation. This problem has never been solved, so there's definitely possible still, obviously, to write for problems that haven't been solved.
This is a fairly tricky calculation, but be very hard for me, even though I know all the, sort of,
the stuff in there, but I'm not so used to doing these calculations.
And the answer is some gamma function stuff. Um…
Okay.
Alright, so this is the results of the benchmark. Um, so here you can…
So when we start… ah, Suessa…
I have a slide from what it looked like when we started, um…
Um, okay, so this is currently the state of the art, but roughly speaking, when we started the benchmark, it looked more like that. Almost nothing at level 5 was solved.
And by now, as you can see, we're at 44% of our hardest problems that have been solved.
Now, by research level, we don't mean entire publications. You should think of this as something like a section in a publication.
Or an appendix in a publication.
Um, certainly not…
Suddenly, if this were 100%, this would certainly not mean humans were useless. Um, this would just mean that…
for these steps of calculations, the models are very powerful.
Um, okay, so that's kind of the state of that, and so, as I said, the interest in having that for me is that if you believe the industry benchmarks, you cannot look into problems, and you don't know what's really going on. Well, this here is a community benchmark that we can look and work on, and so I think this is
Yes, but you can see here, you know, OSS, the, like, the biggest model you can sort of easily run on your laptop,
It's really still really bad at it. Um…
But, uh, um, like, the biggest, you know, public model, the best ischemy again, which, uh, is doing pretty well.
Office 4 and 6, actually not doing that well at the moment. Actually, I talked with a guy on Tropic who asked us whether we had used proper settings the yada yada, so we are investigating those.
Well, it was a really good… So, yeah, there's some, like, and the API has some settings, and they want to be sure that we use the right ones.
I'd love to take up to that. To run a benchmark like this?
you know, uh… another day or so.
Um, so…
the funnel to solve one… No, no, no, the model solves one problem in, like, a minute or so, but there's other 100 problems, and we send them, you know, 5 to 10 times, and so on.
That's cool that you asked me to solve the same problem. Yeah, that's just average of 5 shots here. So this is the average accuracy on 5 trials on this plot.
Is there a containment? I wondered this, having used it for…
Oh, that little time now, like, is there contamination when you ask it to do something? Does it actually retain that and transfer it to the next…
Yeah, not on the API. The API is guaranteed to be fresh.
Um, so it doesn't… yeah, there's no… it doesn't have this internal memory thing here. Yeah, I think so.
There's also the matter of whether we leak it in the training data by putting it in the API, at least, uh…
At Anthropic, you can switch this off. Okay, it's a deep providers handle it differently, you can talk about, you know.
Alright, um, so…
So, is physics close to being solved? So I would… I should say that I'm very, like, I actually am…
Well, as bullish on these models that it maybe sounded so far. Um, so, definitely, as you all know, they are really good tools, they are very helpful, everybody uses them.
Um, but human verification remains a really big problem. Like, if you're… to me, true LGI would be if somebody who doesn't know the physics could write a paper with it, basically. So, without human verification.
And these models, even the best ones, are still…
doing a large amount of… of junk. So, for example, when we do these problems here,
You know, these other 50% of the problems, they look perfectly plausible, the solutions. It's not that a model says, sorry, I don't know, this is wrong. It gives you a perfectly plausible-looking answer, which is totally wrong, and so if you're not a human,
You do not know whether it's right or wrong, and this is, to me, is not a trivial problem to solve. It's not a…
Um, that's not something that seems to be scaling away so easily.
Uh, that we're aware of, people using multiple Asian adversarially, like, they're trying to bullshit each other, and… Yeah, yeah, okay. So, okay, so current, the current stack of solving this thing, right, includes pre-training, supervised fine training,
RLVR, this is the reasoning model training, reinforcement learning was verifiable reward.
An LLM as a judge, that you just said, this is the idea of, well, maybe I can just sample 10 answers, and then I give it to 10 other LLMs, and they ask these 10 other LLMs which of these solutions is the right one,
And so if I play this enough, so using one model to judge the other, then maybe at some point the answer would be correct. And this is called LLM as a judge. And people try this, and in fact, if you use Google's, uh,
Uh, you know, deep think kind of thing, it does something along these lines. Um, so I personally think that, uh,
Models lack an internal sense of whether the result is correct and important, and it does not seem to me to be something that's getting trained out. Since I've been doing this benchmark,
I feel like this has not been…
Qualitatively changed, um…
And models also, as everybody admits, do not learn from… cannot continuously learn. This is also something other labs admit, it's not to solve problems.
And, uh, so I personally do not think if we could just throw a thousand times more compute on this stuff, uh…
physics would be… would be solved. But clearly, as we've seen, like, knowledgeable people, such as Jared Kaplan, I disagree with that, so we'll see who…
Who is right, but um…
My impression was that these problems are not so easy to scale away with.
All right, so I want to talk, this is all sort of older work, we want to talk about some new stuff, um, but, uh…
Um, alright, so…
Sorry. Yeah. Are there any other, uh, benchmarks or where to go beyond problem solving to, you know, like, problem…
creation? Yeah, yeah, the problem is, so whenever you do something that's not always called order verifiable, and then you need human judges, and it's very expensive and hard to run anything like that. Like, you could, of course,
people can try, you know,
come up with a hundred interesting research projects in amplitudes for quantum field theory.
And then give them to humans and ask them to create these ideas or something like that. The problem is that doing something like this takes
at a research level takes extreme expert attention, which nobody has, and so, uh, basically, people do some of these things, like trying, like, some papers have tried to, like, let people judge ideas and things like that, but I would say…
It's a very, uh… it's a bit of a murky business, but of course… People had this thing, right? Yeah, they're starting to emerge, where there's, like, it tries to generate papers, and then…
Yeah, I mean, to some extent, each of us does this, right? When you ask Gemini to talk about your research, you will have some opinion of how good their… this work was or not, but it's hard to make a measurable benchmark out of that, I would say.
Okay, you can talk about this later to us, and then just in time. Alright, so now I want to talk about, uh,
How can we make these models a little bit better by test time scaling?
So this paper is, uh, 6 months old, and so by now already a little outdated, unfortunately, but at the time,
Um, so the problem still remains that test time scaling rate is the idea to invest a ton of compute into solving the problem. You already trained your model, you're not training anything anymore, you want to invest a ton of compute to solve your problem.
The two most naive ways to do this are parallel something, that would be ask the model 100 times, and then perhaps
take the majority vote, for example, take the answer that it must have come up with. That's called parallel something.
There was a well-known paper, which was called Large Language Monkeys, that did that.
Sequential scaling is basically the idea to ask the model to think harder. So, for example,
Like, a simple way to implement this is you do the… it gives you an answer and say, reconsider every step, think again, or something. You can scale this endlessly, obviously, and this would be an example of sequential scaling.
And then, nowadays, people try to do this multi-agent methods, in which this is called scaffolding, so if you're
Google's deep fingers are scaffolding of Gemini, so which will put together different agents that will communicate in some way, and try to validate each other's approaches and so on.
So we haven't evaluated TP Bench on this class of methods, so what we've done is to try this class of methods, and I want to quickly show you.
Yeah, some of that. When we did the Opus 4.6, was it allowed to do deep thinking and all that? Thinking mode? So, yeah, so that's what… this was exactly the question. So we used the Office Pro.6 API, and this is exactly the question that people have anthropic asked us about what were the exact settings we put in the API.
And I actually don't know the answer to this, it was just… we literally on the weekend. Opus for Pen6, all the other ones are out there.
Um, okay, so let's do it… so I want to show you, just to give you an idea of this… I want to talk about the spell of something, okay? Which is still totally done in practice, so it's not… ChatGPT Pro doesn't exactly tell you what to do, but they certainly sample several answers and see which of those are more plausible.
And so, you can do this, let's see, do this with our hardest TP bench problems. Some of our hardest TP bench problems.
Okay, so these here are, like, 11 or so problems, and you can see in red, the unique answers, or signatures should say answers, so for this problem here,
The model came up with 44 different answers.
And two of those were correct.
Well, for this problem here, it came up with 22 answers, and none of them were correct. I won 50 trials, right?
And so the game of test time scaling, as parallel scaling is to pick out the right answer of those. Of course, if you know the right answer, then you don't need to run the thing, but
If you have all these samples, what would you do best?
To get the right answer. The simplest method to do this… so two simple methods to do this would be one of them is majority vote. You pick the answer that the majority agrees,
I guess, I don't know, but if you ask, you know, a large classroom, whether they ask you a classroom, the answer to a physics program, is it better to take the majority word, or ask the student that went to the International Physics Olympia and take this solution? But that's the question of…
But your classroom is filled with food.
With clones. Yeah, yeah, that's true, like, uh…
But, uh, with some randomness in that, right? But yeah, so they don't give you the same answer. One quick question.
So, the blue is, like, the… it was the same correct answer every time, so proximate ODE problem, there were 5 total attempts, and 3 were equivalent.
But, like, the one on the far left. Yes, 3 and 2. There were 5 total attempts, and 3 were equivalent. No, no, there were 50 attempts, of which 47 were wrong, and 3 were right.
Oh, but to… there were only, like, two, like, failure modes.
No, there were two different answers, so they were… the answers were 5 and 10.
And 5 was the right answer, but 5 was only proposed 3 times by 40… while 10 was…
But both parties, 7 times, so… okay.
Alright, so this was our first work mode, so maybe we can… so how can we pick the best answer out of these samples here? So what's the best way to…
To decide which sample to pick, and as I already said, the simplest way would be a majority bot.
The second simplest way, perhaps, is what David said we can…
youth, uh, we could use other LLMs, so we asked queried…
different LLMs 10 times to judge for themselves which of them do you think is the best answer, and then we sort of do whatever gets voted the most often, the most highly we took.
Then we tried to, uh, check, um, algebraic mistakes. So often in these calculations, the problem wasn't a logical reasoning mistake, but some algebra mistakes, so the hope was, can we
Check whether the algebraic calculation was wrong, and so we wrote a simple SymPy agent, and that would do that.
And uh… and I'm gonna show you a comparison of these approaches.
of course, you can never get better than best of NRED, so if you sample in parallel sample, if the correct answer isn't contained in your sample, obviously no way… no method can solve the problem then.
Did you ever do LLM as a judge with different companies and LLMs? No, no, no, we did not, so it is all, like…
They complement each other somehow? Yeah, it's a… this is a good, uh, it definitely is a good direction, and it… you do pretty quickly run into API cost issues there, if you want to do things like that.
Because, you know, you have 50 problems, you send for 50 answers, and then you send it to 5 different companies and so on.
So we've had some paint for this paper, at some point we had spent, like, 5K, and we said, okay, that's it, we're leaving it there.
Right, right. Yeah.
Um, yeah, I showed it to some people in finance who laughed at me that 5K would be a problem, but they spent, apparently, an API called, uh, tens of thousands a day. Anyway, okay, so this is our Symphy verification agent, worked as follows. It divided the solution in steps.
It constructs Symphy code to validate each step, then it executes the code and checks it,
And then it assigns a final grade, and here's an example. So this here is an answer from the model. Let's say, I don't know, 01 or something.
Um, then you can see…
Uh, this here is an example of what our agent did, it took, like, individual calculations, such as this one, and that one.
But this integral here, this integral is wrong.
And then it wrote some PI code to check whether these calculations are correct.
And they use this as a… to pick the solution, so we eliminated solutions that had wrong algebraic steps in them.
And it turned out that it worked pretty well, um, so…
Um, here is how…
Our SunPy verifier compares to majority vote.
So in blue is the Senpai verifier, so you can… obviously, the more samples you get,
the more likely you're correct, and thus majority vote.
And you can see that we gained something by running the Symphy verifier. Of course, it also cost us compute. We had to run the semi verifier to…
Maybe we had to run LLMs to write the SunPy code and so on.
Um, so this is an example of how to…
of how to, you know, construct a physics agent, and you have an agent that is… the most specific task is not theoretical reasoning, but to validate calculations.
Um, but as you can see, it doesn't get arbitrarily good, of course. At some point, you have sort of reached the limit of how good the model is.
These are the earlier fiscal Wi-Fi that, uh, some of the mistakes were algebraic and not logical, so you're saying the rest of the mistakes?
are probably logical? Yeah, that's everything. So our paper has, at some point, has some quantitative, so they definitely make logical mistakes, they…
Yeah, and also some wrong effects. For example, you need a Klipschorden coefficient and poker inputs in the wrong one. That also exists.
And, uh, it does sort of the whole range of errors that humans make, too.
Um, okay, so here, I think there's one interesting direction for research, is to build better tools for verification. So we use SymPy, mostly because Python, like, models are just better at using SymPy than they are at Mathematica.
But definitely, if you're, like, one direction where people can work on is to…
To provide better software package does these agents can use to call to validate their calculations. And I think there is…
The level of what's existing there is not so good. Physicists have their own sort of mathematical packages that can do specific things, but there's not a good
overall structure that organizes those. And here you can see that
You know, tons of manipulation with power integrals and so on could not really… were not verified by SymPy, obviously.
So I think that's, uh, one interesting direction for… for us to do some work on.
Um, okay, so to finish this off, yeah, I just want to say that, uh, so yeah, we did…
Parallel and sequential scaling. Sequential worked really badly for us, it didn't show the results, but currently state-of-the-art would be this multi-agent reasoning systems, and when we wrote the paper, they were not yet.
did not yet appear, but I think one interesting direction is to set up a multi-agent system that has various verifiers. Analytic one, so it's like Mathematica, and the other verifiers, and sort of interacts in a good way.
And then see to what extent that can help with improving reliability. But again, I do not think that that would bring us to anything near Physics AGI or something.
Okay, so that was, uh, what I had about, uh…
these TV bench problems. Um, I'm already waylaid, uh, so that maybe let's keep questions for later, if you have any.
I want to show you something new. This is a paper we just, uh, published, uh, we put on our… submitted to archive today, so you can check it out. I think the website is already working. So, Mad Evolve is sort of our version of Alpha Evolve. Who here has, uh, heard of Alpha Evolve?
Okay, on the one, two…
Um, so Alpha Evalfa was from Google, Alpha Evolve is a way to…
To combine LLMs with evolutionary programming, and sort of they started with a base program that can do something, such as multiplying two matrices, and then the LLM tries to propose changes
to the, uh, to the code, and then benchmarks them, and changes that work, it will keep.
And maybe sometimes it will… so it will have, like, a population of programs, and it evolves them forward, and whenever, like, in genetic programming, whenever some evolution works, then…
this population gets upgraded, and so on, and so you use, sort of, many LLM codes to iterate a course to iteratively.
improve, uh, improve code.
And this was, uh… yeah, this was Google's system called FABL. It's related to funds today, right?
Yeah, outside of that. That's the same, yeah.
Yeah, and such as Pegota. That's one of a bit more, um…
loaded up from one such. That's the same idea. So I'm really… so, cosmology has a lot of algorithms in them, so I'm a cosmologist. One of them would be
The reconstruction of the initial conditions, this is one that we look at. And there are many other algorithms, such as estimating bispectra and partial sky mask, and so there are a lot of algorithms, and people continuously improve algorithms,
And so if LLMs… and so…
Algorithms have not been replaced by neural networks, so people in cosmology try to replace everything with a large neural network black box.
And so far, this will work really poorly, because the simulations aren't…
Good enough, and it's sort of…
It just turns out that the idea to replace the theoretical algorithm with, like, a massive billion-parameter model often doesn't actually work so well.
And so algorithms are physically interpretable, and uh…
And, uh, therefore, yeah, and so I think…
It's really interesting to see whether LLMs can be used to improve these algorithms.
So one advantage of doing this, of algorithm search, is that you have a real feedback loop. So by this… in these theoretical problems, if you don't know the answer, then there's no way, no mathematical way to test whether the answer… whether it was correct or not.
But for these algorithms, there's a target metric, such as the reconstruction quality, just how well does your code perform,
And so even if the LLM reasoning is flawed, it doesn't matter as long as it improves the
the target metric. And so this is a way to use LLMs to do conceptual physics,
But, uh, without, um…
Without the problem that you can't believe anything they're doing.
And so, this is how Medivow works. The main thing that it does different from AlphaEvolve is that we have an extra step of parameter evolution, so the LLMs,
Uh, the LLM proposes auto-differentiable algorithms to do the task we want, and then there's an extra step that runs Autom Differentiable parameter optimization to find the best fit parameters.
Uh, for this algorithms. I'll show an example in a minute.
And so in this way, we decouples all of the conceptual evolution from the parameter tuning.
And as I said, it doesn't fit a large neural network, like a typical amount of parameters would be, like, order 10 or so, not, uh, billions.
So here's the first application we're gonna do. So this one is just be a standard reconstruction, it's called in cosmology. This is a task that is done
very… in practice by Desi and so on. So Desi would be the metal distribution today, so this is on SIMS, but you can imagine these are the galaxy clusters here.
And then you want to know what it was looking like at the Big Bang, the universe.
And to go from here to here, cosmologists have come up by analyzing the forward perturbation theory theoretically, because models have come up with algorithms that go from here to here. I'm going to show you one in a minute.
And here, you could train a neural network to do this in a supervised fashion, but the neural network emulators have certainly been trained, but they're never used in practice, because they are…
Sort of don't generalize to real data, right? This algorithm works on real data. So the help was to find… to use a neural network to make this algorithm better.
Um, and uh, so here is our evolution, right? So this is the base algorithm.
It's really simple, it's called Zelda Watch Reconstruction, um…
It's, uh, those of you who are cosmologists know what it says, um, but, uh, anyway, you calculate some displacement fields, and then, uh,
FLTER, and so on. And so the original algorithm that we put in into Metaverse scored here at the blue line,
So for the target metric, which are some integrated cross-correlation curriculum, that was 75%.
And you can see that after a thousand iterations of Metivorf,
So, 1,000 LLMs proposed code changes,
And this went up by a good amount. Um, and here we use many different models, so this uses Cloud and ChatGPT and so on and so forth.
Um, to get, sort of, an ensemble of different ideas from different models.
And, uh, yeah, as I said, the advantage of this in this case is that there is a clear target metric.
Let me just quickly skip ahead to show you what actually the model does. So what you should think this here is how the base algorithm is implemented. It's just a bunch of code. It implements these equations that were on the slide.
And then after evolution, it looks something like that. So it's still a bunch of code,
That has some, you know, some physical ideas in it. You can see here morphological estimator, fast Hessian estimator, yada yada. These are ideas of the LLM.
And so, they are validated in the sense that, indeed,
The performance of the algorithm goes up, okay?
Um, so are you basically trying to expand at the linear… like, you're saying the linear order
works with the linear order, but the data that you have is…
In nonlinear function scales, and you want to correct… you want to… Correct, yeah. I'm glad I got to this. So what? So now…
So, Matt Evolve now will write afterwards, after the evolution, will write an LLM-generated report of what actually the innovations were that it put in there.
And, uh, these look, here we can have a look at this report. Now, sorry to slow you down, but…
It's okay, you could take a little life. Um, is the man involved being trained on…
synthetic data? No, there's no training on Medivow, it's just LLM calls, and with this evolutionary structure, so it works like…
It pulls a program, and then it tries to, basically, the LM gets a restriction,
Um, change this code block… try to improve this code block to improve the target metric. But the target metric is computed on synthetic… Yeah, punch them, yeah. Oh, yeah. The target metric… Oh, yeah, yeah. Yeah, that's right, okay. But how do you know it overfitting on the synthetic data? Right, we are… so, again, we use the usual test data and validation data, right? So, the algorithm works on independent simulations, but from the same simulator.
solve the problem that
add that simulation codes might give something else, but the hope is by finding an algorithm that is somewhat physically motivated, at least, and that has only 10 parameters, you actually can see how the parameter count went up,
The base algorithm had a few parameters, it went up here by… to 10, but still 10 is not 10 million, right? So the hope is that it will generalize better outside of domain than a normal neural network. Oh, no, that was answering my question. So what type of parameters the LLMs, like, suggest?
So, okay, in this case, so the base parameters here were right where, for example, the filterings.is.
And it suggests similar stuff. So then we get to that. So here is the… now, you're not supposed to read the source bank, I comes out is LLM-generated algorithm summary.
And here at, uh… here we can look at some ideas. It says that its final code has, it claims it has a tensor invariant augmentation,
The algorithm computes the shear tensor invariance, yadda yadda yadda,
I do think, you know, 2L does mimics, 2LPT Lagrosian perturbation theory.
And contains several free parameters that I fit after one.
Then it claims it does something it names spectral dewarping, but you can see that involves higher order terms here.
And so… so the… so the answer is that the model indeed proposed various, um, non-linear terms to add to the algorithm.
that are somewhat motivated by cosmology. So this looks… if you look at the report, it looks sort of superficially…
reasonable, but then if you look in detail, there's a lot of…
Like, for example, the names are very creative, like, nowhere on the internet does the word coherence-gated fusion exist.
Um, but…
But the problem in this case is not as big as when we did… when we tried to do theory before, because here, these things, while the explanations, may be garbage, they nevertheless lead to work, right? So they do work, improve the result on a verifiable metric.
And so, here the problem is not as big. So here you can, uh…
Um, yeah, a human can look through the report and select things that, uh,
Um, that make more or less sense, and then, uh, um…
sort of that prevents the problem, but alleviated.
But still, it's not equivalent to human work, right? It's not what human expert, yeah.
In this case, I mean, we…
You can go to second order. Yeah.
can humans just write down the optimal answers? Well, I must think second order is the most optimal answer. I'm just saying that, like, is what it found? Yeah. Does it go to second order and then go beyond it? I mean… So, yeah, so these terms here are…
Um, you know, some second, some are third order, so… but cosmology is not…
So it does things at scale to the cosmology starts to become somewhat non-linear, so in fact, in cosmology, it's not a completely veto-coupled perturbation theory, right? This translates to the nonlinear regime.
And like in quantum field theory, there may be non-perturbative methods,
that work that the model could come up with. So it's not…
simply a matter of listing
all systematically, you know, power counting, all of these terms, and then fitting them. They can do more than that. Sorry, but it knows all internet, so it knows about cosmological perturbation theory, effective theory… Yeah, it does, it does, it does. It does. It leverages knowledge? So, yeah, that's an interesting… so definitely, I mean, if you read here, it mimics the two LPT, uh,
perturbation theory correction, so obviously it leveraged its knowledge, but did it do this perfectly? Uh, certainly not.
So, in fact, this algorithm here is not quite state-of-the-art, um, so…
Thus when we use the base algorithm, it's the simplest one, it's widely used, but it's not the best known one. And in fact, it's a little below the state of the art, and so now we tried a second run, where we started from the state-of-the-art algorithm,
It's called iterative reconstruction of Initial Condition by Schmitfel and Zelda Riaga. It's up there. And this here is the state-of-the-art algorithm, and then we tried to evolve on top of the existing state-of-the-art algorithm.
And you can see that we found some improvements again. Now, they're not as large anymore, because this algorithm was already really good, and there's a theoretical limit how good it can get.
But again, we found some success, and at least for these simulations, we have therefore set a new state of the art. Now, I'm not saying that our algorithm would work on real data as well as the cell dear algorithm. That might not be the case.
that this is, uh… but certainly, as you can see, um…
The, uh, yeah, on the simulations, on independent test simulations, the model does improve over the algorithm.
Here again, here's, like, how these things compare in terms of the cross-correlation coefficient. You don't have to look at this too much, but here our algorithm is the yellow one.
green one was the one that's, uh…
From the Zelda Riaga group, and you can see that there's some regime where the yellow one is winning.
And uh… and again, what it did was to use various higher-order terms that are somewhat
And did that inspired by things in cosmology, such as EFT and the Halo model?
But they were not used in a…
in the same systematic way, how humans would do it.
Um, well, so briefly, so one other example where actual D games are pretty good.
Okay, so it does here was for this task of initial conditions, a construction for this task, so go from here to here.
And so we ran it on the second thing, um…
It's just called… so anyone sending me the title Reconstruction?
So I, um… I, uh, um…
Okay, if you're not astrophysicists, you will not care so much for this task, but it has some… like, in astrophysics, like, something like the CHIME experiment, I…
Large interferometer has a problem called the foreground wedge.
There are a large number of modes are contaminated by a certain noise that comes from the detector, and
So people try to use the…
uncontaminated modes to reconstruct the contaminated modes, and…
in that process called tidal reconstruction. And this one here came as a surprise. The successor to us came as a surprise, so that it was so good.
So just, our baseline here was from a paper from the group where my grad student was from, so it's a real…
The code is from a real paper that, like, is from a paper that people worked on, and at the time,
And thought was near state-of-the-art, and our algorithm's actually much better than these, so you can see it trained up really quickly.
And then sort of plateaued, so you can see after evolution 50, it barely made any progress. It just introduced new parameters, which were obviously useless. The end algorithm had 60 parameters and isn't better than the algorithm here.
Um, that has, uh…
this one here has, you know, 8 parameters or something. And so, obviously, we picked this one with the few parameters.
And uh… and for this task, it looks like that our algorithm is really good.
And we compared it with one other algorithm from the literature, which was also well below the score. So we think that for this task, we've set the state of the art.
And cosmology is thought to be absolutely sure with statements by us, because we don't have these data challenges. In machine learning, there are these data challenges with unified data sets, and there's a leaderboard, and so you can say precisely how good you were.
But in cosmology, I'm sure particle physics also, there isn't quite this culture, and so we… and we cannot, you know, re-implementing every paper ever written on the topic is out of the question, so you make some judgment calls, but you think is good and reproducible, and we did that, and compared to those that our algorithm won.
Um, so here, how that, how that works? So here, actually, the report makes, uh, more, to me, more sense. So, it discusses a lot about, uh,
How to improve the filtering, and it turns out that, indeed, so it filters the data in a way that
more correctly approximate.
the physics, which looks something like that, so there is…
There's some difference between parallel and perpendicular modes, and it sort of incorporates Dustini algorithm.
And the original human-made method, uh…
did not do this, does algorithmic filtering, and since we know the person who wrote the paper, they said they didn't do it for simplicity and to… because it was computationally easier.
Um, but they were aware that that was suboptimal.
And, uh, indeed, for this task, it looks pretty good, so you can see that
This here was our baseline, this year was an algorithm we found on the literature, um, and that wasn't given to the model, and the Series D.
the final answer. Um…
Yeah. Now, it's not… the answer to these things are not…
Like, the reports don't look like human-written, they are still sort of a patchwork of ideas. It throws a lot of stuff together. There's no derivation, the optimal answer is therefore this, or something like this for humans.
Humans would try to look at certain limits and say, in this limit, when, say, this component is very large, I can write down the analytic answer,
In this other case, I can write down analytic answer as a sample will need to be in between, or something like that. There's no good structural reasoning, uh, along these lines.
But, um… but the resulting algorithms perform pretty well.
Um, so a summary of that part of the talk would be…
Identifying good, verifiable tasks,
That can be done with LLMs, I think, is a promising direction.
This doesn't have to be only these algorithms, even in model building, so if you want to do a computer in model building with, uh…
Both Medivol, for example, or something similar, then if you can have, you know, measurable performance metrics, such as the…
The fit… quality of the fit of the data, the number of free parameters, and uh… maybe your end for a sort of energy conservation by, you know, letting it only change the Lagrangian or something like that.
So if you're… if you can come up with a verifiable task, and then LLMs can already now be really good at doing new, useful work,
And then you can still, as a human, if it finds something that fits the data, you can still, as a human, look into it and see if you can learn from it.
But, as I said, they are not as reasoning as well as humans would do. It's more of a patchwork of different directions.
Um, but yeah, I think it's an exciting direction to use LLMs to search for a space of.
conceptual possibilities.
And then, uh, afterwards examining them by a human, and I think there are many lines along… many lines of research along that.
Um, that People Explore.
Um, okay, so…
I don't know, if you want, I can still talk 5 minutes about reinforcement learning.
Quickly, sorry.
The first thing that does the project that I'm done. So, I've won…
Um, so one thing I'm curious, like, I wanted to know whether we can fine-tune small reasoning models, so say we take a Quen 5 billion parameter model, and we try to make it better at quantum field theory.
And, uh, by training it on quantum field theory training problems. The goal of that would not be to be better than Claude Oppos or something, that's not the goal. The goal is to…
First of all, see if it can be done in academia, and then possibly experiment with training methods. You know, you could try to…
Change the loss function in various ways. I tried to set up some soft play setup, or…
Um, so there are many… there's a lot of possibilities to… to play with training, and for that reason, I…
I'm logging into thus not to try to beat.
industry labs. Um, for those who don't know, right, reinforcement learning is this, like, the…
idea that you have these verifiable problems, and then you can train up the loss curve. This is called RLVR. And so we need a data set, so we made a…
We made a synthetic dataset generator, which uses
Both human prompts and, uh…
And we have an archive agent that looks through the archive and downloads courseworks and takes problem statements from there.
And then, um, so from these two sources, basically, we then use a frontier model to write the problem.
So, in this case, this Gemini 3 Pro, that made us verifiable training data.
And this is just because we cannot pay people to make this dataset, right? When OpenAI trains their models, they pay thousands of people to write the training data. We cannot do this, so we sort of extract it from…
From, uh, Frontier Models. Um…
Then we, uh… then there's some filtering step, and we verify a different functioning model, and so on this way, and this way, we come up with a training dataset for quantum field theory.
And then, um…
Okay, and this here is currently the state of our work, so if you use a…
When, uh, so if you use a Quen 7… no, just… yeah, so Quan 3 is 7 billion model or so.
Um, you can see the CS validation now, so this is the loss on new training programs.
And here, on quantum field theory, so these are easy quantum field theory problems, so sort of…
first level of quantum field theory. You can train up the score of the model, so indeed, it's possible to do RL fine-tuning with academic resources.
We used four…
4H200 machines from perimeter institutes of 4 nodes.
Uh, no, for a machine. So, I don't know, we invested…
I think the hardware that we use costs maybe $200K, and we used it maybe…
Uh, you know, for a couple of weeks or so. Um, and so you can see…
And this is how it's trained with GRPO. That's the thing that got famous by Deep Sig Group, Relative Policy Optimizations, and their various, sort of,
training terms, and you can see it, it does work. Of course, it doesn't reach state-of-the-art.
And as I said, the reason I'm doing this is just for curiosity, so I wanted to see what is changing in the chain of thought of these models from, uh,
have valid trains, so can we identify in the chain of thought what mistakes sort of get trained out during DRL?
And also something we are currently…
We are currently investigating. Can you say a bit more about the RL? So, is it trained to a REFL point?
sort of word for word with a… No, it's RLBR, so the outcome, that's, again, is, like, a number, yeah, a number or a formula, yeah.
And the same as our benchmark. You could reach that number however it wants, but it's trained to get that reward. Yeah. Okay.
Yeah, yeah. This is how deep-seq trained, right? So, like, a year ago, now it feels ancient, but when this plot came out, the Deepstick R1 plot, this was a huge news, and this is just in January last year. This was when, for the first time, when the Chinese, like, the Dow Jones lost… like, the S&P lost, like, 5% a state that day because of this plot, or a few percent.
And that was because the Chinese labs had shown they can do it too, before this OpenAI for their 01 model, they had not told people how they were training it, and this paper sort of showed that it was done with RL with verifiable rewards.
And they showed us on the Amy example, the CS accuracy on Amy, but you can do the same with content theory.
And, uh, the problem is, if we had the…
A ton of compute, of course, we could make it better, but we don't, yeah. Uh, no, RLHF and RLVR are not the same thing. Isn't one just an elaboration of it? No, no, RHF is the…
If the thing where you're… like, RL with human feedback, right? And this is where, like, they have, like, hired people to vote, do you prefer this answer or that answer?
And this is RLHF. RLVR is, um, something like, um, find the answer to this math problem, and then the answer's 5 or 7 or something.
No, our LHF needs a human to sit there and click, RLVR does not. It's both your training the policy… it has a policy to produce some outcome.
Yeah, yeah. I mean, so I'm not saying RL was new, but RL VR, it wasn't so… it wasn't non-openai, didn't wait how they trade their reasoning models, right, at the time. And this was the paper that basically, the DeepSeek paper was the paper that basically gave this away. And I talked to some guy from DeepMind afterwards who told me that, uh, now that the DeepSeq paper had come out, he could talk to me about this topic.
And before the DeepSig paper, this was an industry secret, and apparently everybody in the research labs knew this for, like, half a year or so, that this was working well to solve these math problems.
But they were not allowed to talk about it, and then the Chinese published that, and unfortunately, so… What does it mean when the…
open capitalist society companies are keeping all the secrets of authoritarian, totalitarian dictatorship. Yeah, I think we have to re-evaluate our values there. I'm really open about it.
But I find it incredibly bothersome that the frontier labs do not publish their research. I think it's bad for progress, and it's…
Well, yeah, also, API is obviously such a…
crazy technology that I think everybody should be allowed to participate in developing it. They encourage competition. Here is… This reminds me of the moon rate, where the American program is basically saying communism, and the Russians did, uh…
just capitalism for a little bit. Yeah, that didn't know that.
Okay, yeah, yeah, so just my takeaway… this is a working project, and in progress, so my takeaway is, first of all, getting this RL training to train is hard, so it took us a lot of attempts to get there, even though it doesn't look so impressive.
But, uh, it can be done in academia to some extent, and then you can look… you can do things that you cannot do with Frontier models, because you can look what happened during the training process, right? OpenAI will not give you their training process, so you can look what happens to the train of thought.
I think that's interesting. One thing we saw that's interesting is that
Maybe some of you have heard of those. There was, like, a lot of… there's a lot of debate on going to what extent RL actually
really improves reasoning, and the specific claim was that RL only improves the pass rate, so the correct answer rate at lowK. So RL would, if you give
Okay, and so password 1K means the probability of getting it right if you have one attempt. And so…
And, uh, so the claim that several papers made was that, uh,
Um, RL sort of only helps to reinforce the correct answer,
out of the pre-trained model that already was able to get the correct answer, just not every time. And RL just upgrades this probability.
And so… and now we see some of those in our training, so the pass at 1 goes up, so it gets better at getting it right in first try.
But it doesn't necessarily get it better at, you know, 30th dry or so.
Um, this is… this is an interesting question, because…
This is the only stage where the model doesn't…
really get human training data. Like, RLVR is… there's a human answer, but the way to get there is completely sampled by the model.
And so if all RL does is dig out
the chains of thought that give the right answer, but we're already in the pre-trained model. That sort of means that the…
RL isn't really it.
generating anything new, and the right human reasoning was already in the race, it was just not.
extracted. And so I think that's an interesting claim.
And so, yeah, investigating things like that, I think, is interesting, and definitely physicists can… I think physicists can definitely study what these models do when they reason about physics.
Android and write interesting papers about that, and that has not yet happened.
I think there's a lot to investigate. You don't even have to run RL, you can just take the trained weights, such as from the Kimi model, a public model, and just look at
But what's actually happening in the chain of thought when the thing gets solved?
And, uh, yeah, I think there's a lot of interesting…
things one can do. Okay, that's it. Perfect. Thank you.
Thanks for a really fascinating talk. Um, questions?
Okay.
Um, I believe we said it.
I'm cognizant. Uh, at the very beginning, you showed how the…
more to models solve for a different level of questions, and…
For research problems,
They can be at Wake.
44% accuracy?
Can you say again how you verify whether, like,
If the answer is correct, and… Yeah.
Yeah, um, so, okay, I can, um…
I can show you some…
I mean… I think I've, um…
So, if you go on our website, for example, you can… and that is not kept up to date, but I want to show you how… what actual the code does. So here, of our problems, 10 of our problems are public, the other ones are not public. As I said, you can have them if you use them for research.
But here, let's pick one problem here, slow roll inflation. And so,
This here, here you can see what models actually answered, and so this is the problem, here's the expert solution, it looks like that.
And now let's look at the model answer. So here, the model was asked the question, it does then this calculation here.
And then in the end, it comes up with the answer that's here in the box.
Okay, so does this doc calculation answer. And then the model is asked to translate this here
into a Python function.
that has the signature.
And then it does that, and so…
Um, and then we check whether the function we had to sample some, some, uh, some, um…
Values for phi, say, and for V0, these sample functions.
And then the sample numbers, and then we check whether it gives the same answer as the… as the, like, the reference implementation. And then concludes the statuses correct. And so the way how we grade is to run this code on all these problems many times, so the models will calculate, and then
They come up in the end with a Python function, and the Python function is not there for reasoning, it's just there to check whether or not the model actually got
Uh, the right answer.
Very quiet. Yeah, right, so verifiable means something that can be checked without a human grader, so that the computer can say with certainty afterwards whether the answer was correct.
And this is not a trivial problem, right? For example, I mean…
For example, a mathematical proof, if you have the, you know, then, um, it might take many experts years to say whether the proof is right or not. So verification is not, in general. And it's the same with physics papers, right? If you get
Do you have to referee a paper and you feel it's hard to say whether the answer is right.
And so, the space of verifiable problems is much smaller than, I would say, than the general space of problems, and uh… and only verifiable problems are used here, but it's not just us, like, the industry methods in industry, it's the same. People use verifiable benchmarks, because it's just too much effort to try to do this with humans.
You're assuming… sorry to interrupt, but you're assuming that…
You're not going to have a situation where there's, like, 3 rungs, and then you gotta write, like, or, like, minus signs, just cancel them out.
Yeah, so… I'm just checking the end result. Right, so you want to… I've made several mistakes along the way that somehow didn't matter. That is true, and that doesn't matter. So you want to… ideally, you want to have only problems where the answer cannot be guessed. So, for example, you try to not have any problems where the answer is 0 or 1.
Where you could come up, I guess it. So, the problem should have enough complexity that it's hard to…
To guess it. Although, this is not always perfectly reached in our dataset, but certainly that was the goal, to have unguessable problems set.
Mm-hmm.
This one here?
Right, yeah, yeah.
So we asked, as I said, these problems here are synthetic, so they are written by the likes of Opus 4.6 and Gemini 3 Pro, and we asked, and we get… so a query would look like something, write a undergraduate level…
Quantum field theory problem about…
involving the LSC reduction formula, involving only scalar fields, or something like that, and then the frontier model would write a problem that accords to this specification. And so in the prompt, we specify which of these levels it should have.
And so, weirdly here,
For the, um, as you can see, this step isn't think that post-gradiate should be the lowest, which has not turned out to be the case.
And so that appears to be, so my…
I think that is because these franchise models aren't very good at writing post-graduate-level problems, and so…
What they… I think many of these problems are, essentially, are more information-based, so I think that the…
Lower problems are more calculation-based, and for the postgraduate problems, it used more, maybe, concepts that are hard to know, but they're not, uh,
better logical reasoning isn't so.
isn't so difficult. So I think there's some… there's a difference between the logical difficulty and the problem and the knowledge depth that you need.
And I think that does explain some of this weird behavior.
That's also, like, it's also clearly for what's difficult for models, it's not the same as what's difficult for humans, so they're definitely another
point in intelligence space, and I think there could be more…
study of this matter, because, like many of these French masters, like, one famous guy who contributed a frontier math problem explicitly tweeted about that, that he…
He thought this problem was totally unsolvable, but he didn't appreciate that if you knew every paper on the internet, you could just use the specific lemma, and then it was a trivial step to go from there to there. And I think things like that happen with these LLMs, they just have this extreme knowledge amount, and that makes some problems easy. That would be hard otherwise. Yeah, is there any notion of, like, people sort of talking about, you know, in the space of ideas, you know, interpolation versus
was true. Yeah, yeah. This is really hard, like, I think tons of people think about this, suddenly, like, we also thought about, like, whether is there any way how we can quantitatively… we can…
qualify how… what the logical difficulty of a problem is, or what the, you know,
Um, what… to what extent… and I… you know, a step follows linear and previous reasoning, and to what extent you need, sort of, an insight, but I think it, very hard to come up with something of this.
If it existed, I think logicians would have already done it, and uh… but maybe it's the time to figure that out. I mean, it could… maybe it's just time to understand better what
thinking really means, but it doesn't mean that they're easy to do. Because I think one way they're gonna plateau is, uh, potentially is they're gonna run out of metrics.
Yeah. It solved every problem in the textbooks, or whatever. Yeah, we talked about this before, yeah, and the problem with RL is that you need training data, and so, of course, if aliens came and gave us our LVR training data for quantum gravity, then models would learn quantum gravity,
But since no such training data exists, it's very unclear whether models can sort of make this themselves. Yeah, exactly, and it's very hard to probe this precisely, and one reason is the very large
amount of knowledge. It would be much better if you had an LLM that can equally well reason, but has only very little knowledge, so that you can more easily check whether it can come up with something new. But that seems to be hard to construct, yeah.
Here's a question.
Where there was something…
in literature, that humans put together.
So, when I was…
I guess graduate school or post-op, or something like that.
Couple of very smart people.
took an idea from condensed matter physics, the fact that there were flux tubes in superconductors,
and invented the theory of confinement.
Yeah. And that, you know…
If they… you took a machine that had access to all the data,
on the internet, which didn't exist then, but… Yeah, yeah. Of course, it existed.
It could have known about flux tubes in superconductors. I think so. They could have known about the fact that quarks
are… seem to be there, but they don't come out. Would it have invented confinement? Yeah, yeah. And I suspect the answer is no. I also think no, and…
So, Jennifer, I think, first of all, it surprises hasn't yet happened, right? Models already have insane knowledge, and you would think,
This could already happen, but I think, to me, the primary problem of models is that they are so unreliable, so
If they, you know, if you query it a thousand times, it might come up with this confinement thing, but it will be…
Buried under a mountain of garbage, and the model has no way to intrinsically judge which of these ideas is actually good. And somehow,
Even though models are trained on archives that they, in principle could learn, but humans think is good research, because they see their human papers just like us,
Somehow, models have not managed to become good at that, and to me, it doesn't seem like this is getting scaled out. But other people totally disagree with that.
Regarding verifiable results, has anyone that you know tried to train or develop a tool that would
you feed it a paper that tells them whether the paper is correct or what?
Um, I… I've heard that is not even wrong. As another category. I think many of us ask the models for their opinions on papers, right? I certainly do that.
And my, like, where I can judge this best is my own papers, and so when I ask… Oh, correct.
Obviously, there are no mistakes in my favorites, though. But, uh, like, if I ask a model to write a review for my paper, I usually think the review is garbage, and if I ask it to write a review for something I don't understand well, then it all sounds very plausible, so…
ask you to write your beautiful kid to always fit.
Yeah, I mean, I was kind of shocked. Like, these things…
Like, these things are of the sort that the model proposes things that sound good to the model, and they are sort of combinations of words that somehow make some superficial sense,
But they have nothing to do with the clarity of…
I assume, and that would do.
They would do the same thing. So, yeah.
Okay. So maybe, I don't know, they could… they can definitely write papers that…
Yeah, that look like they're human-made, but if you look in detail, they are.
Okay. Thank you. Thank you very much. Let me know if you want to go to dinner.
Maybe it can be fair.
famous quote around the time that Elon Musk bought Twitter and talking about, like, the coding.
And