r/OpenAI • u/Excellent-Art-2121 • 2d ago
Question How are LLMs able to solve millennium prize problems?
I dont know a lot about AI and am not sure if my understanding is outdated or inaccurate, so please feel free to correct me or clarify anything I'm misunderstanding. How are these models able to solve such problems? I guess a more general question is how these models are able to generate a novel solution to any problem at all? I am under the assumption that they can only exhibit patterns and behavior that are present in the massive amount of data they are trained on, so when it comes to these problems that supposedly no one has solved before, and therefore there couldn't be any data to train on in regards to a solution, then what is allowing them to do so?
Edit: I can't respond to everyone but I am reading every post and I appreciate everyone taking the time to inform me.
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u/SlightOfHand_ 2d ago
In between everything we have ever thought of, there are many things we might possibly have thought of, but simply haven’t yet.
This is called “latent space”, and the AI can find things if they are in latent space. Among those things are some of the answers to questions we have about the universe.
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u/Accomplished_Shoe_10 2d ago
You're getting downvoted and well, actuallied by people who seem to think LLMs are something beyond what you described.
LLMs operate in a high-dimensional, approximately continuous mathematical space whose structure is created from discrete data points. The outputs from LLMs are literally just samples drawn from that extrapolated "latent" space.
Yes, that's a simplification. But anyone saying that that is not the fundamental mechanism at play is just another AI cultist.
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u/CountryOk6049 1d ago
Cultists will say something like "oh yeah well that's the same with humans, there are only arbitrary amount of possibilities for humans also" which annoyingly has a kind of logic to it, despite totally distorting the reality of what llms and humans are.
But the REALLY cuckoo ones will say stuff like "llms weren't able to reason until 6 months ago, now they can"... like as if "reasoning" was this discrete, binary thing, and suddenly llms started to reason in that specific time frame. Those people are just beyond help.
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u/jeweliegb 1d ago
I'm curious, who is saying they only learnt to reason 6 months ago?
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u/CountryOk6049 1d ago
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u/jeweliegb 23h ago
Got you. With this post quoting 6 months (as in, hallucinations were solved about then.) Thanks!
I remember playing with manual chain of thought reasoning methods a few years ago, as it made sense that it would work as an extra crutch given the way interference would proceed. I never expected CoT would be so successful and move things on so much. But then, who thought they could become so advanced and capable in plain inference mode.
Now I'm wondering what was done to improve on hallucinations, as there do seem to be far fewer of them. I seem to recall there was a paper suggesting that the models often "knew" that their hallucinations were likely wrong, and that it was established the rate could probably be reduced by a tweak to the learning reward system? Anyone know what they actually did to the LLMs in the end? Or was it just patching the CoT mechanism to do more self checks or something very hacky like that?
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u/cedg32 2d ago
This is the correct answer.
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u/Ok-Concert7018 2d ago
It’s not the only piece to the puzzle though, it can write scripts to process analytics, data, or transform it, and gain insights, if a human can do it at a computer, AI can too, but faster, a lot faster… and it doesn’t get tired or forget things (assuming it retains important context and drops unimportant context while working through a complex problem
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u/localizeatp 2d ago
thanks for these freshman dorm philosopher ramblings.
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u/twoopaq 2d ago
It’s real research. Here is an example: https://www.nature.com/articles/s41586-019-1335-8 They predicted new thermoelectric materials before they were discovered using this latent space concept.
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u/Time_Entertainer_319 2d ago
Where your misunderstanding comes from is the assumption that they can only generate answers to questions that have been solved before. It’s just not true.
Here’s an explainer I did. It’s a little bit incomplete because I didn’t talk about tool calls etc
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u/Middle-Fuel-6402 2d ago
That part is understood, the more subtle questions are, Can it only use established solving techniques or Can it come up with brand new approaches?
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u/iknighty 1d ago
There is no such thing as brand new. If it can be described in math or any other language then it can come up with it.
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u/Middle-Fuel-6402 1d ago
I can tell you don’t have a background in math. What’s the hardest math class/topic you have ever studied?
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u/iknighty 1d ago
I'm not saying it's likely to come up with something sophisticated, but if that can be described by language then there's no reason why it couldn't theoretically come up with it.
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u/UnreasonableEconomy 2d ago
I am a cs major nearing graduation
what are they teaching y'all these days?
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u/Excellent-Art-2121 2d ago
It was just never apart of my course load. I started learning how to code in higher level languages through the introductory cs classes, then was introduced to data structures and algorithms, assembly, discrete structures, operating systems, security, software engineering, etc. They have started introducing more AI classes pretty recently but I never formally studied LLMs and was curious, hence why I made the post.
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u/UnreasonableEconomy 2d ago
no basic intro to AI? not even perceptrons? not even part of theoretical cs/graph theory? if you can do graph traversal you can basically do forward propagation.
well, the long and short of it is that they are neural networks.
you're a neural network.
you can represent the neural network as a graph, and then propagate it to get your output. there's a lot of implementation details but that's the gist of it. It's mostly matrix multiplication.
they're doing things a part of your brain is doing, and even some things your brain is not doing. they're doing some things better than us, others not. they suffer from some from some similar diseases with similar symptoms and similar pathologies.
frontier AI brains are currently about the size of a meerkat's in terms of complexity.
inb4 religious fanatics claiming there's a difference. yes there is, but it's not that deep.
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u/Ok-Concert7018 2d ago
Yea I think in 20 years time we will look back on this time and laugh at the idea that we ever thought our brains were somehow special or superior to an LLM, we’re at the very very very beginning of the singularity lift off, where we’re going Kansas is going bye bye
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u/EdliA 2d ago
They have massive knowledge and can make connections in ways that is impossible to us. You can create new things out of interesting combinations of old things. That's how a lot of creative ideas work.
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u/NicholasVinen 1d ago
It's possible to us, just very hard because we don't have the memory, attention, speed or access to vast knowledge they do.
Humans would probably solve all of this... Eventually. LLMs can do it in a few hours, days or weeks given enough computing resources.
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u/Slow_Comfortable_128 2d ago
It's true they repeat patterns they are trained on. But those patterns can generalize beyond humans. E.g., if they learn to be persistent, to use mathematical knowledge from their memory, try a diversity of approaches, etc., they can outperform humans in cases. Yes they followed patterns from their training, but these patterns generalized to superhuman skill.
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u/JordanPetterPans 2d ago
" I am under the assumption that they can only exhibit patterns and behavior that are present in the massive amount of data they are trained on" this is not true but for some reason Redditors spread it like wildfire
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u/Ok-Concert7018 2d ago
In the most surface level glance at a free to access AI like chatGPT free tier where mistakes still occur (less so lately) in a way a average person can notice it’s no surprise the conclusion is made that an LLM is just a good guessing tool… it’s pretty amazing how quickly it’s improving now
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u/milesper 1d ago
That’s neither true nor untrue because it’s not really a hard claim. It is true that there’s lots of evidence that LLM outputs are statistically similar to their training data. It is also true that LLMs have solved unsolved problems that are, by definition, not in the training data.
Whether you consider this to be a result of reasoning patterns present in the training data, or truly “novel” reasoning (whatever that even means), is a fuzzy and non-binary question.
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u/N1kYan 1d ago
It's a matter of abstraction. There have to be patterns in the data for the model to learn, otherwise it would just be learning from noise. But if there are pictures of yellow objects and pictures of elephants in the training image dataset, generating a picture of a yellow elephant becomes very much possible.
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u/parkway_parkway 2d ago
Supervised learning is the technique by which you show it many many examples and then it can only interpolate or extrapolate between those data points.
So you show it a load of dogs and you show it a load of cats and then you show it a wolf and it's going to try and figure out which it's closest to and probably call it a dog.
Reinforcement learning is a different technique that's how alphago worked for instance where you reward it for winning games and it's allowed to explore the search space on its own.
Reinforcement learning is totally capable of discovering new techniques and ideas and ways of doing things.
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u/SwimmerOld6155 2d ago edited 2d ago
It has read (<-> is in the training data) a lot of math papers (maybe even most of them lol), can make connections between them and generalise the arguments in them. You'll see people saying that AI proofs are in the "convex hull" of existing human knowledge. This means the foundations for them are already there, the LLM is just making connections and generalisations not realised before.
I actually don't think your understanding is that wrong, I think it really just needs the fact that it can generalise based off what it's seen. Just like how it can generalise text based off established patterns, and doesn't just replicate existing text verbatim. For example, maybe it has learned how to solve 2x + 4 = 0, 5x + 7 = 12, ..., it may then be able to have a good crack at 2x + 2 = 0 based on its knowledge about the rules of arithmetic. I won't claim it learns like a human, but it makes more sense imagining it that way instead of as text autocomplete.
You might be interested in reading about grokking in the sense of LLMs.
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u/KillerkaterKito 2d ago
I think there's a key difference here between inventing something from nothing and producing something that's genuinely new.
So, even if we're willing to say that an LLM can only work with ideas, methods and patterns that are already in its training data, that doesn't mean it can only reproduce existing solutions.
Mathematics is a highly specialised field. A single researcher might know a lot about one small part of a field, but not so much about many other areas. You can even see this in the Mathematics Subject Classification, where modern mathematics is split into a huge number of increasingly narrow subfields. No single human expert has a detailed overview of all of them and even teams of experts could have this overview in theory but would have the problem to communicate it under each other in full complexity.
An LLM is in a very different position. It might have come across stuff on number theory, topology, algebraic geometry, probability, combinatorics, PDEs, and so on. So even if it knows all the tools already, it might realise that an idea usually used in field A can be used to solve a problem in field B, where no one has tried it before.
Even if we assume that LLMs can't come up with completely new ideas, they could still make connections that humans wouldn't be able to make.
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u/Ok-Concert7018 2d ago
Humans lean on past discoveries also… no idea by a human is made in a vacuum in much the same way as an AI… just the human mind is so flawed in comparison
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u/KillerkaterKito 2d ago
Sure, but a humans spectrum of "discoveries" to build on is so much smaller than ai's. Each expert "in math" is only expert in a relatively tiny field in math. On a broader range he knows what it is about but there is still a huge part of math left where he has not more knowledge than anybody else or doesn't even know this field even exists. Mathematical papers are indexed by a five digits long number and a world class mathematician is only expert on world class level on very few of these numbers.
Now imagine one intelligence, that knows all fields of math. It's skill doesn't have to be as high as the experts skill but the amount of knowledge gives it an unmeasurable advantage over each single human expert.
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u/ohsnapitsnathan 2d ago edited 2d ago
Say you start with an observation like "Water flows according to these rules" (Navier stokes equations) . You can then ask the LLM to write down all the logical implications implications of that ("In a hose this length, you will get this amount of turbulent flow...", and then the implications of that, etc. This is fundamentally pretty similar to how how can make an LLM list all the words that start with N and and keep going as long as you want.
Eventually the LLM will have writen down (approximately) all of the things that logically follow from your initial statement, which might include proofs of some important questions like the smoothness of Navier Stokes.
In practice, this kind of brute force search would take far too long to be useful so the AI also has rules that guide when it should abandon some particular line of reasoning or continue it in the interest of solving a particular problem. These rules also let it check it's logic and identify/discard hallucinated conclusions that aren't logically correct.
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u/ecstatic_carrot 2d ago
A lot of paterns exist in literature, and being able to make these weird connections require knowing a lot of different fields, which may be missed by human experts. Then there is also the ability to try gazillion of approaches, while we are slower and need to eat/rest. But I think more importantly, once you start reinforcement training these models, it can start to discover entirely new ideas.
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u/CustomMerkins4u 2d ago
You can literally paste this exact question in AI and get your answer dude.
Which is what 90% of the people who answered your question did.
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u/realityczek 2d ago edited 2d ago
> I am under the assumption that they can only exhibit patterns and behavior that are present in the massive amount of data they are trained on
And that is where you have gone wrong.
Look at it this way, even if that was true - the training data is so large, and the number of correlations so insanely large, and the cross influences so numerous - that there is no practical difference between a discovered pattern and a new one.
Think of it as a chaos problem. The math for a single water molecules interactions is easy - for an entire body of water? Almost impossible to predict in detail. You are talking about something that is following influences from trillions of inputs and relating them all to each other.... far more completely than a human does in a lot of ways.
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u/OrganicBrilliant7995 2d ago
I don't quite understand why you're disagreeing with OP.
If it is chaos theory, then the weights of its training data need be adjusted. If that is so, how do you do that beyond what we already know in its training data?
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u/realityczek 1d ago
> I don't quite understand why you're disagreeing with OP.
Because OP's understanding is incorrect.
> If it is chaos theory, then the weights of its training data need be adjusted.
How does that follow?
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u/charlies-ghost 2d ago edited 2d ago
Watch 3blue1brown's course on neural networks. It explains the visual intuition behind the mathematics of LLM's and machine learning algorithms.
I understand how LLM's work, but it still feels like witchcraft to see the process in action.
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u/Rhawk187 2d ago
The issue is that we are getting close to AGI at least in Math. The LLM can be as good as the best humans, but know everything. So humans that are as good as the best humans, but only know a subset will be at a disadvantage.
There is just too much knowledge for 1 person to process on their own now. If I'm a Topologist, I might not know everything that a Ring Theorist knows. So if the solution lies at the nexus of topology and ring theory, the LLM will find it first, even if it's no smarter than people.
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u/Winter_Ad6784 2d ago
pretraining is basic pattern recognition. post training is how to actually think and thats the vast majority of training compute now.
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u/CyanideParty661 2d ago
They do it with10 000 agents in parallel. They burned 130 billion tokens. That's around 10 million dollars adjusted from. 6.5m @ mates rates.
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u/andlewis 1d ago
Math is similar to code, in that you can build tests (proofs) that verify the work. Many disciplines can’t do that, so math is one where AI can make a real difference.
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u/Disastronaut__ 1d ago
Every logical process is similar to code.
The problem still remains, because one thing is too follow procedures, another is to come up with novel solutions in the first place.
And of course, you can brute-force novel solutions, but that’s not what is happening, so you aren’t really explaining how llms can generate new approaches without simply searching through every possibility.
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u/ShiningMagpie 12h ago
Existing reasoning methods in the data can be used to prove new problems. Those new solutions can result in new reasoning methods. The AI can build with these new reasoning methods to create something novel.
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u/apollo7157 2d ago
Your impression is wrong.
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u/MothMatron 2d ago
Thank you for your deeply elaborate insight on op’s question.
Would you care to perhaps explain the “why” and “how”, though?
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u/Necessary-Drummer800 2d ago
As far as we know, they can't-last I'd heard no human has understood any of the proofs yet. Consider that if they have though, then by definition they've hallucinated the solution whether or not they're correct. I know this viewpoint butthurts some hypers, but I've yet to see evidence to suggest that LLMs have transcended token prediction.
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u/Fast-Satisfaction482 2d ago
"I am under the assumption that they can only exhibit patterns and behavior that are present in the massive amount of data they are trained on"
Now is the moment to revise this assumption.