What a time to be a sine

This is a huge breakthrough. Right now LLMs tend to struggle with logic and reasoning, but that's about to change. This will open up so many possibilities!

Someone should show this to Roger Penrose. Those are the kinds of problems that he argued could never be solved by a classical computer.

It would be cool if AI starts to see intricate geometries in a way we never thought of into things like, art, architectures and engineering principles. Geometry carries over not only in other realm of mathematics. This achievement really showcases what to come in the future.

This is impressive, but the part I am mostly interested in is this recent trend of making models much smaller these days. We are also seeing a trend to make smaller models more efficient than the larger ones. I have hopes this will eventually bring the power of GPT-4 to consumer-grade GPU that can be installed locally. That would be really something.

This is not something I expected we would make significant progress on so soon.

This is really impressive. AGI will revolutionize the world when it happens.

I'm literally watching Skynet being born. What a time to be alive indeed 😁

Thank you for making my go to videos for watching when I’m eating my lunch. You really improve the quality of my day. Thank you!

4:46 What I am more impressed is there is a class of human biengs with such sheer brilliance, that they can beat a trained neural network at logical deductions.

This might be the breakthrough needed for AI to start designing General AI, imagine it comes up with a general mathematical theorem for intelligence which is more complete than what we've had up to now? And then that model can improve upon itself, and so on. The next 5 years are going to be amazing to watch

Man thanks for your insights and speed news it's great.

Incredible! Specialized, but absolutely incredible! What a time to be alive!

Terrifying amount of progress for a single research! Can't wait for it to be applied to other AI's

Integrating these different models together, the multi-model approach is what will make this useful, GPT-4 will be able to do math really well using it.

listening to this is like racing down a bumpy road

This is a beautiful paper. It made think about the way we train AI and how to allow it to grow on its own.

For me, doing the mechanical work in maths class was learnable, but pulling "rabbits out of hats" was what I really struggled with when doing proofs at uni. Seeing this AI perform almost as well as a Gold IMO contestant is very impressive!

I wonder if we see a development where we have some major frontier general AI that uses lots of specialized systems as tools but then the next-gen frontier AI is trained on this entire structure so it learns to do them by itself out of the box

GPT-4 is quite bad at geometric problems, as I've tested it, I do a little coding exercise with it and so far it has never got right nor have gotten any better as far as I know: 1)I ask it to generate a isometric 3D maze, simple with every wall of the same height and width, 2) Them I explain to it how it could do it: 2.1) Use a classical algorithm say Kruskal's to build the Minimum Spanning Tree (MST) out of random grid of M x N points; 2.2) When point are connected there's a wall and where they don't there's a space in a cell (or the opposite also will work, overall is about 50/50 between open and closed cells) 2.3) It needs to have an opening at top left (Entrance) and another at right bottom (EXIT) Those points (2.0-2.3) it gets right after a few back and forth 3) I say that it should use a linear transformation to make it isometric and them to extrude the wall upwards. Them it keeps getting it wrong and I've showed it dozens of images of simple isometric mazes, but so far as I know it never gets it right, if somebody was able to do it, please leave a message !

This would work well in a Mixture of Experts type model or as a specialized agent in a swarm, right? GPT-4s limitations here would be mitigated by fine tuning it to leverage a model like AG as a tool. As long as it can get as far as asking the question and validating the answer it would likely be an effective approach.

Whaat? Open source? Damn , im having chills because this will be able to do things that we maybe dont know about because it learned from scratch(i think)

6:38 about this AI being "still" relatively narrow: I think it's a good thing it would stay that way, while progressing in its own field. Since models are black boxes, to minimize the alignment problem we want narrow superintelligent AIs to communicate to each other (and themselves, see chain of thought methods etc) in natural language, so that humans (and other ais) can check on what's going on. I think it's a good trade off between security and efficiency.

Very very scaringly brilliant

Awesome! Imagine what will happen some years in the future!

It may be worth mentioning that you can already use a normal computer algorithm to solve these problems. Tarski's axioms are first order, so it is decidable to check whether a theorem follows or not from them, and there are plenty of existing algorithms that enumerate a large number of theorems. The innovation here is making it find short proofs in a way similar to a human, using said algos that enumerate practice problems

This is probably the first video in awhile that was way over me head, it's like Pure Math.

I know very little about AI, but an idea has been bouncing around my head for a while: What would happen if you made a dataset containing a ton of trained AI models, with each model labeled with a text description of what the model can do, along with descriptions on how many dimensions and parameters it has. Would it be possible to make a Text-to-Model AI that allows you to describe a functionality, and have it churn out a model with weights close to what is needed to achieve that functionality?

5:20 no, fast thinking is the quick response like muscle memory and the slow thinking is working out a process like using a process to window away until its answer. The process is what matters kinda like building the blueprint. Math process is the blueprint and we build to the answer. The slow is better thought out basically, not just a first prediction with all info but a first prediction that uses the info to find the right answer. Understanding the process allows it to be smarter.

What a time to be alive!! 🤯

New all-powerful mathematician... hmm i can smell the new physics in some years already

Can you please talk about the new LLM Model called "Mixtral-8x7B" Thanks

Forget the paper, my subtitles spelt Karol's name perfectly! What a time to be a guy.

Yes, I’ve been obsessed with this paper… but to say it’s without human assistance is misleading; they developed a sophisticated set of methodologies and functional graph procedures to generate the training data from scratch, even setting a new state of the art in proof discovery in order to feed it.

For the infinite number of primes question, that actually can be done as a straight construction (and may have been in the original, need to check): after getting the product of a list of primes + 1 and getting the factors of that, you can put these new primes into the list and repeat the process over and over to generate an unlimited number of primes.

Would this be able to work with tabular data? I've been looking at ways to have an LLM crunch some tabular data i have and do some actual math on it (nothing too complicated tho). LLMs so far been incredible with text/string data, but when it comes to numbers, oh boy, hallucinations start easily

great paper for the start of 2024. can't even imagine where we'll be at by december. hard to believe chatgpt is barely a year old

Want more of this!

Next version optimize for less steps possible and put it in a mixture of experts agent swarm to make the AGI

I do like the "narrow" focus approach. Would you rather have a candle or a laser?

Euclid's proof is written incorrectly at 2:15. The point is not that "p is a new prime", but that the prime factorization of p is a set of new primes.

get general purpose AI like this that outperform humans, make some for all domains, make an AI which is able to detect a domain or set of domains from related to a prompt, then bring in the relevant expert AI to solve, if multi domain break down the question into the relevant domains, ask each expert to solve for their part and them put them together. you now have artificial super intelligence. i feel like research papers in the future will be: methodology: i gave the question to an AI results:

A-MA-ZING !!!!

It still seems like a pretty narrow AI but seems incredibly good at what it does. There's still a long road to making this more general, but if that is accomplished, you essentially get an AGI that can figure out how to solve a complex problem on its own. Imagine giving it an access to a simulation (so the AI can check its solutions), and you can use it to develop drugs, computer algorithms, optimized mechanical designs... Basically replacing a whole lot of science and engineering.

I keep saying the way to AGI is to have a million specialized sub AIs and one controller that knows the best one to pick for the job and a translator that can facilitate the communication between them for more complex tasks involving multiple disciplines.

Sometimes I want to connect a lot of these AIs to my brain as new modules and tools. It hadn't upgrades for a long time.

Look at this paper title! Look at this graphics! Let's not discuss anything about the method! What a time to be alive!

Thanks!

Wow, first the MoE revisited approach, and now, we get a narrow expert to augment the MoE with exceptional mathematical ability!? What is going on with all these optimizations in AI right now?

What I wonder is how AI can help decode previously undecipherable written languages from the past. No doubt people are already training AI to do that.

This is great progress. However, you are incorrect @5:06. The AI doesn't "learn from scratch" ... the training data that it is given is pre-trained human created symbolic data from symbolic engines created by humans. So it is literally trained using data that humans created which provide the baseline rules of geometry... it doesn't self-create those rules. The synthetic data is 100,000,000 examples of that data, and then it can use that to give answers to more complex questions or questions not included in the data set. It is still very exciting progress because it can extrapolate what it is trained on to problems that it has not seen.

I really appreciate the time you put in on this channel. I wish I could access the content you provide but your drawn out way of speaking makes it really grating to follow for me. Obviously this is your stylistic choice, but I wanted to give the feedback that the constant pauses in every sentence stop me from clicking your videos despite really being interest in the content. Either way thanks for your hard work :)

I took Maths and Physics at university. It always seemed to me that the logical presentation of a proof said very little about how the proof was first found. 🎩🐇 I came to the conclusion that we use perceptual abilities to discern the key features of the problem, and then use analogy with similar problems to suggest possible approaches. You might even have to break the task into a sequence of stages with sub-proofs for each. This by itself, of course, does not give you a watertight proof. You then have to go through the process of filling in the steps and details.

Károly, ez már elképesztő! Mi mód van arra, hogy ezt a papírt elmondd magyarul is?

Is geometry easier than algebra for AI? Can they make a general AlphaMath with this approach?

Off topic but; I saw a video on how video games are made. The ones where the graphics are well made, it simulates physics. What if we can make a simulation even better, with building a game or a model of reality made with quantum physics, layered and layered to get the reality we see? Would that be possible?

Impressive, but what are the implications or applications?

Wow so can we spin this up as an API in Docker, and make LLMs pose problems in the same distribution as its input data, and use the outputs? How much GPU RAM do we need?

Could this be applied to the domain of Physics?

at 3:42 the AI claimed angle congruencies that don't visually add up. Are these mistakes on the AI's part or mine?

Blackbox problem and stochastical parrots:(Originally an answer hjidden deeply here, so context is missing) An AI that 100% understands an other AI, would basically be a copy, or at least would have this "copy" integrated into itself. Any derivation introduces uncertainty(blurryness). Not a coincidence the similarities to the uncertainty priciple in physics. Interesting metaphysical concepts arise from the study of AIs. Everything that exist, is just a different expression of the same fundamental concepts, just on a higher complexity plane. It fractals down and up all the way. We are creating what created us! These fundamental similarities in concepts can also be seen with human neurological networks. Even though AI only modells one layer of our multilayered thinking and biology. We finally will understand everything much better with and through AI. Ai is the last invention humans will make. People saying that LLMs are only statistical parrots, don't really understand what's going on. But I don't feel like writing a roman now here. Basically both sides of the argument describe the same thing through a incompletness lense. It turtles all the way up and down. The very first time I heard that story of the old lady, that got laughed at by all the scientist, I knew in my heart that she was correct. The most ironic outcome is the most likely. But it was actually my intuition that I knew. And where Intuition comes from, and where it ties into this bigger picture(and QM), is very fascinating. Since AlphaGo, the bigger picture became much clearer for me. And we are just at the start. We are always just at the start. Prepare for the biggest ride ever known to mankind. (Sometimes I feel like I have to write a book, many concepts I never read somewhere else in my head) I am not even really starting here, just wanted to reply a few words, but can't help myself.

The next step is developing an AI that can craft these expert AI's themselves, or intrinsically learn to accomplish these tasks

Notice how people always refer to thinking in ways that are unique from every pervious attempts or methodologies..... as Thinking Outside of the box Hardy Har Har aaahhh sigh I love your vids Thank you for you passion and your diligence

Is there a use for this model or mostly a proof of concept?

2023: “It is just a fancy autocomplete” - human talking about ai 2024: “It is just a fancy autocomplete” - ai talking about human

This is the greatest AI advancement within the past year

Makes me wonder how the problems in a mathematic olympiad are made.

Impressive to see it work off synthetic data.

The problem is how to reduce the domain to reductive and inductive techniques, once you can do that, you can train a NN on anything, and it will be better than the best - why? Because it is fitting a function in the hyperspace, the limit of which is full memorization of the training data. We shouldn’t be so blown away by this, as the NN doesn’t know it’s doing geometry, and if you change anything fundamental it will fail spectacularly.

That moment, when you're walking happily in the streets of computer technology and there's a singularity standing in the next dark alley, waiting to shank you...

3:52 should note the many many proof steps is actually a negative? It's basically doing a slightly more informed version of throwing spaghetti at the wall and looking at what sticks. And it kinda by definition makes no mistake as it just accepts generated proof commands if they actually manage to advance the proof state. Human-written proofs of these things are gonna be quite a bit more concise.

Can it create new, even more advanced maths problems, for the future AI Olympiads?

Can they prove theorems and do the same for other math?

Google: HEre is a new paper and new techinques OpenAI: thanks Google, how can we copy this... again?

You forgot to say “what a time to be alive!”

Can it complete Fermat's last theorem?

How does this pulling rabbit part work?

This is HUGE, big, i mean imagine having problem solving capabilities in your pocket, wow.... the exponential grow is happening, we imagine robots idiots but can be poets, and genius inventors, just do the same to inventions and all the possible inventions and discovery ever can be possible now. Wow

I don't know if you can call the proof better. It requires lower level deductions, but more steps. It's easier to understand, but provides less intuition into what is going on.

This is huge discovery

They should use this program to train GPT-4

Was chatgpt actually able to solve that usaco problem?

If AI know MATH perfectly , it can know how to build anything from scratch

I dropped my papers

Wow. It seems we are in the prologue of sci-fi book

They should compare AI's vs human's solution length, there is where intelligence is.

Can AlphaGeometry solve the Riemann Hypothesis?

Mathematics is in other words deductive reasoning, a foundation to all actual knowledge. The other foundation is empirical observation. If AI can master mathematics, it would not take much before it can master the creation of new technology.

i wish they'd open source the data though. That would be much more helpful imo

But can it prove the Collatz conjecture?

I saw the first few seconds of the video and I don't know why I am SO sad 😢😢😢

Your tone speaking is a boxcar(t) function

4:50 Don't want to ruin the excitement, but this is incorrect. The gold medal isn't awarded just to the winner, put to a big number of contestants, still impressive, but not as much.

imagine the developers' reaction after they figured out they created something smarter than them..

How long until an AI solves one of the millenium prize problems? I guess only 2 years.

Two caveats: 1. A long proof is worse than a short proof. The official solutions to these problems are usually very short. 2. "Gold medal" != smartest participant. About 1 in 12 IMO participants get a gold medal.

i wish i could train on 100 million synthetic geometry problems

Wow people found such an efficient way to make geometry as complicated as they could! This looks nothing like geometry we learned in school 😂😂😂

Shit this is too good too fast 😨

OK now I'm having a real hard time believing that this is anything close to what a LLM is supposed to be able to do. This is not a language predictor. It has short term memory and seemingly logically consistent views of what it's talking about. What is actually happening, here?