1025: Word Gravity: How Transformers Bend Space, with Dr. Luis Serrano

25:04that I think is hard to replace for a machine.

25:07Jon Krohn:Yeah, I think another one of the great advantages of a book is that it's kind of, it's a convenient collection of everything like at the right time. And you can just know that in a well-written book, you can go from the beginning to the end and you're going to get this great arc. It's going to cover all the key topics you need to know. There was an editorial team. There were people who advised on what should be in the syllabus of the book in the first place. and so I think you typically end up with a really great product and at least not at the time of recording we can't yet completely have the book generated by an LLM maybe by the time this is published maybe we'll generate podcasts too for sure maybe this podcast right now is generated how do we know just the hands, five fingers, five fingers still us All right.

26:03Jon Krohn:So in addition to your new book coming out, something you've been writing, something you've been working on, something else that you published is actually a new paper. So you published last November with, I'm going to try not to butcher their names, Ricardo Di Sipio and Jairo Diaz Rodriguez. Yes. Very good. Yeah. I really put a lot of effort and thought into that. you guys wrote a paper together about the curved space-time of transformer architectures. Yes. And that is pretty mind-blowing. I think we're going to spend a bunch of time on that right now because we'll learn about transformer architectures in a way, but I think we're also going to learn about space-time and relativity and these kinds of concepts.

26:52Yes, this was definitely very exciting. Definitely very exciting to work on. And yeah, definitely for the physicists listening, we use the word relativity, but in a very loose way. It's basically a space-time curvature analogy, a weak analogy of what's happening inside a transformer. But I think it opens the door to what's happening underneath. And the fact that physics-related things start appearing, I found it mind-blowing. The story of that is that in order to understand attention, it never clicked to me with the People say it's like a search table with a query and a key never made sense to me.

27:32Then they said, oh, the words pay attention to other words never made sense to me. Then they gave me the formula made even less sense. It's a soft max of KQ divided by square root of DK times V. Nothing for me. So I started looking at videos and looking at other things and looking at just writing and like watching videos and somewhere, somewhere in the process, somebody, which I bless his soul. I don't remember which channel was this. I think it was a kind of an underrated channel that didn't have a subscribe. but this person is just kind of like made a, like this is a beautiful description where at some point they did a linear combination of the words and they said, this word becomes more like that one.

28:21And the linear combination added to one, the coefficients added to one because there's a soft max. So, you know, you turn your word apple into 70 % of apple and 30 % of orange. If you said the two words consecutively, say orange, apple, you know what I mean? so the word becomes a percentage of itself and and the rest of percentage of another word and to me that's moving in a line right like if you have if I have two points and then I take a percentage of one of the position of one point and the other I'm moving in the line between them and so I thought maybe words are moving in a line and I started rewriting all the equations as in like words are in a position in space because embeddings words are in a position in space and then attention just moves them in a line toward each other.

29:07And I immediately thought, oh my God, that's gravity or magnetism, right? Words pull each other. And I thought that makes a lot of sense because if I'm saying the quintessential example is the river bank. Bank is a bank in the financial sector of the embedding around stocks and bonds. And then you say river bank and the bank just becomes a nature thing. So the word river just pulled it towards itself into the nature region of the embedding, because in the nature region of the embedding lives a river and tree and stream and sea and all that stuff. And so it just pulled it. It infused itself with it, right?

29:48It infused some properties of it. For example, the nature property. It didn't infuse all the properties. There are some that don't, but the nature property, it moved in that. So the moving actually works in different directions. It's not towards it because of the value matrix. But anyway, the fact is, words, I started calling it word gravity. And as I said, any physics words that I say is a very loose analogy. But I started calling it word gravity, word gravity, word gravity. And then one day I gave a talk in the Toronto Machine Learning Summit. And Ricardo Di Sipio, physicist, I also, by the way, I hope I'm pronouncing it well because I don't know Italian.

30:27And Ricardo is a physicist who was sitting in the first row. And then he came to me and said, hey, what you have is actually, you know, when Newton was talking about gravitation and then Einstein came, which is a force between objects, he died and he had no idea why this force happened. And then Einstein came hundreds of years later and he said, it was not a force. The masses are bending the space. Like, you know, the reason you fall towards the earth or the earth falls towards the sun is not because the sun exerts a force, it's because the sun bends space. And all of a sudden, the line in which the earth should be flying in a straight line, it's curved because of the sun and it happens to be curved around the sun.

31:07And that's why we're there, you know? So he said, I think it's the same concept. Like you're talking about word gravity as like a force between words. I think it's more like it's probably a space-time curvature thing. Like it probably words are bending space in a way that they just pull towards each other. Right. And so we started working on that and he worked out the math a lot. He knows the physics a lot more than me. So he actually worked out the geodesics and very much like the matrices that appear in the geodesics appear in are the key query and value matrices. And then we started working with another friend, a higher of the as a professor at York University in data science and statistics to run a lot of experiments.

31:50So these two guys are wonderful. They actually know a lot more about that than me and worked out both the physics and a bunch of experiments that really study this analogy. And so we're very excited actually of this. I mean, it provides an analogy. I think it's more of a visual work. We meant it as a visual work. We've gotten notices of like labs that are working with it for something else. So I'd love to see applications of it. But as of right now, we thought of it as like a fun analogy, like physics analogy of what's happening inside chat GPT or inside the brain of these models.

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33:06Jon Krohn:Beyond the training, ODSC AI West brings the AI community together with networking events, meetups, the AI expo, and more, giving you the chance to learn, practice, and connect all in one place. Super Data Science listeners can use the code SUPER at checkout on odsc.ai for an additional 15 % off your pass. See you there. Odsc AI West, October 27th to 29th in San Francisco. In that analogy, what plays the role of gravity in the same way that you described the sun bending space so that the earth comes toward it. Yeah. What's gravity in a transformer? Yeah, that's a great question. So it's not the same gravity as in mass one, mass two times R squared in particular, because mass doesn't make sense.

33:55Like if you have a big mass, it attracts every word, right? But here is not the case. For example, river really attracts bank, but it doesn't attract other words, right? Like, you know, if I say river tree, it's still the same tree uh so it's not a matter of how close you are because tree is close to river doesn't get pulled as much as bank which is farther away so it's not it's not that that words independently have an information of how much you pull and they pull everything based on the distance and the mass of the air word it's for every pair there's an actual quantity of pool and it's not symmetric because for example, bank doesn't pull river.

34:37If I say the river and the word bank comes before, it's still a river. You know what I mean? Unless they name something bank, a river of something, then yes. But as of right now, the pool is not symmetric. A word can pull another one, but the other one can't pull. So it's weirder than gravity in many ways. And the formula is not GM1M2 divided by R squared. It's soft max of KQ blah, blah. And it's based on the dot product of the words, but when you multiply them by K and Q. So K and Q, what they do, the key and the query matrices, is they extract all the features of a word that would influence other words for key.

35:18And the query extracts all the features of a word that get influenced by other words. So in river bank, then the key of river extracts the nature part and says, you know what? If a word comes with some nature, the river will pull it. And the query does that for bank. Yeah. And then you multiply those. So it's very dependent on the key and the query matrices that basically transform your space into something else where the dot product says more than just similarity. So it's a similarity. It's a two directional similarity. And then the V matrix comes out and says, you know what? you want to move in this direction, but I actually want to move you in a different direction because some properties are movable and some are not.

36:08I can add nature to the word bank and turn it into a more nature word, but there's a bunch of properties that are not. For example, bank is a noun. I can't change that no matter how much I pull it, right? So for example, in the book, I have the example canoeing bank. So canoeing is a verb and it pulls bank, but it's never going to bring it to become a verb. Right. It's going to bring it towards nature. So out of the all the descriptors of a word, if there are 1024 numbers in your embedding, a bunch of them are movable, a bunch of them are not. So V does that. And interestingly enough, in the analog for relativity, K and Q make a lot of sense, but the V just came out of nowhere.

36:50So it even has extra stuff, but I'm getting ahead of myself.

36:54Jon Krohn:Luis, you're talking about the bank bending towards the river. It reminds me of an analogy that happens in the paper that I found fascinating. And this isn't really that related to data science or AI. It's, I guess, more an astronomical thing, but maybe it'll help people understand the same kind of transformer idea as it was helpful for you. I'd love you to tell us more about Eddington's 1919 eclipse experiment. Yeah, that's one of my favorite experiments, because what happened is you can't really see space-time curvature, right? Like we feel like we live in a giant 3D cube, but we don't know it's bent in different ways.

37:36You know, you can see bending in 2D because we can sort of see the earth being round, but you can't really see the universe being curved if all we have is 3d vision right so um so what eddington did uh was he he thought about a star that was sort of behind the sun and in a certain eclipse and and you would see it not behind but and in another place like you would see it sort of in a place where it's not and the reason is because the light of the star came in and bent thanks to the sun and then got to our eyes, but we could see it right behind. We could see it like it was above the sun. And so we have an analog of that experiment, which is we have the word, and it's always with bank and river, but basically bank, it takes the place of the star and river is the place of the sun.

38:31A fun story. I actually wanted to find the right example where the word would be sun and the word light would be bent, you know, something like maybe there was so much sun that I had to pick up the suitcase and it was light, something like that. Anyway, I couldn't work it out. So if it ever happens, I'll have an experiment with the word sun and star or light or something. But we had to do bank and river. And basically we just looked at space is the embedding, right? And the analog for time is the layers in the neural network. So the first layer is the beginning of time and each layer is a snapshot in time.

39:08And obviously, then that's a problem because time is discrete in our analog. But we can't really mimic the continuity of time. We can only take snapshots. That's a limitation. But actually, we had an... What's the opposite of limitation? We had actually something that was easier, which is that you could see the entire trajectory, whereas Eddington could only see the end of it, right? Like, where do I see the star? He doesn't know where the light went because he can't look at that. We could actually take the position of river and bank in every single layer. So there's a pro and a con. But basically, yeah, I mean, like the word bank flies through the embeddings, the embedding in every snapshot, in every layer.

39:52And it's like bank is here, then it's there, then it's there, then it's there. And eventually it appears in another place at the final layer. and when we added the word river in the sentence then it would basically go around river and the other in a different path so we would see the path of the path of bank is this but when you add river then the path of river is this so we had no choice then to say well river must have must have been the space around it for it to take a different route it's interesting to be able to

40:23Jon Krohn:see that happening through all the layers of the neural network in that transformer. That is very cool. One of the counterintuitive findings of doing that kind of analysis was that I think you found that function words like to, like T-O, which are like, they don't seem like they have much semantic meaning, but they actually showed some of the sharpest curvature in your experiments as opposed to semantically heavy words. What do you make of that. Yeah, that was a really interesting experiment because some words are pretty flat. Like, for example, the word the doesn't get influenced very much. The is the, you know.

41:01On the other hand, two can be influenced a lot because it can mean different things based on what's before, right? Like two can be to something or like, like there's a lot of meanings of it. So in some, in some layers, it really showed a lot of curvature because it was, it was easily influenceable. So that's something interesting we found. We also found that like each layer takes care of certain things. So like sometimes words had a big curvature around them in some layer and in another one, not so much. And that just lets us think that, you know, different layers are taking care of semantics or meaning or things like that.

41:40Jon Krohn:For sure. That's something that we've known about deep neural networks forever, where, yeah, you have different layers that come to represent different kinds of meaning. And so, yeah, in some layers, two doesn't need to change, but in others, it needs to change wildly in order to be able to make sense of some sentence or document or what have you. Very cool. Well, thanks for talking us through that paper, The Curved Spacetime of Transformer Architectures, Decipio, Diaz-Rodriguez, and Serrano. I'll have a link to that in the show notes for sure. let's move on to agents agents are i don't think we've talked about them at all yet in this episode which is pretty amazing because it's hard to go very far without talking about them you actually just wrapped a course called it's your first paid cohort course you can tell us what that means what the cohort course is all about but it's called grokking agents in production and it's with some more names that I'm going to struggle with.

42:46Jon Krohn:I am giving you some. Miguel Otero Pedrido and Antonio Zauros. Zaraoos. Although if I was in Spain, I wouldn't say Zaraoos. I would say Zaraoos. Zaraoos Moreno. There you go. I was saying it wrong, actually. I was saying Miguel Otero Pedrido, and it's Pedrido. Yeah. I didn't even hear a difference between those two. Pedrido versus Pedrido. Okay. So, yeah, even I mess up the Spanish. But yes, yes, I'm very, this course was very fun. It was a six-week course. It was dense. It was really more of an eight-week course. I'm rocking with Miguel Otero and Antonio Zarauz from, they make the Neural Maze, which, by the way, this is an amazing channel.

43:31They have so much, the Substack subscribers and very, like, they make so much content. If anyone wants to learn agents, definitely the Neural Maze, you should check it out. And so I worked with them on this course and I was doing sort of the, it was the same breakdown as I normally do. They have the technical side and the deployment side. And I was doing this sort of conceptual explanations on agents. And it was a lot of fun. I learned a lot about agents. For example, I had a conversation with Miguel where actually we're recording a video because it was such an interesting thing. I used to think that RAG was an agent, you know?

44:16So I would say, you know, RAG is an agent. Whenever you have an LLM doing things, that's an agent. And then I quickly found out, he corrected me and said, no, RAG is not an agent because it's an LLM workflow. So one thing is an LLM that does stuff. And another thing is an agent. An LLM workflow is when you tell the LLM what to do. Like you go, okay, you do this. And if this happens, you do this and then you nod, you close and that's it. And agent is when the LLM makes a decision, right? So when the LLM says, oh, I need to look for more information. I go look for information. Now I feel like I can answer this question, but I'm missing something.

44:57Like when the LLM is in charge, it's an agent. So that's one of the, that's one of the interesting things I learned. And yeah, other than that, it was a lot of new stuff and basically a zero to 100 on agents with deployment.

45:15Jon Krohn:Yeah, lots of the unglamorous parts, containerization, IM, observability, CICD. And it seems like the tagline for the course is demo agents are trivially easy to create, but production agents get hired. Yeah, and that's what the course does. Like it's end to end, like the project was to build a PDF reader that can read everything on your PDF using different techniques, chunking OCR, all that kind of stuff. And I combined them and then answer questions on it. And every, like every module had its own sort of deployment part. We use Google Cloud and then Cohere for the LLM. So it's pretty, yeah, it's pretty interesting.

46:02I learned a lot.

46:02Jon Krohn:In 2024, when you were on this episode previously, you predicted agents and tool use as the next big wave right after multimodality. And you got both of those right. Are there things that happened faster over the past two years than you expected? Or do you think there's parts of agents, multimodality that are still overhyped? I'm so glad my prediction went right. Thank you. You're so kind that if I had done something wrong, you would have erased it, right? But I'm glad it worked out. Yeah, no, I mean, definitely that was the vibe at Cohere when I was leaving. The vibe was tool use, tool use. It wasn't even call agents.

46:37It was tool usage. Like you got the thing to talk. You now have to make it do things. Like it's the next thing because it's the next thing with everything, right? Like with the internet, first it was like text coming in and coming out. And then it started doing things like a bank transaction or something. And it looked weird at a time. Like it looks weird to get the model to do things for you. But that was definitely the trend. No, I mean, I think it went, I didn't predict any speed for it. I knew it was going to be fast that we're going to start getting this to do things. Something that I found interesting is that in my head, the LLM already talks and now you make it do things.

47:24Go open your calendar, go write an email. What I actually didn't occur to me and I found it really interesting. I mean, it was there, but it just clicked, is that you can use agents to make the LLM do better things, right? Like you can have an agent, if you want to write a book, you don't just tell the LLM to write a book. You have a multi-agent system where one writes the syllabus and the other one makes the chapters and the other one checks it and the other one checks the grammar and there's a loop and there's like a manager that decides what part you need more. And so definitely the fact that you can make the LLM talk better by making it do things.

48:03That was a nice addition.

48:07Jon Krohn:regular listeners will already be aware that i'm obsessed with anthropic's fable 5 model and it has taken over my working life i'm writing a technical book that includes latex files mathematical notation python code examples and fable 5 and cloud code handles requests i make across whole chapters with accompanying jupiter notebooks end-to-end work that a few short months ago would have been dozens of separate requests with way more manual fiddling required with fable 5 it just works, essentially like magic, first time. Claude is the AI for problem solvers. It's the collaborator that understands your entire workflow and thinks with you, not for you.

48:44Jon Krohn:Whether you're debugging code at midnight, building a financial model, or strategizing your next business move, Claude extends your thinking to tackle the problems that matter. For problems worth solving, get started with Claude at claude.ai slash superdata. That's claude.ai slash superdata. and check out Claude Pro, which includes access to all of the features mentioned in today's episode. Claude.ai slash superdata. Yeah, worth checking out for folks who want to get into getting agents into production, get the grokking agents in production course. Definitely. You can, of course, an easy place.

49:19Jon Krohn:Of course, I'll have a link to that in the show notes, but again, you can find all of this at serrano.academy in one convenient location. Yeah, definitely check it out. We're going to run another cohort. We had a lot of students. and it was a lot of work, a lot of interaction, a lot of office hours, and then we're definitely going to run it again later in the year. So keep an eye if you want to learn agents. Fantastic. Thank you for all the great courses, Luis. Thank you. Two of your six agent course modules were on evaluation. So things like golden test sets, trajectory scoring, LLM as judge, evaluated deployments.

49:55Jon Krohn:Why is agent evaluation so much harder than say, rag evaluation? Yeah. I mean, I feel like ML evaluation gets harder and harder, right? 10 years ago, it was like evaluating a multiple choice test when it was predictive machine learning, right? Then LLMs came in and it's like evaluating an essay much harder because you have to evaluate conceptual writing. And then one step even harder than that is evaluating doing stuff, right? Like how do you evaluate someone who's doing a job? Like that's even harder than grading an essay. So definitely agent evaluation is one step harder than LLM evaluation.

50:34And the reason is because there's so many things to take care of, right? Like if you only look at the final result, that has to be good, but that doesn't tell the whole story. And then you have to see every single step along the way. Now, every single step is, did you do this step or did you do the step right? Huge difference, but you have to check if the step was done. And sometimes it's hard because let's say something simple in an LLM doing rag, you ask it something and it just answers out of memory and it answers correctly. So you just go good, but no, it didn't, it didn't use rag. And if I'm going to ask it something like, what's the weather today?

51:15It has to use rag, you know, it has to use the tool. So I can't just rely on, did it, did it do the thing right? Right. So basically the modules on that were something as simple as check if all the tools were called, then check if the result was good, then check every tool separately using different ways, you know, root score, just basically comparing words, using an LLM as a judge is also quite interesting. And those two are basically need to be done because there are cases where, yeah, you just check if the right words appear in the answer. But other times you need to check if you need an LLM to check if the answer was, the question was answered.

52:03So there's a lot of little moving pieces that you somehow have to combine into a big evaluation step. But we made a big deal on that because that is less common to see. Like a lot of the work and agencies do it and deploy it. And we're like, no, you have to make sure it works well. I mean, you need to be very responsible on this thing. So we add a lot of material on evaluation, like I do with everything. I think it's very important.

52:32Jon Krohn:Yeah, super important. This is something that we run into a lot with my consulting firm, YCaret. We have enterprise clients, we have government clients, and it is essential for them that if agents are deployed, they can be trusted. And it's these kinds of evals that allow that to happen. So thank you for creating a course like this. In addition to the agents course, you've also built a whole free course and video series on reinforcement learning for LLM. So you cover RLHF, PPO, DPO, GRPO. If we had all the time in the world, I would have you go in and explain all those different things. But so instead, I'm just going to skip to GRPO because that seems to be a reinforcement learning approach that has really mattered a lot, particularly with the DeepSeek explosion from last year.

53:23Yeah. I'm very interested in GRPO and I love it. And yeah, I worked on that. And the video series on GRPO was a lot of fun for me because it was just learning stuff from scratch. And we talk about that in the course a lot, in the course I have with the Rackpack. and it's basically, here's the interesting thing of GRPO versus PPO, right? Basically, GRPO is for reasoning models. It's for making the model not just talk, but do math or write code or do logic, which are much harder. But when you look at GRPO, it's not an actor-critic model. It's really just an actor. Whereas PPO is actor-critic model.

54:08So I'm going to sort of over generalized, but in my head, PPO is more meant to make the model talk well. And GRPO is make the model do math well. And there's one difficulty and one thing that is easier. One thing is that's harder, which makes GRPO what it is. If you want to make the model talk, that's easier than making the model doing math. I'll tell you why in a minute. But if you want to evaluate a model talking, that's harder than evaluating a model doing math. For the simple reason that if you write an essay, that's hard to grade. But if you do a math test whose answers are numbers, that's easy to grade.

54:52Right? So we kind of have a two by two square where we say, okay, talking is easy. Doing math is hard. But evaluating talking is hard and evaluating math is easy. So PPO has an okay actor that talks and a really good evaluator that evaluates. And GRPO has a really strong talker that does math and an evaluator that is not as strong. Obviously, it's strong. But where does it come that the evaluator in GRPO is not as sophisticated as the evaluator in PPO? The evaluating PPO is a model that gets trained. So you're training the talker and the evaluator at the same time. The model talks, the other one evaluates, the one talks, the one evaluates, and they both get better.

55:44On GRPO, you're only training the talker. Your evaluator is fixed. And the evaluator is simple. It's a formula that grades your responses and it doesn't get any better. It just gets trained. It uses LLMs. It uses other stuff. It uses compilers for compiling the code. It uses math engines to check the math. It uses a lot of stuff, but it's not a model that gets trained. So all you have is the actor and the evaluator is sort of this big formula they have in the paper where you have, it's basically a big loss formula. But that's what I find interesting of your PO because you would have thought in order to make the model do math, I need to make everything better, but it's not.

56:29I need to make the model stronger, but the evaluator actually, there's a lot of stuff I can use in the fact that the model is reasoning instead of talking that I can take advantage on. And at the end of the day, I did say another thing that I want to clarify. I said talking is easy and doing math is hard. Obviously, talking is not easy for a model. but what I mean is that probabilistically talking is easier for a model because the model doesn't go for the right answer. The model throws a dart in the vicinity of the answers because it's a probabilistic model and it gets some answer that is close to what you meant to say.

57:11If the perfect answer is here and you throw a dart, you get something close. But in text, that's no problem because if I live in text space and I pick a sentence that's close enough, I'm likely to say the right thing worded differently. You try that in math, that don't work. Because if the answer is two plus two equals four, and I move one millimeter, I get two plus two equals 4.1. And that's not correct. So math is a hostile space where a right answer is surrounded by wrong answers. Code is the same. A right line of code is surrounded by wrong answers where you change a colon into a semicolon.

57:44Whereas text, for the most part, if I land very close to what I wanted to say, I'm okay, right? So in some way, then we have this two by two matrix where we have top left, we have talking is easy. Top right, we have evaluating talking is hard. Bottom left, we have doing math is hard. And bottom right, we have evaluating math is easy. And the top row is PPO and the bottom row is GRPO, basically.

58:11Jon Krohn:That was a really fantastic explanation of GRPO, which I don't think I even said is called group relative policy optimization. That's what GRPO stands for. And I'll have a link to materials on that, of course, in the show notes as well. But fantastic explanation there. And particularly for why it's important, that mathematical reasoning. And it seems like that's a key part of this. Like there was a, GRPO was actually introduced in a paper called DeepSeek Math. Yes, yes, yes, yes, exactly. pushing the limits of mathematical reasoning in open language models. So aligns very nicely with what you're saying there.

58:49Jon Krohn:Luis, you used to work on quantum computers at Zapata Computing. What's been happening in the world of quantum as it relates to ML or AI? Have there been any big innovations in recent years? I think there's been hardware things happening. The computers have been getting bigger. There was this topological qubit thing happening. So I think in terms of that, yes, I don't know. And maybe it's just that I haven't been sort of that up to date, but I don't know in terms of algorithms, at least in machine learning or something. But yeah, I've been out of the world a bit, but definitely hardware advantages have been happening.

59:35And then hopefully we'll have a quantum computer sometime. That I don't know if I can predict, but I'll just, you know what? I'll say the two things and we'll have both recordings. And you're so nice that in two years, you'll put in the podcast the one that was right. Like I'll say that quantum computers are never going to work. And then I'll say we're a year away from our quantum computer and we'll make sure the right video appears. How's that?

59:59Jon Krohn:Nice. Sounds great, Luis. Last technical question for you here. It's actually not that technical, but it's related to a technical topic. So the International Math Olympiad, You're very familiar with it because you won the Broadens Medal in the International Math Olympiad years ago. And in 2025, AI models hit a gold medal standard for the IMO, for the International Math Olympiad. And it seems like in 2026, they did even better. We haven't had full reports out yet. What goes through your mind when you see a machine being able to act at that level on math. Is it just exciting for you? I find it very exciting.

1:00:44I mean, I think there's always a tiny bit of nostalgia saying, oh, I worked so hard to get this and like a machine can do it. But I think that's 0.1 % because I'm 99.9 % very excited to see models being able to solve these problems. These problems at the end, I mean, require a lot of creativity, but a lot of it is using a lot of tools that exist, which is not that different from a game of Go or a game of chess, where it requires tons of creativity. But the fact that you have a finite set of moves, and that a computer can do, can search in a space so humongous, then definitely, I mean, Olympiad mathematics is a game like that.

1:01:29And I actually was really hoping that it would be, that a model would perfect it. Um, I think it doesn't take away from, from the competition in the same way that we still watch people run, even though cars are faster.

1:01:46Jon Krohn:And even in, in, in intellectual pursuits like chess that you already mentioned. Yeah. We still watch chess, you know, goal is still interesting, even though a computer, uh, can be there. So, you know, computers can, can, if we can watch the Olympics with, with machines and it'll be less fun, but they will win. Uh, we could watch two models playing chess, but we still watch two humans playing chess, you know, because I think there's still the fact that we do it with our, with our limited computer in our head and, and we use different, you know, creativity and things like that. I think it's exciting.

1:02:17So I still, I still follow IMO results, very, very excited. And I, and I think it's not going to go away. And I think that's the same thought that I, I talk with a lot of, a lot of IMO people and I see nothing but excitement. I mean, I think, I think it's, it's great to see models that can, that can build on. It's a good benchmark. And I mean, I, I, it's already like research mathematics is already in, in reach. And I think I'm, I'm excited about it because at the end of the day, the, the, the human is going to pass to a higher level of saying, okay, what do I want to, the direction of this field to go?

1:02:55What do I want to, the big problems I want to solve. And for things like, like solving the problems, I mean, mathematics at the end of the day is, is a game we have a finite number of axioms and from the axioms you build lemmas or you build small you know from the lemmas you build theorems and it's it's no different than walking in a very high dimensional world trying to find a needle in a haystack so models models can do that very well and they can they can i mean go has more positions in the board than atoms in the known universe and it's able to navigate that space very well and find the tiniest needle in the biggest haystack.

1:03:38So I'm excited. I'm excited of seeing it solve mathematics. And, you know, people would work, like Terry Tau, for example, is the best mathematician. He's done a lot of work on AI and mathematics. And there's a lot of other famous mathematicians doing that work. Timothy Gowers and other fields of my atlis is also working on that. So yeah, there's definitely interest there.

1:04:02Jon Krohn:Hey, hey, this is your host, John Krohn. In addition to hosting this podcast, did you know that I run an AI consulting firm called Y-Carrot? Yes, that's the letter Y and the deliciously crunchy veggie. At Y-Carrot, our team pairs decades of ML and software engineering experience with recognized expertise in the latest AI techniques, such as all the key generative and agentic approaches. From problem scoping and proof of concept through to high volume production deployments, we've got you covered at every stage of the AI project lifecycle. To learn more, head to ycarat.com. From there, you can click partner with us to give us some context on how we can help.

1:04:40Jon Krohn:We're looking forward to hearing from you. Again, that's ycarat, Y-C-A-R-R-O-T.com.

1:04:51Jon Krohn:Well, fascinating conversation today, Luis. Across the board, reinforcement learning, agents, curved space-time of Transformers, and of course, Grokking Machine Learning, the second edition, which will be available to listeners very soon. In addition to your own books, do you have any book recommendations for us? Yeah, I think I was checking that I gave you someone's last time. So I wanted to not repeat myself, but there's one that actually someone has been in your, on your channel. There's on your podcast, Kathy O 'Neill, Weapons of Math Destruction, Math, like M-A-T-H. That's a really good one.

1:05:32So that, that, that one I recommend. What else is good? I mean, good friends of mine, JLMR and Martin Grotendorf are getting one out on agents pretty soon. So that's, that's one to, to definitely check out.

1:05:45Jon Krohn:It's pretty funny that, am I correct in thinking this when you were giving the Spanish, like the way that someone would say something in Spanish, like in, in, in Spanish from Spain, would they say weapons of math destruction? They would say weapons of math destruction. I think so. Yeah. Maybe that's definitely, oh, that's, that's the perfect way to teach the Spanish set. If you say math versus math. That's how you would say the Z and the C in Spain. Whereas in Latin America, we just say S, Z, and C in the same ways. Yeah, yeah, yeah. Really cool. That's funny. Good to have a laugh with you again.

1:06:27Jon Krohn:If people want to follow you after this show, which I encourage them to do, obviously we know they can go to serrano.academy. Is there anywhere else they should follow you on social media or something like that? Yeah. The page Serrano.academy, the channel Serrano Academy, the YouTube channel is where I put all the stuff I know goes there. LinkedIn. I'm also quite active on LinkedIn. So I'm just Luis Serrano on LinkedIn. Those are the main places. Perfect. We'll have links to all of that in the show notes. Luis, I always enjoy spending time with you. You are a treat. So friendly, so fun, so intelligent, and you tell it like it is.

1:07:05Jon Krohn:So I hope we'll have the honor of having you back on the show again sometime soon. Thank you so much for taking the time out of all the work that you're doing these days to join us. Thank you so much, John. I'm a great fan of your podcast and you're a wonderful person to talk to now. And I know that in person and in virtually. So I definitely look forward to our next conversations. So thank you so much for having me. So it's a treat for me to be here. What a fun episode with Luis Serrano. In it, he detailed his new paper on the curved space-time of transformers, how his team recreated Eddington's famous 1919 eclipse experiment inside a transformer, tracing the word bank through every layer of the network and watching its path curve around the word river.

1:07:47Jon Krohn:He talked about the crucial distinction between an LLM workflow, where you tell the model exactly what to do, and an agent, where the model itself decides what it needs to do next. He talked about why agent evaluation is so much harder than evaluating a chatbot, his elegant explanation of why GRPO powers reasoning models for a probabilistic model, talking is easy but hard to evaluate, while math is hard but easy to evaluate. And he talked about why, as an international math Olympiad medalist himself, he's thrilled, rather than threatened by AI hitting gold medal standard on the IMO, comparing it to how we still watch humans race even though cars are faster.

1:08:25Jon Krohn:As always, you can get all the show notes, including the transcript of this episode, the video recording, any materials mentioned on the show, the URLs for, or the URLs for Luis's social media profiles, as well as my own at superdatascience.com slash 1025. Thanks to everyone on the Super Data Science podcast team for another great episode. We've got our podcast manager, Sonja Brejevic, media editor, Mario Pombo, our partnerships manager, Natalie Zajski, researcher, Serge Macisse, and our founder, Kirill Aromenko. Thanks to all of them for producing such a fascinating and fun episode for us today.

1:09:04Jon Krohn:For enabling that super team to create this free podcast for you, we are deeply grateful to our sponsors. You can support this show by checking out our sponsors links, which you can find in the show notes. And if you'd ever like to sponsor an episode yourself, you can get the details on how by making your way to johnkrone.com slash podcast. Otherwise, please help us out by sharing this episode with other nerds that would enjoy this deep dive that Luis took us on. Review this podcast on your favorite podcasting platform or the YouTube video that you're watching. If you write in an Apple podcast review, that is particularly helpful to us.

1:09:45Jon Krohn:And I will eventually actually read it on the show if you do that. Subscribe, obviously, if you're not already a subscriber. But most importantly, I hope you'll just keep on tuning in. I'm so grateful to have you listening and I hope I can continue to make episodes you love for years and years to come. Until next time, keep on rocking it out there and I'm looking forward to enjoying another round of the Super Data Science Podcast with you very soon.

1:10:22you