Information Theory for Language Models: Jack Morris

Our last AI PhD grad student feature was Shunyu Yao, who happened to focus on Language Agents for his thesis and immediately went to work on them for OpenAI. Our pick this year is Jack Morris, who bucks the “hot” trends by -not- working on agents, benchmarks, or VS Code forks, but is rather known for his work on the information theoretic understanding of LLMs, starting from embedding models and latent space representations (always close to our heart). Jack is an unusual combination of doing underrated research but somehow still being to explain them well to a mass audience, so we felt this was a good opportunity to do a different kind of episode going through the greatest hits of a high profile AI PhD, and relate them to questions from AI Engineering. Papers and References made * AI grad school: * A new type of information theory: * Embeddings * Text Embeddings Reveal (Almost) As Much As Text: https://arxiv.org/abs/2310.06816 * Contextual document embeddings https://arxiv.org/abs/2410.02525 Harnessing the Universal Geometry of Embeddings: https://arxiv.org/abs/2505.12540 * Language models * GPT-style language models memorize 3.6 bits per param: * Approximating Language Model Training Data from Weights: https://arxiv.org/abs/2506.15553 * LLM Inversion * “There Are No New Ideas In AI.... Only New Datasets” * misc reference: https://junyanz.github.io/CycleGAN/ — for others hiring AI PhDs, Jack also wanted to shout out his coauthor Zach Nussbaum, his coauthor on Nomic Embed: Training a Reproducible Long Context Text Embedder. Full Video Episode Timestamps 00:00 https://www.youtube.com/watch?v=SWIKyLSUBIc Introduction to Jack Morris01:18 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=78s Career in AI03:29 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=209s The Shift to AI Companies03:57 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=237s The Impact of ChatGPT04:26 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=266s The Role of Academia in AI05:49 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=349s The Emergence of Reasoning Models07:07 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=427s Challenges in Academia: GPUs and HPC Training11:04 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=664s The Value of GPU Knowledge14:24 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=864s Introduction to Jack's Research15:28 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=928s Information Theory17:10 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=1030s Understanding Deep Learning Systems19:00 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=1140s The "Bit" in Deep Learning20:25 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=1225s Wikipedia and Information Storage23:50 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=1430s Text Embeddings and Information Compression27:08 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=1628s The Research Journey of Embedding Inversion31:22 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=1882s Harnessing the Universal Geometry of Embeddings34:54 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=2094s Implications of Embedding Inversion36:02 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=2162s Limitations of Embedding Inversion38:08 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=2288s The Capacity of Language Models40:23 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=2423s The Cognitive Core and Model Efficiency50:40 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=3040s The Future of AI and Model Scaling52:47 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=3167s Approximating Language Model Training Data from Weights01:06:50 https://www.youtube.com/watch?v=SWIKyLSUBIc&t=4010s The "No New Ideas, Only New Datasets" Thesis This is a public episode. If you'd like to discuss this with other subscribers or get access to bonus episodes, visit www.latent.space/subscribe https://www.latent.space/subscribe?utm_medium=podcast&utm_campaign=CTA_2

• 0:03Speaker 00

  Hello, this is Late in Space, just switch today with our special guest, Jack Morris, a guest from Columbia, that's your affiliation right now.

• 0:12Speaker 01

  Cornell.

• 0:14Speaker 01

  It's actually confusing because I'm in the New York City outpost of Cornell, so you have the city, right? But it's Cornell Tech, which is like a small Cornell campus in New York.

• 0:28Speaker 00

  I just, you're a student of Sasha Rush, who teaches at Cornell, so I shouldn't have made that connection, okay, yeah, I'm sorry. Well, that's a horrible mistake to make right off the bat, but you're one of, look, you're one of, there are not that many PhD students that make an impact with their research. The last time someone like this happens was Shun Yu from Princeton, and he joined the OpenAI operator team quite shortly after he graduated. So like, you're one of those like, high-profile PhD students at least, that's like, coming out of the program, and like, I figured like, it was a good time to just like, talk about your work, and also the fact that you're looking for like, which lab you're gonna join.

• 1:11Speaker 00

  That's like a whole interesting meta discussion, especially with like, the insane market for AI talent these days. What's it like to be an AI grad student these days?

• 1:21Speaker 01

  Yeah, and thanks for having me. I guess maybe we can go back to when things first started, or like, put yourself in my shoes. In 2017, 2018, I really learned a lot about machine learning, and at my, I went to a state university, it's a good school, but they didn't have like, a deep learning research department or anything. They had people doing it, but it was just not as big at that time. But I was getting really interested in those topics, especially as applied to language. And then in 2019, I kind of was starting to do research, and I think, thinking about my career, I mean, at that point, I was 20, 21, I was thinking about, like, where do I wanna be career-wise? Or like, who's doing the coolest stuff right now?

• 2:06Speaker 01

  Like, looking at, like, what kind of stuff is coming out of that time? I mean, I think- AlphaGo, I thought AlphaGo was really good. At that time, I was playing a lot with like BERT and BERT based models. So like, you know, Google, DeepMind, they're doing great work. GPT-2, GPT-1 from OpenAI were like interesting, but I think most people were into BERT at that time. I still have a soft spot for like that parameter class of like hundred million to one billion scale models. But this is all to say, I think at that time, I felt like the people doing a lot of the most impactful work were like professors and PhD students, like just a ton of like interesting ideas being explored and cool opportunities in academia. So I ended up applying to grad

• 2:51Speaker 01

  school. Well, at first I did this Google AI residency program, which was mostly during the pandemic, like 2020 and then 2021. And then I was also applying to grad school, started grad school in 2021. That's still what was going on at that time, like around when I guess GPT-3, 175 billion had been released, but not Instruct GPT. So like, we had pre-training and sort of the science of pre-training was emerging, but that's where the models were. And I still think like, I'm glad that I went to grad school and like I had a great experience, but the last five years have changed a lot. Like the whole meta has shifted, you know, like the kind of power

• 3:35Speaker 01

  dynamics are completely different. The ideas are coming from different places. Most stuff is open. Now most of it's not open. The types of questions people are asking are different. And so, yeah, I mean, for better or for worse, I did go to do the full grad school thing and here I am. It's been really interesting perspective, watching the science kind of emerge with the products. Like, the biggest thing that happened by far was like ChatGPT coming out, and which was right in the middle, like, what, 2022, before Christmas, like November? I remember that year, like, my grandma was asking me about it. And that's when it hit me like, oh, this is actually becoming like a real area that people will know about and understand. Like, I was trying to

• 4:20Speaker 01

  explain it to my parents. And that's when I think things really started to change in terms of the types of questions you wanted to ask. Can't always be answered with academic resources. So a lot of the like fundamental kind of like boundary pushing in AI science moved into companies.

• 4:37Speaker 00

  That was the year when like, you know, just around Europe as well. Everyone in NLP and deep learning were like very confused at like. I think some people were like kind of expecting this already in a sense that they had. They were obviously more clued into large language models. But I think that the sheer amount of consumer level interests that had that was around at the time in 2022. That completely changed the world like now. Now we're just like in a different sphere. Did you have to pivot your research? Or were you already, you just went from BERT to like other stuff? You've done a lot of embeddings work.

• 5:12Speaker 01

  I mean, you're always heads down, working on a problem. So I don't think most people in academia are the type to say, oh, look at this new product that came out. I'm going to abandon everything I'm doing.

• 5:24Speaker 00

  That could be the right move, you know?

• 5:26Speaker 01

  Oh, it definitely can. Honestly, if I were to give advice to a younger grad student. I think the way to do it would be literally just like sit and wait until the next kind of paradigm shift. And then just immediately start working as fast as you can to like re-implement it. Like I, I don't think that's like maybe the best way to do science, but it's probably the best way to play the sort of academic game in the, in the days of AI. Like you've seen that so many times, most recently probably with the reasoning models like. Oh, one came out of OpenAI September 2024 last year. And then there's just been this explosion of like you build like abstraction ladders on top of that. Like first it was re-implementation, like how do we even do this?

• 6:10Speaker 01

  And now it's like a lot about the data. What's the right data? What are the right evals? What are the right training schemes? Like there are so many different axes you can test and. Publish research in and like I think the easiest way to do that probably is just work in a field like that that like has it only existed for less than one year? And so no one has any like big advantage, I guess.

• 6:32Speaker 00

  That is mostly correct. I think anyone who jumped on reasoning and RL for L labs is doing super well. I just saw this morning that one of the recent Stanford grad students who worked on RL, they just started their company and they're worth 500 million. It's it's like absolutely bonkers right now. It's just like no product, just three dudes, you know, sitting in some basement somewhere. I mean, undoubtedly cracked, but like also not worth 500 million.

• 7:01Speaker 01

  Yeah, but maybe it's not paying for the product, right? It's like the

• 7:04Speaker 00

  The potential.

• 7:05Speaker 01

  Ideas behind it or the, yeah, yeah. There was this big shift from in scale of working with 100 million parameter models. Really what happened is like, I think the company has invested a ton more into training and infra. And like, we all kind of had to catch up, like, you know, me, I go to Cornell, work with a professor there. He has to buy GPUs, like, should he buy last year's GPUs or this year's GPUs? How many should he get? That we were kind of like trying to figure that out. And there was, there was like a big lag, I think, where basically the the seven and eight billion parameter scale, like there's a huge difference between the bird size models, which are 125 million parameters to 200. And then like the eight billion parameters. I mean, obviously it's two orders of magnitude, but just like

• 7:51Speaker 01

  this idea of emergence, like if you're talking to a model that's 100 million parameters, no matter how well it's trained, it knows nothing. Like if you ask it, like, what's the capital of a state? Or like, if you ask it, who's, who was president of the United States in 1990 or whatever? It'll just always say George Washington because it just associates the words like president, United States with George Washington. And then when you get to the eight billion parameter scale, suddenly it knows every single president. It knows every single capital of every single country. And I really do think that changes the type of research you can do. And so like, it took us a while, I think, in academia to catch up. Like getting good seven billion parameter models and then running them and getting GPUs to run them.

• 8:34Speaker 01

  Now I think things have stabilized a lot, like we have access to compute and we can kind of like fine tune and inference that scale of models and that's like kind of fine. But there was like kind of two years where everyone in academia was working on like smaller models and none of it really mattered.

• 8:49Speaker 00

  I can sort of branch that discussion in two ways and we should, we should sort of go to your research at some point. But I'm enjoying this because I think like we don't get to talk about this on the podcast too often. One is there, there's, there's an often, there's an often bit of advice from the industry people to grad students, which is give up, don't work on models, just do benchmarks, right? Like a really good benchmarks will, will get our attention and then we'll hire you and then you can switch to models later. You have for better or worse avoided that, which is cool. And we can talk about that as well. But the other thing I think is that around about seven, eight B, maybe four B is when you start switching from like a single GPU setup to like a distributed setup. And I'm wondering, like, do grad students get HPC training?

• 9:32Speaker 00

  How much they teach you of like just how to work with like large clusters of stuff?

• 9:38Speaker 01

  Oh, to be clear, they don't teach you anything, like anything, like if you see a paper coming out from even, you know, Stanford, they're probably the best school in AI if you had to choose. And it's not like they're learning how to do like multi-node distributed FSDP training, like with whatever deep speed. You have to learn that from the internet and from other people. And like, there's no classes that really do that. I mean, that's, that's hard to facilitate, like as one person. I would say most grad students are doing stuff on single GPU. Some people are doing multi GPU training. There's probably basically no grad students doing multi-node training.

• 10:19Speaker 01

  I mean, there's probably a few, especially if they have like company affiliations, but that's really unusual, I think.

• 10:24Speaker 00

  Okay, for grad students who are looking to get up to speed on that, I would recommend the GPU mode Discord, where basically the PyTorch team is hanging out in there just waiting to help you. And then the other one would be the Fast AI team. If you have some kind of. Thing Jeremy Howard will basically help you out and they have some distributed training. Honestly, try to reach out to the DeepSpeed team at Microsoft. Like actually, they're reasonably accessible. Nobody talks to them. Like, it's so, so funny. I like met them at Europe's and like they had nobody at their, like there was presenting speech three. I was the only one asking questions, like, um, yeah.

• 11:00Speaker 01

  Yeah, that's good. That's good advice. Listen to this guy.

• 11:03Speaker 00

  Yeah, I mean, just basically like the people are there if you want to ask. This is very, very valuable experience. Once you're like a GPU god, like you're basically, you know, in a like a different tier as a researcher. Because you don't rely on someone else helping you out, like you can just be your own research engineer, you know?

• 11:20Speaker 01

  Yeah, I'll comment on that quickly because if someone has been listening to this and also following me online for a while. I think I've made a couple of comments like saying something like you shouldn't learn about CUDA or things to that nature. And I'll, I'll give some more color to that. So it's definitely a great idea to learn CUDA if you can. I think my point was that if you're trying to enter this space, like learn about the models, learn about how they're trained, what the data looks like, what the compute looks like. One axis of that is how to do more efficient training and inference. And one part of doing more efficient training and inference is studying the hardware, which is GPUs.

• 12:03Speaker 01

  So like, I think that's a very small subset of all possible knowledge that you could acquire. And it's probably not the best place for a lot of people to start. That said, if you do it, you've got to be one of the most hireable people in the world. Like if you like really deeply understand the architecture of the new GPUs coming out and how to control it. You're in a very small handful of people and like everyone will want to hire you.

• 12:29Speaker 00

  Actually, the sweet spot is not even CUDA right now. I would say actually it is Mojo. I don't know if you've been paying attention to modular Mojo.

• 12:37Speaker 01

  Oh, I listened to your podcast, man. You had that guy on the other day.

• 12:41Speaker 00

  The whole story is Chris Lattner, industry legends, LVM, Swift, all these things. And now he's turned his attention to the Python CUDA relationship, right? And he wants to basically. Create a viable CUDA replacement. It's basically Python married with Rust. For the last two and a half years, it was basically kind of stealth, not ready for production. When he came on our podcast, he was basically announcing to the world, like, we're open for business. Like, you can use this now for for most models. And like, we actually are faster than like the native, like, uh, sometimes the PTX implementation. I don't know how that works precisely, but he's a compiler language is God. I think there's a there's one of those windows now, like, like you said, like, you know, bet early on something that's this is this is shift. It's one of those windows now where you try to implement things.

• 13:27Speaker 00

  You basically like, you know, modular is a hundred people. If you run into issues, you'll get Chris's personal help on things. Like, I'm not promising it, but like, probably, you know, like, because he wants to work on improving the toolkit. And all you have to do is just like, it's not really about becoming a CUDA God. Because obviously, like, once you wrap up on the the general concepts and principles, you can probably translate ecosystems pretty effectively. A lot of people switch from like JAX to CUDA. But like, the the thing is just like being able to experiment very quickly on a limited budget. Like, efficiency is not just because you are trying to be an efficiency guru and that's your career and that's kind of boring. But it's really also just about being able to experiment very quickly and finding these like these ideas.

• 14:10Speaker 01

  I also think uh, VLM and SG Lang seem like really good and important and here to stay. Like, they'll probably just get larger and more complex to accommodate future systems. But if I were like, uh, starting out grad student and working in that area, I'd probably like want to learn more about how they work.

• 14:31Speaker 00

  Awesome. Let's go to your research. I like to mention that I I first came across you because of CDE, the contextual document in bidding paper. You can uh, tell me the story about that, but I just want to show you proof that, you know, I get one slot per day to highlight the number one AI story. And you were the slot of the day for October 5th.

• 14:51Speaker 01

  Oh, no way.

• 14:52Speaker 00

  I mean, obviously, you were producing work before that, but like, I thought CDE was a really cool exploration of like, oh, yeah, you know, embedding models are kind of like stuck in a rut. Like, here's actually how to make them very efficient by just doing it in two stages. That seems like a, you know, relatively simple insight that was done very well. But you have a general, maybe information theory thing that maybe we should start with, and then we can sort of. Green is in our way.

• 15:17Speaker 01

  Yeah, sure. That sounds good. So we can, we can circle back on that. That's, that's really cool that you wrote about it. What was that? Almost coming up on two years ago? Yeah, this is the post I wrote. I called it a new type of information theory. We don't need to go into the, there, there's this paper about a concept called V information. Maybe I'll give like the most simple explanation, which is if you say you have two text files. One text file contains a paragraph of information about New York City. And then the other text file contains the same text, but encrypted with like SHA, whatever encryption algorithm.

• 15:56Speaker 01

  So it looks like random letters, but if you decrypt it, it has the same text as the first text file. From the perspective of like Shannon's information theory, these two files contain the same information content. Like relative to everything, they have the same number of bits, but it's, it's very clear to the observer that the first text file, which is plain English text, is like much easier to read and easier to process, even though they have the same information. And so there's this theoretical framework proposed in this paper, which is a theory of usable information under computational constraints from 2020.

• 16:38Speaker 01

  It really doesn't have that much press. There not, aren't as many citations as you would think. But I think it's a really, really neat idea. It's like, we should measure information with computational power as a constraint. So like they have this idea, they called V information of how much information is extractable from a given like file or code. So in that case, we could say the left text file actually has more extractable information than the, the right text file. I think that's like really good. That captures a lot of our ideas of how these deep learning systems work. Like, why does pre-training work? Like, if you have two sets of weights and you, you want to train on some downstream data set, one set of weights is pre-trained, one set of weights is randomly initialized.

• 17:22Speaker 01

  Why is the pre-trained model better? At all, even though it's never seen your data. Maybe one way of looking at that is that it has like, it makes the information like more extractable somehow like there's this concept of like computational processing that you can almost like store up. I like this as a, just like a lens to view problems with like, how much information is stored where like if you, if you get a a set of model weights or like an activation vector and you open it up like, print some tensor, an umpi array. It looks like random numbers, right? Like there's nothing human intelligible about that. But really it's this complex combination of

• 18:05Speaker 01

  like the training data and the training algorithm which get compressed into model weights. And then the actual computation that the model is doing, which involves like manipulating these numbers in ways that we don't understand. So it's like this really highly compressed nonlinear combination of all these information sources mixed with like computation. And I just think we don't have like the right words of, of discussing this. I think, I like the information theory analogy because back in the day, you know, we had phones and like telegraphs and, and people were just sort of like building the phone system with these crazy heuristics to like send information across the country or send telegraphs across the Atlantic.

• 18:47Speaker 01

  People were just like trying stuff and then uh, we kind of found stuff that worked and we, we ran with it, but it wasn't really optimal. And it wasn't until someone came along and proposed this concept of like a bit, like a one or a zero that tells you something. And once we have a bit, we can do all these things. We can like count the amount of information a signal. We can do really good error correction. We can measure properties of distributions of things and, and we can build like a really good system for, for phones. And then eventually which led to computers. I'm bringing this all up because I don't think we have, I don't think we know what a bit is yet in terms of like deep learning models.

• 19:27Speaker 01

  I'm going to graduate from my PhD this year, but I didn't figure it out. So if you're listening to this, maybe you can like, I don't know, spend more time on it or you're smarter than me or you have a, you know, a group of collaborators. You can all get together and figure out what the right lens to look at this stuff is. But even by just asking these questions, I think I was able to conduct this research agenda that I'm kind of still working on actually.

• 19:52Speaker 00

  Yeah, uh, what do you call this field?

• 19:55Speaker 01

  Oh, I don't know. I don't know. I called the post a new type of information theory. I don't think it exists yet, I guess, so maybe it'll it'll get a name once someone actually comes up with the right set of definitions. I think the information is a really good start.

• 20:12Speaker 00

  There's a couple of related threads. So first of all, you don't know this, but I actually have been trying to accumulate in data about Shannon, like this is just like a Shannon information theory view of language models. I have a lot of notes. This is actually on my GitHub for people who are watching along. But, um, you know, at the limit, if a language model has 175 billion parameters, using 16 bit, you could, it would take up 350 gigabytes. You can compare that to Wikipedia. Wikipedia is about 150 gigabytes. You know, let's say GPT-3 can store two Wikipedias. But like, is that a relevant measure of information storage, right? It is not because you can compress Wikipedia a lot. There's a lot of repeated patterns. Tokenization is like the first form of compression.

• 20:56Speaker 00

  But I think there's a there's a related talk from Ilya Sutskever about how deep learning is, machine learning is kind of is compression. Like you have a data set, you compress it into a model that is smaller than a data set, but generalizes and like has like, you know, some some amount of acceptable loss. I think that one of your commenters on the on the post made this direct comparison with common ground complexity, which is what Ilya, how Ilya sees it. So I think like people have this information theory idea or approach to language models. It is just not precise because exactly what you say, like it's, we don't know what a bit really means. We don't know what like the most legible, legibility is a word that comes to mind in terms of like,

• 21:39Speaker 00

  like it matters to us that it's human readable, like even if it's shot one, shot two, five, six, I don't care. But like, that is less readable and therefore there's more, I guess, I don't know. Entropy is not the word because it's it's directly convertible. But it's just less useful.

• 21:56Speaker 01

  Yeah, yeah, yeah. Useful is a good word. I think maybe useful information or usable information is the right lens. And Komagorov is a really interesting connection, like Komagorov complexity. I think that's a really good concept for for computer scientists. So I'm not sure exactly about this specific talk or like what he was trying to say, but I I think that we have a very good understanding of language model pre-training. And there's a deep connection between language models and and compression. Actually, maybe let's let's start with the embeddings. So we can come back to that.

• 22:29Speaker 00

  Okay. So is this, are we going to the first paper?

• 22:32Speaker 01

  Actually, let's go to your Wikipedia numbers, if you still have access to that. So this 50 gigabytes for text of Wikipedia, that sounds like a pretty high to me. Is that that's uncompressed like text files?

• 22:45Speaker 00

  I don't know. I grabbed it from Andrew Ng. So I don't know.

• 22:49Speaker 01

  Okay, okay. No, no, I'm probably off. I just sort of have the sense that like, when you store text, it's generally like very, very small, especially when you zip it.

• 22:58Speaker 00

  Maybe he's including all the languages, all the edits. I don't know.

• 23:01Speaker 01

  Yeah, yeah, that can make sense. That can make sense. Because I guess what you you say from, you know, if you want to do apples to apples comparisons, GPT-3 can store two Wikipedias. Is that right? Two point three Wikipedias?

• 23:13Speaker 00

  Two point something, yeah.

• 23:14Speaker 01

  So I thought it would be a lot more. And this is actually an experiment that you could do. You could like, just train a model on Wikipedia and keep training it until you can perfectly extract all of Wikipedia. And that would be like a good way of knowing like how many Wikipedias can GPT store. I like I like that idea. But I think this type of like back of the envelope math is, it's really useful for thinking about problems and like grounding yourself in the real world, even if you can never quite answer the questions you want to answer, at least like in four years. If we think about embeddings, you know, vectors that people use for search, we can do the exact same kind of math. So if you use the OpenAI embeddings, which last time I checked, I think have 1,536 dimensions.

• 23:59Speaker 01

  So that if you say there's 16 bits per dimension and like half precision floating

• 24:06Speaker 01

  Point, it's something like 20 kilobytes of information in a vector. And if you want to store 20 kilobytes of text, that's a lot of text, like many, many paragraphs that you can perfectly compress into 20 kilobytes. And so I think this is kind of like the idea we had. I'll give you the practical explanation, which was I'm, well, first of all, I'm a second year grad student. I'm like going to these conferences, seeing all these other things people working on and thinking, you know, like, what the heck? Like, how am I gonna like have my own little area to do work in that no one else is working in already? And so I spent a lot of time coming up with bad ideas. And my advisor would say, no, like, that's not a good idea to work on. Many times this happened.

• 24:48Speaker 01

  And like even my first year and a half of grad school was like a lot of exploration and a lot of like coming up with bad ideas. And then honestly, I'd be interested to see how he remembers it. But I think I wrote a sequence of proposals about different projects. And then I came up with this idea, I was like, oh, we should just try to do as well as we can to reverse engineer the text that's in embeddings. And I, and then we were talking about it. He was like, oh yeah, you should just do that. And then that was the end of the proposals. And then that was just working on that problem for a long time. Which at the time I was really motivated by that because I was like, cool. Like my first, as a grad student, my first sort of like official, like sign off on like coming up with a good research idea.

• 25:31Speaker 01

  And at the same time, there was this big rise of this startup business model called like a vector database. And there are all these companies popping up, raising money, raising money, getting like crazy funding. And then actual applications being built that do something where instead of exchanging customer data, they exchange vectors. So we had this like very grounded question of like, what data are they actually sending when they, when they send the vectors? Like, first of all, you have this information theoretic argument that when you send one vector, there should be a lot of text recoverable, just in terms of like, a lot of these things represent very short documents, but they actually have many, many bits. So like the problem seems tractable. And then second of all, we had this

• 26:16Speaker 01

  Justification of how the product is actually being used. Like, if someone hacks into a vector database, what do they actually find, if that makes sense? So we were working on that for a while.

• 26:26Speaker 00

  I think I have the talk that you did from, that Sasha highlighted is this one.

• 26:31Speaker 01

  Oh, yeah, yeah.

• 26:32Speaker 00

  Maybe that has the graphic that would kind of.

• 26:35Speaker 01

  Oh, go one before, I think.

• 26:37Speaker 00

  One before?

• 26:37Speaker 01

  This is actually, yeah, this one's good. Yeah.

• 26:40Speaker 00

  I like having Visual Aid. I like giving people breadcrumbs to follow up if they're interested in digging more. But yeah, I remember this is a pretty hot area of research at the time.

• 26:50Speaker 01

  And there's been some really interesting follow-ups. Like, we ended up building a system that can do this quite well, like, taking and embedding. And I think our highlight number is like at a certain length, like a long sentence length, we can get 90% of the text back exactly. And a lot of people were able to do stuff with that. Like, they can, for example, I know these people that work on a problem of like de-biasing embeddings. And like, in one dataset, they do something. They have a procedure for like removing all latent features that correlate with gender. So they can produce like useful embeddings that, from some perspective, have no like information or usable information about gender.

• 27:35Speaker 01

  And they'd been doing that for a while, and then they actually just used our tool. And they, so like, they would put in a sentence like, "This woman is a doctor at Weill Cornell Hospital in New York." Or you'd say, "This woman is a doctor. She works at Weill Cornell." And then they would run their procedure, and then they run our embedding to text model. And now it would say like, "This person is a doctor. They work at Weill Cornell," which is pretty cool. So they have like sort of text-based evidence that their method is actually removing gender features. But let me talk for a second about the research phase here because I thought it would be. I mean, I know if you ever heard me talk about this, I probably told you about it.

• 28:17Speaker 01

  But just for a wider audience, I like thinking back on this because it was probably my, in some sense, like my greatest victory of grad school was like working on this embedding inversion problem for a while, for quite a while and proposing a lot of approaches and like testing stuff. I think sometimes you do stuff and it's clear it was a bad idea. Sometimes you think you should have figured it out earlier. And then sometimes you do stuff and you kind of realize it's really complicated and probably not worth it. So I was testing different decoding algorithms for embeddings that are closer or text that's closer to the text that's in embeddings. And I was testing these kind of like inference time adaptation models for samplers.

• 29:02Speaker 01

  I think we tried a lot of architecture and like kind of training tweaks. We should have tried RL. I think that would work. But finally we found something that ended up working. And I guess I'm just saying this all because I thought it was like so rewarding. Like we were just banging our heads against the wall. I'd have bi-weekly meetings with my advisor who kind of suggests things. Sometimes we would agree we were mutually stuck. Sometimes I would get feedback one way or another and try something new or try a couple of things. And we had this idea that it was possible from the information theory arguments. And this other thing where we would, we would kind of like take our best guess at what the text was and re-embed it and see that it was kind of far from the true embedding.

• 29:44Speaker 01

  So we had this proof that like a better method could like leverage this kind of information. And then when we finally solved it, it was, it was awesome. Like we had this number that was like 30 for months. I think at one point I got it to 35. And actually I think I was like, oh, I'm done. Like I got it to 35 and my advisor told me, I'm not like that's, you can't really just propose a new problem and show you push a metric from 30 to 35. That's like confusing and probably not that meaningful to people. And I think I was, you know, that was kind of like a local minimum for me where I was like bummed. But then we ended up getting the number to like 97 or something, which neither of us knew were possible. We were all just, we were just kind of staring at this graph like, oh my God, like, who knew you could get this much information from an embedding?

• 30:29Speaker 01

  And that was like. So great, like, um, just sort of this, it was so rewarding and so it was invigorating, honestly, like that research process of like, we picked a good problem and then we spent so long trying stuff that didn't work, which I'm probably forgetting how frustrating that was. I'm sure it was terrible, but then like actually solving, or at least like coming up with a much better way of solving the problem. I don't know if I'd say we solved it, but we definitely learned a lot from where we started was like, was great. And it completely solidified for me the fact that I should have gone to grad school to have this like life experience and like makes me want to do research forever.

• 31:09Speaker 00

  You're clearly, clearly, um, sort of in love with the, the, the journey, uh, which I think is, is important because this is what keeps you going through the, the tough parts. Is this a good time to talk about the universal geometry side then?

• 31:20Speaker 01

  Yeah, yeah, yeah. Let's, let's do that next. I think that's a good idea. So, so we have this more recent follow-up and the, so the first part I was talking about ended up in this paper called Text Embeddings Reveal Almost As Much As Text, which was published in 2023. And then we recently had a paper come out on archive, which will hopefully be published at some point, and it's called Harnessing the Universal Geometry of Embeddings, which was also, that was probably like the only other time I felt like we've made like, maybe there have been two more times, but that, that was probably the, the second of three times where I felt like we made like a real discovery about like the unknown. And it was like very rewarding just for its own

• 32:02Speaker 01

  intrinsic kind of elusiveness. And I'll start from explaining it in terms of the prior paper. So we, we built a system that can, you know, do embeddings to text and it, and it works very well. And we're, we're very pleased with ourselves. And then we, we went to a conference, we talked to people about it. We talked to like the vector databases. I think some of them changed our privacy policies, which was like somewhat gratifying. Um, and then we kept getting this perpetual question, which is like, well, you're just assuming we use the OpenAI model, or you're just assuming we use the most popular text embedding model, if they fine tune their own model, or if they use a model that you're not training an adversary for, then you can't solve the problem, which is like true. Like none of the vector to text

• 32:46Speaker 01

  stuff works unless you have this assumption of like knowing the encoder and also being able to make a lot of queries to it. But we had this kind of underlying theory that all of the models learn very similar things. Like, we have some preliminary evidence for that, like, certain models that are fine tuned from the same base, you can kind of swap their representations without doing much. Or if you look at the nearest neighbors, a lot of the models will give you the exact same nearest neighbors, even though they have completely different training bases. And then there's this paper that came out last year called "The Platonic Representation Hypothesis" from some folks at MIT, which is really, really compelling. And I think just like, great intersection of philosophy, representation learning, deep learning research.

• 33:29Speaker 01

  Like, I love this paper, and it's such a beautiful idea, which is something like, all models are trained on data from the world. And there's only one world. And so, as the models get better by scaling data and scaling model size, they're sort of converging to learn the exact same thing. And in this paper, they have evidence based on correlations for doing this with vision and language models. It's very neat. And so, we saw this. So, basically, think about, you know, you're us, you see this Platonic Representation Hypothesis paper. A lot of people have this shared idea, like, you know, Claude and GPT-4 probably do a lot of very similar internal computation, because both of them are trained on trillions

• 34:14Speaker 01

  of tokens of human-written text. Even if they have different architectures, like, maybe, you know, the actual basis or like, the numbers, if you look at them, look different. But in some way, they're like, kind of computing the same thing. And I think it's even more true with these, like, embedding models, which have, like, really only one objective that works. And they're probably all trained on, like, MS Marco, which is a really popular dataset, and pre-trained maybe on Wikipedia. But we wanted to basically combine this Platonic Representation Hypothesis idea with the vector text thing, and produce a system that can, like, align models, so that we can do embedding inversion.

• 34:53Speaker 00

  But you know, it's valuable for more than just embedding inversion. But you can use this to kind of glue together models. Like, that's what actually got me like super excited. And by the way, like, I think there's a few related threads. Uh, I think we did an episode with Nicholas Carlini where he had an extraction attack uh, on, on one of the GPT models and they, they got it fixed. The other thing I want to, I really just really want to spell out for people, just in case they're not thinking it through. Being able to invert embeddings also means that you can, you can back out uh, like secret prompts or contexts that might leak customer information. That's potentially harmful and like obviously a, a tax vector issue. I think one of the things I, I had a question about was whether or not position embedding

• 35:35Speaker 00

  does affect it and like the extension of position embeddings affect it because obviously that like contexts are going to get longer and longer. Your ability to invert will obviously decrease with longer context. What now, you know, uh, maybe not that important.

• 35:48Speaker 01

  No, no, no, you're totally right. So we're operating in this space in, in our work where the sequences are relatively short and the embeddings are relatively large. Like, I think we're kind of at a great advantage from that perspective. And you're definitely right, like if you embed an entire book to a five hundred dimensional vector.

• 36:12Speaker 00

  Yeah, no way.

• 36:13Speaker 01

  There's just no way you could get the entire book back. Like, there must be this, these kinds of collisions, like, you know, in information theory, like if you have lossy compression, two different inputs mapped to the same code, which means that you can never determine which input formed the code. And I think that's probably what will start to happen. Like, if you have two books and you swap just one word and you embed them, I don't know, someone can try this. You'll probably get like a perfect collision. And in that case, inversion is impossible. And even like, when you don't take it to the limit, it probably just gets very, very hard. Like, things get super compressed. So I don't know how well this work scales. Like, it's a great question, like exactly how much information you can sort of cram into one of these vectors. And I, I don't have a sense of where the boundary is.

• 36:58Speaker 00

  It'd be interesting to talk to some, one of the like linear algebra people from like the math department on like, how literally can we take inversion? Like, you know, how, like, what, what measures of a matrix do they have where we can like kind of run that? And like, try to get some meaningful information out of that. This is like where information theory starts to collide with linear algebra and all the, all the other stuff. Totally, yeah.

• 37:21Speaker 01

  There's always this this detail where we're running these on computers. And so we don't actually have like real decimal numbers or real numbers. We have like floating point representations of numbers, which are like very, it's kind of like throws a wrench into the mix.

• 37:38Speaker 00

  Do you have any consideration of like superposition? When like sort of nonlinearity, like you keep like stuff information in the lower bits. But I don't know if that matters. I really don't. It's just like a nice thing to think about.

• 37:51Speaker 01

  Yeah, yeah, it is a great question. And I get a sense that like a lot of the less important bits are more useful for computation. And maybe the higher order bits are more important for like storing data or something like that. But I'm not sure. These are the kinds of questions I'm actually hoping to explore over the next few years. Like, um, I'll skip ahead for a second. So we have this result that's like maybe the third sort of like discovery I was alluding to, which is like a way to measure the exact capacity of a language model. And we get this number. If you train a language model on a ton of random data and you measure its rate of memorization. Yeah, can you open the right curve? This is sort of the discovery I'm talking about.

• 38:31Speaker 01

  Like, no matter how you scale the training size, you hit this like perfect, perfect-ish plateau in auto memorization, which we call the model capacity. And the question I've been stuck on in the back of my mind for a while is like, how is that actually implemented? So like, this is a transformer that is trained for many, many data points and many, many training steps. And so like, it's almost like if you have, okay, the 10 to the sixth point on the X axis, the capacity, uh, we don't have to actually say the numbers, but it's basically perfectly dividing its computation between all of the data points. Like every one of the 10 to the sixth data points gets like a tiny sliver of the model parameters

• 39:15Speaker 01

  because they're completely independent random strings. So I don't really know if superposition is occurring here. Like, it seems possible to me that the model would learn like these completely independent columns of computation, one per data point, but it's also. So possible it's learning some kind of like combined thing where it's maybe it learns like a load and a store and it's like sort of like loading and storing that's using these generic operations and then in the end it reconstructs the random string. So even though like the data is completely independent, the kind of like compute is is very similar in terms of like predicting random strings. But yeah, I guess this is all to say like about superposition and everything.

• 39:58Speaker 01

  I have no idea how the mechanisms are actually implemented inside the models and that's like one thing I'm hoping to learn about in the next couple of years.

• 40:05Speaker 00

  It's a reasonable question whether it's meaningful to learn. I think there's a lot of things that is like nice to know, but maybe not that useful. Late in space, late in space alignment is very, very useful. Data set efficiency in theory, cool, but like practically people are just gonna go for the biggest data set they can. Like, like the scaling laws are kind of worked out insofar as like the relationship of compute and data. Amount of memorization, I don't know. I think maybe this is a good point to maybe also bring in the idea that Andre has been pushing for the last, I think, year and a bit of the cognitive core. Like, what is the dumbest possible model that knows nothing?

• 40:48Speaker 00

  But is you is smart enough for tool use to do everything else, right? So you can run it on device and fast inference is open source, whatever. So Gemma three N is like a really good candidate right now because it's like a four B model that is like claimed to be better than Lama four and GPT four point one, according to, you know, certain arenas that shall not be named.

• 41:09Speaker 01

  This is where things get complicated. Like, it feels like language models kind of implement things and know things almost in the same way. And it's like really difficult to disentangle like whether they're memorizing facts from whether they're like learning useful ways to generalize about new stuff. But I agree, this would be really nice. I don't think we have a lot of evidence that we can build a system like this that like is really, really good at reasoning, but really dumb about the world. Like, I don't know if we have the tools.

• 41:41Speaker 00

  Yeah, maybe, maybe not. I think the existence proof is humans, right? People always lean on humans as like the existence proof. It's not a great existence proof because I think if you've talked to people about the number of neurons that we have and you make a neuron roughly equivalent to a parameter, we have something like a hundred trillion in our brains. So like, and like, we consume like twenty watts of energy, like it's nothing. Like, we're so much better than, than, uh, language models. It's not even funny. And then the, the last feature of us is that we're self-pruning, which is, uh, not something that language models do as well.

• 42:13Speaker 01

  Oh, like we were forget stuff?

• 42:15Speaker 00

  No, like, we are not deeply densely connected, like, we, like, connections will drop, therefore we're more efficient, you know?

• 42:21Speaker 01

  See, I see, I'm like a language model where everything is always connected all the time.

• 42:25Speaker 00

  Yeah, or you're like, you, you preset the skip layers or whatever and that, that's it. You know, like, it's not, it's not really actually anything we've evolved with learning. It's just like something you do based on ablations and like guestimates.

• 42:38Speaker 01

  Even if we did want that, I'm not sure if we have like the right frameworks or methods for actually building like what you're talking about yet.

• 42:46Speaker 00

  I think the world is much closer to where you're at, to where Andre is at. Andre is like kind of wishing for a, a, an optimistic world. Our conversation with Noam Brown was like, yeah, reasoning is emergent. If you gave the O one harness on top of G P T two, you would get nothing because G P T two didn't know enough. You need a G P T three and G P T four in order to then get O one, like as, as G P T four is the base model. Which is like, yeah, that's, I mean, that's, that's reasonable. The way I put it is like, in order to use tools, you need to, like, in order to search Google, you need to know at least search terms in order to like then search Google and then learn what you need. And if you don't know what, what to search, then like you might just be too dumb.

• 43:28Speaker 01

  I like the kind of ethos, like maybe you could do some kind of. Pre-training or whenever the model doesn't know something, it can just Google for it. And that way you try to encourage it to learn words without or like to guess words correctly without actually storing the information into its weights.

• 43:46Speaker 00

  Yeah.

• 43:46Speaker 01

  It seems like a nice like goal at least.

• 43:49Speaker 00

  Yeah, you need some kind of online learning probably or memory and some combination of that.

• 43:56Speaker 01

  Yeah.

• 43:57Speaker 00

  It's exciting, you know, like I think like if that is the the direction of of where this all ends up, that's great, but like people are not doing that. Instead, we're building, you know, $500 billion data centers in the middle of Texas. And like, you know, all hail the the God cluster that just all, you know, eventually wrap around the sun and consume solar energy because that's what we need. Do we finish out the universal geometry thing?

• 44:23Speaker 01

  Let me finish the kind of a methodological description. So so we had this goal. So yeah, back to the embedding universality. We started with going from embeddings to text. We know about this platonic representation hypothesis. And maybe I'll skip over the details, but basically we had total inspiration from computer vision in this model from 2017 called CycleGAN, which is, among other things, it's a way to map between two different distributions without any underlying notion of like which thing should be mapped where. It's just based on some kind of idea of closeness.

• 45:04Speaker 01

  So like the cool thing about this, if you look at the top left, so I guess the the top left is Monet. So impressionist paintings and this picture on the right is a photograph. So like it's learning this kind of like semantic notion of what content goes where just by mapping a distribution of Monet pictures to a distribution of photographs without actually telling it which. Monet picture should map to which photograph? It's kind of a subtle point I'm making. It takes a little bit of time to wrap your head around, or maybe like go to the middle one, if you don't mind, the zebras and the horses. So like, it's clearly learning like what an animal is and what legs are and sort of like more abstract stuff, like what the camera position should be

• 45:49Speaker 01

  and what grass is and stuff like that. And it's learning like what a horse that looks like a zebra is, which is actually like a complicated semantic concept. Like, we don't have a data set that has a horse and then that horse as a zebra. We just have separate horses and separate zebras. But somehow this GAN system is able to like elicit this sort of mapping property. It's like kind of a magical connection that it learns. And I'm still like in awe that it's possible at all. But we more or less like repurpose this system and like we built our own, but like this idea, we took it and we applied it to model embeddings, where instead of zebras and horses,

• 46:31Speaker 01

  we have like BERT embeddings and GPT embeddings, or like two completely different models with different architectures. So I think these are GTR, which is a T5-based retrieval model, and GTE, which is based on BERT. So they have different training data, different architectures, different downstream objectives, different embeddings. But yet, when we do this cycle GAN in the embedding space, they just perfectly sort of snap to the same place, which is amazing and has some pretty deep implications of like the platonic stuff. Like, maybe the models actually are learning a lot of the same functions or something. And in some semantic way, they're like very close. And yeah, this is a diagram of how our system looks.

• 47:11Speaker 00

  It's weird to me how profound it seems. You seem deeply impressed by it. And then the other thing is like, when we talked to Emmanuel from Anthropic, who did the circuit tracing and mechanistic interpretability work, they were like excited that like the same thing in different languages maps to the same circuits. And I'm like, what you would expect?

• 47:36Speaker 01

  Yeah.

• 47:36Speaker 00

  I don't know like, I don't know like, why like, I, I, I, I, I don't know. I think, I feel like this, this feels more profound to you than it does to me. I'm like, yeah, obviously.

• 47:44Speaker 01

  No, that's, that's so fair. Maybe it's just like self congratulatory and we're happy that we're like the people that got it to work.

• 47:51Speaker 00

  Yeah, exactly.

• 47:52Speaker 01

  Yeah, it does. It does seem obvious in retrospect. And I think that's like constant feedback I've gotten from research from, you know, people will tell you that this seems obvious to them. But you have to realize that like, you came from a perspective of no one ever having done this before. And they're coming from a perspective of you telling them it's true. And like, if someone had told you that this was true, it would be like, maybe obvious to you too, if that makes sense.

• 48:18Speaker 00

  The way I put it is that we have the intuition, but not the proof. You have to, you did the work. And you have at least some evidence that it's true, whereas we just have intuitions, right? So, uh, part of research is just confirming intuitions. The applied part comes from like, okay, now that you know this for a fact, what do you do with it?

• 48:37Speaker 01

  Yeah, right. I think the details can be really interesting, like the details of the proof, like which models are most similar to one another? And to what degree can you get them to align and on which distributions does this property actually emerge? And like, that's why reading papers can be fun sometimes is because they kind of answer all those little question.

• 48:55Speaker 00

  Yeah, I would say, uh, okay, I pulled up something very current, uh, which is Gemma three N, which launched, which, uh, sort of was, uh, generally available yesterday. I would say that for me, and you can correct me if I'm wrong, the most immediate implication is mapping adapters to language models. So the, the dream is that you have a language model backbone, let's say this and it's like a to be language model backbone. And then you offload your vision. So you only, you only load in the vision and parameters of the, the vision adapter when you need vision. You only load in audio, you don't, you only, only speech, uh, text to speech whenever you need it. Uh, because these are all separately trained, you're, you're just sort of aligning latent spaces.

• 49:34Speaker 00

  And you can sort of train them separately. And I think like, this helps to make us more confident in, uh, one is, it's more efficient. That's a, that's a given. Two, it makes, helps makes us confident that we can just, just add capabilities without taking away or catastrophically forgetting others.

• 49:51Speaker 01

  So they're just sort of like stacking more parameters.

• 49:54Speaker 00

  Just stackable.

• 49:55Speaker 01

  So that's very cool. Yeah.

• 49:56Speaker 00

  Swappable, stackable. It's like a fatter version of Laura's that is not really

• 50:02Speaker 01

  Yeah.

• 50:03Speaker 00

  that model specific. I would say Apple and Google are pursuing this for their on-device stuff is where is my sense.

• 50:10Speaker 01

  Is this open source?

• 50:11Speaker 00

  Gemma, yeah. For a given definition, open source, which is like we release the way so hugging face, here you go.

• 50:16Speaker 01

  Oh, that sounds like open source to me.

• 50:18Speaker 00

  Eh.

• 50:19Speaker 01

  Oh, yeah, I guess it's open weights, but not the data.

• 50:23Speaker 00

  Not the data, not the code.

• 50:24Speaker 01

  Not the code. Yeah, right.

• 50:26Speaker 00

  Yeah, I would say that this is quite soda in terms of efficient models. Maybe a small LM also from hugging face would be also in that in that category. It's not that many people working on very good, very efficient models.

• 50:38Speaker 01

  Yeah, this is a very deeply related question and something that really interests me, which is like, what is the limit of like a hundred million parameter model? Like, if you imagine, you know, a hundred years from now, when we have maybe our computers are gelatinous blobs and we all communicate through telepathy, will we have hundred million parameter models that are at the level of today's O three pro or whatever? And like, if so, like, how would that even be the case? Like, based on scaling laws, like, do we have special data? Do we come up with like a brilliant new training scheme or some type of magical architecture? Like, I really don't know. Or maybe we really are on the at the plateau already. I don't know.

• 51:21Speaker 00

  It seems like when we are doing things like calling a small model like a 27B model as small, like that's what Miss Charles doing.

• 51:32Speaker 00

  You know, we've plateaued a little bit in terms of like what we can do to compress things. I have a fun theory that this is where we mix quantum computing with models. Like, we have to change what a parameter means. We have to search through very high dimensional space and resolve them much quicker than we can with like conventional compute. That would be my pie in the sky thing.

• 51:53Speaker 01

  I said a hundred years. That's very reasonable to me.

• 51:56Speaker 00

  Throw quantum at it.

• 52:00Speaker 01

  Yeah, I probably have to get a second PhD to know what's going on there. I think that we should establish the definition of small model as being a model that a grad student can infer at a reasonable time on a single.

• 52:17Speaker 01

  GPU, which is probably like 7B, maybe. I don't think 27 is small under any reasonable. Is it, was it an MOE?

• 52:26Speaker 00

  Mistral? Uh, I don't think so. I think I'll, I think their stuff is default dense. Don't quote me on that. Uh, this is, uh, this is coming off of, um, just a lot of pre-trained data that is, that is, uh, potentially collided. Okay, there was one, there's two more papers that we wanted to cover and then we can, we can sort of wrap it. You had an approximating, you had a language model training data. I think this is a little bit, uh, also newer. How does this rank in terms of your, your overall work?

• 52:53Speaker 01

  Yeah, let's return to the kind of information theory question. So, yeah, maybe we'll, we'll skip over the contextual embeddings in the case of time, but we'll group those papers. Great paper. Hopefully people start training with that technique. It's kind of a free lunch. Those questions are all about information and model activations. Like, how much can we recover from this given vector? Or like, what data does this vector represent? Or what computation does this vector represent? And there's really two types of, like, if you want to taxonomize, there's, there's two types of, whatever you call it, dense information storage mechanisms. One of them is activations or embeddings, which we were discussing already.

• 53:37Speaker 01

  And then the other is weights, which are the things that are used to perform the computation, but not the computation itself. And so we have now two papers in this direction of what is stored in the weights. The first one is about language model capacity, which is called, how much can language models memorize? Or how much do language models memorize? I never remember which one we settled on. And then the other one is called approximating language model training data from weights. The first one is like, I, I think has a lot of deep messages about how language models store information and how they work in general. The second thing is like a proof of concept of maybe like a longer term research project. Let's start with the capacity stuff, if that's good with you.

• 54:21Speaker 00

  Do I have the paper for that? I don't. I don't know.

• 54:24Speaker 01

  You know, we can return to the question you asked me, which is something like, why do we care? Or like, what is this useful for? And I don't know if I have a good answer for this. I think this is, this is somewhat profound. Like, it's kind of like in, in physics, you know, when they try to measure these constants. Like, gravity, people tried to measure the rate of acceleration of gravity for a long time. Or like those Greek guys, like back in, in the B C era, when they were trying to, to approximate the radius of the earth based on shadows. We're trying to take the G P T architecture, like the main one, and just measure how much information it can store. And we did this through the, the lens of memorization, which I think we can skip over for the podcast.

• 55:08Speaker 01

  And, and we'll just talk about like information, storage and, and weights. Like, these curves to me are, are pretty crazy. Again, maybe, maybe it's like the sort of discoverers' folly or something where I'm like, oh, this didn't exist before. So it seems so cool, but then you're saying like, it seems somewhat obvious?

• 55:27Speaker 00

  No, no, no, don't, don't let me take that away from you. Yeah, no. Again, like, I, I independently was asking, how come there's not enough people exploring all elements from information theory? And then like you come along and your bidding's works become like an information theory exploration. And I'm like, suddenly, like, I'm very aligned to like exploring this, promoting this, and encouraging more people to, to figure it out. Because like, that's ultimately how we figure out this whole compression issue and, you know, what, what Andre wants, which is like the cognitive core, right? The most efficient model for the most capability, like, that is an information theory question.

• 55:58Speaker 01

  Totally agree with that. We could start here, like, so, so transformers that are trained in thirty-two bit precision, we approximate can store about three point six bits of information to maybe three point nine bits, somewhere in there, per parameter. And like, why is this? I mean, for some perspective, this is, this is quite bad. Like, if you have thirty-two bits available and you can only use three to four of them, like you're-

• 56:27Speaker 00

  Just store thirty-two, bro.

• 56:30Speaker 01

  Yeah, yeah, then you'll like, you know, you could build your own AI lab if you can make the these models that much more efficient. I don't know how they're implementing this mechanism or where the kind of bottlenecks come from, or even now that we know this, what it's necessarily useful for. I guess the tools that would be interesting to me are knowing, like, given a data set, if you could predetermine the exact model size and maybe architectural properties required to get a certain level of performance, that would be really neat. And like, we don't even know how to do that. We don't even know what the difference is between doing lower training, which trains less than 1% of the parameters, and full fine tuning, which trains all the parameters. We don't even really understand the difference there.

• 57:15Speaker 01

  So I think this is like, maybe like a baby step sort of in that direction, but there's a lot of unknown ahead of us.

• 57:20Speaker 00

  Okay. Do you think this is a hard limit? Do you think someone can come up with a better algorithm, but better architecture and then sort of just change the slope?

• 57:28Speaker 01

  There are two axes here. One is the ability of the model to store data. And I think we can definitely improve that. I think like, maybe even if we tested this with the Lama architecture, like, there's sort of like a GPT++ architecture, like, I would guess that can store better data just because the kind of numerical flow is a little bit better, the nonlinearities are maybe like, a little bit more suitable to training, like that will probably raise the bound a little bit. And then the second axis is that our measurement tools are just not that good. Like this is, you know, me, I'm a grad student, I'm running all these hyperparameter sweeps and sort of like, we draw conclusions from them, but even that being said, like, there are probably ways to measure this better, but all that would do is push the number up. So it's possible, like,

• 58:13Speaker 01

  there is a way to store five bits per parameter if you have like, a better optimization technique, or if you were a super genius and you could just perfectly set the weights to store the data, then maybe you can do better. And this is just sort of like what we can reach through optimization is this 3.6 bits per parameter. But I would be happy if someone came along with a much better measurement tool, like,

• 58:38Speaker 01

  this is just sort of like the first measurement. I mean, I would, I would guess in the future, like, you know, people will look back and say like, this is like somewhat oh, in one direction or another, for whatever reason. And that's just how science goes, and I have no problem with it.

• 58:52Speaker 00

  What we do is we call, we, we call this the Morse concert, 3.6, right?

• 58:58Speaker 01

  I would never.

• 58:59Speaker 00

  And then we we said like a like a challenge, like a leaderboard of like, beat this, right? And like, let let people go.

• 59:06Speaker 01

  Yeah, that assumes that we know the true constant ahead of time and we can measure the error rate.

• 59:12Speaker 00

  It's doable. You laid it out here.

• 59:14Speaker 01

  Yeah, yeah, yeah, yeah. That makes sense.

• 59:16Speaker 00

  One minor doubt I have is like, the goal actually isn't memorization, it's generalization, right?

• 59:22Speaker 01

  Mm hmm.

• 59:23Speaker 00

  The best memorizer model may not be the best generalizer model. And you're like, this incentivizing people to to max this number might actually just be fruitless in terms of actual intelligence. Like, you just get the best actual compressor. Like, you're just gonna get GZed.

• 59:39Speaker 01

  That's totally true. And there's this pattern in research, you know, time after time, it's like, someone poses a question and then people answer it over and over and over again, but it's it's often much more fruitful to just ask a new question. Maybe it just doesn't matter how much GPT models can store, and you should just like work on something else.

• 59:59Speaker 00

  We'll figure that out. Uh, did you wanna uh dwell on this this side at all?

• 1:00:03Speaker 01

  Yeah, let's just talk about it real quick. Uh, definitely not the algorithm itself.

• 1:00:08Speaker 00

  By the way, what are your tools for doing these kinds of charts uh and these kinds of diagrams? Like, I just come kind of curious of behind the scenes on the tools.

• 1:00:14Speaker 01

  I think like visualization has definitely been sun hobby of mine during grad school. This one actually, Oscar, my co-author, made this one. Maybe I gave some like prompting, but he made it. I I think most the last few papers have all been in diagrams, Google diagrams. I was using Figma for a while and Illustrator. I think Illustrator actually is is the best tool.

• 1:00:41Speaker 00

  Oh, did you know the Transformers Transformers diagram was in Adobe Illustrator?

• 1:00:45Speaker 01

  Oh, yeah, yeah, I did know that, actually. Yeah, because that's the only way you can get arrows that sort of like curve like that. Um, and they they have good shadows. Diagrams is like the least robust, but it's the most accessible. And honestly, if you if you're good, you can make pretty good stuff. Excalidraw is is nice, too, if it's not going in a a paper.

• 1:01:06Speaker 00

  Yeah, it's just too rough for a paper, but you. Need something professional looking, you know? It helps like if you're gonna publish your work, you need to make it look nice and professional and like official, right? So this is what it is.

• 1:01:16Speaker 01

  Yeah, yeah, and I think there's something worthwhile about saying like, okay, if I'm gonna put my name behind this, like I wanna spend time making all the references perfect and all the diagrams professional, all the captions are correct. And I think it's like important to put that level of detail into your work. That's a little chuggy, but let's finish this off. So, okay, we're talking about bits, information theory, what information sort of embeddings? We were talking about language model capacity. I think a much more question, more practical question is maybe, maybe this is more analogous to the vector database hacking embedding threat model we discussed is like if you have access to a set of model weights, what can you learn about the data?

• 1:01:58Speaker 01

  So like you were just mentioning, Gemma 3B came out yesterday and you can download it and it takes up a certain amount of space on disk. And it was trained on some data, but we have no insight into what the data was. I mean, it's probably English, it's probably some distribution of web text. I would guess there's a lot of code. And we seem to have a lot of information about the model, right? You have this file and there's like many ones and zeros, which means something. But it's kind of like a very highly compressed version of the training data. But I, I, I would be extremely surprised if they do any type of like private training, like there are these mechanisms for doing like differentially private language model training or even just anonymization in the pre-training pipeline. I bet they don't do any of that.

• 1:02:42Speaker 01

  They just sort of like train on the data. And then they kind of know that we don't have the right tools to decrypt the model weights. And so that's like my dream is we can come up with some way of translating model weights back into text data sets. And so in the, the most recent kind of drop, paper drop is that paper approximating language model training data from weights. And it turns out to be a really hard problem, like trying to go from model weights to text is really hard. And we do something a lot simpler, which is like. Well, there's, there's two ways we make it simpler. The first thing is we assume access to two checkpoints, which I think is probably not the case in Gemma.

• 1:03:25Speaker 01

  But in, in the case of DeepSeek, if you download the 400 billion parameter model weights, it's this giant file and you can actually get two of them. You can get the base model weights and the fine tune model weights. So the way we put this, you have this kind of like difference in parameter space, telling you what DeepSeek fine tuned on. And it's very controversial. I mean, they're sort of like geopolitical. Definitely at the corporation level, they're really interested in the implications of like, what did DeepSeek train on? And they've released this kind of treasure trove of information of what they trained on, which is the actual model weights. But we have no tool for like interpreting or kind of decrypting this weight difference.

• 1:04:08Speaker 01

  And so we started with something really simple, which is instead of even just trying to like regenerate the training data, we take just a web corpus and try to do selection of training data that kind of like looks like the true training data and gives us performance that's as close as possible to the true training data. So there is this complicated method, but it's something like you just sort of like, look at the data point gradient and see if it points in the direction in weight space of the fine tune. And then you take like the top data set. There are some tricks to it, but it's basically just like gradient based selection based on this weight difference. And it seems to be okay. Like it can get us pretty good training data.

• 1:04:52Speaker 01

  So I guess if you actually wanted to use this, it would be like your competitor releases a base model and a fine tune and you're trying to recreate their data set. So you can take this weight difference and take a giant web data set. Like if I was doing this at a company, I'd probably try to scale it up to trillions of tokens and then select the exact data points that try to produce the model. And it turns out you can train a pretty good model with that. We don't get to quite the performance of the original model, but it does seem to be like trending in that direction.

• 1:05:24Speaker 00

  This is like very creative. I don't know what the, the, the use of it.

• 1:05:30Speaker 01

  Yeah, like, when would you be in this exact situation?

• 1:05:33Speaker 00

  Decently often for the open model labs, like even DeepSeek R1 like has released an update. Mistral does it pretty frequently, Llama does it frequently. It's not impossible, but like I, I think it's like, it's like, I think that I really like the creativity in using quote unquote synthetic checkpoints to do this, which is, I don't think I've heard less from any other place. So I don't know if you, you came up with the idea.

• 1:05:57Speaker 01

  It's like linear interpolation in, in weight space.

• 1:06:00Speaker 00

  Okay, um, that's a bunch of the recent work. Uh, I wanted to sort of cap things off with the data sets question, if, if that's, is, is that a good?

• 1:06:07Speaker 01

  You can ask me whatever you want.

• 1:06:09Speaker 00

  Well, it's not, it's not a good, it's not an ask. It's just like, I think this is a very good thesis. Uh, I think it's a hot take. I almost invited you to speak based on just this alone, but it was, it was a little bit late.

• 1:06:21Speaker 01

  Oh, for the, for the conference.

• 1:06:22Speaker 00

  Yes. When I look for conference keynotes, I look for something that has a broad overview that can I put the last few years in perspective, or it's an insight that you can reasonably rely on to like last for a while, so you can get some mileage out of it, you know? And I think a lot of ideas in AI come and go, but like things that are trend, these things are scaling laws, things are trend lines, things are, things that are like, uh, there's, you know, there's no new ideas in AI. That I pay attention to. So maybe you want to recap, like, what's, what's the backstory if, if there was one?

• 1:06:52Speaker 01

  Yeah, yeah, sure. So the, the meta backstory is I've sort of started writing on Substack. And this is a post that I wrote a, a few months ago.

• 1:07:00Speaker 00

  The highest art form of humanity.

• 1:07:03Speaker 01

  Yeah, yeah.

• 1:07:06Speaker 01

  Yeah, publishing papers wasn't doing it for me anymore and, and I moved to Substack. And this is the name of the post, there are no new ideas in AI, only new data sets. One, one guy pledged me, but then I found out he was like my former student from a class I was teaching. So I, I don't think it really counts.

• 1:07:24Speaker 00

  It counts, he's a friend, he's your first supporter.

• 1:07:27Speaker 01

  A pledge is a pledge, man, I'll take whatever I can get. So, so the underlying thesis is that whenever, maybe I'll, I'll lay out this framework first. So there's this, uh, this book called The Structure of Scientific Revolutions by Thomas Kuhn.

• 1:07:44Speaker 01

  That I read near the beginning of my PhD, which suggests that science kind of moves in these cycles where not very often, there's something he calls a paradigm shift, which is like, you could think of it as a zero to one innovation where everything changes. And then it's followed by a rapid period of small innovations, a lot of like reapplication of previous techniques, pre-paradigm shift techniques to the new era. And then things sort of slow down as we wait for a new paradigm shift. And I was kind of asking myself, what's unique to the paradigm shifts that we've seen in AI? And by the way, to me, AI and language models are somewhat synonymous at this point, like at least for the foreseeable future.

• 1:08:27Speaker 01

  I'm certain that will change, but basically everything that's pushed the boundary to whatever we have now that resembles like intelligence has come from language models. And so those breakthroughs came in a few steps. So I think the idea is also like a meta-commentary on the research community, because what everyone wants as a researcher is some kind of like cute new method that no one has thought of before that just works on the existing data better than the previous methods. That's like, for whatever reason, like the kind of most glamorous thing people think you can do as a researcher, like Mamba, it's like, it's like a transformer, but it's like more efficient and works better.

• 1:09:10Speaker 01

  So that's what a good idea looks like. And I think everyone wants to like find something like that. But if you look at what's actually borne out in practice, it's never been like that. I think like all of the things that I would consider paradigm shifts in the Kuhnian sense came from a new technique, but trained on new data. And I think the new data is super, super important. So I wrote it as a series of four paradigm shifts. The first is the emergence of deep neural networks with AlexNet, which I think was like 2010 to 2012 era, where we just started training on ImageNet, which is like a scale no one had ever seen before of millions of images. And then the second thing was transformers and

• 1:09:54Speaker 01

  And this attention is all you need paper twenty seventeen, the first GPT twenty eighteen, which is web scale pre-training, like no one had ever done that before. No one had ever tried to scrape all the text off the internet and then tokenize it and feed it into models. Like, it's a crazy idea. And I think like, we should be honest. I mean, transformers are incredible and like their staying power is never going to cease to amaze me. They're like much more optimal than I think anyone ever knew. And I don't know if we'll ever beat them, but the real innovation is web scale pre-training. And I think like, we honestly probably could have gotten this with R N Ns. I know like the scaling laws paper shows that R N Ns have worse curves for scaling, but

• 1:10:37Speaker 01

  probably people would have been like, I bet you could have built chat GPT with a very sophisticated R N N. Like you didn't even need transformers. What you need is web scale pre-training and the third innovation, which is instruction tuning. And we thought it it came with like reinforcement learning, but I think the big innovation of instruction tuning is actually the human preference data, which is like gathering positive and negative pairs of what looks good. Like in terms of a chatbot interface. And actually, it turns out you can do supervised learning on that, too. You can do D P O, which is a form of supervised learning. You don't even need the the instruct GPT techniques. You just need the data. So like, I'm sort of playing devil's advocate here, but I actually think this is true that like,

• 1:11:19Speaker 01

  if we had the right data sets, we almost could have scaled like twenty fifteen era techniques and gotten something that looks like at least instruct GPT. Reasoning models are are a little different, like they're, I I'm not sure if we could have that with R N Ns or not. Like, I don't know if I'm in a position to comment on that with certainty, but they do fall into this framework, which is they really did emerge from a new data source. In this case, it's something like a little different. It's like verification with symbolic systems like math calculators, coding environments, unit tests, like things where we can provide numerical feedback to language model outputs. But we we built a way to to learn that and leverage it to get

• 1:12:01Speaker 01

  more intelligent systems. And so whatever the fifth thing is, whether it's video or embodied A I or some kind of crazy innovation on reasoning models. Whatever comes next will probably be some type of new data source that we're not using yet.

• 1:12:18Speaker 00

  That's a really good thesis. I would say that the researchers I talked to would somewhat disagree. Yeah, obviously, this is like a hot take type of thing. And like you already acknowledged that R N Ns don't don't scale to the same extent. Like they operate on the slope of the curve. Whereas, you know, I guess like the amount of data or the type of data or the core insight just changes the order of magnitude of the X axis, right? That that we are mostly working on. But like both are important. The way that I think someone put it to me was an improvement on compute or data efficiency is the equivalent of having a whole bunch more data that we, you know, that otherwise would be a lot more expensive to collect. It's likely that, you know, the frontier models right now are just a collection of

• 1:13:03Speaker 00

  hundreds of these small little experiments that just stack up. You mentioned Muon in your in your post, which seems to be the atom killer. Curiously enough, like still none of the big models use Muon, but like vibes are good.

• 1:13:19Speaker 01

  Yeah, yeah. And the value of building better optimizers is really incredible. Like it's just a free launch. You can just sort of like plug in a slightly better training mechanism. And then you save like a ton of compute and a ton of training time. That's like hugely valuable.

• 1:13:34Speaker 00

  I think this is cool because I think like it puts us in a mode of like, if you were ever to ask what comes after reasoning, it has to be something on the order of this. And most ideas are not, most ideas are not. And so this is cool in a sense of like, it just jolts you out of incremental thinking into like what really is missing for the next paradigm. And I don't have an answer. Do you have one? Do you have, do you have candidates?

• 1:13:58Speaker 01

  Oh, I really haven't even considered that too much. I guess like scaling reasoning.

• 1:14:03Speaker 00

  You gotta do the autocomplete.

• 1:14:05Speaker 01

  First step five.

• 1:14:06Speaker 00

  I mean, you got us all the way there and you're like, you know, you gotta show us the way now.

• 1:14:11Speaker 01

  We can say it's an exercise left to the reader. But I mean, the reality is like predicting the future is too damn hard, you know? Like I, maybe it'll be obvious to me in hindsight in five years, but sitting here today, I really can't derive from first principles what the next wave of innovation will come from.

• 1:14:29Speaker 00

  Yeah, I think we have a few years left. Like each of these phases lasted for a few years. Reasoning just started last year, kind of. We got some juice on this one. Cool. I think that is a broad overview. We've went way over time, but like I really enjoyed this. I guess my parting question for you is kind of a meta one. So I'm not an academic. I'm like kind of self taught. I just read a bunch of papers and like I talk to people all day as part of the podcast. How do I rate in terms of like my, my questions? As though like, could I pass as a grad student? Like, or like, what's my distribution? Like, maybe I was maybe more industry oriented than academics.

• 1:15:10Speaker 01

  I think you got to realize that like, the only person that's an expert in your area as a grad student is you. And even like eventually your advisor defers to you for a small set of questions that fall within your very niche expertise. So like, I think you're clearly like a very good generalist and have like a huge amount of background on these topics. And to the point where I would say you're passing the grad student Turing test. And I think if you went to a talk, like people would just assume you have some weird research area of your own that they don't understand, you know?

• 1:15:45Speaker 00

  My research area is AI engineering. Like I'm, I'm sort of like making it up as I go. But no, this is super helpful. Okay, well, I, I, that's about all we prepared. All the best in your search, all the best in your PhD. I assume like apparently the current PhD meta is you just do a bunch of small papers. You staple them together and like find like an overall theme. You do a defense and that's it. Like, that's the journey, which is kind of cool. Like I would, I would love to do that. I'm too old to do it, but like, it's cool.

• 1:16:13Speaker 01

  Yeah, yeah, it's, it's a great thing to do at, at any age.

• 1:16:16Speaker 00

  Well, it's better to do a Substack, right? And then you have like people like subscribing and pledging along the way and like getting validation. And like, yeah, that's, that's better than a PhD. Substack.

• 1:16:30Speaker 00

  That's the title of the episode, like Substack better than PhD.

• 1:16:35Speaker 00

  But no, thanks. Yeah, thanks for your time. This is really great. Where can people find you? What are you looking for really?

• 1:16:41Speaker 01

  I'm online, you know, you can follow my Substack and Twitter. I tweet pretty consistently. And you're putting papers out. I guess like the most meaningful thing, to be honest, is to engage with the research and send me an email. If you really care, that's amazing. And like, I love having those kinds of discussions. And you mean like what I'm looking for in a job or out of life?

• 1:17:05Speaker 00

  Your research direction, like what interests you over anything else that's like if if there's someone out there looking who has a problem and is looking for someone to help them on it, like you are the guy for underscore.

• 1:17:17Speaker 01

  Oh, yeah. Hopefully, if you listen this long, like, I think like my research is a lot more well-connected than some people's PhD research in that it all falls into like a very small manifold of like all possible problems. And so if you if you want to work on anything within that space, or that's sort of like adjacent to the problems that we discussed in terms of like language model, maybe not even language model, but model, weight and activation, information. I think anything that can be described as that is very interesting to me and I would love to talk.

• 1:17:54Speaker 00

  Awesome. Well, we'll put your contact info in the show notes and thanks for your time.

• 1:17:59Speaker 01

  Thank you.