Lex Fridman Podcast - #75 – Marcus Hutter: Universal Artificial Intelligence, AIXI, and AGI

Episode Date: February 26, 2020

Marcus Hutter is a senior research scientist at DeepMind and professor at Australian National University. Throughout his career of research, including with Jürgen Schmidhuber and Shane Legg, he has proposed a lot of interesting ideas in and around the field of artificial general intelligence, including the development of the AIXI model which is a mathematical approach to AGI that incorporates ideas of Kolmogorov complexity, Solomonoff induction, and reinforcement learning. EPISODE LINKS: Hutter Prize: http://prize.hutter1.net Marcus web: http://www.hutter1.net Books mentioned: - Universal AI: https://amzn.to/2waIAuw - AI: A Modern Approach: https://amzn.to/3camxnY - Reinforcement Learning: https://amzn.to/2PoANj9 - Theory of Knowledge: https://amzn.to/3a6Vp7x This conversation is part of the Artificial Intelligence podcast. If you would like to get more information about this podcast go to https://lexfridman.com/ai or connect with @lexfridman on Twitter, LinkedIn, Facebook, Medium, or YouTube where you can watch the video versions of these conversations. If you enjoy the podcast, please rate it 5 stars on Apple Podcasts, follow on Spotify, or support it on Patreon. This episode is presented by Cash App. Download it (App Store, Google Play), use code "LexPodcast".  Here's the outline of the episode. On some podcast players you should be able to click the timestamp to jump to that time. OUTLINE: 00:00 - Introduction 03:32 - Universe as a computer 05:48 - Occam's razor 09:26 - Solomonoff induction 15:05 - Kolmogorov complexity 20:06 - Cellular automata 26:03 - What is intelligence? 35:26 - AIXI - Universal Artificial Intelligence 1:05:24 - Where do rewards come from? 1:12:14 - Reward function for human existence 1:13:32 - Bounded rationality 1:16:07 - Approximation in AIXI 1:18:01 - Godel machines 1:21:51 - Consciousness 1:27:15 - AGI community 1:32:36 - Book recommendations 1:36:07 - Two moments to relive (past and future)

The following is a conversation with Marcus Hutter, senior research scientist at Google Deep Mind. Throughout his career of research, including with Yergen Schmidt, Hooper, and Shane Legg, he has proposed a lot of interesting ideas in and around the field of artificial general intelligence, including the development of IXI, spelled A-I-X-I model, which is a mathematical approach to aGI that incorporates ideas of comagurov complexity, solemn enough induction, and reinforcement learning. In 2006, Marcus launched the 50,000-year-old Hutter prize for lossless compression of human knowledge. The idea behind this prize is that the ability to compress well is closely related to intelligence.

This, to me, is a profound idea. Specifically, if you can compress the first 100 megabytes or 1 gigabyte of Wikipedia better than your predecessors, your compressor likely has to also be smarter. The intention of this prize is to encourage the development of intelligent compressors as a path to AGI. In conjunction with this podcast release, just a few days ago, Marcus announced a 10X increase in several aspects of this prize, including the money, to 500,000 euros. The better your compress works, relatives of the pre-gest winners, the higher fraction of that prize money is awarded to you. You can learn more about it if you

Google simply, Hutter prize. I have a big fan of benchmarks for developing AI systems and the Hutter prize may indeed be one that will spark some good ideas for approaches that will make progress on the path of developing AGI systems. This is the Artificial Intelligence Podcast. If you enjoy it, subscribe on YouTube, give it 5 stars and Apple podcasts, support it on Patreon or simply connect with me on Twitter, at Lex Friedman spelled F-R-I-D-M-A-N. As usual, I'll do one or two minutes of ads now and never any ads in the middle that

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for young people around the world. And now here's my conversation with Marcus Hutter. Do you think of the universe as a computer or maybe an information processing system? Let's go with a big question first. Okay, I have a big question first. I think it's a very interesting hypothesis or idea. And I have a background in physics. So I know a little bit about physical theories, the standard model of particle physics,

and general relativity theory. And they are amazing and describe virtually everything in the universe. And they're all in a sense, computable theories. I mean, they're very hard to compute. And it's very elegant, simple theories, which describe virtually everything in the universe. So there's a strong indication that somehow the universe is computable, but it's a plausible

hypothesis. So, what do you think, just like you said, general relativity, quantum field theory? What do you think that the laws of physics are so nice and beautiful and simple and compressible. Do you think our universe was designed is naturally this way? Are we just focusing on the parts that are especially compressible? Are human minds just enjoy something about that simplicity? And in fact, there's other things that are not so compressible. No, I strongly believe and I'm pretty convinced that the universe is inherently beautiful, elegant and simpler and described by these equations

and we're not just picking that. I mean, if the versa phenomenon which cannot be neatly described, scientists would try that, right? And you know, there's biology which is more messy but we understand that it's an emerging phenomena, and it's complex systems, but they still follow the same rules, right? Of quantum and electrodynamics, all of chemistry follows that, and we know that. I mean, we cannot compute everything because we have limited computational resources. No, I think it's not a bias of the humans, but it's objectively simple. I mean, of course, you never know, you know, maybe there's some corners very far out in the universe or super, super tiny below the nucleus of of of atoms or well parallel universes where which are not nice and simple, but there's no evidence for that. And we should apply Occam's razor and, you know,

choose the simplest tree consistent with it, but although it's a little bit self-referential. So maybe a quick pause, what is Arkham's razor? So Arkham's razor says that you should not multiply entities beyond necessity, which sort of if you translate that into proper English, means, and you know, in the scientific context, means that if you have two series or hypothesis or models, which equally well describe the phenomenon you have studied or the data, you should choose the more simple one.

So that's just a principle? Yes. So that's not like a provable law, perhaps, perhaps we'll kind of discuss it and think about it, but what's the intuition of why the simpler answer is the one that is likely to be more correct descriptor of whatever we're talking about? I believe that outcomes razor is probably the most important principle in science. I mean, of course, we'll be logically deduction if we do experimental design, but science is about finding understanding the world, finding models of the world, and we can come up with crazy, complex models which explain everything but predict nothing,

but the simple model seems to have predictive power, and it's a valid question why. And there are two answers to that. You can just accept it. That is the principle of science. And we use this principle and it seems to be successful. We don't know why, but it just happens to be. Or you can try, you know, find another principle which explains or comes to razor. And if we start with assumption that the world is governed

by simple rules, then there's a bias towards simplicity. And applying Occam's razor is the mechanism to finding these rules. And actually in a more quantitative sense and we come back to that later in case of Solomon deduction, you can rigorously prove that you should assume that the world is simple, then Occam's razor is the best you can do, you know, certain sense. So I apologize for the romanticized question, but why do you think outside of its effectiveness,

why do we do you think we find simplicity so appealing as human beings? Why does it just, why does E Cosmacy squared seem so beautiful to us humans. I guess mostly in general many things can be explained by an evolutionary argument and you know there's some artifacts in humans which you know are just artifacts and not in the evolutionary necessary but with this beauty and simplicity it's believe, at least the core is about, like science, finding regularities in the world, understanding the world, which is necessary for survival, right? You know, if I look at a bush, right, and I just see Norris, and there is a tiger, right, and it's me, then I'm dead.

But if I try to find a pattern, and we know that humans are prone to find more patterns in data than they are, you know, like the Mars face and all these things. But this bias towards finding patterns even if they are not, but I mean it's best of course if they are, yeah, helps us for survival. Yeah, that's fascinating. I haven't thought really about the, I thought I just loved science, but they're indeed from in terms of just survival purposes. There is an evolutionary argument for why, why we find the work of Einstein so beautiful. Maybe a quick small tangent, could you describe what Salmon of induction is?

Yeah, so that's a theory which I claim and Racer Lominoff sort of claimed a long time ago that this solves the big philosophical problem of induction and I believe the claim is essentially true the ability of the claim is essentially true. And what it does is the following. So, okay, for the picky listener, induction can be interpreted narrowly and widely, narrow means inferring models from data. And widely means also then using these models for doing predictions or predictions

also part of the induction. So I'm a little sloppy sort of with the terminology and maybe it comes from, right, so long enough, you know, being sloppy, maybe I shouldn't say that. We can't complain anymore. So let me explain a little bit this theory in simple terms. So assume we have a data sequence, make it very simple, the simplest ones say 111111 and you see if 100 ones. What do you think comes next? The natural order I'm going to speed up a little bit, the natural answer is of course, you know, one. Okay. And the question is why. Okay. Well, we see a pattern there. Yeah. Okay. There's a one and we repeat it. And why should it suddenly

after 100 ones be different? So what we're looking for is simple explanations or models for the data we have. Now the question is, a model has to be presented in a certain language, in which language to be used. In science, we want formal languages and we can use mathematics or we can use programs on a computer, so abstractly on a touring machine for instance, or can be a general purpose computer. So, and there, of course, lots of models of you can say, maybe it's 101, and then 100 zeros and 101s, that's a model, right? But there are simpler models. There's a model print one loop, that also explains the data.

And if you push that to the extreme, you are looking for the shortest program, which, if you run this program, reproduces the data you have. It will not stop, it will continue naturally. And this you take for your prediction. And on the sequence of ones, it's very plausible, right? That print one loop is the shortest program. We can give some more complex examples, like 1, 2, 3, 4, 5. What comes next, the short program is, again, you know, counter. And so that again, you know, counter.

And so that is roughly speaking how a lot of induction works. The extra twist is that it can also deal with noisy data. So if you have, for instance, a coin flip, say a biased coin which comes up head with 60% probability, then it will predict. It will learn and figure this out. And after a while, it predicts, oh, the next coin flip will be head with probability 60%. So it's the stochastic version of that. But the goal is the dream is always the search for the short program. Yes. Yeah. Well, in Solomon of Induction, precisely what you do is, so you combine. So

looking for the shortest program is like applying Opax Racer, so looking for the shortest program is like applying OPAX Razer, like looking for the simple theory. There's also Epicoros Principle which says, if you have multiple hypothesis which equally well described your data, don't discard any of them, keep all of them around you never know. And you can put that together and say, okay, I have a bias towards simplicity, but I don't rule out the larger models and technically what we do is we weigh the shorter models higher and the longer models lower and you use a beige

technique you have a prior and which is precisely two to the minus the complexity of the program and You weigh all this hypothesis and takes this mixture and then you get also this to have a statistician Yeah, like many of your ideas, that's just a beautiful idea of weighing based on the simplicity of the programmer. I love that, that seems to me maybe very human-centric concept, seems to be a very appealing way of discovering good programs in this world. You've used the term compression quite a bit. I think it's a beautiful idea. We just talked about simplicity and maybe science or just all of our intellectual pursuits is

basically the attempt to compress the complexity all around us into something simple. So, what does this word mean to you compression? I essentially have all explained it. So it compression means for me, finding short programs for the data or the phenomenon and hand, you could interpret it more widely as you know, finding simple theories, which can be mathematical theories, or maybe even informal, you know, just inverts. Compression means finding short descriptions,

explanations, programs for the data. Do you see science as a kind of our human attempt at compression? So we're speaking more generally, because when you say programs, you're kind of zooming in at a particular sort of, almost like a computer science, artificial intelligence, focus, but do you see all of human endeavor as a kind of compression?

Well, at least all of science, I see, as a, and develop compression, not all of humanity, maybe. And, well, there are some other aspects of science like experimental design, right? I mean, we, we, we create experiments specifically to get extra knowledge. And this is, that is in part of the decision making process. But once we have the data to understand the data is essentially compression. So I don't see any difference between compression, understanding and prediction. So we're jumping around topics a little bit, but returning back to simplicity, a fascinating concept of comagurov complexity.

So in your sense, the most objects in our mathematical universe have high comagurov complexity. And maybe what is, first of all, what is comagurov complexity? Okay, comagurov complexity is a notion of simplicity or complexity and it takes the compression view to the extreme. So I explained before that if you have some data sequence, just think about a file in a computer

and best sort of, you know, just a string of bits. And if you, and we have data compressors like we compress big files into, say, zip files with certain worse compressors and you can ask what is the ultimate compressor? So what is the shortest possible Self-extracting RKF you could produce for certain Data set here which reproduces the data set and the length of this is called the Kolmogorv complexity and Arguably that is the information content in the data set. I mean, if the data set is very redundant or very boring,

you can compress it very well. So the information content should be low and it is lower according to this difference. So the length of the shortest program that summarizes the data. Yes, yeah. And what's your sense of our universe when we think about the different

the different objects in our universe that we try concepts or whatever at every level do they have higher or low comical complexity. So what's the hope? Do we have a lot of hope and be able to summarize much of our world? That's a tricky and difficult question. So as I said before, I believe that the whole universe based on the evidence we have is very simple. So it has a very short description. Sorry to linger on that. The whole universe, what does that mean? Do you mean at the very basic fundamental level in order to create the universe? Yes, yeah. So you need a very short program and you run it to get the thing going. You get the thing going and then it will reproduce our universe. There's a problem

with noise. We can come back to the later possibly. There's no is a problem or is it a bug or a feature? I would say it makes our life as a scientist really, really much harder. I mean, think about it without noise. We wouldn't need all of the statistics. But that maybe we wouldn't feel like there's a free will. Maybe we need that for the... Yeah, this is an illusion that noise can give you free will. That's the reason that way it's a feature.

But also, if you don't have noise, you have caotic phenomena which are effectively like noise. So we can't get away with statistics even then. I mean, think about rolling a dice and forget about quantum mechanics and you know exactly how you throw it. But I mean, it's still so hard to compute the trajectory that effectively it is best to model it as coming know, as you know, coming out with a number, this probability one over six. But from this set of philosophical, Kolmogor, a complexity perspective,

if we didn't have noise, then arguably you could describe the whole universe as, well, as standard model plus general relativity. I mean, we don't have a theory of everything yet, but assuming we are close to it or have it here, plus the initial conditions, which may hopefully be simple. And then you just run it and then you would reproduce the universe.

But that's spoiled by noise or by chaotic systems or by initial conditions, which may be complex. So now, if we don't take the whole universe, we're just a subset, you know, just take planet Earth. Planet Earth cannot be compressed, you know, into a couple of equations. This is a hugely complex system. So interesting.

So when you look at the window, like the whole thing might be simple, but when you just take a small window, then it may become complex. And that may be counterintuitive, but there's a very nice analogy. The book, the library of all books. So imagine you have a normal library with interesting books and you go there, great, lots of information and huge, quite complex. So now I create a library which contains all possible books, say, of 500 pages.

So the first book just has AA over all the pages. The next book AA and ends with B. And so on, I create this library of all books. I can write a super short program which creates this library. So this library which has all books has zero information content. And you take a subset of this library and certainly have a lot of information in there. So that's fascinating. I think one of the most beautiful object mathematical objects that at least today seems to be understudied or under-talked

about is cellular automata. What lessons do you draw from the game of life or cellular automata where you start with a simple rule, just like you're describing with a universe and somehow complexity emerges? Do you feel like you have an intuitive grasp on the fascinating behavior of such systems where like you said, some chaotic behavior could happen, some complexity could emerge, some it could die out in some very

rigid structures. Do you have a sense about cellular tomat or that somehow transfers maybe to the bigger questions of our universe? It's a cellar-lautomata, and especially a conversed game of life, is really great, because the jewelers are so simple, you can explain it to every child. And even by hand, you can simulate a little bit.

And you see this beautiful patterns emerge. And people have proven that it's even touring complete. You cannot just use a computer to simulate game of life, but you can also use game of life to simulate any computer. That is truly amazing. And it's the prime example probably to demonstrate that very simple rules can lead to very rich phenomena. And people, you know, sometimes, you know, how can, how is chemistry and biology so rich? I mean, this can't be based on simple rules, yeah? But no, we know quantum electrodynamics describes all of chemistry and and we come later back to that. I claim intelligence can be explained or described in one single equation this very rich phenomenon. You asked also about whether, you know, I understand this phenomenon.

It's probably not. And this is saying you never understand really things you just get used to them. I think it was pretty used to sell it automatically. So you believe that you understand now why this phenomenon happens. But I give you a different example. I didn't play too much with this Converse Game of Life, but a little bit more with fractals and with the mandal bronze set. And it's beautiful, you know, patterns just look mandal bronze set. And well, when the computers were really slow and they just had a black and white monitor and a programed my own programs on an assembler to to get these practice on the screen and it was mesmerized and much later so I returned to this you know every couple of years and then I tried to understand what is going on and you can

understand a little bit so I try to derive the locations, you know, there are these circles and the apple shape. And then you have smaller mandal broad sets recursively in this set. And there's a way to mathematically by solving high auto polynomials to figure out where these centers are and what size they are approximately. And by sort of mathematically approaching this problem,

you slowly get a feeling of why things are like they are. And that sort of isn't, you know, first step to understanding why this rich phenomena. Do you think it's possible, what's your intuition? Do you think it's possible to reverse's your intuition? Do you think it's possible to reverse engineer and find a short program that generated these fractals by looking at the fractals? Well, in principle, yes.

So I mean, in principle, what you can do is you take any data set, you take these fractals or you take whatever your data set, whatever you have. So a picture of Converse Game of Life. And you run through all programs, you take a program of size 1, 2, 3, 4, and all these programs around them all in parallel in so-called dovetailing fashion, give them computational resources, first one 50% second one half resources and so on, and let them run. Wait until they hold, give an compare it to your data and if some of these programs produce the correct data, then you stop and then you have already some program. It may be a long program because it's faster. And then you continue and you get shorter and shorter programs until you

eventually find the shortest program. The interesting thing you can never know whether it's a shortest program because there could be an even shorter program, which is just even slower. I just have to wait here, but asymptotically and actually after final time, you have this shortest program. So this is a theoretical but completely impractical way of finding the underlying structure in every dataset. And that is a lot more of induction that has a common goal of complexity. In practice, of course, we have to approach the problem more intelligently.

And then if you take resource limitations into account, there's, once the field of pseudo random numbers, yeah. And these are random numbers. So these are deterministic sequences. But no algorithm which is fast, fast means runs in polynomial time can detect that it's actually deterministic. So we can produce interesting, I mean random numbers, maybe not that interesting, but just an example. We can produce complex looking data and we can then prove that no fast algorithm can detect the underlying pattern.

Which is unfortunately, that's a big challenge for our search for simple programs in the space of artificial intelligence, perhaps. Yes, it definitely is one to the vision intelligence, and it's quite surprising that it's, I can't say easy, I mean, it's really hard to find. It's theory, but apparently it was possible for human minds to find this simple rules in the universe. It could have been different, right? It could have been different. It's, it's awe-inspiring. So let me ask another absurdly big question. What is intelligence in your view? So I have, of course, a definition.

I wasn't sure what you're going to say, because you could have just as easy said, I have no clue. Which many people would say, but I'm not modest in this question. So the informal version, which I've worked out together with Shane Lack, who co-founded DeepMind, is that intelligence measures and agents' ability to perform well in a wide range of environments. So that doesn't sound very impressive, So that doesn't sound very impressive, but these words have been very carefully chosen. And there is a mathematical theory behind that, and we come back to that later. And if you look at this definition, by itself, it seems like, yeah, okay, but it seems

a lot of things are missing. But if you think it through, then you realize that most, and I claim, all of the other traits, at least of rational intelligence, which we usually associate with intelligence, are emergent phenomena from this definition, like, you know, creativity, memorization, planning, knowledge, you all need that in order to perform well in a wide range of environments. So you don't have to explicitly mention that in order to perform well in a wide range of environments. So you don't have to explicitly mention that in a definition.

Interesting. So yeah, so the consciousness, abstract reasoning, all these kinds of things are just emergent phenomena that help you in towards, can you say the definition against multiple environments? Did you mention the word goals? No, but we have an alternative definition instead of performing value constructs, replace it by gold. So intelligence measures and agent ability to achieve goals in a wide range of environments. That's

more or less equal. But it's because in there, there's an injection of the word goals. So you want to specify there should be a goal. Yeah, but perform well is sort of what does it mean? It's the same problem. Yeah. There's a little bit gray area, but it well is sort of what does it mean? It's the same problem. Yeah There's a little bit gray area, but it's much closer to something that could be formalized are in your view are humans? Where do humans fit into that definition? Are they

general intelligence systems that are able to perform in like how good are they at fulfilling that definition at performing well in multiple environments? Yeah that's a big question. I mean the humans are performing best among all species and earths. Species we know we know earth yeah depends you could say that trees and plants are doing better job they'll probably outlast us. So. But they are in a much more narrow environment, right? I mean, you just, you know, I have a little bit of air pollution, and these trees die, and we can adapt, right? We build houses, we build filters, we do geoengineering, so multiple environment parts.

Yeah, that is very important, yes. So that distinguishes narrow intelligence from wide intelligence intelligence also in the AI research. So let me ask the the Alan Turing question can machines think can machines be intelligent? So in your view, I have to kind of ask the answers probably yes But I want to kind of hear with your thoughts on it can machines be made to fulfill this definition of intelligence, to achieve intelligence? Well, we are sort of getting there and on a small scale we are already there. The wide range of environments is missing. But we have self-driving cars, we have programs to play go and chess, we have speech recognition.

So it's pretty amazing, but you can, you know, these are narrow environments. But if you look at Alpha Zero, that was also developed by DeepMind. I mean, but famous with Alpha Go and then came Alpha Zero a year later. That was truly amazing. So, uh, reinforcement learning, algorithm, which is able, just by self-play, to play chess, and then also go. And I mean, yes, they're both games, but they're quite different games. And you know, this, you didn't don't feed them the rules of the game. And the most remarkable thing, which is still a mystery to me, that usually for any decent chess program, I don't know much about go, you need opening books and endgame tables and so on to and

Nothing in there nothing was put in there special alpha zero the self-play mechanism starting from scratch being able to learn To actually new strategies is Yeah, it is really really discovered, you know all these famous openings within four hours by itself What it was really happy about, I'm a terrible chess player, but I like Queen Gambi. And Alpha Zero figured out that this is the best opening. Finally, somebody proved you correct. So yes, to answer your question, yes, I believe the general intelligence is possible. And it also, it depends how you define it. Do you say AGI with general intelligence, artificial intelligence only refers to if you achieve human

level or a subhuman level, but quite broad. Is it also general intelligence? So we have to distinguish or it's only super human intelligence general artificial intelligence. Is there a test in your mind like the touring test, or natural language, or some other test that would impress the heck out of you that would kind of cross the line of your sense of intelligence within the framework that you said? Well, the touring test has been criticized a lot, but I think it's not as bad as some people.

I think some people think it's too strong, so it tests not just for a system to be intelligent, but it also has to fake human deception. This deception, right, which is much harder. And on the other hand, this is too weak, because it just maybe fakes emotions or intelligent behavior. It's not real. But I don't think that's the problem or big problem. So if you would pass the touring test, so a conversation over terminal with a bot for an hour or maybe a day or so and you can fool a human into, you know, not knowing whether

this is a human or not, that it's the touring test. I would be truly impressed. And we have this annual competition, the Lepna price. And I mean, it started with Eliza, that was the first conversational program. And what is it called? The Japanese Mitsuku or so, that's the winner of the last, you know, couple of years. And well, it's impressive. Yeah, it's quite impressive. And then the last couple of years. Yeah. And well, it's impressive. Yeah, it's quite impressive. And then Google has developed Mina, right?

Just recently, that's an open domain conversational bot. Just a couple of weeks ago, I think. Yeah, I kind of like the metric that sort of the Alexa price has proposed. I mean, maybe it's obvious to you, it wasn't to me, of setting sort of a length of a conversation. Like you want the bot to be sufficiently interesting that you'd want to keep talking to it for like 20 minutes.

And that's a surprisingly effective and aggregate metric because you really like nobody has the patience to be able to talk to a bot that's not interesting in intelligent and witty and Is able to go on the different ages jump domains be able to you know say something interesting to maintain your attention Maybe many humans who also failed this test Unfortunately, we set just with autonomous vehicles with chatbots We also set a bar that's way too hard to reach. I said the touring test is not as bad as some people believe, but what is really not useful about the touring test, it gives us no guidance on how to develop these systems in the first place.

Of course, we can develop them by trial and error and do whatever and then run the test and see whether it works or not. But a mathematical definition of intelligence gives us an objective which we can then analyze by theoretical tools or computational and maybe even prove how close we are. And we will come back to that later with the Ixi model. So I mentioned the compression, right? So in that language processing, they have achieved amazing results. And one way to test this, of course, you're gonna take the system, you're training it,

and then you see how well it performs on the task. But a lot of performance measurement is done by so-called perplexity, which is essentially the same as complexity or compression length. So the NLP community develops new systems and then they measure the compression length and then they have ranking and leaks because there's a strong correlation between compressing well and then the system's performing well at the task at hand. It's not perfect, but it's good enough for them as an intermediate aim. So you mean a measure? So this is kind of almost returning to the common girls complexity.

So you're saying good compression usually means good intelligence. Yes. So you mentioned you're one of the one of the only people who dared boldly to try to formalize the idea of artificial general intelligence to have a a mathematical framework for intelligence. Just like as we mentioned, termed IXC, AIXI. So let me ask the basic question, what is IXC? Okay, so let me first say what it stands for because- What it stands for actually, that's probably the more basic question.

What is the first question is usually how it's pronounced, but finally I put it on the website, how it's pronounced. And you'll figured it out. The name comes from AI, Artificial Intelligence, and the X-I is the Greek letter X-I, which are used for Solomon of Distribution, for quite stupid reasons, which I'm not willing to repeat here and from the camera. So let us happen to be more or less arbitrary. I chose this Xi. But it also has nice other interpretations. So there are actions and perceptions in this model. Right in the agent has actions and perceptions and over time. So this is A index i x index i.

So this is the action at time i and then followed by perception at time i yeah um we'll go with that i'll edit out the first point yeah i'm just kidding i have some more interpretations yeah so at some point maybe five years ago or ten years ago i discovered in uh in Barcelona it was on a big church uh there was in stone engraved some text and the word Iksia appeared there Very surprised and happy about it and I looked it up. So it is a Catalan language and it means with some Interpretation of that's it. That's the right thing to do. Yeah, Horika. Oh, so it's almost like destined somehow came yeah came to you in a dream the right thing to do, yeah, hoi rica. Oh, so it's almost like destined. Somehow came to you in a dream.

So, similar, there's a Chinese word, I, she also written like I, see if you transcribed it to pinjen. And the final one is that is AI, crossed with induction because that is, and that's going more to the content now. So good old fashioned AI is more about, planning and known deterministic

world and induction is more about often your IID data and inferring models and essentially what this IXI model does is combining these two. And I actually also recently I think heard that in Japanese AI means love. So if you can combine XIs somehow with that, I think we can, there might be some interesting ideas there. So I see that's going to take the next step. Can you maybe talk at the big level of what is this mathematical framework? Yeah, so it consists essentially of two parts.

One is the learning and induction and prediction part, and the other one is the planning part. So let's come first to the learning induction prediction part, which essentially I explained already before. So what we need for any agent to act well is that it can somehow predict what happens. I mean, you have no idea what your actions do. How can you decide which action are good or not? So you need to have some model of what your actions affect. So what you do is you have some experience, you build models like scientists, you know, of your experience,

then you hope these models are roughly correct, and then you use these models for prediction. And a model is sorry to interrupt, a model is based on the perception of the world, how your actions will affect that world. That's not the important part. But it is technically important. But at this stage, we can just think about predicting, say, stock market data, whether data or IQ sequences, one, two, three, four, five, what comes next, yeah. So, of course, our actions affect what we're doing, what I come back to that in a second. So, and I'll keep just interrupting. So just to draw a line between prediction and planning, what do you mean by prediction in this way? It's trying to predict the environment without your long term action in the environment without your long-term action in the environment, what is prediction?

Okay, if you want to put the actions in now, okay, then let's put it in now. Yeah. So we don't have to put them down. Yeah, scratch it, scratch it, don't question. Okay, so the simplest form of prediction is that you just have data that you passively observe and you want to predict what happens without interfering. As I said, weather forecasting, stock market, IQ sequences, or just anything. Okay. And Solomano's theory of induction based on compression. So you look for the shortest program which describes your data sequence, and then you take this program run it, which reproduces your data sequence by definition, and then you let it continue running,

and then it will produce some predictions. And you can rigorously prove that for any prediction task, this is essentially the best possible predictor. Of course, if there's a prediction task, or a task which is unpredictable, like you have fair coin flips, yeah, I cannot predict the next one. But Solomanof task says okay next head is probably 50%.

It's the best you can do. So if something is unpredictable Solomanof will also not magically predict it. But if there is some pattern and predictability then Solomanof induction will figure that out eventually and not just eventually but rather quickly and you can have proof convergence rates. Whatever your data is. So that is pure magic in a sense. What's the catch? Well, the catch is that it's not computable and we come back to that later.

You cannot just implement it in even this Google resources here and run it and predict the stock market and become rich. Raise a lot more of already. Try it at the time. But the basic task is you're in the environment and you're interacting with the environment to try to learn a model of the environment and the model is in the space of all these programs and your goal is to get a bunch of programs that are simple. And so let's go to the actions now, but actually good that you asked, usually, I skipped this part. Also, there is also a minor contribution, which I did, so the action part, but actually good that you are usually skipped this part, although there is also a minor contribution

which I did, so the action part, but they usually sort of just jump to the decision part. So let me explain to the action part now. Thanks for asking. So you have to modify it a little bit. By now, not just predicting a sequence, which just comes to you, but you have an observation, then you act somehow, and then you want to predict the next observation based on the past observation and your action. Then you take the next action, you don't care about predicting it because you're doing it.

And then you get the next observation, and you want, well, before you get it, you want to predict it again based on your past action and observation sequence. It just condition extra on your actions. There's an interesting alternative that you also try to predict your own actions. If you want. In the past or the future? In the future. In the future actions.

That's interesting. Yeah. Wait, let me wrap. I think my brain is broke. We should maybe discuss that later after I've explained the Iximole. That's an interesting variation. But that is a really interesting variation.

And a quick comment, I don't know if you want to insert that in here, but you're looking at the, in terms of observations, you're looking at the entire, the big history, the long history of the observations. Exactly, that's very important, the whole history from birth sort of of the agent. And we can come back to that also, while this is important, you know, in RL, you have MTPs, macro decision processes, which are much more limiting.

Okay. So now, we can predict conditioned on actions, so even if the influence environment, but prediction is not all we want to do, right? We also want to act really in the world. And the question is how to choose the actions and we don't want to greedily choose the actions You know just you know what is best in in the next time step and we first I should say you know what is you know How do we measure performance so we measure performance by giving the agent reward? That's the so-called reinforcement learning framework so every step, you can give it a positive reward or negative reward.

Or maybe no reward. It could be a very scarce, right? Like if you play chess just at the end of the game, you give plus one for winning or minus one for losing. So in the IXI framework, that's completely sufficient. So occasionally you give a reward signal and you ask the agent to maximize the reward, but not greedily sort of, you know, the next one, the one, because that's very bad in the long run, if you agree, so, but over the lifetime of the agent. So let's assume the agent lives for M timestamps as they are dies in sort of 100 years, sharp. That's just, you know, the simplest model to explain. So it looks at the future, Revert Sum, and ask, what is my action sequence? Actually more precisely my policy, which leads in expectation

because I don't know the world, to the maximum river of some. Let me give you an analogy. In chess, for instance, we know how to play optimally in theory. It's just a mini-max strategy. I play the move which seems best to me under the assumption that the opponent plays the move which is best for him so best so worst for me under the assumption that he I play again the best move and then you have this expect him x3 to the end of the game and then you back propagate and then you get the best possible move. So that is the optimal strategy which for Neumann already figured out a long time ago for playing adversarial games. Luckily, or maybe unluckily for the theory, it becomes harder, the world is not always adversarial.

So it can be, if the other human's even cooperative, or nature is usually, I mean, the dead nature is stochastic, you know, things just happen randomly, or don't care about you. So what you have to take into account is a noise, and not necessarily at the ZRLT. So you replace the minimum on the opponent's side by an expectation, which is general enough to include also adversarial cases.

So now instead of a minimax strategy, you have an expected max strategy. So far, it's a good so that is well known. It's called sequential decision theory. But the question is, on which probability distribution do you base that? If I have the true probability distribution, like say I play Begamen, right? There's dice, and there's certain randomness involved. Yeah, I can calculate probabilities and feed it in the expected max or the sequential decision tree come up with the optimal decision if I have enough

compute. But in the for the real world, we don't know that, you know, what is the probability that the driver in front of me breaks? I don't know. So, it depends on all kinds of things, and especially new situations, I don't know. So, this is this unknown thing about prediction, and there's where Solomonov comes in. So, what you do is in sequential decisionry, you just replace the true distribution, which we don't know by this universal distribution. I didn't explicitly talk about it, but this is used for universal prediction and plug it into the sequential decisionry mechanism.

And then you get the best of both worlds. You have a long-term planning agent, but it doesn't need to know anything about the world because the Solomon Vinduction part learns. Can you explicitly try to describe the universal distribution and how Solomon's induction plays a role here? Yeah, let's try to understand. So what he does it, so in the simplest case, I said, take the shortest program, describing your data, run it, have a prediction which would be deterministic. Yes. Okay. But you I said, take the shortest program, describing your data, run it, have a prediction which would be deterministic. Yes.

Okay. But you should not just take the shortest program, but also consider the longer ones, but give it lower, up-reviewer probability. So in the Bayesian framework, you say up-reviewer any distribution, which is a model or a stochastic program, has a certain upper-year probability, which is 2 to the minus and y to the minus length, you know, I can explain. Lengths of this program, so longer programs are punished, upper-year, and then you multiply it

with a so-called likelihood function, which is, as the name suggests, is how likely is this model given the data at hand. So if you have a very wrong model, it's very unlikely that this model is true, so it is very small number. So even if the model is simple, it gets penalized by that. And what you do is then you take just the sum, this is the average over it. And this gives you a probability distribution. So it's a universal distribution also a lumen of distribution.

So it's weighed by the simplicity of the program and likelihood. Yes. It's kind of a nice idea. Yeah. So, okay. And then you said there's you're playing N or M or forgot the letter, it steps into the future.

So how difficult is that problem? What's involved there? Okay, so there's a optimization problem. What do we do? Yeah, so you have a planning problem up to Horizon M. And that's exponential time in the Horizon M, which is, I mean, it's computable, but interactable. I mean, even for chess, it's already interactable to do that exactly. And, you know, for go, but it could be also discounted kind of framework. Yeah, so having a heart horizon at 100 years,

it's just for simplicity of discussing the model. And also sometimes the master simple. But there are lots of variations actually quite interesting parameter. It's there's nothing really problematic about it, but it's very interesting. So for instance, you think, no, let's let's let's let the parameter m tend to infinity, right? You want an agent which lives forever, right?

If you do it, now we have two problems. First, the mathematics breaks down because you have an infinite reward sum, which may give infinity, and getting reward 0.1 in the time step is infinity, and giving reward 1 every time step is infinity, so equally good. Not really what we want. Other problem is that if you have an infinite life you can be lazy for as long as you want for 10 years and then catch up with the same expected reward and think about yourself or maybe some friends or so. If they're new, they they lived forever, why work hard now? You just enjoy your life and then catch up later. So that's another problem with the infinite

horizon. And you mentioned, yes, we can go to discounting. But then the standard discounting is so called geometric discounting. So a dollar today is about worth as much as you know one dollar and five cents tomorrow So if you do this so called geometric discounting you have introduced an effective horizon So the age is now motivated to look ahead a certain amount of time effectively. It's like a moving horizon and for any fixed effective horizon There is a problem To solve which requires larger horizon. So if I look ahead, you know, five time steps, I'm a terrible chess player, right? I'll need to

look ahead long. If I play Go, I probably have to look ahead even longer. So for every problem, now for every horizon, there is a problem which this horizon cannot solve. But I introduced the so-called near harmonic horizon, which goes down with 1 over T rather than exponentially T, which produces an agent, which effectively looks into the future, proportional to each age. So if it's 5 years old, it plans for 5 years, if it's 100 years old, it then plans for 100 years. And it's a little bit similar to humans too, right?

I mean, children don't plan. I had very long, but then we get adult, we play, I had more longer, maybe when we get very old, I mean, we know that we don't live forever. And maybe then how are rising shrinks again? So that's really so just adjusting the horizon. What is there some mathematical benefit of that of Orges is just a nice, I mean, intuitively empirically, it will probably be a good idea to sort of push the horizon back to extend the horizon as you experience more of the world, but is there some mathematical conclusions here that are beneficial? With the Lomon Hvitaxi, the prediction part would be extremely strong finite time, finite

data results. So you have so much data, then you lose so much so the deterioration is really great. With the Ixi model with the planning part, many results are only asymptotic. Which, well, this is what is asymptotic means you can prove, for instance, that in the long run, if the agent acts long enough, then you know, it performs optimal or some nice thing happens. So, but you don't know how fast it converges Yeah, so it may converge fast, but we are just not able to prove it because it's a difficult problem or maybe there's a bug

in the in the in the model so that it's really that slow yeah, so so that is what asymptotic means sort of eventually, but we don't know how fast and If I give the agent a fixed horizon M, then I cannot prove asymptotic results, right? So I mean, sort of if it dies in 100 years, then in 100 years is over, I cannot say eventually. So this is the advantage of the discounting that I can prove asymptotic results. So just to clarify, so I, okay, I made,

I've built up a model well now in a moment I've Have this way of looking several steps ahead. How do I pick what action I will take? It's like with a playing chess, right? You do this mini max in this case here Do expect the max based on the solombr of distribution? you propagate back and then, while an action falls out, the action which maximizes the future expected rewatch on the Solomon of Distribution, and then you just take this action. And then repeat.

And then you get a new observation, and you feed it in this action and observation, then you repeat. And the reward, so on. Yeah, so you're eroded too, yeah. And then maybe you can even predict your own action. I love that idea. But okay, this big framework, what is it, I mean,

it's kind of a beautiful mathematical framework to think about artificial general intelligence. What can you, what does it help you into it about how to build such systems or maybe from another perspective, what does it help us in understanding AGI? So when I started in the field, I was always interested in two things. One was in an AGI, the name didn't exist then, what kind of generally I or strong AI.

And physics here everything. So I switched back and forth between computer science and physics quite often. You said the theory of everything. The theory of everything here, there's a link. There's basically these problems before all humanity. Yeah, I can explain if you wanted some later time, you know, why I'm interested in these two questions. Cassley, and a small tangent. If, if, uh, if one to be, it was one to be solved, which one would you?

If one, if you were, if an apple fell in your head, and there was a brilliant insight, and you could arrive at the solution to one, would it be AGI or the theory of everything? Definitely AGI because once the AGI problem solved, I can ask the AGI to solve the other problem for me. Yeah, brilliant. I put it. Okay. So, as you were saying about it. Okay, so, and the reason why I didn't settle, I mean, this thought about, you know, once you've solved AGI, it solves all kinds of other, not just the theory of every problem, but all kinds of useful, more useful problems to humanity is very appealing to many people. And, you know, I think so also, but I was quite disappointed with the state of the art

of the field AI. There was some theory about logical reasoning, but I was never convinced that this will fly. And then there was this homo-horistic approaches with neural networks, and I didn't like these heuristics. So, and also I didn't have any good idea myself. So that's the reason why I took it back and forth quite

some violent invoices for a couple of years and a company developing software or something completely unrelated. But then I had this idea about the Ixi model. What it gives you, it gives you a gold standard. I have proven that this is the most intelligent agents which anybody could build in quotation mark because it's just mathematical and you need infinite compute. But this is the limit.

And this is completely specified. It's not just a framework. And every year, tens of frameworks are developed, which are skeletons and then pieces are missing and usually this missing pieces turn out to be really, really difficult. And so this is completely and uniquely defined. And pieces are missing and usually this missing pieces turn out to be really, really difficult. And so this is completely and uniquely defined.

And we can analyze that mathematically. And we've also developed some approximations. I can talk about that a little bit later. That would be sort of the top down approach, like say for Neumann's Minimax theory, that's the theoretical optimal play of games. And now we need to approximate it, put the risks in, prune the three blah blah blah and so on. So we can do that also with the Iximole model, but for generally high, it can also inspire those and most of most researchers go bottom up, right?

They have their systems that try to make it more general, more intelligent. It can inspire in which direction to go. What do you mean by that? So if you have some choice to make, right? So how should I evaluate my system if I can't do cross validation? How should I do my learning if my standard regularization doesn't work well? Yeah. So the answer is always this, we have a system which does everything that's

I see. It's just, you know, completely in the ivory ivory tower completely useless from a practical point of view. But you can look at it and see, ah, yeah, maybe, you know, I can take some aspects. And, you know, instead of Kolmogorov complexity, they just take some compressors which has been developed so far. And for the planning, well, we have UCT, which has also, you know, been used and go. And it at least it inspired me a lot to have this formal definition. And if you look at other fields, you know, like I always come back to physics because I was a physics background, think about the phenomena of energy. That was a long time, a mysterious concept. And at some point it was completely formalized and that really helped a lot and

you can point out a lot of these things which were first mysterious and awake and then they have been rigorously formalized. Speed and acceleration has been confused, right, until it was formally defined, there was a time like this. And people, you know, often, you know, who don't have any background, you know, still confuse it. So, and this Ixy model or the intelligence definitions, which is sort of the dual to it, we come back to that later, formalizes the notion of intelligence uniquely and rigorously. So in a sense, it serves as kind of the light at the end of the tunnel. So for, yeah.

I mean, there's a million questions I could ask her. So maybe kind of, okay, let's feel her out in the dark a little bit. So, there's been here a deep mind, but in general, been a lot of breakthrough ideas, just like we've been saying, around reinforcement learning. So how do you see the progress in reinforcement learning is different? Like, which subset of IACE does it occupy the current, like you said, maybe the mark of assumptions made quite often in reinforcement learning, the other assumptions made in order to make the system work.

What do you see as the difference connection between reinforcement reinforcement learning in IACC. So the major difference is that essentially all other approaches, they make strong assumptions. So in reinforcement learning, the Markov assumption is that the next state or next observation only depends on the previous observation and not the whole history, which makes of course the mathematics much easier rather than dealing with histories. Of course, they profit from it also because then you have algorithms that run on current computers and do something practically useful. But for generally, I, all the assumptions which are made by other approaches, we know already now they are limiting.

So, for instance, usually you need a godicity assumption in the mdp framework in order to learn. I got this essentially means that you can recover from your mistakes and that they are not traps in the environment. And if you make this assumption, then essentially you can go back to a previous state, go there a couple of times, and then learn what statistics and what the state is like and then in the long run perform well in this state, but there are no fundamental problems. But in real life we know there can be one single action, one second of being inattentive while driving a car

fast, you know, can ruin the rest of my life, I can become quite replete you or whatever. So there's no recovery anymore. So the real world is not ergodica or we say, you know, there are traps and there are situations where you are not recovered from. And very little theory has been developed for this case. What about what do you see in the context of IACC as the role of exploration? Sort of, you mentioned, you know, in the real world, and get into trouble

when we make the wrong decisions and really pay for it, but exploration seems to be fundamentally important for learning about this world, for gaining new knowledge. So is exploration baked in? Another way to ask it, what are the parameters of this of IACC that can be controlled? Yeah, I say the good thing is that there are no parameters to control. Some other people try to control and you can do that. I mean, you can modify IACC so that you have some knobs to play with if you want to. But the exploration is directly baked in.

And that comes from the Bayesian learning and the long-term planning. So these together already imply exploration. You can nicely and explicitly prove that for simple problems like so-called bandit problems where you say to give a real word example say you have two medical treatments, A and B, you don't know the effectiveness, you try A a little bit, B a little bit, but you don't want to harm too many patients, so you have to sort of trade of exploring and at some point you want to explore and you can do the mathematics and figure out the

optimal strategy. It took a Bayesian agent, also non-B Bayesian agents but it shows that this Bayesian framework by taking a prior or possible worlds during the Bayesian mixture, then the base optimal decision with long term planning that is important automatically implies exploration also to the proper extent, not too much exploration and not too little. In this very simple settings, in the Ixi model I was also able to prove that it is a self-optimizing theory or asymptotic optimality themes, although it only asymptotic not finite time bounds.

So it seems like the long-term planning is a really important, but the long-term part of the plan is really important. And also, maybe a quick tangent, how important do you think is removing the mark of assumption and looking at the full history? Sort of intuitively, of course, it's important, but is it fundamentally transformative

to the entirety of the problem? What's your sense of it? Because we make that assumption quite often. It's just throwing away the past. Now, I think it's absolutely crucial. The question is whether there's a way to deal with it in a more holistic and still sufficiently well-waved.

So I have to come up with an example and fly, but you know, you have some key event in your life, you know, long time ago, you know, in some city or something, you realize, you know, that's a really dangerous street or whatever, right? Yeah. And you want to remember that forever, right? In case you come back there, kind of a selective kind of memory. So you remember all the important events in the past, but somehow selecting the important, is it is very hard. Yeah. And I'm not concerned about, you know, just storing the whole history, just you can calculate, you know, human life says, sorry, 100 years doesn't matter, right? How much data comes in through the vision system

and the auditory system, you compress it a little bit, in this case, lossily, and store it. We are soon in the means of just storing it. But you still need to dis-election for the planning part and the compression for the understanding part. The raw storage, I'm really not concerned about. And I think we should just store if you develop an agent, preferably just just store all the interaction history.

And then you build of course models on top of it and you compress it and you are selective, but occasionally you go back to the old data and re-analyze it based on your new experience you have. Sometimes you're in school, you learn all these things, you think it's totally useless and you know much later you read us, aren't they? But not, you know, it's so useless as you thought. I'm looking at you in your algebra. Right. So maybe let me ask about objective functions because that rewards. It seems to be an important part. The rewards are kind of given to the system. For a lot of people, the specification of the objective function is a key part of intelligence.

The agent itself figuring out what is important. What do you think about that? Is it possible within NICC framework to yourself discover that a word based on which you should operate? Okay, that will be a long answer. So, and that is a very interesting question and I'm asked a lot about this question, where do the rewards come from? And that depends, yeah. So, and I'll give you now a couple of answers. So, if we want to build agents, now let's start simple. So, let's assume we want to build an, now let's start simple. So let's assume we want to build an agent

based on the IXI model, which performs a particular task. Let's start with something super simple, like I mean super simple, like playing chess, or go or something, yeah. Then you just, you know, the reward is, you know, winning the game is plus one, losing the game is minus one done.

You apply this agent, if you have enough compute, you let itself play, and it will learn the rules of the game is plus one, losing the game is minus one, done. You apply this agent, if you have enough compute, you let itself play and it will learn the rules of the game, will play perfect chess after some while, problem solved. So if you have more complicated problems, then you may believe that you have the right reward, but it's not. So a nice, cute example is the elevator control. There is also in Rich Sutton's book, which is a great book, by the way. So you control the elevator and you think, well, maybe the reward should be coupled to how long people wait in front of the elevator. You know, a long way to spare.

You program it and you do it. And what happens is the elevator eagerly picks up all the people but never drops them off. So you realize that maybe the time in the elevator also counts. So you minimize the sum. Yeah. And the elevator does that, but never picks up the people in the 10th floor and the top floor because in expectation, it's not worth it. Just let them stay. growth, just let them stay. So, so even in apparently simple problems, you can make mistakes. Yeah, and that's what in our serious context, say, ag, I say, if you research, just consider. So now let's go back to general agents.

So assume we want to build an agent which is generally useful to humans. Yeah, so you have a household robot, yeah robot and it should do all kinds of tasks. So in this case, the human should give the reward on the fly. I mean, maybe it's pre-trained in the factory and that there's some sort of internal reward for the battery level or whatever. But so it does the dishes badly. You punish the robot, it does it good, you revert the robot and then train it to a new task, you know, you punish the robot, you know, does it good, you revert the robot and then trying to do a new task, you know, like a child, right?

So you need the human in the loop. If you want a system, which is useful to the human, and as long as this agent stays sub-human level, that should work reasonably well, apart from, you know, these examples. It becomes critically if they become, you know, on a human level. It's like, Mr. Children, small children, you have a reason to be well under control. They become older. The reward technique doesn't work so well anymore. So then finally, so this would be agents which are just, you could say slaves to the humans, yeah. So if you are more ambitious and just say we want to build a new space of intelligent

beings, we put them on a new planet and we want them to develop this planet or whatever. So we don't give them any reward. So what could we do? And you could try to come up with some reward functions like it should maintain itself the robot, it should maybe multiply, build more robots, right? And you know, maybe, well, all kinds of things that you find useful, but that's pretty hard, right? You know, what, what does self maintenance mean? You know, what does it mean to build a copy? Should it be exact copy on approximate copy? And so that's really hard, but, um, Laurent also also a deep mind, deep mind developed a beautiful model. So it just took the Ixi model and coupled the rewards to information gain. So he said the reward is proportional to how much the agent had learned about the world.

And you can rigorously formally, uniquely define that in terms of other versions. So if you put that in, you get a completely autonomous agent. And actually, interestingly, for this agent, we can prove much stronger result than for the general agent, which is also nice. And if you let this agent lose, it will be, in a sense, the optimal scientist.

This is absolutely curious to learn as much as possible about the world. And of course, it will also have a lot of instrumental goals, in order to learn, it needs to at least survive, right? That agent is not good for anything. So it needs to have self-preservation. And if it builds small helpers acquiring more information, it will do that, yeah, if exploration, space exploration or whatever is necessary, right? To gathering information and develop it. So it has a lot of instrumental goals falling on this information gain.

And this agent is completely autonomous of us. No rewards necessary anymore. Yeah, of course, you could find a way to game the concept of information and get stuck in that library that you mentioned beforehand with a very large number of books. The first agent had this problem, and it would get stuck in front of an old TV screen because it has a wide noise. The second version can deal with at least stochasticity. What about curiosity, this kind of word, curiosity, creativity,

What about curiosity, this kind of word, curiosity, creativity? Is that kind of the reward function being of getting new information? Is that similar to idea of kind of injecting exploration for its own sake inside the reward function? Do you find this at all appealing? Interesting. I think that's a nice definition. Curiosity is a reward. Sorry, curiosity is exploration for its own sake. Yeah, I would accept that, but most curiosity, while in humans and especially in children, yeah, is not just for its own sake, but for actually learning about the environment and for behaving

sake but for actually learning about the environment and for behaving better. So I think most curiosity is tied in the end to what's performing better. Well okay, so if intelligent systems need to have this reward function, let me, you're an intelligent system, currently passing the torrent test quite effectively. What's the reward function of our human intelligence existence? What's the reward function that Marcus Hunter is operating under? Okay, to the first question, the biological reward function is to survive and to spread and very few humans are able to overcome this biological reward function. survive into spread and very few humans are able to overcome this biologically reward function. But we live in a very nice world where we have lots of spare time

and can still survive and spread, so we can develop arbitrary other interests, which is quite interesting on top of that. But the survival and spreading sort of is I would say the goal or the reward function of humans that the core one. I like how you avoided answering the second question, which a good intelligence said I would. So my, the your own meaning of life and reward function. My own meaning of life and reward function is to find an AGI to build it. Beautiful. But, okay, let's dissect that X even further. So one of the assumptions is kind of infinity keeps creeping up everywhere.

Which, what are your thoughts on kind of bounded rationality and sort of the nature of our existence and intelligent systems is that we're operating those under constraints under you know limited time, limited resources, how does that, how do you think about that within the IxI framework within trying to create an AGI system that operates under these constraints? Yeah, that is one of the criticisms about IXE that ignores computation uncompletely and some people believe that intelligence is inherently tied to what's bounded resources. What do you think on this one point? Do you think it's the, do you think the bounded research is fundamental to intelligence?

I would say that an intelligence notion which ignores computational limits is extremely useful. A good intelligence notion, which includes this resources would be even more useful, but we don't have that yet. And so look at other fields, outside of computer science. Computational aspects never play a fundamental role. You develop biological models for cells, something in physics,

these theories, I mean, become more and more crazy and harder and harder to compute. Well, in the end, of course, we need to do something with this model, but this more nuisance than a feature. And I'm sometimes wondering if artificial intelligence would not sit in a computer science department but in a philosophy department, then this computational focus would be probably significantly less.

I mean, think about the induction problem is more in the philosophy department. There's usually no paper who cares about, you know, how long it takes to compute the answer. That is completely secondary. Of course, once we have figured out the first problem, so intelligence without computational resources, then the next and very good question is, could we improve it by including computational resources, but nobody was able to do that so far, even halfway satisfactory manner. I like that. That's in the long run, the right department to belong to is philosophy. It's actually quite a deep idea, or even to at least just think about big picture-phosophil questions, big picture questions, even in the computer science department. But you've mentioned approximation.

So there's a lot of infinity, a lot of huge resources needed. Are there approximations to IACC that within the IACC framework that are useful? Yeah, we have to develop a couple of approximations. And what we do there is that the Solomov induction part, which was find the shortest program describing your data, which just replaces by standard data compressors. And the better compressors get, the better this part will become.

We focus on a particular compressor called context-free waiting, which is pretty amazing, not so well-known. It has beautiful theoretical properties, also works reasonably well in practice. So we used that for the approximation of the induction and the learning and the prediction part. And for the planning part, we essentially just took the ideas from a computer girl from 2006. It was Java,

CPS, Paris, also now I deep mind, who developed the so-called UCT algorithm, upper confidence bound for trees algorithm, top of the Monte Carlo tree search, so we approximate this planning part by sampling. And it's successful on some small toy problems. We don't want to lose the generality, right? And that's sort of the handicap, right? If you want to be general, you have to give up something. So, but this single agent was able to play, you know, small games like Coon Poker and Tik Tok Toe and even Pac-Man.

And to the same architecture, no change. The agent doesn't know the rules of the game. There's nothing at all by player with these environments. So, here's an instrument who will propose something called Gatorn Machines, which is a self-improving program that rewrites its own code. It's sort of mathematically, philosophically, what's the relationship in your eyes if you're

familiar with it between IX and the Gator Machines? Yeah, familiar with it, he developed it while I was in his lab. So the Gator Machines explained it briefly. You give it a task. It could be a simple task as you know, finding prime factors in numbers, right? You can formally write it down. There's a very slow algorithm to do that, just to try all the factors, yeah?

Or play chess, right? Optimally, you write the algorithm to minimax to the end of the game, so you write down what the girl machine should do. Then it will take part of its resources to run this program and other part of its sources to improve this program. And when it finds an improved version which provably computes the same answer, so that's the key part. It needs to prove by itself that this change of program still satisfies the original specification.

And if it does so, then it replaces the original program by the improved program. And by definition, it does the same job, but just faster. And then it proves over it and over it. And it's developing a way that all parts of this good machine can self-improve, but it stays provably consistent with the original specification. So, from this perspective, it has nothing to do with IxC. But if you would now put IxC as the starting axioms in,

it would run IxC, but you know, that takes forever. But then if it finds a provable speed up of IxC, it would replace it by this and like this and this and maybe eventually it comes up with a model which is still the IxC model. It cannot be, I mean just for the knowledgeable reader, IxC is incomputable and I can prove that therefore there cannot be a computable exact algorithm compute is there needs to be some approximations and this is not dealt with the goodle machine. So you have to do something about it. But there's the ICTL model which is finally computable, which we could put in which part of

IX is a non-computable. There's so long one of induction part. Yeah, actually. Okay. So, but there is ways of getting computable approximations of the Ixi model. So then it's at least computable. It is still way beyond any resources anybody will ever have. But then the girdle machine could sort of improve it further in an exact way. So is this theoretically possible that the the the Gural machine process could improve? Isn't isn't isn isn't actually already optimal?

It is optimal in terms of the reward collected over its interaction cycles, but it takes infinite time to produce one action. And the world, you know, continues whether you want it or not, yeah. So the model is assuming had an Oracle which, you know, solved this problem and then in the next 100 milliseconds or the reaction time you need gives the answer, then Ix is optimal.

So it's optimally in sense of date, also from learning efficiency and data efficiency, but not in terms of computation time. And then the guy on the machine in theory, but probably not provably could make it go faster. Yes. OK. And those two components are super interesting.

The perfect intelligence combined with self-improvement, sort of provable self-improvement, since you're always getting the correct answer in your approving. Beautiful ideas. Okay, so you've also mentioned that different kinds of things in the chase of solving this reward, sort of optimizing for the goal, interesting human things could emerge. So is there a place for consciousness with an IACI?

Where does maybe you can comment because I suppose we humans are just another Instunciation by X agents and we seem to have consciousness. You say humans are an instantiation of an IACI agent. Yes Oh, that would be amazing, but I think that's not even for the smartest and most rational humans. I think maybe we have very crude approximations. Interesting. I mean, I tend to believe, again, I'm Russian. So I tend to believe our flaws are part of the optimal. So the we tend to laugh off and criticize our flaws and I tend to think that that's actually close to optimal behavior But some flaws if you think more carefully about it are actually not flaws. Yeah, but I think they are still enough flaws I don't know. It's unclear as a student of history. I think all the suffering that we've endured is a civilization

It's possible that that's the optimal amount of suffering we need to endure to minimize long-term suffering. That's your Russian background, aren't we? That's the Russian. Whether humans are or not instantiations of an AXI agent, do you think there's consciousness of something that could emerge in a computational form of framework like IXC. Did you also ask your question, do you think I'm conscious?

That's a good question. That tie is confusing me, but I think that makes me unconscious because it strangles me or if an agent were to solve the imitation game posed by touring, I think that would be dressed similarly to you, that because there's a kind of flamboyant, interesting, complex behavior pattern that sells that you're human, you're conscious. But why do you ask? Was it a yes or was it a no? Yes, I think you're conscious. But why do you ask? Was it a yes or was it a no? Yes, I think you're conscious, yes.

So, and you explain somehow why. But you infer that from my behavior, right? You can never be sure about that. And I think the same thing will happen with any intelligent agent we develop. If it behaves in a way sufficiently close to humans, or maybe if not humans, I mean, you know, maybe a dog is also sometimes a little bit self-conscious, right? So if it behaves in a way where we attribute typically consciousness, we would attribute

consciousness to these intelligent systems and, you know, actually probably in particular, that of course doesn't answer the question whether it's really conscious. And that's and, you know, I see probably in particular, that of course doesn't answer the question whether it's really conscious. And that's the, you know, the big hard problem of consciousness, you know, maybe I'm a zombie, I mean, not the movie zombie, but the philosophical zombie. It's to you, the display of consciousness close enough to consciousness from a perspective of AGI that the distinction of the heart problem of consciousness is not an interesting one.

I think we don't have to worry about the consciousness problem, especially the heart problem for developing AGI. I think, you know, we progress at some point we have solved all the technical problems and this system will behave intelligent and then super intelligent and this consciousness will emerge. I mean, definitely it will display behavior which we will interpret as conscious. And then it's a philosophical question, did this consciousness really emerge or is it a zombie which just you know fakes everything? We still don't have to figure that out although it may be interesting, at least from a philosophical point of view figure that out. Although it may be interesting, at least

from a philosophical point of view, it's very interesting, but it may also be sort of practically interesting. You know, there's some people saying, you know, if it's just fake in consciousness and feelings, you know, then we don't need to have to be concerned about, you know, rights, but if it's real conscious and has feelings, then we need to be concerned. I can't wait till the day where AI systems exhibit consciousness because it'll truly be some of the hardest ethical questions I would do with that. It is rather easy to build systems

which people ask for consciousness. And I give you an analogy. I mean, remember, maybe it must be before you were born the time of Gocchi. Yeah. We could born a deri sir. Why, that's the, yeah. I mean, remember, maybe it must be before you were born the Tamagotchi. Frick of a boy. How dare you, sir. Why, that's the... Yeah, but you're young, right?

Yes, that's a good thing. Yeah, thank you. Thank you very much. But I was also in the Soviet Union. We didn't have... We'd never knew those fun things. But you have heard about this Tamagotchi, because, you know, really, really primitive, actually, for the time it was...

And, you know, you could race, you know, this... And actually, for the time it was, and you could raise this, and kids got so attached to it and didn't want to let it die. If we would have asked the children, do you think this is tomogot, this conscious? They would have a beautiful thing, actually, because that consciousness, ascribing consciousness, beautiful thing actually, because that consciousness, a scribing consciousness, seems to create a deeper connection, which is a powerful thing. But we'll have to be careful on the ethics side of that. Well, let me ask about the AGI community broadly.

You kind of represent some of the most serious work on AGI as of at least earlier in deep mind, represents serious work in AGI these days. But why in your sense is the AGI community so small or has been so small until maybe deep mind came along? Like why aren't more people seriously working on human level and superhuman level intelligence from a formal perspective. Okay, from a formal perspective, that sort of, you know, an extra point. So I think there are a couple of reasons. I mean AI came in waves, right? You know, AI winters, AI summers, and then there were big promises which were not fulfilled. And people got disappointed, but narrow AI solving particular problems, which seemed to require intelligence, was always to some extent successful and there were improvements, small steps.

And if you build something which is useful for society or industrial useful, then there's a lot of funding. So I guess it was in parts of the money, which drives people to develop specific systems solving specific tasks. But you would think that, you know, at least in university, you should be able to do ivory tower research. And that was probably a better long time ago, but even nowadays there's quite some pressure of doing applied research or translational research and harder to get grants as a theorist. So that also drives people away. It's maybe also harder attacking the general intelligence problem.

So I think enough people, I mean, maybe a small number, we're still interested in formalizing intelligence and and thinking of general intelligence, but you know, not much came up, right or not not much great stuff came up. So what do you think we talked about the formal big? Light at the end of the tunnel, but from the engineering perspective, what do you think it takes to build an AGI system? Is it, and I don't know if that's a stupid question, or a distinct question from everything we've been talking about, IAXE, but what do you see as the steps that are necessary to take to start to try to build something?

So you want to blueprint now and then you go up and do it? It's the whole point of this conversation, trying to squeeze that in there. Now, is there, I mean, what's your intuition? Is it, is it in the robotic space or something that has a body and tries to exploit the world? Is it in the reinforcement learning space? Like the effort to the Alpha Zero and Alpha Star, they're kind of exploring how you can solve it through in the simulation in the gaming world? Is there stuff in sort of the other transformer,

work in natural language processing, sort of maybe attacking the open domain dialogue? Like, what do you see in promising pathways? Let me pick the embodiment maybe. So embodiment is important, yes and no. I don't believe that we need a physical robot walking or rolling around interacting with the real world in order to achieve AGI. in order to achieve AGI. And I think it's more of a distraction probably than helpful. It's sort of confusing the body with the mind.

For industrial applications or near-term applications, of course we need robots for all kinds of things, but for solving the big problem, at least at this stage, I think it's not necessary. But the answer is also yes, that I think the most promising approach is that you have an agent, and that can be a virtual agent, you know, you know, a computer interacting with an environment, possibly, you know, a 3D simulated environment, like in many computer games and you train and learn the agent. Even if you don't intend to later put it sort of, you know, this algorithm in a robot brain and leave it forever in

the virtual reality, getting experience in a, although it's just simulated 3D world is possibly and as I possibly, important to understand things on a similar level as humans do, especially if the agent or primarily if the agent needs to interact with the humans, right? If you talk about objects on top of each other in space and flying in cars and so on, and the agent has no experience with even virtual 3D worlds. It's probably hard to grasp. So if you develop an abstract agent, say we take the mathematical path

and we just want to build an agent which can prove theorems and becomes a better and better mathematician, then this agent needs to be able to reason in very abstract spaces. And then maybe sort of putting it into 3D environments in a related note is even harmful. It should sort of, you put it in, I don't know,

an environment which it creates itself or so. It seems like you have an interesting, rich, complex trajectory through life in terms of your journey of ideas. So it's interesting to ask what books, technical fiction, philosophical books, ideas, people had a transformative effect. Books are most interesting because maybe people could also read those books and see if they could be inspired as well.

Yeah, luckily, there are books and not singular books. It's very hard and I try to pin down one book. And I can do that at the end. So the most, the books which were most transformative for me or which I can most highly recommend to people interested in AI. Both perhaps. I would always start with Russell and Norvik, Artificial Intelligence, a modern approach. That's the AI Bible. It's an amazing book. It's very broad. It covers, you know, all approaches to AI. And even if you focus on one approach, I think that is the minimum you should know about the other approaches out there. So that should be your first book. Fourth edition should be coming out soon. Oh, okay, interesting. There's a deep learning chapter now, so there must be written by Ian Goodfellow.

Okay. And then the next book I would recommend, the reinforcement only book by Satin and Bartol. There's a beautiful book. If there's any problem with the book, it makes RL feel and look much easier than it actually is. It's very gentle book, very nice to read and exercise. You can very quickly, you know, get some RL systems to run, you know, and very toy problems, but it's a lot of fun and you very in a couple of days you feel feel you know, you know what I realize about, but it's much harder than the book.

Yeah. It's come on now. It's an awesome book. Yeah. No, it is. Yeah. And maybe, I mean, there's so many books out there. If you like the information theoretic approach, then there's Konmogolf complexity by Lee and Vitani, but probably

you know, some short article is enough. You don't need to read a whole book, but it's a great book. And if you have to mention one all-time favorite book, it's a different flavor. That's a book which is used in the international baccalaureate for high school students in several countries. That's from Nicholas Alchen, Theory of Knowledge. Second edition, or first, not the third, please. The third one, they took out all the fun. So this asks all the interesting,

or to me, interesting philosophical questions about how we acquire knowledge from all perspectives, from art, from physics and ask how can we know anything. A book is called Theory of Knowledge. From which is this almost like a philosophical exploration of how we get knowledge from anything? Yes, I mean can religion tell us you know about something about the world? Can science tell us something about the world? Can mathematics, so is it just playing with symbols? And you're in this open-ended questions. And I mean, it's for high school students, so they have 10 resources from Hikers, Guy to the Galaxy, and from Star Wars, and the chicken crossed the road. And it's fun to read,

and but it's also quite deep. If you could live one day of your life over again, because it made you truly happy, or maybe like we said with the books, it was truly transformative. What day, what moment would you choose? Does something pop into your mind? Does it need to be a day in the past or can it be a day in the future? Well, space time is an emergent phenomena, so it's all the same anyway. Okay.

Okay, from the past, you're really good at saying from the future. I love it. No, I will tell you from the future. From the past, I would say when I discovered my axiomodel, I mean, it was not in one day, but it was one moment where I realized Commodore of complexity and didn't even know that it existed, but I discovered sort of this compression idea myself, but immediately I knew I can't be the first one, but I had this idea. And then I knew about

sequential decisionary, and I knew if I put it together, this is the right thing. And yeah, I still still been thinking back about this moment. I'm super excited about this. Was there any more details and context at that moment in Apple falling your head? So if you look at Ian Goodfell talking about Gans, there was beer involved. Is there some more context of what sparked your thought?

Was it just that? No, it was much more mundane. So I worked in this company. So in this sense, the 4.5 years was not completely wasted. So and I worked on an image interpolation problem. And I developed a quite neat new interpolation techniques and they got patented. And then I, you know, which happens quite often, I got sort of overboard and thought about, you know, yeah, that's pretty good, but it's not the best. So what is the best possible way of doing in the interpolation? And then I thought, yeah, you want a simple picture, which is if you coarse-grant recovers your original picture and then I thought about this simplicity concept more in quantitative terms and then everything developed.

And somehow the full beautiful mix of also being a physicist and thinking about the big picture of it then led you to probably the big would I. Yeah, yeah. So as a physicist I was probably trained not to always think in computational terms, you know, just ignore that and think about the fundamental properties which you want to have. So what about if you could really one day in the future? All day. Well, what would that be? When I solved the AGI problem. I don't know. In practice. In practice. So in theory, I have solved it with Ixi model by the practice. And then I asked the first question. What would be the first question? What's the meaning of life? I don't think there's

a better way to end it. Thank you so much for talking today as a huge honor to finally meet you. Yeah, thank you, too. I was a pleasure of mindset, too. Thanks for listening to this conversation with Marcus Hunter. And thank you to our pleasure of my side too. If you enjoy this podcast, subscribe on YouTube, give it 5 stars and Apple podcasts, support it on Patreon or simply connect with me on Twitter at Lex Friedman. And now let me leave you with some words of wisdom from Albert Einstein. The measure of intelligence is the ability to change. Thank you for listening and hope to see you next time. you