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Feb. 26, 2020 - Lex Fridman Podcast

01:39:41

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

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	The following is a conversation with Marcus Hodder, senior research scientist at Google DeepMind.
	Throughout his career of research, including with Jürgen Schmidt-Huber and Shane Legge, he has proposed a lot of interesting ideas in and around the field of artificial general intelligence.
	Including the development of AIXI, spelled A-I-X-I model, which is a mathematical approach to AGI that incorporates ideas of Kalmogorov complexity, Solomonov induction, and reinforcement learning.
	In 2006, Marcus launched the 50,000 Euro 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 one 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 compressor works relative to the previous 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'm 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 on 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 can break the flow of the conversation.
	I hope that works for you and doesn't hurt the listening experience.
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	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 why do you think, just like you said, general relativity, quantum field theory, why 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?
	Our 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 simple and described by these equations.
	And we're not just picking that.
	I mean, if there were some phenomena 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 emergent phenomena.
	And, you know, 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 atoms or, well, parallel universes 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 simple street consistent with it.
	But also it's a little bit self-referential.
	Yeah. So, maybe a quick pause.
	What is Occam's Razor? So, Occam'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 theories or hypotheses 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. 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 likelier to be more correct, descriptor of whatever we're talking about?
	I believe that there comes razor is Probably the most important principle in science.
	I mean, of course, we lead logical deduction and 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, you know, explain everything but predict nothing.
	But the simple model seemed to have predictive power.
	And it's a valid question.
	Why? 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 Occam's razor.
	And if we start with the 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 terms of somnolom deduction, you can rigorously prove that.
	If you assume that the world is simple, then Occam's razor is the best you can do in a certain sense.
	I apologize for the romanticized question, but why do you think, outside of its effectiveness, why do you think we find simplicity so appealing as human beings?
	Why does E equals MC 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 evolutionary and necessary.
	But with this beauty and simplicity, it's, I 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 noise, and there is a tiger, right, and eats 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 indeed, in terms of just for survival purposes, there is an evolutionary argument for why we find the work of Einstein so beautiful.
	Maybe a quick small tangent.
	Could you describe what Solomon of induction is?
	Yeah, so that's a theory which I claim, and Reza Lomanoff sort of claimed a long time ago, that this solves the big philosophical problem of induction.
	And I believe 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.
	So prediction is also part of the induction.
	So I'm a little bit sloppy sort of with the terminology and maybe that comes from Ray Solomonov, 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 11111 and you see if 100 ones.
	What do you think comes next?
	The natural answer, I'm going to speed up a little bit.
	The natural answer is, of course, one.
	And the question is, why?
	Well, we see a pattern there.
	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.
	And now the question is, a model has to be presented in a certain language.
	In which language do we use?
	In science, we want formal languages, and we can use mathematics, or we can use programs on a computer, so abstractly on a Turing machine, for instance, or it can be a general-purpose computer.
	And there are, of course, lots of models.
	You can say maybe it's 100 ones, and then 100 zeros, and 100 ones.
	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 it 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 one, two, three, four, five.
	What comes next? The short program is again, you know, a counter.
	And so that is, roughly speaking, how Solomov 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 Solomanov induction, precisely what you do is, so you combine, so looking for the shortest program is like applying Opus Razor, like looking for the simplest theory.
	There's also Epicurus principle, which says if you have multiple hypotheses, which equally well describe 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 Bayesian technique.
	You have a prior, which is precisely two to the minus the complexity of the program.
	And you weigh all this hypothesis and take this mixture, and then you get also the stochasticity in.
	Yeah, like many of your ideas, that's just a beautiful idea of weighing based on the simplicity of the program.
	I love that. That seems to me maybe a very human-centric concept.
	It 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 already explained it.
	So compression means, for me, finding short programs for the data or the phenomenon at hand.
	You could interpret it more widely as finding simple theories, which can be mathematical theories, or maybe even informal, like just in words.
	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 on 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 an endeavor of compression, not all of humanity, maybe.
	And, well, there are also some other aspects of science, like experimental design, right?
	I mean, we create experiments specifically to get extra knowledge, and that isn't 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 Kalmogorov complexity.
	So in your sense, do most objects in our mathematical universe have high Kalmogorov complexity?
	And maybe what is, first of all, what is Kalmogorov complexity?
	Kolmogorov 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 on a computer and best sort of, you know, just a string of bits.
	And we have data compressors, like we compress big files into, say, zip files with certain compressors.
	And you can also produce self-extracting archive.
	That means as an executable, if you run it, it reproduces your original file without needing an extra decompressor.
	It's just a decompressor plus the archive together in one.
	And now there are better and worse compressors.
	And you can ask, what is the ultimate compressor?
	So what is the shortest possible self-extracting archive you could produce for a certain dataset, which reproduces the dataset?
	And the length of this is called the Kolmogorov complexity.
	And arguably, that is the information content in the dataset.
	I mean, if the dataset is very redundant or very boring, you can compress it very well, so the information content should be low, and it is low according to this definition.
	So it's the length of the shortest program that summarizes the data?
	Yes. And what's your sense of our universe when we think about the different The different objects in our universe, concepts or whatever, at every level, do they have high or low Kolmogorov complexity?
	So what's the hope? Do we have a lot of hope in being able to summarize much of our world?
	That's a tricky and difficult question.
	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. To get the thing going and then it will reproduce our universe.
	There's a problem with noise.
	We can come back to that later, possibly.
	Is noise 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 without noise, we wouldn't need all of the statistics.
	But then maybe we wouldn't feel like there's a free will.
	Maybe we need that for the...
	This is an illusion that noise can give you free will.
	At least in that way, it's a feature.
	But also, if you don't have noise, you have chaotic phenomena, which are effectively like noise.
	So we can't, you know, get away with statistics even then.
	I mean, think about rolling a dice and, you know, 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, you know, as, you know, coming out this...
	A number with probability 1 over 6.
	But from this set of philosophical Kolmogorov complexity perspective, if we didn't have noise, then arguably you could describe the whole universe as, well, as a standard model plus generativity.
	I mean, we don't have a theory of everything yet, but sort of assuming we are close to it or have it, 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 with just a subset, just take planet Earth.
	Planet Earth cannot be compressed 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, It may become complex and that may be counterintuitive, but there's a very nice analogy, the library of all books.
	So imagine you have a normal library with interesting books and you go there, great, lots of information and quite complex.
	So now I create a library which contains all possible books, say, of 500 pages.
	So the first book just has A, A, A, A over all the pages.
	The next book A, A, A 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 suddenly you 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 sort of the game of life or cellular automata where you start with the simple rules just like you're describing with the 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, it could die out in some very rigid structures.
	Do you have a sense about cellular automata that somehow transfers maybe to the bigger questions of our universe?
	The Cellular Automata and especially the Conway's Game of Life is really great because these rules are so simple.
	You can explain it to every child and even by hand you can simulate a little bit.
	And you see these beautiful patterns emerge and people have proven that it's even too incomplete.
	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 is chemistry and biology so rich?
	I mean, this can't be based on simple rules.
	But no, we know quantum electrodynamics describes all of chemistry.
	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 I understand this phenomenon.
	It's probably not.
	And there's this saying, you never understand really things, you just get used to them.
	I think we're pretty used to cellular automata.
	So you believe that you understand now why this phenomenon happens.
	But I'll give you a different example.
	I didn't play too much with Conway's Game of Life, but a little bit more with fractals and with the Mandelbrot set and these beautiful patterns.
	Just look Mandelbrot set.
	And, well, when the computers were really slow and I just had a black and white monitor and programmed my own programs in Assembler, too.
	Assembler, wow. Wow.
	You're legit. To get these fractals 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 tried to... Derive the locations, you know, there are these circles and the apple shape.
	And then you have smaller Mandelbrot sets recursively in this set.
	And there's a way to mathematically, by solving high order 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 appears.
	Do you think it's possible?
	What's your intuition? Do you think it's possible to reverse engineer and find the 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, you know, any data set, you know, you take these fractals or you take whatever your data set, whatever you have, say a picture of Conway's Game of Life, and you run through all programs.
	You take a program size one, two, three, four, and all these programs, run 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 output, 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 the shortest program because there could be an even shorter program, which is just even slower, I mean, you just have to wait, yeah?
	But asymptotically, and actually after finite time, you have the shortest program.
	So this is a theoretical but completely impractical way of finding the underlying structure in every dataset, and that is what Solomov induction does and Kolmogorov complexity.
	In practice, of course, we have to approach the problem more intelligently.
	And then If you take resource limitations into account, there's, for instance, 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 for artificial intelligence, and it's quite surprising that it's, I can't say easy.
	I mean, physicists worked really hard to find these theories, but apparently it was possible for human minds to find these simple rules in the universe.
	It could have been different, right?
	It could have been different.
	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 were going to say, because you could have just as easily said, I have no clue.
	Which many people would say, but I'm not modest in this question.
	So the informal version, which I worked out together with Shane Leck, Co-founded DeepMind, is that intelligence measures an agent's ability to perform well in a wide range of environments.
	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'll 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 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 a definition.
	Interesting. So yeah, so the consciousness, abstract reasoning, all these kinds of things are just emerging phenomena that help you in towards, can you say the definition again?
	So multiple environments.
	Did you mention the word goals?
	No, but we have an alternative definition.
	Instead of performing well, you can just replace it by goal.
	So intelligence measures an agent's ability to achieve goals in a wide range of environments.
	That's more or less equal. But it's interesting because in there, there's an injection of the word goals.
	So we 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 of a gray area, but it's much closer to something that could be formalized.
	In your view, are humans...
	Where do humans fit into that definition?
	Are they general intelligence systems that are able to perform in...
	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 we know of.
	Depends. You could say that trees and plants are doing a better job.
	They'll probably outlast us.
	Yeah, but they are in a much more narrow environment, right?
	I mean, you just have a little bit of air pollution and these trees die and we can adapt, right?
	We build houses, we build filters, we...
	We do geoengineering.
	So the multiple environment part.
	Yes, that is very important, yes.
	So that distinguishes narrow intelligence from wide intelligence, also in the AI research.
	So let me ask the Alan Turing question.
	Can machines think?
	Can machines be intelligent?
	In your view, I have to kind of ask, the answer is probably yes, but I want to kind of hear 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, you know, on a small scale, we are already there.
	The wide range of environments are still missing.
	But we have self-driving cars, we have programs which 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 AlphaZero, that was also developed by DeepMind.
	I mean, but famous with AlphaGo and then came AlphaZero a year later.
	That was truly amazing.
	So a 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, 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 end game tables and so on too.
	And nothing in there, nothing was put in there.
	Especially with AlphaZero, the self-play mechanism, starting from scratch, being able to learn Actually, new strategies.
	Yeah, it rediscovered all these famous openings within four hours by itself.
	What I was really happy about, I'm a terrible chess player, but I like Queen Gambi, and AlphaZero figured out that this is the best opening.
	Finally! Somebody proved you correct.
	So yes, to answer your question, yes, I believe that general intelligence is possible.
	And it also, I mean, 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 Turing test for 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 Turing test Well, it has been criticized a lot, but I think it's not as bad as some people 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, which is much harder.
	And on the other hand, they say it's 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 a big problem.
	So if we would pass the Turing test So a conversation of a 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 Turing test.
	I would be truly impressed.
	And we have this annual competition at Löbner.
	I mean, it started with Eliza.
	That was the first conversational program.
	And what is it called?
	The Japanese? Mitsuko or so.
	That's the winner of the last couple of years.
	It's quite 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 in aggregate metric.
	Because it really, like nobody has the patience To be able to talk to a bot that's not interesting and intelligent and witty and is able to go on to different tangents, jump domains, be able to say something interesting to maintain your attention.
	Maybe many humans will also fail this test.
	Unfortunately, we set, just like with autonomous vehicles, with chatbots, we also set a bar that's way too high to reach.
	I said the Turing test is not as bad as some people believe, but what is really not useful about the Turing test,
	it gives us no guidance 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 ICSI model.
	I mentioned the compression, right?
	So in natural language processing, They have achieved amazing results.
	And one way to test this, of course, you take the system, you train 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 systems 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 goal of complexity.
	So you're saying good compression usually means good intelligence?
	Yes. So you mentioned you're one of the only people who dared boldly to try to formalize the idea of artificial general intelligence, to have a mathematical framework for intelligence, just like as we mentioned, termed AIXI, A-I-X-I. So let me ask the basic question.
	What is AIXI? Okay, so let me first say what it stands for.
	What it stands for? Actually, that's probably the more basic question.
	The first question is usually how it's pronounced, but finally I put it on the website how it's pronounced, and you figured it out.
	The name comes from AI, artificial intelligence, and the X, I, is the Greek letter Xi, which are used for Solomanov's distribution.
	For quite stupid reasons, which I'm not willing to repeat here in front of camera.
	So it just happened to be more or less arbitrary.
	I chose Xi. But it also has nice other interpretations.
	So there are actions and perceptions in this model, right?
	An agent has actions and perceptions.
	And over time, so this is A index I, X index I. So there's the action at time I and then followed by perception at time I. We'll go with that.
	I'll edit out the first part.
	I'm just kidding. I have some more interpretations.
	At some point, maybe five years ago or 10 years ago, I discovered in Barcelona, it was in a big church.
	There was a stone engraved, some text.
	And the word Aixi appeared there a couple of times.
	I was very surprised and happy about it.
	And I looked it up, so it is a Catalan language and it means, with some interpretation, that's it, that's the right thing to do.
	Oh, so it's almost like destined, somehow came to you in a dream.
	And similar, there's a Chinese word, Aixi, also written like Aixi, if you transcribe it to Pinjin.
	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, you know, planning and known deterministic world and induction is more about often, you know, IID data and inferring models.
	And essentially what this ICSI model does is combining these two.
	And I actually also recently, I think, heard that in Japanese, AI means love.
	Oh! So, if you can combine XI somehow with that, I think we can...
	There might be some interesting ideas there.
	So, Aixi, let's then 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, if you have no idea what your actions do, how can you decide which actions are good or not?
	So you need to have some model of what your actions effect.
	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 the model is, sorry to interrupt, and the model is based on your perception of the world, how your actions will affect that world.
	That's not the important part.
	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.
	So, of course, our actions Affect what we're doing, but I'll come back to that in a second.
	And I'll keep just interrupting.
	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.
	What is prediction? Okay, if you want to put the actions in now, okay, then let's put it in now.
	So... We don't have to put them now.
	Scratch it. Scratch it.
	Dumb question. Okay. So the simplest form of prediction is that you just have data which you passively observe.
	And you want to predict what happens without, you know, interfering.
	As I said, weather forecasting, stock market, IQ sequences, or just anything, okay?
	And Solominov'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.
	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 know, you have fair coin flips.
	Yeah, I cannot predict the next fair coin flip.
	What Solominov does is says, okay, next head is probably 50%.
	It's the best you can do.
	So if something is unpredictable, Solominov will also not magically predict it.
	But if there is some pattern and predictability, then Solominov 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, even with Google resources here, and run it and predict the stock market and become rich.
	I mean, Ray Solominov already tried it at the time.
	So the basic task is you're in the environment, and you're interacting with that environment to try to learn a model of that 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.
	So let's go to the actions now.
	But actually good that you asked. Usually I skip this part, although that is also a minor contribution, which I did.
	So the action part, but I usually sort of just jump to the decision part.
	So let me explain 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.
	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.
	You just condition extra on your actions.
	There's an interesting alternative that you also try to predict your own actions.
	In the past or the future?
	Your future actions.
	That's interesting. Wait, let me wrap.
	I think my brain is broke.
	We should maybe discuss that later, after I've explained the ICSI model.
	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.
	That's very important, the whole history from birth of the agent.
	And we can come back to that also why this is important here.
	Often, you know, in RL, you have MDPs, macro decision processes, which are much more limiting.
	Okay, so now we can predict...
	We're conditioned on actions, so even if we influence the 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 the next time step.
	And 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 time step, you can give it a positive reward or negative reward or maybe no reward.
	It could be 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 IXE framework, that's completely sufficient.
	So occasionally you give a reward signal and you ask the agent to maximize reward, but not greedily sort of, you know, the next one, next one, because that's very bad in the long run if you're greedy.
	So, but over the lifetime of the agent.
	So let's assume the agent lives for m time steps, let's say dies in sort of 100 years, sharp.
	That's just, you know, the simplest model to explain.
	So it looks at the future reward sum and asks what is my action sequence, or actually more precisely my policy, which leads in expectation, because I don't know the world, to the maximum reward sum.
	Let me give you an analogy.
	In chess, for instance, we know how to play optimally in theory.
	It's just a minimax 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 worst for me.
	Under the assumption that I play, again, the best move.
	And then you have this expectimax tree to the end of the game.
	And then you backpropagate and then you get the best possible move.
	So that is the optimal strategy, which von 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 there are other humans, even cooperative.
	Or nature is usually, I mean, the dead nature is stochastic.
	Things just happen randomly or don't care about you.
	So what you have to take into account is the noise and not necessarily adversariality.
	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, we have an expectimax strategy.
	So far so 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 Begammon, right?
	There's dice and there's certain randomness involved.
	Yeah, I can calculate probabilities and feed it in the expectimax or the sequential decision tree, come up with the optimal decision if I have enough compute.
	But for the real world, we don't know that.
	What is the probability the driver in front of me breaks?
	I don't know. So it depends on all kinds of things, and especially in new situations, I don't know.
	So this is this unknown thing about prediction, and there's where Solominov comes in.
	So what you do is in sequential decision tree, 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 decision tree 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 of Induction part learns.
	Can you explicitly try to describe the universal distribution and how Solomon of Induction plays a role here?
	Yes. I'm trying to understand. So what it 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 should not just take the shortest program, but also consider the longer ones, but give it lower a priori probability.
	So in the Bayesian framework, you say a priori any distribution.
	Which is a model or a stochastic program has a certain a priori probability, which is 2 to the minus, and why 2 to the minus length?
	You know, I could explain length of this program.
	So longer programs are punished a priori.
	And then you multiply it with the 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, and so it's a 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, or this is the average over it.
	And this gives you a probability distribution, a so-called universal distribution or Solomanov distribution.
	So it's weighed by the simplicity of the program and the likelihood.
	Yes. It's kind of a nice idea.
	Yeah. So, okay.
	And then you said you're planning N or M, or forgot the letter, steps into the future.
	So how difficult is that problem?
	What's involved there? It's a basic optimization problem, what are we talking about?
	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 intractable.
	I mean, even for chess, it's already intractable to do that exactly, and, you know, for Go.
	But it could be also a discounted kind of framework where...
	Yeah, so having a hard horizon, you know, at 100 years, it's just for simplicity of discussing the model, and also sometimes the math is simple.
	But there are lots of variations.
	It's actually a quite interesting parameter.
	There's nothing really problematic about it, but it's very interesting.
	So, for instance, you think, no, let's let the parameter m tend to infinity, right?
	You want an agent which lives forever, right?
	If you do it naively, you have two problems.
	First, the mathematics breaks down because you have an infinite reward sum, which may give infinity, and getting reward 0.1 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, you know, think about yourself or, you know, or maybe, you know, some friends or so.
	If they knew they lived forever, you know, why work hard now?
	You know, just enjoy your life, you know, and then catch up later.
	So that's another problem with 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 $1.05 tomorrow.
	So if you do this so-called geometric discounting, you have introduced an effective horizon.
	So the agent 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 horizons.
	So if I look ahead, you know, five time steps, I'm a terrible chess player, right?
	I need to look ahead longer.
	If I play Go, I probably have to look ahead even longer.
	So for every problem, for every horizon, there is a problem which this horizon cannot solve.
	Yes. But I introduced the so-called near-harmonic horizon, which goes down with 1 over T rather than exponentially in T, which produces an agent which effectively looks into the future proportional to each age.
	So if it's five years old, it plans for five years.
	If it's 100 years old, it then plans for 100 years.
	Interesting. And it's a little bit similar to humans too, right?
	I mean, children don't plan ahead very long, but then we get adult, we play ahead more longer.
	Maybe when we get very old, I mean, we know that we don't live forever, maybe then our horizon shrinks again.
	So that's really interesting.
	So adjusting the horizon, is there some mathematical benefit of that?
	Or is it just a nice...
	I mean, intuitively, empirically, it would probably be a good idea to sort of push the horizon back, extend the horizon as you experience more of the world.
	But is there some mathematical conclusions here that are beneficial?
	With the long-modern induction sort of prediction part, we have extremely strong finite time, or finite data results.
	So you have so-and-so much data, then you lose so-and-so much.
	So the theory is really great.
	With the ICSI model, with the planning part, Many results are only asymptotic, which, well, this is...
	What does asymptotic mean? Asymptotic means you can prove, for instance, that in the long run, if the agent acts long enough, then it performs optimal or some nice thing happens.
	But you don't know how fast it converges.
	So it may converge fast, but we're just not able to prove it because it's a difficult problem.
	Or maybe there's a bug in the model so that it's really that slow.
	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, it's over.
	I cannot say eventually. So this is the advantage of the discounting that I can prove asymptotic results.
	So just to clarify, so okay, I've built up a model.
	Well, now in the moment, I 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 minimax. In this case here, do expectimax based on the Solomanov distribution.
	You propagate back, and then, well, an action falls out.
	The action which maximizes the future expected reward under Solomanov 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 it.
	And the reward, so on.
	Yeah, so you rewrote 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 intuit 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, you know, AGI, the name didn't exist then, what's called general AI or strong AI, and the physics theory of everything.
	So I switched back and forth between computer science and physics quite often.
	You said the theory of everything.
	The theory of everything. Those are basically the two biggest problems before all of humanity.
	Yeah, I can explain if you wanted some later time, you know, why I'm interested in these two questions.
	Can I ask you, on a small tangent, if it was one to be solved, which one would you, 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 is solved, I can ask the AGI to solve the other problem for me.
	Yeah, brilliantly put.
	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 have solved AGI, it solves all kinds of other, not just the theory of every problem, but all kinds of more useful problems to humanity is very appealing to many people.
	And, you know, I had this thought also.
	But I was quite disappointed with the state of the art of the field of AI. There was some theory, you know, about logical reasoning, but I was never convinced that this will fly.
	And then there was this more heuristic approaches with neural networks, and I didn't like These heuristics.
	And also I didn't have any good idea myself.
	So that's the reason why I toggled back and forth quite some while and even worked four and a half years in a company developing software or something completely unrelated.
	But then I had this idea about the ICSI model.
	And so what it gives you, it gives you a gold standard.
	So I have proven that this is the most intelligent agents which anybody could Built 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.
	Every year, tens of frameworks are developed, which are skeletons, and then pieces are missing, and usually these missing pieces turn out to be really, really difficult.
	And so this is completely and uniquely defined, and we can analyze that mathematically.
	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 heuristics in, prune the tree, blah, blah, blah, and so on.
	So we can do that also with the ICSI model, but for general AI. It can also inspire those, and most of...
	Most researchers go bottom-up, right?
	They have their systems. They 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?
	So the answer is always this.
	We have a system which does everything.
	That's ICSI. It's just, you know...
	Completely in the 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'll 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 in Go.
	And at least it's 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 have a physics background.
	Think about the phenomenon of energy.
	That was 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 vague, and then they have been rigorously formalized.
	Speed and acceleration has been confused until it was formally defined.
	There was a time like this.
	And people often who don't have any background still confuse it.
	And this ICSI 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.
	Yes, yeah. I mean, there's a million questions I could ask her.
	So maybe kind of, okay, let's feel it around in the dark a little bit.
	So there's been here at DeepMind, 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?
	Which subset of IEXE does it occupy?
	The current, like you said, maybe the Markov assumption is made quite often in reinforcement learning.
	There's other assumptions made in order to make the system work.
	What do you see as the difference connection between reinforcement learning and IEXE? So the major difference is that essentially all other approaches, they make stronger 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 general AI, all the assumptions which are made by other approaches, we know already now they are limiting.
	So, for instance, usually you need an egoticity assumption in the MDP frameworks in order to learn.
	Egoticity 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 factors.
	Problems. But in real life, we know, you know, there can be one single action, you know, one second of being inattentive while driving a car fast, you know, can ruin the rest of my life.
	I can become quadriplegic or whatever.
	So there's no recovery anymore.
	So the real world is not ergodic, I always say.
	You know, there are traps and there are situations where you are not to recover from.
	And very little theory has been developed for this case.
	What about... What do you see in the context of Aixie as the role of exploration?
	Sort of... You mentioned in the real world we can 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 IEXE that can be controlled?
	Yeah, I say the good thing is that there are no parameters to control.
	Some other people try knobs to control and you can do that.
	I mean, you can modify axes 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-world 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 off exploring, and at some point you want to explore, and you can do the mathematics and figure out the optimal strategy.
	The so-called Bayesian agents are also non-Bayesian agents, but it shows that this Bayesian framework, by taking a prior over possible worlds, doing the Bayesian mixture, then the Bayes 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.
	It is very simple settings.
	In the ICSI model, I was also able to prove that it is a self-optimizing theorem or asymptotic optimality theorems, although they're only asymptotic, not finite time bounds.
	It seems like the long-term planning is really important, but the long-term part of the planning is really important.
	And also, maybe a quick tangent, how important do you think is removing the Markov assumption and looking at the full history?
	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, just throwing away the past.
	I think it's absolutely crucial.
	The question is whether there's a way to deal with it in a more heuristic and still sufficiently well way.
	So I have to come up with an example and fly, but you have some key event in your life a long time ago in some city or something.
	You realize that's a really dangerous street or whatever, right?
	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 importance is...
	That's very hard, yeah.
	And I'm not concerned about, you know, just storing the whole history.
	Just, you can calculate, you know, human life is 30 or 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 do the selection.
	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 we develop an agent, preferably 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 reanalyze it based on your new experience you have.
	Sometimes you are in school, you learn all these things you think is totally useless, and much later you realize, oh, they were not so useless as you thought.
	I'm looking at you, linear 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 IXE framework to yourself discover the reward based on which you should operate?
	Okay, that will be a long answer.
	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.
	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 agent based on the ICSI model which performs a particular task.
	Let's start with something super simple like playing chess or Go or something.
	Then, the reward is winning the game is plus one, losing the game is minus one.
	Done. You apply this agent.
	If you have enough compute, you let it self-play and it will learn the rules of the game.
	We'll play perfect chess after some while.
	Problem solved. So, if you have more complicated problems, then you may believe that you have the right rewrote, but it's not.
	So, a nice, cute example is Elevator Control that 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, long wait is bad.
	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 then you realize, maybe the time in the elevator also counts, so you minimize the sum.
	And the elevator does that, but never picks up the people in the 10th floor, in the top floor, because in expectation, it's not worth it.
	Just let them stay. So even in apparently simple problems, you can make mistakes.
	And that's what, in more serious contexts, AAGI safety researchers consider.
	Now let's go back to general agents.
	Assume we want to build an agent which is generally useful to humans.
	We have a household robot and it should do all kinds of tasks.
	In this case, The human should give the reward on the fly.
	I mean, maybe it's pre-trained in the factory and there's some sort of internal reward for the battery level or whatever.
	So it does the dishes badly.
	You punish the robot. It does it good.
	You reward the robot and then train it to a new task, 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 these agents stay subhuman level, that should work reasonably well,
	apart from, you know, these examples.
	It becomes critical if they become, you know, on a human level.
	It's the same as children.
	Small children you have reasonably 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 species 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, you know, come up with some reward functions like, you know, it should maintain itself, the robot.
	It should maybe multiply, build more robots, right?
	And, you know, maybe...
	Well, all kinds of things which you find useful, but that's pretty hard, right?
	You know, what does self-maintenance mean?
	You know, what does it mean to build a copy?
	Should it be an exact copy, an approximate copy?
	And so that's really hard.
	But Laurent Assault, also at DeepMind, developed a beautiful model.
	So it just took the ICSI 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 our 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 loose, it will be, in a sense, the optimal scientist.
	It is absolutely curious to learn as much as possible about the world.
	And of course, it will also have a lot of instrumental goals, right?
	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?
	Exploration, space exploration or whatever is necessary, right, to gather information and develop it.
	So it has a lot of instrumental goals following on this information gain.
	And this agent is completely autonomous of us.
	No rewards necessary anymore.
	Yeah, of course it 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.
	It would get stuck in front of an old TV screen which has just a white noise.
	Yeah, white noise, yeah. But the second version can deal with at least stochasticity.
	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 reward, sorry, curiosity is exploration for its own sake.
	Yeah, I would accept that.
	But most curiosity, well, in humans, and especially in children, is not just for its own 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 intelligence systems need to have this reward function, you're an intelligence system.
	Currently passing the Turing test quite effectively.
	What's the reward function of our human intelligence existence?
	What's the reward function that Marcus Hutter 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.
	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.
	On top of that, yeah. But the survival and spreading sort of is, I would say, the goal or the reward function of humans, the core one.
	I like how you avoided answering the second question, which a good intelligence system would.
	Your own meaning of life and reward function.
	My own meaning of life and reward function is to find an AGI to build it.
	Beautifully put. Okay. Let's dissect eggs even further.
	So one of the assumptions is kind of infinity keeps creeping up everywhere.
	What are your thoughts on kind of bounded rationality and sort of the nature of our existence and intelligence systems is that we're operating always under constraints, under You know, limited time, limited resources.
	How does that, how do you think about that within the IXE framework within trying to create an EGI system that operates under these constraints?
	Yeah, that is one of the criticisms about ICSI, that it ignores computation completely, and some people believe that intelligence is inherently tied towards bounded resources.
	What do you think on this one point?
	Do you think the bounded resources are fundamental to intelligence?
	I would say that an intelligence notion which ignores computational limits is extremely useful.
	A good intelligence notion, which includes these 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 is more a 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 in an even halfway satisfactory manner.
	I like that, that in the long run, the right department to belong to is philosophy.
	It's actually quite a deep idea, or at least to think about big picture philosophical questions, big picture questions, even in the computer science department.
	But you've mentioned approximation.
	Sort of, there's a lot of infinity, a lot of huge resources needed.
	Are there approximations to IXE within the IXE framework that are useful?
	Yeah, we have developed a couple of approximations.
	And what we do there is that the Solomov induction part Which was, you know, find the shortest program describing your data.
	We just replace it by standard data compressors, right?
	And the better compressors get, you know, the better this part will become.
	We focused on a particular compressor called context-free weighting, 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 Chava Zepespari, also now at DeepMind, who developed the so-called UCT algorithm, upper confidence bound for trees algorithm, on 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.
	But this single agent was able to play small games like Coon Poker and Tic-Tac-Toe and even Pac-Man.
	It's the same architecture, no change.
	The agent doesn't know the rules of the game.
	We're doing nothing all by self or by player with these environments.
	So Jürgen Schmidhuber proposed something called Gatel machines, which is a self-improving program that rewrites its own code.
	Sort of mathematically or philosophically, what's the relationship in your eyes, if you're familiar with it, between AXI and the Gödel machines?
	Yeah, familiar with it.
	He developed it while I was in his lab.
	Yeah, so the Gödel machine To explain 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 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 Gödel machine should do.
	Then it will take part of its resources to run this program and other part of the resources 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 developed in a way that...
	All parts of this Gödel machine can self-improve, but it stays provably consistent with the original specification.
	So, from this perspective, it has nothing to do with ICSI, but if you would now put ICSI as the starting axioms in, It would run ICSI, but, you know, that takes forever.
	But then if it finds a provable speedup of ICSI, it would replace it by this, and this, and this, and maybe eventually it comes up with a model which is still the ICSI model.
	It cannot be... I mean, just for the knowledgeable reader, ICSI is incomputable, and I can prove that, therefore, there cannot be a computable exact...
	Algorithm computers. There needs to be some approximations, and this is not dealt with the Gödel machine, so you have to do something about it.
	But there's the ICTL model, which is finitely computable, which we could put in.
	Which part of ICTL is noncomputable?
	The Solomanov induction part.
	The induction. Okay, so...
	But there's ways of...
	Getting computable approximations of the ICSI model, so then it's at least computable.
	It is still way beyond any resources anybody will ever have, but then the Gödel machine could sort of improve it further and further in an exact way.
	So is this theoretically possible that the Gödel machine process could improve?
	Isn't AXE 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 continues whether you want it or not.
	So the model is, assuming you had an oracle which solved this problem and then in the next 100 milliseconds or the reaction time you need gives the answer, then AXE is optimal.
	It's optimal in the sense of data, also from learning efficiency and data efficiency, but not in terms of computation time.
	And then the government machine in theory, but probably not provably, could make it go faster.
	Yes. Okay.
	Interesting. 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 and you're improving.
	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 within IXE? Maybe you can comment, because I suppose we humans are just another instantiation of IX agents and we seem to have consciousness.
	You say humans are an instantiation of an IX agent?
	Yes. Oh, that would be amazing.
	But I think that's not true 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 we tend to laugh off and criticize our flaws, and I tend to think that that's actually close to an optimal behavior.
	Well, some flaws, if you think more carefully about it, are actually not flaws, yeah, but I think there 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 as 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, I think.
	That's the Russian. Whether humans are or not instantiations of an AXE agent, do you think there's consciousness of something that could emerge in a computational form or framework like AXE? Let me also ask you a question.
	Do you think I'm conscious?
	That's a good question.
	That tie is confusing me, but I think so.
	You think that makes me unconscious because it strangles me?
	If an agent were to solve the imitation game posed by Turing, I think that would be dressed similarly to you.
	Because there's a kind of flamboyant, interesting It's a complex behavior pattern that sells that you're human and you're conscious.
	But why do you ask?
	Was it a yes or was it a no?
	Yes, I think you're conscious, yes.
	And you explained 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 even 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 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.
	Is 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 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, 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 faking consciousness and feelings, you know, then we don't need 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 of what we do with that.
	It is rather easy to build systems which people ascribe consciousness.
	And I give you an analogy.
	I mean, remember, maybe it was before you were born, the Tamagotchi.
	How dare you, sir.
	Why? It means that you're young, right?
	Yes, it's good. Thank you.
	Thank you very much. But I was also in the Soviet Union.
	We didn't have any of those fun things.
	But you have heard about this Tamagotchi, which was, you know, really, really primitive, actually, for the time it was...
	And, you know, you could race, you know, this...
	And kids got so attached to it and, you know, didn't want to let it die and...
	If we would have asked the children, do you think this Tamagotchi is conscious?
	They would have said yes. I think that's kind of a beautiful thing, actually, because that consciousness, ascribing consciousness, seems to create a deeper connection, which is a powerful thing.
	But we 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, at least earlier, and DeepMind represents serious work on AGI these days.
	But why in your sense is the AGI community so small or has been so small until maybe DeepMind came along?
	Why aren't more people seriously working on human-level, superhuman-level intelligence from a formal perspective?
	Okay, from a formal perspective, that's sort of an extra point.
	So I think there are a couple of reasons.
	I mean, AI came in waves, right?
	You know, AI winters and AI summers, and then there were big promises which were not fulfilled.
	And people got disappointed.
	But narrow AI, solving particular problems, which seem to require intelligence, was always to some extent successful and there were improvements, small steps.
	And if you build something which is, you know, useful for society or industrial useful, then there's a lot of funding.
	So I guess it was in parts 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 better a long time ago.
	But even nowadays, there's quite some pressure of doing applied research or translational research.
	And, you know, it's 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, maybe a small number, were still interested in formalizing intelligence and thinking of general intelligence.
	But not much came up, right?
	Or 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?
	I don't know if that's a stupid question or a distinct question from everything we've been talking about IXE, but what do you see as the steps that are necessary to take to start to try to build something?
	So you want a blueprint now and then you go up and do it?
	That's the whole point of this conversation.
	I'm trying to squeeze that in there.
	I mean, what's your intuition?
	Is it in the robotics space or something that has a body and tries to explore the world?
	Is it in the reinforcement learning space, like the efforts of AlphaZero and AlphaStar that are kind of exploring how you can solve it through in the simulation in the gaming world?
	Is there stuff in sort of all the transformer work in natural language processing, sort of maybe attacking the open domain dialogue?
	Where do you see the 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. 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.
	I think the most promising approach is that you have an agent.
	And that can be a virtual agent in a computer interacting with an environment, possibly 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 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 I say 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?
	You know, if you talk about objects on top of each other in space and flying and cars and so on, and the agent has no experience with even virtual 3D worlds, it's probably hard to grasp.
	But if we 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 mathematician, then this agent needs to be able to reason in very abstract spaces and then maybe sort of putting it into a 3D environment simulated or not 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 I asked books and not a singular book.
	It's very hard and I tried to pin down one book.
	And I can do that at the end.
	So the books which were most transformative for me or which I can most...
	Highly recommend to people interested in AI. Both, perhaps.
	Yeah, both. I would always start with Russell and Norbeck, 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 Learning book by Sutton and Bartow.
	That'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 a very gentle book.
	It's very nice to read and exercises to do.
	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 in a couple of days, you feel, you know, you know what RL is about.
	But it's much harder than the book.
	Yeah. Oh, come on now.
	It's an awesome book. Yeah, it is, yeah.
	And... Maybe, I mean, there's so many books out there.
	If you like the information theoretic approach, then there's Kolmogorov Complexity by Lien 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.
	If you have to mention one all-time favorite book, it's of different flavor.
	That's a book which is used in the International Baccalaureate for high school students in several countries.
	That's from Nikolaus 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 math, from art, from physics, and ask how can we know anything.
	And the book is called Theory of Knowledge.
	It's almost like a philosophical exploration of how we get knowledge from anything.
	Yes, yeah. I mean, can religion tell us, you know, about something about the world?
	Can science tell us something about the world?
	Can mathematics, or is it just playing with symbols?
	And, you know, open-ended questions.
	And, I mean, it's for high school students, so they have then resources from Hitchhiker's Guide to the Galaxy and from Star Wars and The Chicken Cross the Road, yeah?
	And it's fun to read, 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 emerging phenomena, so it's all the same anyway.
	Okay. Okay, from the past...
	You're really going to say from the future.
	I love it. No, I will tell you from the future.
	Okay, from the past. So from the past, I would say when I discovered my Aixi model, I mean, it was not in one day, but it was one moment where I realized Kolmogorov complexity.
	I 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 decisionry, and I knew if I put it together, this is the right thing.
	And yeah, still when I think back about this moment, I'm super excited about it.
	Was there any more details and context at that moment?
	Did an apple fall in your head?
	If you look at Ian Goodfellow talking about GANs, there was beer involved.
	Is there some more context of what sparked your thought or was it just...
	No, it was much more mundane.
	So I worked in this company.
	So in this sense, the four and a half years was not completely wasted.
	And I worked on an image interpolation problem.
	And I developed a quite neat new interpolation techniques and they got patented.
	And then, 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 interpolation?
	And then I thought, yeah, you want the simplest picture, which is if your core screen, it recovers your original picture.
	And then I, you know, thought about the 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 think big with Ike.
	So as a physicist I was probably trained not to always think in computational terms.
	Just ignore that and think about the fundamental properties which you want to have.
	So what about if you could relive one day in the future?
	What would that be?
	When I solve the AGI problem.
	In practice. So in theory, I've solved it with the EICSI model, but in practice.
	And then I ask 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.
	It's a huge honor to finally meet you.
	Yeah, thank you too. It was a pleasure off my side too.
	Thanks for listening to this conversation with Marcus Hutter, and thank you to our presenting sponsor, Cash App.
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	And now, let me leave you with some words of wisdom from Albert Einstein.
	The measure of intelligence is the ability to change.

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