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[S1] Uh, this is changing H and N conserve quantity, uh, which is what they believe is, is, uh, they predict it's going to be some more, the energy. You can see the baseline neural network, which is just the, uh, the F, basically, just F. [S2] Mm-hmm. [S1] Uh, quickly loses energy, and therefore, this is going to lead to much worse predictions. On the left, you can see the MSE goes up. [S2] Mm-hmm. [S1] Um, if you fully impose energy, well, this is a much better inductive bias, the fact that energy is conserved. And you can see that, uh, the predictions are much better.
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[S1] And then, uh, we also, uh, had Professor Josh Tenenbaum from, uh, MIT Cognitive Science and Kenji Kawaguchi, uh, from the University of Singapore. [S2] Cool. Excellent. Well, Ferran, thank you so much for being here with us, uh, today. [S1] Thank you. [S2] And, and all the, all the best. I hope you have great, great ideas in the future.
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[S1] Welcome, everyone. Uh, today I have with me right here, Stefan Dascholi, who is the first author of the paper, Deep Symbolic Regression for Recurrent Sequences. Stefan, welcome. Thank you very much for being here. [S2] Yeah, pleasure. Bad timing to have COVID, but I'll try my best to- [S1] Yeah.
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[S1] ... taking a, a, a matrix and then, uh, outputting its inverse or stuff like that. And so, uh, a natural continuation of this was to start from numeric data and go to a symbolic formula, and that's basically, uh, symbolic regression, which means you take a function, uh, you only see its values and you have to try and infer the expression of the function. [S2] Mm-hmm. [S1] And, uh, indeed, it's kind of surprising that the, this has been studied quite a lot for, for,
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[S1] This one is actually a good example. It's kind of hard to recognize for us. And if you look at the formula that the model gave us, uh, you can actually figure out why, uh, it predicted that formula. It's UN minus one plus N. Uh, and the reason for that is that NN plus one divided by two is the formula for the sum of integers. And so the way it built this formula is just to take Peter's turn, add N- [S2] Mm-hmm. [S1] ... and then take the modulus with respect to 10 because that gives you the final digit. So it's kind of a, a clever thing that, you know, would be kind of, um, hard to figure out.
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[S1] Um, actually, it turns out that it's better to use a, a long, um, a larger base because if you lose a, use a larger base, well, you're going to have a bigger vocabulary, but you're going to have shorter sequences. And typically, you know, transformers have a quadratic complexity. They struggle a bit with very long sequences. [S2] Mm-hmm. [S1] Uh, which is why, yeah, we, we, we prefer to use a large base. Here we use 10,000 as our, as our base.
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[S1] Yeah. So this is, this will be base 30 and obviously in base 10,000, I think it's important to note that every single number from zero to 9,999 is its own token, right? [S2] Exactly. [S1] The model has no inherent knowledge of, you know, three comes after two and four comes after three and so on. All of this has to be learned. It seems- [S2] Exactly. [S1] It, it seems so weird to, to say, you know, uh, it is better
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[S1] Exactly. Yeah. So, so that's what's really interesting is that that is one approach. And actually we had a couple of discussions on this, like how can we feed in our inductive bias on, on numbers directly into the model. And well, I mean, the problem with this is that here we're dealing with like just, uh, one-dimensional vectors in some sense. Transformers need, you know, high dimensional vectors as inputs. [S2] Mm-hmm. [S1] And it's not obvious how you represent these numbers in, in a high dimension, um, you know, because the, as I was saying just before, the problem is that these numbers have very,
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[S1] Yeah. [S2] Yeah. [S1] And the float embeddings are, are very similar, right? In that you encode them as like a, a, a, a sign, a mantissa, and an exponent. And again, the mantissa, if I understand correctly, same deal, that you have a token per number between zero and, and 10,000. [S2] Mm-hmm. [S1] And the, and the exponent, um, is that correct? That you have, you say you have exponent from negative 100 to 100. So one token would be
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[S1] ... big, big model. We, we've embedding dimension 512. [S2] Mm-hmm. [S1] Actually, when we were using a smaller model, uh, with a smaller embedding dimension, we saw a really neat pattern, um, which was basically the fact that it, the model was learning the, uh, arithmetic properties of integers. So it was basically creating a line with two, four, six, eight, 10, et cetera. [S2] Yeah. [S1] Then three, six, nine, et cetera. And here it's a bit less obvious, probably because the big model is learning something even more complex that we can't interpret as easily. [S2] Mm-hmm. [S1] Um, if you go in the
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[S1] So these plots, just to, to make it clear, these are the cosine similarities between each of the tokens. So the tokens would be distributed on the, on the axis here. [S2] Exactly. [S1] These are tokens and these are tokens, and then we plot the, uh, the cosine similarities between every two tokens. So naturally, obviously, every token's gonna be very similar to itself, but also-
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[S1] very similar to its immediate neighbors. So it seems to really learn this, uh, the ordering of all the tokens. But then also, yeah, what, what I found special, um, there is this, this structure of the, the common, sort of the common factors, uh, common divisors between the- [S2] Exactly. [S1] ... the tokens. That's, that's really cool, yeah.
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[S1] Oh, sorry, no, they're, they're repeated in part, but also, um, there are more in the float formulas. And then you just generate in, um, reverse Polish notation, is that correct? [S2] Exactly. [S1] So you generate reverse Polish notation formulas given these, these things, and you can also have integer prefactors, right, for, for all the things. So either you sample integers or you sample- [S2] Or you can try, yeah. [S1] You sample,
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[S1] Rather different things in the two setups. Really in the integer setup, we're focusing on sort of arithmetics and arithmetic properties of numbers. Whereas in the float setup, we're really interested in a, let's say a more classic, uh, symbolic regression problem with, with complex operators. [S2] Yeah. [S1] And yeah, as you said, our generation process is basically to build a mathematical tree. Uh, so a unary binary tree. Uh, this is like previous works by- [S2] Mm-hmm. [S1] ... by Francois and- and Guillaume. And then
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[S1] Yeah, probably we could have, like, tuned these parameters somehow, but here we really wanted to have the, the simplest choice possible, uh, on the rationale that basically our, our dataset is so huge, uh, that it's, eventually we're gonna see all possible, uh, formulas at some point. [S2] Yeah. [S1] Uh, it doesn't matter that much, the specific values we choose, and we don't want to tune them to a specific problem. [S2] Mm-hmm. [S1] Um, and so this is why we really chose,
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[S1] even numbers you divide by two. That's a rule which is possible to express with a, a mathematical expression. Essentially what you do is say, is write it as N modulus two times what you do if it's, uh, even plus- [S2] Yeah. [S1] ... one minus- [S2] N modulus one minus that. Yeah. [S1] But that's-
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[S1] Basically, always been good at the problems we've given them. Uh, likely, I mean, one natural justification is that, uh, as we saw for the outputs, you can represent math as a language in a, in a very easy way. It's actually, we can see here that it's much harder to represent the inputs as, as tokens, but the formulas themselves are very easy to represent as, as a language with this Polish notation thing. [S2] Mm-hmm. [S1] And so it's very natural to use transformers because they're our best models to, to deal with language. Um, so yeah, I th- I think that's the,
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[S1] ... kinda defined, even though there are infinite possibilities. Like, you, you, do you know a little bit what I mean? Is it more like- [S2] Yeah, yeah, yeah. [S1] ... a property of humanity or of, of mathematics? [S2] I think it's probably two different things. So, as far as humans is concerned, indeed we, we,
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[S1] ... tend to prefer simplicity. That's like our OCam's razor principle. We, we like going for the compressing information and going for the simplest representation. Um, in terms of, of our algorithm here, we didn't put at all this simplicity inductive bias, uh, from a explicit point of view. We didn't tell the model, "Give us the, the simplest formula." Actually, we could have done so because we could have, for example, given a penalty to like the decoder when it generates too long sequences, for example. [S2] Mm-hmm. [S1] But we didn't have to do this at all because the inductive bias comes from,
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[S1] ... presentation of the world. [S2] Of course, yeah. [S1] I could, you know, be, be, do much more powerful planning. Is there, are you thinking of applications like these when you develop this, right? Beyond- [S2] Definitely. [S1] ... number sequences or is there any- [S2] Yeah. [S1] ... interesting ones that, you know, come to your mind?
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[S1] Um, you can have the two criterions. The criterion you, we choose in the papers, we want the, uh, the evaluations to be the same. [S2] Mm-hmm. [S1] Mm-hmm. [S2] So even if it comes up with, like, a different formula, it's, it's fine as long as, like, the, the ones you tested on, uh, match.
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[S1] Euler's const, okay. So, n times the, s- the sine of gamma squared. So, the entire thing on the right-hand side is a, oh, sorry, is a constant, right? So, it's essentially n times a constant. [S2] Yeah. [S1] Uh, so the, the model, what it has to do is it has to somehow figure out the expression for the constant as a formula, right? Because it, it can't, it, it- [S2] Yeah.
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[S1] ... that the model could, you know, figure it out from the data points it has. By the way, the, the green background, that's the input, right? The blue background- [S2] Exactly. [S1] ... that's, that's the, what it has to predict. [S2] Yeah. [S1] So the next one I find particularly interesting. It is, the formula is the tan of the, the tangent of N plus N times the last element.
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[S1] When it fails on the right-hand side, it not only fails outside the input points, but also on the input points. It's not even able to fit the points you gave it. [S2] Yeah. [S1] So this really shows a big difference. [S2] We can see this a little bit, I think. So on the bottom left, there is a, there is a nice case where it, it can, it already fails, yeah, on the inputs. Like that's the best formula it can come up with. You do have a beam search in there, right?
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[S1] ... that tiny bit off. [S2] Exactly. [S1] And th- that, that gets worse and worse as the, sort of, the output progresses. Okay. [S2] Yeah. Yeah. [S1] So, yeah, th- there are a bunch of, a bu- a bunch of other funny ones, like this one. Again, these, the scale here is, um, the scale here is absurd. It's like a, a, a, the exponent is 224, and there's just this one output that it's supposed to match, and, I mean, that's just, that's just mean to the model, honestly. [S2] Yeah.
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[S1] Yeah, exactly. Yeah. Uh, a Nurek model is, is generally gonna be better indeed when, when there isn't a simple formula but you can still infer logic. It's- [S2] Yeah. [S1] Yeah. Sometimes, I mean, you, you give very...
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[S1] Okay. It's interesting because I think we interviewed, we interviewed, uh, Guillaume and, and, and co-authors on a previous paper on the machine learning street talk. I asked them, uh, pretty much, I think, the same question, and that they're, they already said, like, "No, you know, kinda we plugged it in and it, you know, it worked out and, you know, it was, it was cool." So I think this is like, uh, maybe it's, it's forbidden knowledge, but this might be like a field of deep learning where there's, you know- [S2] Where things actually work. [S1] ... still, you, you, you, you,
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[S1] can get, you can get like results. It, it kind of, it works maybe, or maybe let's say you get started with something that works pretty quickly. [S2] Yeah. [S1] Whereas, whereas if you're in like reinforcement learning, you spend months until something actually starts working. [S2] Yeah, and the explanation is simple. It's basically just that you have this synthetic, uh, task and so you have infinite data. And the big problem of, of
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[S1] All right. So I think this, this, is there anything you wanna like special that we haven't come to you, you wanna mention about the paper itself? [S2] No, that was, that was great for me. Thanks for your questions. [S1] I think that was great for me as well. I, I'm always happy if I can ask like all my, all my dumb questions, uh, to the people themselves. In this case, Stefan, thank you very much. Uh, thank you and your co-authors for, for writing the paper, and thank you so much for being here. This was really, really fun. [S2] Thanks a lot.
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[S1] Hello, everyone. Today, here with me, I have Patrick Mino, who is a neuroscientist, uh, slash blogger, slash anything else that you might imagine in between, uh, deep learning and the human brain. Uh, welcome, Patrick, to the channel, uh, for this bit of a, a special episode, I guess. [S2] [LAUGHS] Thanks. Uh, it's great to be here. [S1] I got, I got,
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[S1] Uh, presenting deep learning to the world and saying like, "This is ready. This is a big deal," was ImageNet 2012. [S2] Mm-hmm. [S1] Right? Um, as you know. So that was, uh, during my PhD. So at the, uh, the very start of my, um, um,
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[S1] Well, that, it, it seems like it was an exciting time. I do remember Theano as well, so I'm definitely dated, dated the same. Um, so you, the dorsal stream, just to make clear, that's part of, sort of the visual, the visual stream, uh, into the brain. Is that correct or- [S2] Yeah, yeah, yeah. [S1] ... [S2] So-
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[S1] ... differences in luminance between like a center and a surround or differences in time. Um, so you can think of it as a camera with like a little bit of linear filtering. Um, and, uh, it then gets forwarded to, um, different areas of the brain. First to the lateral geniculate nucleus and then to the back of the brain, the occipital por- cortex, which is called the primary visual cortex. [S2] Yeah. [S1] So that's a huge area, a huge chunk of the brain. And you have tons of, uh, neurons,
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[S1] ... Visual processing splits into two different substreams. Uh, there's the, uh, ventral visual stream, which is the object stream. Um, so if you think, like, what does a, you know, ResNet-50, that's trained on, uh, on ImageNet, do, maybe it's something similar to that, and we can get into that later. [S2] Mm-hmm. [S1] And, uh, then there's a, another set of areas, which is the dorsal stream. Um, again, organized in a hierarchical fashion. Again, you have, like,
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[S1] ... these, uh, you, you know, you've, uh, for instance, you have increases in the size of receptive fields, you have increases in the size of, in the complexity of things that these neurons respond to. But this time, they don't care about form. They don't care whether, uh, they don't care about texture. Uh, what they really care about is motion. [S2] Mm-hmm. [S1] Uh, so, you know, you're gonna poke at,
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[S1] Uh, a neuron in, uh, let's say the middle temporal area, which is part of the dorsal stream, and 80 or 90% of the neurons will respond when you show them the right moving stimulus. [S2] Yeah. [S1] Uh, which is, which is, uh, remarkable.
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[S1] understanding how the brain does certain things. And the answer is- [S2] Absolutely. [S1] Right? The answer is a little bit yes and a little bit no. Like, there's still, there's still questions. But you point out a bunch of areas of where progress has been made in, uh, correlating, let's say, neural activities in deep neural networks with neural activities in, in brains. So,
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[S1] ... they would be, uh, it, it wouldn't matter the, the precise location of, uh, of this line in question. And it wouldn't matter the, the contrast. So it could be white to black or it could be black to white. [S2] Yeah. [S1] It, it, uh, it wouldn't matter. And so their hunch was that, okay, well, you have this, this transformation that happens. First of all, you have a selectivity operation which create that simple cell.
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[S1] ... that looked inside of these deep neural networks and found that, you know, the kinds of selectivity that you see inside the cells, they're very, very similar to what you would, to what a neurophysiologist would describe in areas like V1, V2, V4, inferotemporal cortex. Um, so the combination of the quantitative and qualitative tells us like, "Hey, maybe, maybe there's a kind of, these are kind of like little brains." [S2] Yeah. [S1] One very, very specific part of the brain I, I want to be at- [S2] You get into a lot of trouble
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[S1] Sure, just like the idea of, look, how, like, what, what do we, what do we measure? Like, you know, is it a number, is it a correlation, or is it, uh, am I training a regression model from one signal to the other signal? Like, how, how can I make the statement that- [S2] Yeah. So the- [S1] ... this neural- [S2] Oh, yeah. [S1] ... this neural network explains some function in the brain.
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[S1] ... down sampling or whatever. Um, and then you measure the output of that deep neural network, uh, with respect to some stimulus ensemble. [S2] Mm-hmm. [S1] So, which gives you a big matrix, big X, uh, which has a bunch of rows for the different examples and a bunch of, of columns for the different features.
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[S1] and then you just regress that, uh, against neural data that's, uh, that's recorded with the same, um, im- with the same images. [S2] And, yeah, that- [S1] So it's just a regression, so you can add, like, a bunch of, of different spices into your, your basic recipe. So you can, uh, add some, uh, some sparseness priors. You can, uh, try to, well, usually you'll use a, a ridge regression rather than a straight regression because, uh, that will,
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[S1] Definitely, yeah, uh, the, the regular regression will usually crash and burn. Neural data is, is very noisy. [S2] Yeah. [S1] That's, uh, something that people don't, uh, often appreciate. Um, and so it's a regression. Let's just put it that way. [S2] Yeah. [S1] Now- [S2] That would be so, sort of, so, for example, fMRI data when we talk about neural data.
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[S1] I think. [S2] [LAUGHS] We just say MEG. Um, and, or it could be a single neuron recordings or array recordings. [S1] Yeah. [S2] So those are taken inside the brain. [S1] Mm-hmm. [S2] Or it might be ECOG, which is just on the surface of the brain. So there's different kinds of, uh, of recordings. Now, it happens that, uh, fMRI and MEG are much more popular. [S1] Mm-hmm. [S2] Um,
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[S1] Yeah, so that's super exciting. [S2] Yeah. [S1] And the reason is that I, I think that everybody got very excited when they saw that these networks, which were trained for ImageNet, they could be aligned for, to the ventral stream, uh, to that object recognition stream. [S2] Yeah. [S1] Because now it's something that, you know, you have this in-silico thing, and it kinda looks like it does the same thing as the brain. [S2] Yeah. [S1] And so it's kind of a model of the brain. [S2] Yeah. [S1] Super exciting. You can do a lot of things with it.
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[S1] Um, but there's different ways in which something can be a model of, of, of the brain. And some of these are, are a little bit more useful than others. [S2] Yeah. [S1] And, and one of the ways I, one of the big flaws I think for, uh, uh, for supervised learning
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[S1] Is that it's not like really a way, it's not really a model of how the brain would learn a task. [S2] Mm-hmm. [S1] Uh, because, you know, I'm not walking around as a baby and like, you know, my, uh, my parent, uh, just tells me like, "Dog, dog, dog, dog, dog." [S2] Mm-hmm. [S1] "Cat."
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[S1] So people generally like unsupervised learning and self-supervised learning better for that reason, because you don't have to, you know, come up with this like, uh, weird concept that- [S2] Yeah. [S1] ... dog, dog, dog, cat. Um,
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[S1] And, and, uh, but you do have to do the math to make sure that it actually does work out in practice and that, you know, the right, the, the kinds of, the, the quantity of examples that you feed into, um, into the model is similar to the kinds of, to the, the quantity of examples that you would feed into a human- [S2] Yeah. [S1] ... for instance.
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[S1] I think you have, you have a- [S2] So, uh- [S1] ... in your conclusion, you have a little bit of an example that, uh, it would, like, the language models that we train, such as GPT-3, would be equivalent to, like, years and years and years of, of human- [S2] Of just constant- [S1] Yeah. [S2] ... constant- [S1] Yeah. [S2] ... talking and talking and talking. [S1] And babies are able- [S2] Right, 'cause GPT- [S1] ... to do it by age, what, four or so, or two.
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[S1] Uh, exactly. So, uh, so I think that there's still a, a, a big gap- [S2] Mm-hmm. [S1] ... there that comes from that. You still, I mean, we're off, I think I calculated that we're off by four orders of magnitude in terms of- [S2] Yeah. [S1] ... the efficiency. Um, but, y- you know, I'm, uh, th- th- to score everybody on the same kind of curve. I mean, the GPT-3 is not made as a model of the brain. [S2] Sure. [S1] I mean, it's made as a language model and to solve all these, these problems in zero-shot settings and it works very well for,
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[S1] ... trying to solve these, uh, uh, these problems. So, um, so for, for instance, there's a lot of work on, um, trying to fit the same kinds of unsupervised learning models, but with streams of data that look more like what a baby would- [S2] Yeah. [S1] ... would see in, uh, in their early years. Uh, in which the camera is not always pointed at that- [S2] Yeah. [S1] ... at the right things, uh, because babies tend to- [S2] I see. Yeah, yeah. Yeah. [S1] [LAUGHS] Do a lot of gesturing. [S2] It's, but it's,
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[S1] ... a lot of gesturing. [S2] But it's also, it's also, also, there it's special because the baby, with time, is able to move its head, right? And, and therefore, it's also not the same as just placing a camera somewhere because whatever captures attention will be actively looked at more. So it's, it's definitely like, I think there's a long way to go, uh, in any of these things. [S1] Oh, yeah. Oh, yeah, absolutely. I, I think, uh, um,
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[S1] So to close the, uh, the, the- [S2] Yeah. [S1] ... just, just that, uh, that one paper, 'cause we've been on it for, [LAUGHS] like 15 minutes. But super cool that you can have, uh, you can train a model in a unsupervised or self-supervised manner, and it turns out to be just as good at explaining, you know, V1, V4, and IT- [S2] Yeah. [S1] ... all these different sub-areas of the ventral stream. And then there's a kind of hierarchy that happens between the, uh, the different, um,
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[S1] Oh, yeah. So, uh, so I'll, I'll just go very rapidly with, uh, true that actually the second one is, uh, ventral stream. [S2] Oh, sorry. [S1] Uh, again. And so that's, uh, from, uh, Talia Kanko, um, and very, very, uh, consistent, uh, data. So they use fMRI rather than- [S2] Mm-hmm. [S1] ... than single neuron data. But, I mean, the data is,
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[S1] actually is, um, I was going about this, uh, very naively, but I, I just looked into, like, the torch vision models. [S2] Yeah. [S1] You know, the, they have, like, some, uh, some model database and just downloaded all the models that were trained on, um, video recognition. Uh, so all the models that were trained on, um, uh,
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[S1] I, I'm drawing a blank here. [S2] Yeah. [S1] Kinetics 400, uh, which is a task where you have to look at a video of somebody juggling and say, "Oh, it's juggling," rather than unicycling, rather than soccer or whatever. And so the special thing about these models is that they look at 3D data. Uh, by 3D, I mean spatial-temporal, right, in time. And so that means that
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[S1] And so I looked at these models and I did, uh, the kinds of visualization tricks that, uh, Crisola and, uh, and Yang do at, uh, at OpenAI to, uh, look inside. 'Cause I was curious, you know, do they learn motion? Do they align with, uh, with the brain? And I found that they were actually, like, really terrible. [S2] Yeah. [S1] Which surprised me because, uh, if you look into the methods of, uh, of these papers, it's like we trained, uh,
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[S1] Yeah. So vertical is like kind of a, sorry. [S2] [LAUGHS] [S1] This is like a weird non-secular. But, um, vertical is kind of a, a funny thing, right? Because it's an inner ear problem. [S2] Yeah. [S1] Right? So you have your vestibule and it kind of, it basically tells you there's acceleration in ways that there shouldn't be acceleration and that gives you a, an impression of being dizzy.
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[S1] But also gives you like these weird visual effects. [S2] Yeah. [S1] Right? Which is, uh, uh, which is strange. Or, you know, if you drink a little too much, you might have that, uh, that same kind of feeling. Um, so there's an area in the brain, which is called MST, which has these neurons which receive both visual input and vestibular input. [S2] Mm-hmm.
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[S1] And the way that they receive, uh, visual input is, uh, they have a lot of selectivity for things like rotation and expansion and, uh, and wide field translation. [S2] Yeah. [S1] And so we think that they're really involved in navigation. So if you're going forward, uh,
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[S1] In a, in a line, uh, you have these neurons which receive both the vestibular input, so they know how you're accelerating and where gravity is, and they receive all this white field optic flow, which is, tells you, uh, where you're, uh, where you're heading. So we said, why don't we train a deep neural network to, uh, solve a, a navigation task so that the network can, uh, can orient itself, uh, in space, essentially. [S2] Yeah. [S1] So, um, so I used a, uh, an environment
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[S1] Uh, it's an environment for, uh, drone simulations. [S2] Yeah. [S1] It's called AirSim. And, uh, it's really fun. Uh, so it's an, uh, Unreal engine. [S2] Yeah. [S1] Uh, and you can, [LAUGHS] you can, uh, basically fly a drone in these suburban environments. [S2] Yeah. [S1] And, uh, back out these sequences of videos. And then you can train a, a convolutional neural net, uh, uh, 3D ResNet to solve the problem of figuring out, uh, what is the, from a, a little sequence of, uh,
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[S1] ... for, uh, for translation and, um, translation, but they don't care about the pattern that underlies the, uh, the translation. And in particular, you see these cells, like the one that you're, that you're visualizing here, that like things like spirals, uh, and some of the higher level layers of, uh, of this network, which was, um, which was super exciting because those look a lot like what you would see in an estate. [S2] So the, yeah. [S1] So basically we- [S2] The, the networks that try to just predict
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[S1] ... anything from a video that contains motion weren't, aren't, like, turns out these neural ne- sorry, the deep networks, uh, I have to stop saying neural networks here because it's ambiguous. Um, [S2] Ah, yes, yes, yes. [S1] ... the deep networks that, that train on vi- any kind of video data, they're not super well aligned with the brain. However, as soon as it, as you go maybe to, like, some sort of an ego perspective, right, and you, especially you predict y- your own parameters of motion. So from the
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[S1] One, um, one big question that, uh, came up during the review is that, you know, we claimed originally this was, uh, unsupervised or self-supervised. [S2] Yeah. [S1] In the abstract. And then the reviewers came back and said, "Well, it's not really unsupervised or self-supervised. It's a supervised network because, you know, you know what the answer is. You're just training in a, in a, in a supervised fashion." [S2] Yeah.
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[S1] My feeling is that it is, uh, self-supervised in the sense of when you embody this in an agent. So when I'm, when I'm a baby, [LAUGHS] let's, let's imagine that I'm a baby and I'm walking around the world. I have some control over where I'm heading. [S2] Yeah. [S1] Right? So I can say, like, I'm gonna turn this way, I'm gonna turn that way. [S2] Yeah. [S1] I'm gonna move forward, I'm gonna go get that cookie. Uh, I'm gonna look at, uh, my parent, uh, and so forth. So I am an agent. [S2] Yeah. [S1] So that means that I control-
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[S1] ... control the motion that comes into my eyes. [S2] Yeah. [S1] Uh, because the vast majority of motion that we see in the world comes from, uh, from our self-motion. [S2] Mm-hmm. [S1] And so I can correlate my motor plans with what I see in the world. And that means that, uh, it's a, it's a much easier kind of problem to correlate these two things than, uh, to say I,
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[S1] Here's found data. [S2] Yeah. [S1] Which is the, the case of ImageNet, and figure out something to, to, to model with this. [S2] Yeah, exactly. [S1] Right? [S2] Yeah.
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[S1] Yeah, absolutely. So, I think it looks more like the bottom part of this diagram, uh, that you see there, where you have these two things which are happening in the present, but one, uh, part is occluded and the other part is visible. [S2] Yeah. [S1] So, you're doing multimodal masking, in other words, right? So, you have the vision, but now you're trying to predict the vestibular. [S2] Yeah. [S1] Or you have the vestibular and you're trying to predict the vision. [S2] Yeah. [S1] And so, if you look something like, um, uh, clip,
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[S1] You know, in a way, you're trying to predict, um, language from, uh, from vision. But it's really, uh, this, this kind of, uh, of masking, and it's a, I think it's a more general approach to solving, uh, this, uh, this type of problem. So, yeah, I agree with you, embodied agents, I'm 100% on board. [S2] Yeah. [S1] Uh, they're, they're definitely going to be awesome, and, uh, uh, and actually, questions about, you know, what do reinforcement learning agents learn? Do they learn, like, good self-motion representations, for instance, when they're,
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[S1] When they have a visual task, I think like those are super interesting. Like what do you need to put in there- [S2] Yeah. [S1] ... uh, in order to get that, uh, that effect. [S2] Yeah, that, that con-
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[S1] ... this, this paper you're describing, it tackles the question- [S2] Oh, it's the same people. [S1] It is actually, it is actually, I just saw, I just saw in my notes, that is again one of, one of your papers. Yeah. [S2] Yeah. [S1] It is the question, why are there even two different of these visual streams in, in the brain? Like, it maybe makes sense if we, if we sit down, but also you find some actual empirical evidence for why it might be, um, might be that we even have two streams, right?
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[S1] I worked on, um, looking at what, what it would take to, to recreate both ventral and dorsal stream. [S2] Mm-hmm. [S1] And, uh, I think the remarkable thing that he found is if you train a, uh, a network like, uh, a CPC network, so a contrastive predictive coding network, which is one form of self-supervised learning in which, uh, you're trying to, uh, essentially discriminate between different futures, um, if you will. So you're trying to, you
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[S1] on just, uh, on just one GPU. And so what they decided arbitrarily is to split it up into two parts, especially at the, uh, uh, at the early part. [S2] Yeah. [S1] And then basically they, so they were independent, but they could re-communicate a little bit later on. [S2] Mm-hmm. [S1] Um, so, which was,
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[S1] ... a pretty unique feature, uh, back then. People didn't really do that. [S2] Yeah. [S1] Uh, but now it's, it's quite common to, you know, chop up the channels in different ways and all sorts of things. [S2] Mm-hmm. [S1] Um, but what they found is that there's this, this, uh, there's this very interesting self-organization principle where
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[S1] All the, all the, uh, the, the filters on one GPU turned out to be color selective, and all the filters on the other GPU turned out to be, uh, to, to be black and white. [S2] Yeah. [S1] Which is, whoa, that's weird. [S2] Just, just by the fact of, of splitting up.
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[S1] ... extreme. [S2] Yeah. So in that, in that case, in the early Alex- [S1] Mm-hmm. [S2] ... that paper, actually both, uh, of the types of filters are different sub- types that you see in, uh, in V1. But they are, you know, functionally- [S1] Yeah. [S2] ... different, and they have different roles. But it was like kind of an interesting proof of concept- [S1] Mm-hmm. [S2] ... that if you just set a separation, arbitrary separation down the middle, you don't say anything else, like you don't say, like, "You have to respond- [S1] Yeah. [S2] ... to color, you have to respond to this." But just, you set a separation,
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[S1] pushing the network very, very slightly out of, of equilibrium. [S2] Yeah. [S1] And that's enough to self-organize into this thing. And so, uh, Shahab found a, a very similar phenomenon in the context of these networks which are trained in an unsupervised manner in CDC. [S2] Mm-hmm. [S1] And, um, so being trained on videos was able to find
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[S1] Um, and was able to correlate that with some, um, some data that we have in, uh, in mouse where there's tons and tons of data on what's the relative selectivity of the, of these different things and found some, uh, some really nice correlations. [S2] Cool. [S1] Uh, so that means that you can,
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[S1] Uh, all you would need basically is a little bit of a nudge. [S2] Yeah. [S1] Right? And, uh, so, so which is, is, is this great idea. Like maybe you just initialize the network in a sl- so that, like, the two things are just very slightly asymmetric. [S2] Mm-hmm. [S1] Because one thing I should say is that, um,
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[S1] ... the, uh, the two networks don't always get the same label, right? So if you train the network twice, one time it's going to be dorsal-ventral, and the other time it's going to be ventral-dorsal. Whereas the brain, every time that you train it- [S2] It's the same, yeah. [S1] ... [LAUGHS] that we know of. [S2] So there, there are some- [S1] Exactly. It's all, ventral is ventral, dorsal is dorsal. [S2] There's some prior- [S1] So there's some, like, inbuilt asymmetry, but it's a very, probably like a very small asymmetry. [S2] Yeah.
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[S1] Uh, because if you train it with real data, uh, and then it will automatically, you know, self-generate into this, uh, in, in bloom into this particular activity. [S2] Cool. Um- [S1] So very exciting. [S2] Yeah, this could be- [S1] Uh, that the brain can organize itself for something that's, uh, that's useful just from- [S2] Yeah, this could be useful.
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[S1] Is it this paper? [S2] Oh, that's, this as well. I think, like, uh, I, I think that there's been a lot of movement in this subfield. And by the way, I want to tell your viewers, 'cause I know a lot of you viewers are coming from a machine learning background versus, uh, a, a neuroscience background. And, uh, you know, it's hard to get into NeurIPS, but I think if, you know, it's such a wide open field to, in, uh, in neuroscience. [S1] Yeah. [S2] Um, there are so many questions that if you care a lot about representation learning, you know, it's, it's a pretty easy, uh, field to, to jump
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[S1] ... jump onto and, uh, and have positive reception. So, um, there's, there's still a, a bunch of, uh, a bunch of questions, so grab your nearest neuroscientist and go write a paper. Uh, encourage everybody to do it. [S2] Yep. Definitely. How to, how to hack, how to hack the right publications. There you go. [S1] Um, yeah, there you go. So, uh, yeah, so, uh, Clip. Uh, Clip is, Clip is weird. [S2] [LAUGHS]
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[S1] Um, and, uh, so in this particular instance, they, uh, they presented different kinds of, uh, of concepts and images. And one of the cells that they found had this, like, amazing property that if you just show the words Jennifer Aniston, it would respond. If you showed the face of Jennifer Aniston- [S2] Mm-hmm. [S1] ... it would response. If you showed, uh,
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[S1] Um, so, uh, ever since then, uh, people have been, like, fascinated by this idea, although it's a, it's a much older idea, you know, this idea that you have, like, a cell in your hippocampus that responds- [S2] Yeah. [S1] ... to your grandmother. It's the grandmother cell idea. But, um, um, one thing that was very interesting when we first saw Clip is that you have, cells can respond both to text and to, um,
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[S1] Um, so it sounds very hippocampus-like to me. And so in this particular paper, they, uh, they actually looked at, um, at this problem and found that out of all the different models that, uh, that they could look, um, they, they, they found that, uh, Clip could explain, uh, the most, uh, hippocampal data, which is super exciting. I'm sure that people are really going to drill down further into this, uh- [S2] Yeah. [S1] ... into this finding. [S2] Yeah.
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[S1] But it's Clip specifically. [S2] Yeah. Yeah. [S1] 'Cause there's a lot of other unsupervised models and, uh, somehow Clip is the best and we still don't understand why this is. I mean, it's like the delta between it and the, uh, the, the second best model is- [S2] Yeah. [S1] ... is huge. But why? Uh, I, I think no one knows right now. And, um,
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[S1] Yeah. And, uh, and one thing that's, uh, that's interesting, in particular for babies, you know, if, uh, if you ever interacted with babies, they really like to have toys- [S2] Yeah. [S1] ... which make lots of noise, which drives parents crazy. And, but I think that there's a reason for that, right? Like, why would you want a, like, a toy that makes, like, a lot of noise? 'Cause clearly, there's a lot of pressure on making the noise as silent as possible because the parents are just, like, trying to sleep. Um, but I think that the kids just prefer that because- [S2] Yeah. [S1] ... it's a multimodal stimuli and you can do all sorts of
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[S1] ... Because you could like- [S2] ... on that neuron. [S1] So you, you could rotate the entire space, it would still make sense, right? So there's no, there's no reason why an individual neuron should align with just like one axis in, in that particular subspace.
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[S1] Mm-hmm. [S2] Yeah, exactly. Um, so, but, uh, neuroscientists really like, uh, labeled axes. [S1] Yeah. [S2] [LAUGHS] That's, that's one thing that, uh, that they're very fond of. Um, so, you know, you can imagine that you have, like, an axis. I don't know if you're in, in Unity or in Unreal. [S1] Yeah. [S2] You know, you have, like, my avatar, and then you just, like, hit, like, one switch, and I just go, "It, do. It, do." [LAUGHS]
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[S1] Yeah, it's, uh, it's too bad. So I still print out papers because there's been research that shows that you retain more when you print something out, rather, when you read it in a, um, on a printed document rather than- [S2] Yeah. [S1] ... reading it on the, but it's just becoming so, so inconvenient that I think I'm gonna have to abandon soon. Uh, okay, so starting back then and, uh, I apologize. Where do you want me to, to restart?
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[S1] Yes, yes, exactly. And that might be because, uh, you know, neuroscientists like to name things, and if something is not nameable, they'll say it's mixed selectivity or whatever, and then they'll just forget about it. [S2] Yeah. [S1] [LAUGHS] That's also a very good assumption. Um, so both of these things can be happening at the same time. Uh, but in this paper, they found that, uh, if you train a, a beta, a VAE, which is a VAE which has a, a stronger, uh, weight on, on one of the
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[S1] How the, what the distribution of responses is over, uh, a stimulus ensemble is very important, uh, for how efficient, uh, the code is. Because remember, neurons are super noisy, right? [S2] Yeah. [S1] Uh, so you want them, you, you wanna have like a nice exponential distribution of, uh, of responses, uh, in order to have an efficient code, um, given that you have this Poisson-like noise- [S2] Yeah. [S1] ... in the data.
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[S1] ... that, you know, the, the, the result of there being eyebrows is that they look a certain way. [S2] Yeah. [S1] And then it would make sense, again, that they are encoded, like the structural prior is encoded in one space, and then simply the manifestation of that is the picture we see. [S2] Yeah, yeah, yeah. Maybe I misused the, the term causal here. Uh, I don't wanna mistake it for causal inference and, uh, I- [S1] Sure, sure, yeah. [S2] [LAUGHS]
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[S1] Um, but I think that what I mean, uh, by this is a, is a forward model for how, like, one individual- [S2] Yeah, exactly. [S1] Uh, so you, you can think of, uh, you, you can think of a, uh, of a directed acyclic graph in which, you know, there's a bunch of different factors. One of them is whether or not I wake up with a mustache today. Another one is how close my eyes are. Another one is- [S2] Yeah. [S1] ... is my nose. And these factors are, you know, disentangled, so that means that, um, you know, they're independent from, uh, from each other. And then I can just, like,
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[S1] ... I turn on and off the switch and generate different, uh, different, uh- [S2] Yeah. [S1] ... faces. So that's, uh, I think, like, the underlying naive model is the Mr. Potato Head, uh, model, right? In which you just, like, switch out the different, uh, the, the different components. Uh, and of course, there are specific, you know, holes that you can put the, uh, [LAUGHS] the different, uh, the different things in. Um, so I think, uh, that,
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[S1] I, I guess, like, the question is, like, are these factors in this, uh, this factor graph, are they, like, can you put labels on them and they correspond to one thing that we would identify as something that is independently changeable? So, for instance, like, we understand that age and lighting, for instance, like, those are two totally disentangled, uh, things that have nothing to do with each other. [S2] Yeah. [S1] Um,
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[S1] So, uh, so the question is, are they, are they different factors or are you rotated like one is square root of two, like one over square root of two times age minus, uh, one over square root of two times, uh, uh, lighting and, and so on and so forth. And it looks like they're really aligned towards, um, towards the, uh, the factors that we can label and that are indeed independent. [S2] It- [S1] Both in brands and in this particular model. [S2] Do you think that-
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