On models of the mind - with Grace Lindsay - #1

[Music] Welcome to the first episode of the new theoretical neuroscience podcast. I'm the host, Kairat Einwell. The guest of today's episode is Grace Lindsay, author of the popular science book "Models of the Mind", excellently describing the theoretical neuroscience field. Before I start, I thought I should mention why I decided to make this theoretical neuroscience podcast series. I've been making podcasts for four years now, so I'm covering topics of science and other topics of interest. Podcasts is called "The Tovitenskop", or mostly in Norwegian, but has a few episodes in English as well. As for now, I have made 80 episodes and I really enjoy making them. So why a new podcast series focusing on theoretical neuroscience? Theoretical neuroscience can be said to be a sparse field, meaning that we are rather few people compared to the number of topics that we address. Only a few percent of neuroscientists would identify themselves as theoretical or computational neuroscientists. So students or researchers doing theoretical neuroscience often don't have a large community of other malm-like-minded neuroscientists around them. Being a competition neuroscientist myself, I decided to make this podcast with the hope that it can help in contributing to a lively and generous theoretical neuroscience community. I've been inspired by the podcast Brain Inspired, focusing on research at the interface between neuroscience and AI. I follow this podcast regularly, and for me it's much easier and more enjoyable to listen to a podcast lasting an hour or two to learn about the new topic, rather than reading a paper. I suspect it's the same for many other scientists. I will however have some costs related to the production of the podcast that I hope to get covered. I prefer not to have commercials in the podcast, and I also don't want money issues to get in the way, for people who would like to listen to it. So for now, I have decided to simply make the old version free, and this will be available on all major podcast platforms, and also through the web page, TheoreticalNurerscience.no. On this web page, we'll also find info about episodes with links to relevant material. However, I have made a patron page where you can subscribe and get not only the older podcast, but also the video version of the podcast as well as transcripts of each episode. If you want to support the podcast, go to patreon.com/TheoreticalNurersciencePodcast and choose a membership of your liking, for example at the cost of one euro per episode. Even if you're happy with listening to only the older versions of the podcast, I hope that many of you will sign up as patron supporters to support the production of it. I can assure you that I will not pocket any of the money for myself, everything will go into the production of the podcast, mainly to help with the technical aspects. But now to the first episode itself, where I'm very happy to have Grace Lindsay as a first guest. Grace is a competition neuroscientist working at New York University, and she published a book "Models of the Mind" a few years ago, which gives a popular account of the history of Theoretical or Competition Nurerscience, and also the problems that the field is interested in. I'm quite impressed by this book, and I like it a lot, and I recommend it for all neuroscientists, computational or otherwise. In the episode we talk about the history of biophysical modeling of neurons from the discovery of bielectricity by Galvani 200 years ago, to Hotschkin Huxley's "Modeling of the Action Potential" and onwards from there. Before we discuss the modeling of information flow and competition, starting with a seminal paper of pits and my colloc, published 80 years ago, that also had a major impact on the start of the AI field. Next we discuss some highlights from computational modeling of networks, for example, Opfield's memory model and the balanced excitation inhibition ID, explaining the noisy fire nerve neurons in cortex. We also talk about the recent development where deep networks from AI are used to investigate biological vision. This is Grace's own research field, and finally we speculate a bit about the future of our field. Okay, here we go. Welcome to the podcast, Grace Nancy. Thank you. Happy to be here. Yeah, so I mean, when I decided to make this new podcast on theoretical neuroscience, my first thought was that I should have you as a guest for the inaugural episode, because I think you've written this really excellent and impressive book, models of what is it, models of the mind? That's right. Yeah, and which then I think sort of both gives a very nice historical introduction to the field of theoretical neuroscience, computational neuroscience, and also in very much covers many of the problems that the field is now working on. First, I mean, Kenes says, why did you do this? I mean, you must have been active popularizing it before, because I'm quite ambitious thing, I think you were a postdoc at the time. Yeah, I was just starting a postdoc and during grad school, I had done a decent amount of science writing on my own blog and other outlets, and then I also had a podcast for a few years. That was unsupervised thinking. That's right. That was about computational neuroscience and artificial intelligence and neuroscience, and that sort of thing. So I always kind of was interested in getting a broad view of the field, and kind of thinking of maybe the more like meta science level of how it works, and why mathematical models are a good idea. And so, yeah, and then through the writing that I did, I got to know people who had written popular science books, and it kind of became a more tangible, possible thing. And then, yeah, there was a publisher, the publisher I didn't use, Bloomsbury Sigma was looking for more authors, and I had a conversation with the editor and kind of just snowballed from there to being an actual book. Wow. Yeah. So this is, I think, as. Well, when I read this book, I thought this must. Well, it seems like it should be written by a person who's been like many decades in the field, and you were just a starter. So that was quite impressive. You also came up, there's a lot of metaphors that you have in there, that about sort of like out sort of to describe what's going on in the rural system. So you made. Most of them I haven't heard before. Did you make them up yourself? Yeah, yeah, for the most part. I mean, I knew. So, you know, there are a lot of people who are in the field, or in an adjacent field that have read the book, and I figured that would happen. But also it's supposed to be a book that's accessible to a general audience. So I wanted to make sure that, you know, even if you didn't get the exact scientific description, that you could capture the general vibe by having these metaphors. So yeah, it's usually just kind of thinking about how I'm visualizing the concept in my head and trying to come up with something in the real world, in like the normal everyday world that relates to that to kind of get the idea across. So, yeah, so anyway, so I think just to start, I think this should be a book that. Well, this is a book that belongs in the bookshelf of any computational neuroscientist and lots of other people, or also just interested in what's going on in the field. I think it gave a very nice and accurate description of what's going on and sort of like the main ideas and so on. So good else to you. And I thought I should start with like going back to the. I guess to the start of some sense of, I guess, maybe computation neuroscience or even at the beginning of neuroscience with the discovery of electricity in the brain, with Galvani. So what did he do? Yeah, so he was an Italian scientist who was studying a lot of different things as scientists of that time did. They didn't really specialize yet. So he was studying biology and electricity and physics and all of those different things. And through kind of an accident in his lab, he discovered that if you apply electricity to a frog's leg, it twitches. And then that suggests that biological beings are using electricity in some way. They're using it to conduct signals or to cause movements. And so he kind of followed that up with more experiments of saying, yes, if we apply electricity to different organisms, you can get responses and that kind of set off, you know, a long debate amongst people as to whether electricity is really used by animals natively. Or if this was just something that kind of you could get to happen. If you apply electricity, but it doesn't actually speak to how the body really works. That was kind of the debate that he set up. But one thing that one very concrete thing that got out of it was this novel Frankenstein. Yeah, yeah. So yeah, because this was the time when, you know, the boundary between different types of science was weak in the boundary between a scientist and a lay person tinkering in their, you know, in their own home was kind of weak as well. The notion of electricity creating life or reanimating things was spread throughout popular science. or through popular culture rather, and people were playing with some of these devices, like a laden jar is a device that can hold charge, but it's pretty simple and easy to build, and so people could play with these things in their home, and it really just spread through the popular imagination. What electricity could do and how it could relate to life and how life is generated? I haven't heard that people were traveling around with corpses giving them electric shocks so that they could scare people in the audience. I would be scared by that. Me too. But then, I mean, we've maybe also heard about Volta, at least that's another Italian who has the unit for electric potential, named after him, Volta, but he, he sort of, even though he made batteries and stuff, he still didn't believe that maybe that electricity was something that muscles or the biological tissues or brain could make by myself. Yeah, the nature of the experiments were not ones where you could observe electricity in the body. It was just this foreign application of it, and so without being able to observe electricity directly, without it being applied externally, there was just for Volta, not enough reason to believe that this was happening and ate in the animal, that it was just a response or a result of external electricity, but didn't necessarily speak to what was happening biologically. Because even you even, I mentioned in a book that this is very important physiology book by some miller or something that he sort of, like 1840, didn't really believe that electricity was that important to understand the body. Yeah, so he was a vitalist, so he said that, yeah, it's not electricity that's part of how nerve, signaling, communicate, or that leads to control or animation, but also this vitalist camp is kind of of the mindset that you can't describe what it is. You're not going to be able to give a physical explanation to what animates the body. And so from, you know, if you're starting from that point, then yeah, you're not going to believe it's electricity, you're not going to believe it's anything. And Muleur, you know, particularly was also on the side of like experiments where you apply the electricity, those are no good, what you want is just observation. You just want to be able to observe and see what happens and draw conclusions from that. So yeah, for Rhees and similar to Volta, he didn't believe in the electricity, but also for these more kind of fundamental philosophical reasons, he probably wasn't going to believe in anything because his whole claim was that there's this, you know, life force. And that's the answer, but the life force isn't definable in physical, chemical terms or anything like that, which is kind of a difficult position to stomach. I think if you're having a scientific mindset to something, you kind of believe that you can figure it out and that it's not just going to be, you don't have to just appeal to something that's by definition immeasurable. But yeah, that was the state of kind of the study of life at the time, which is kind of analogous to the study of consciousness now in a way where people kind of appeal to the fact that there's something that can be measured. But yeah, it was, he wasn't, Miller wasn't the only person who believed this, but he was a prominent person who believed it. But, you know, eventually the actual experiments with electricity won out. Yeah, but because I guess also this was like the early days of our electric studies. So I guess it also questioned about like amplifiers, whereas it was like difficult to have like to get the right signal to noise ratio. But soon rather soon after there was like this guy, the boy Raymond and also then Bernstein, Julius Bernstein, that was able to measure real well, well clear electric signals from I guess muscles and brain cells and so on. Yeah, so Bernstein was a student of Raymond and yeah, they were developing the necessary technology to actually be able to pick up the very weak electrical signal that can come from nerves. They were still working in the realm of nerves, not even individual neurons, but bundles of neurons. But yeah, they were able to stimulate the neuron on one end and then, you know, put the recording device at a different end and be able to see at some time point later that there would be this kind of electrical disturbance in the cell itself. And therefore that the cell was using electricity to communicate, it wasn't just the result of externally applied electricity. As of the Bernstein was he did this work I think in 1868 where he measured the actual potential. So that was sort of like I guess it's 150 years ago or something. Yeah, well, when you think about it like that, it's like neuroscience is pretty young. The actual potential is kind of core to the whole endeavor. Yeah, so what could you do before it? Yeah, so that's true. So, and I guess also I think the first I just do because our group we have been working on this extra cell of signals and stuff and I think the first extra cell of the signal that was measured from the brain was the ECOG, which was like 1870 or something, which is also something. Yeah, so that was also when they had the guys amplifiers which were good enough so that you can sort of yeah. Methodology is very important. Yeah, so but then and then for those, I mean many of us in the field have learned about the integrated fire model and then it's often referred to the University of this person La Pic in I think 1907 or something. So what did what did he do? Yeah, so he took you know at this point there was a lot of evidence of how neurons respond or nerves at least respond to applied voltage and you know you know the idea that they're using electricity was accepted but his goal was to quantify it more and kind of come up with a description of what was happening that had some mechanistic truth to it. And so to do that he focused on the question of if you stimulate the neuron it was known that you know you stimulate the neuron with some electricity and the muscle or the neuron will have some response later on. And so his question was you know if you apply voltage of different strengths at what time point will the the nerve or the muscle respond to that application because it was clear that weaker voltage led to a longer delay and higher voltage led to a quicker response from the neuron. And so he wanted to be able to come up with an equation that captured that relationship and to do so he just kind of took very directly the mathematical framework of how people describe electrical circuits. So just thinking of the neuron as its own electrical circuit and using the same mathematical tools that you would use to describe you know wires and things he used that to describe the neuron and what's called an equivalent circuit model of the neuron. And so that just was quite important conceptual events. Yes yeah to say because then it just it makes this very clear connection between the two fields and you know all the tools that are developed in one can then be used in the other. And so yeah he described the neuron as having a capacitor that could hold charge which is played by the role of the cell membrane. And then also he acknowledged though that it wasn't a perfect capacitor it didn't hold all of the charge that was put on it. It had some kind of leak to it and that was played by the role of resistor in the equivalent circuit model. And through that he was able to make this connection between how much voltage you applied and when the nerve would respond by assuming that the voltage had to read some sort of threshold in order to respond. So he was able to kind of fit the data that he had with this equivalent circuit model. So then the response was then what we now call the spike or the action potential. But they didn't really know what exactly happened at this action potential that was that's my these I would just like the membrane was sure circuit that there's something that was just opened up and became a whole unit or like yeah. Yeah so the peak model definitely doesn't try to explain what the action potential actually is. He's just saying there's a response that happens and it happens at some threshold and that's all that that he was trying to capture. And yeah so the actual kind of you know if you really like zoom in on the action potential it has a very characteristic shape to it. The dynamics of the voltage of the shell of the cell has a very characteristic shape. And yeah the theories initially from people like Burns 9 were that the cell membrane just kind of dissolves a little bit and that's how the the difference in charge between the two sides of the cell brain how cell membrane how that weakens during the action potential. But that wasn't a very good model because it doesn't describe some of the more kind of extreme features of the action potential shape. If it was just that the membrane was getting a little bit looser and letting more things through you wouldn't get the shape of the action potential that's actually seen. One element of that theory is that there is a potential difference between the inside on the outside and to begin with sort of like in in in rest. And I guess this was sort of like this idea with the nourished potential that that there's like if you pump up or if you have different or unnatural concentrations of some sort of these ions of sodium and potassium I guess and chloride. In particular then you get this this membrane potential to begin with. So I guess that was also another pioneer was this nourished. Yeah. Yeah that also put this yeah that that also made this and then but then I guess next big milestone stone to jump until like the 1950 or something was the Hodgkin and Huxley because they then took it a step further and aimed to, well not only aimed to try to make more quite successful in explaining what actually happened when they get this particular spike because it's not just that the membrane breaks down. It's like more particular picture about with iron currents, iron selective channels. Yeah, so Hodgkin and Huxley had to do a bunch of experiments with these different ion types by taking neurons and putting them in different solutions that contained, or didn't contain different ions to see which part of the action potential would change if there was not an sodium or not an potassium or something like that. And so through that they were able to see that there is a lot of very specific ion concentrations at play that it's not just kind of a generic charge calculation. It matters the type of ions. And so they therefore built a kind of new equivalent circuit model still based on the same basic principles, but here they added these extra resistances to the model. And those resistances were meant to kind of model the ion channels that were specific to different ion types. And also those ion channels, it turns out are voltage sensitive, they're voltage dependent, they'll change how resistant they are based on the voltage of the cell. So that creates this rather complex system with a lot of interdependencies and a lot of interesting dynamics. And through that you get the shape of the action potential that that we know of where the voltage changes in both directions and kind of goes reverse as a potential and comes back down and everything. And so their model through having the right kind of ion channel dynamics, the right understanding of those ion channel dynamics, they were able to capture the actual shape of the action potential. And at that point you needed computers or at least like some handcranked some comia to do the numerics because it was just you couldn't really do compute the consequences with pen and paper easily. Yeah, even yeah, even just for one single point neuron model, it already gets too complicated. And there's a quote in the book from Hodgkin doing those calculations where he says that he was he's been surprised by the outcome of it. Like he's putting in the calculations and he's calculating the voltage at the next time step and he thinks it's going to lead to like a full action potential, but it dies out instead. And just this idea that our intuitions for these really complex systems are just they're not very helpful. We don't we don't have intuitions for these complex systems. Exactly. And that's kind of the whole point of doing mathematical modeling is you know, you you figure out the basic principles and you can write down the equations, but you can't guess how they're actually going to play out. Exactly. And that's I guess that's one of the reasons why when you're able to do mathematical modeling, it's so attractive because because the rules are so well, I mean, you can follow the logic. I mean, you can trust the outcome if you do the maths, right, even though if you don't have intuition about it, right, because it's such a so that's much more difficult with with like, I mean models in words, that's they're difficult to sort of to come up with really unintuitive things. Yeah, usually you're just kind of restating your intuition with words, whereas the models can actually, you know, return something pretty surprising. So then we were in terms of modeling neurons, then I mean, we still we still didn't have like a good way to or we didn't sort of so far the focus hadn't been mentioned then writes, right. But then the next then the computation neuroscience hero Wilfred Drahl, I guess, at the stage. So what did he do? Yeah, so he just kind of continued on with this idea that neurons are electrical circuits and therefore you can use the tools that we use to mathematically model electrical circuits. You can use them to describe neurons and build models of neurons. And in the case of dendrites, he's associated with the cable theory where you basically just treat dendrites kind of as wires that have some resistance and but they can carry the the current to the soma. And so by adding in the morphology of the dendrites, just according to the basic equations by which you have model wires in an electrical circuit, then you can capture some of the functionality of dendrites in neurons. And so you know, something that comes out of that is just this idea that the pattern of stimulation on the dendrite can matter. So we want order you're stimulating different inputs because they're physically located in different places. They can lead to different results at the soma and that that itself can be involved in computation. And I guess this with that sort of like and so he out of all time. And I guess also if you so if well, if you look at the Hodgkin Huxley, what they contributed was one thing they had like came up with this so demand, but that's him channels that actually was sort of the right form to explain this action potential generation and propagation in this and squid giant axons. But they also the formalism they introduced was also then could be easily adapted to other ion channels. And I think now with this much well, this cable acuation description overall and this Hodgkin Huxley description of ion channel currents, we sort of have the it's like that sort of the backbone of what's what's called multi-compartmental modeling or like biophysic radita in modeling and neuroscience. So so the principles of that is sort of like I guess was established in the 60s or 70s or something. Yeah, or even with the peak as early as you know, 1907. But yeah, building on that by being able to collect data from real neurons and then use that to get the parameters from the model, but having the kind of mathematical tool set to be able to put in almost anything you could find in a real neuron, you can pretty straightforwardly put it into one of these models, like extended models. And then this was then then then you also needed some some models for the mathematical expression for the synaptic currents. But after that, you could start making putting it together in this large large networks and maybe the most well-known of this large game networks is this blue brain model that came out in 2015 from this this group in Switzerland. So what was the what did that model do? Yeah, so that model yeah kind of took these basic ideas and just really went crazy on scale with them basically. So collecting data about all different types of neurons in the rat cortex and you know the shape of the neurons and their properties about their member potentials and ion channels and all of that along with how they connect to other cell types and all of that to create just a really large model of a bunch of interconnected thousands of interconnected neurons which are governed by millions of equations basically and just running that simulation you know on supercomputers to be able to take these basic principles of how you model individual neurons and then say can we from that build a model that's actually more representative of an area of cortex, a very small area of cortex but still some region of cortex kind of going from these small bio physical models to still bio physical models but at this really large scale which is for the most part of very technically challenging thing to do both in terms of collecting all the data you need to get the parameters and then actually running the simulations on computers. One, I mean of course this large we are also involved in doing this and well in this collaborating with people at Allen Institute with the mouse primary visual cortex model and of course it's very difficult to analyze the results it's sort of like and and what to deal with these models but this one one example maybe where which for a simpler system with this stomato gastric what is called stomato gastric angle in the crab and then with even harder and collaborators so they have sort of been able to study I guess that's one of the well best successes of sort of studying modeling a particular network system in the living system. Yeah that's an example that's rare in the sense that there is kind of a lot known about it it's not a very large circuit of cells and it's used to control digestion but it's well characterized like the data has been collected on the cell types and how they connect to each other and all of that and you know its function is pretty clear it's supposed to be generating these oscillations and so I would say it's not that setting is not super representative of what of the challenges that face most neuroscientists because usually you don't have the the structure and the low level details that well characterized and sometimes you're so many neurons are there's like ten or twenty yeah so yeah and a lot of times you're not even that sure about what the function is but yeah there have been because it's so well characterized you can kind of say things with more certainty and derive kind of principles that could be relevant for for everyone for whatever your study and so one of the the kind of arguments that Eve martyr makes you know is that the relationship between the structure of the circuit and its function is not that type especially if you're really defining structure as kind of the pattern of connections between the neurons she's shown that you know you can have the same connections you can have have the same circuit really, but based on the different neuro-monkey. that are present, it can display very different rhythms. And so the function of it changes based on the presence of these neuromodulators that don't really change the physical connectivity necessarily, but change some maybe properties of how the cell responds or maybe like scale the weights of the synaptic connections to some extent. So yeah, so the idea that a single structure can have many different functions is one side of it. And then also the flip side is that the same function can be produced by many different structures. So different individuals, individuals in this species will have slightly different structural connectivity, but they all still are able to produce the rhythms that are necessary for the digestive system. A flip side, maybe for the, not for the animal probably, because it makes them more robust that there are many ways to have the solution. But in terms of for the modular, if you want to look for some kind of unique solution, it sort of is, it makes it more, and sometimes it's ill-posed, it makes it more difficult. But I guess it's also, I mean, if you sort of like this thing of doing this biophysically detailed modeling, if you go take a computation neuroscience course around the world, you typically are introduced to cable description and Hodgkin Huxley. And you maybe do, I mean, do some simulation or build a model and are like these tools like neuron genesis and arbor, you can do these things. And then, so that's sort of like the standard approach. And then you typically decide what science you want to have in it, and then you sort of have to choose this density, so these different science, how they are spread. But I guess like some people have also started to look at, maybe this is like, you could go one level deeper and maybe instead of modeling the densities of putting in choosing the densities of science as parameters to sort of models or the transcription or whatever, or like how these are, because these are dynamically regulated to begin with, right? So because this subcellular level has not been so much, I mean, what's going on inside cell? That hasn't really typically been the realm of computation neuroscience, not too many computational neuroscientists are getting it. Yeah, I think there are people who are applying computational approaches to that, but they're not, they don't fall under the category of neuroscience. And they're maybe doing it in a more generic way for how cells regulate these processes in general. But without the motivation in terms of how these subcellular processes lead to things that are particularly important for the brain and how the brain functions. Yeah, a lot of computational neuroscientists have ignored them. And that's the art of computational modeling, is that you ignore the things that you think don't matter. And so ignoring subcellular stuff is a pretty easy argument to make a lot of times. But I think there is, there can be areas where people turn to that if they think it's important for what they're trying to understand. And one area that I've seen developing kind of spurred by progress in artificial neural networks and thinking about how those learn and how that compares to biological learning is looking at subcellular, maybe long time scale processes that occur in order to support synaptic changes for learning. So yeah. So things that's going on inside synapses, maybe some up regulation, down regulation. Yeah, inside synapses. And also maybe just things that are tracking kind of overall activity levels of the cell to have a sense of how active the cell has been recently and relate that to outcomes of the animals behavior to say, you know, the activity of this cell is associated with good things happening or not. So that kind of thing and yeah, being able to integrate different sources of information to do a calculation about how the synapse should change. All of that are things that could be happening subcellularly and it would kind of be helpful from an algorithmic perspective if they were. So now, now, computational neuroscientists of a certain variety are happy to look at what subcellular people have been studying for a while. Yeah, because one field under there is also this, I mean, I'm a physicist by training. So this molecular dynamic simulations where they're simulates or like how they can, for example, simulate like a represent ion channels in terms of proteins going back and forth through the membrane and sort of model it at atomic level. So there are, and this is of course used, this is used a lot in sort of to study other, I mean protein folding and stuff like that. So there's also this field working on at that level. And I guess if you sort of look at the Hodgkin-Huxley model, they had these key expressions for how these openings and closing of the channels depend on voltage. And this was sort of something they fitted to data. But in principle, these should be able to be computable maybe from from molecular dynamics simulations. Yeah, at least in principle, right? So there are sort of, there is a level below there that sort of most we typically don't go into as competition. Going for a really long time. That's true. Okay, so now we have sort of talked about the biophysical aspects. And this could have been about any body part, right? Whether it's brain or any other body part, I mean, it's a biophysics. We haven't really talked about coding and information processing. But that I guess there was this, that's the start of that avenue or that branch of competition neuroscience was really this paper by my color and pits and 43. So what was that paper about? Yeah, so that paper kind of demonstrated a way in which you could use what was known about neurons at the time, kind of their basic properties, you know, that they fire an action potential and they have connections between each other and some of those connections are excitatory, meaning that they make the other neuron more likely to fire and some are inhibitory, meaning they stop the firing of the neuron. Using those basic facts, you could string neurons together in a way that they could implement logical functions. So the idea that a neuron is either firing or not that can be related to Boolean binary logic, the idea that a statement is true or false. And then the connections between the neurons can implement these logical operators. So if you had a neuron that got two inputs from two different neurons and it needed both of its inputs to be firing for it to fire, then that neuron is implementing the or the AND function. It's saying I need my first input and my second input to be true to be RUN for me to be on, for me to represent true. And so through that, you know, you could string together, I mean, infinite numbers of these to create more and more complex logical statements. And if you can do that, if you can make neurons do logic that you're opening the door to explaining a lot of the things that the brain can do about logic and reasoning and all of that. So that was their major contribution in terms of taking the first of the brain, making the physical details that were being studied by physiologists and biologists and giving them some kind of purpose in a larger computational system to actually explain the outcome of the brain, more explaining the mind using these physical details. And my comic was this physiologist, right? I'm working in Chicago, but Pitz was this very interesting character. And also this child prodigy, who sort of grew up in really difficult circumstances. So I think it's a fascinating story. Maybe the most interesting person in neuroscience that I've come across. Yeah, he grew up in Detroit, but he ran away from home when he was a teenager to actually go to the University of Chicago, not to attend it as a student, but just to like go hang out because Bertrand Russell was visiting there and he wanted to hear his lectures and stuff. So he just kind of hung out at the University. And Bertrand Russell was his really famous mathematician, right? Yeah, that. And philosopher. Yeah, who had a lot to say about logic and mathematics and all of that. And so yeah, so Pitz just kind of hung out there. He was homeless for a bit, but he just wanted to learn more about these things that he had read about as a kid. And clearly just had some innate ability to grasp these very complex abstract, logical, mathematical ideas. And so yeah, he never really had a formal education or certification or anything like that. But he ended up functioning, you know, as a scientist, as a professor, kind of person in the field. But he also, you know, for a variety of reasons, kind of struggled towards the end of his life and died rather young because of some of the difficulties in his own life and in the science that he was doing. And also I, for those who have seen Goodwill hunting, like a movie from some decades ago with Matt Damon playing this prodigy and that sneaks in sort of like sort of correcting what sneaks in is like mathematical notes onto the professor's desk and sort of gets, gets discovered that way. And that was a little bit similar to what happened to Pitz, right? But it wasn't really this, this, this, this, my colleague Pitz paper didn't make a big splash in neuroscience. Yeah, the neuroscientists and the biologists and physiologists of the time, they didn't really know what they were doing. what to make of it because it didn't really explain their experimental data in any specific way. It didn't address questions that they had amongst themselves. It didn't tell them what they should look for in future experiments. It was just kind of making this claim that look you could, you can do logic with neurons and they were like, okay, but no one was trying to connect neurons to computation or logic at the time. So it was a solution to a problem that didn't exist and also it was hard to read like the paper is not very clearly written, not even in retrospect. The notation of the paper and style didn't catch on. So yeah, it wasn't taken up by the neuroscientists in any enthusiastic way. It was difficult to do. It didn't really, it wasn't any specific experiments that you could do to test it maybe or. Yeah, not so clearly. But it was sort of a starting point of another community, which is also obviously very important for the computational neuroscience community, the AI community. So how was that? So that was like this 56 conference or workshop somewhere in Dartmouth. Is there something? Yeah, so that's kind of the starting point of AI properly. But even before that, there were these Macy Foundation conferences or workshops where people that were kind of swirling around this topic area like McCulloch and Pitts and John Van Neumann and all of them kind of in this realm of cybernetics or whatever it was called at the time that were really planting the seeds for all of that. And so through that vein, McCulloch and Pitts had influence on this very burgeoning, very young field that eventually got the label of artificial intelligence. But it was really in its starting point at this time. And then because one thing that is sort of not so different or at least had this maybe this logic idea was this perceptron with a Rosenblatt. So what was that about? Yeah, the perceptron came in like 1958 and it is also an artificial neural network in the sense that it uses neuron-like elements like the McCulloch and Pitts system does to implement computations. But it has a lot of differences. I mean, one, it was like the Rosenblatt actually built a physical machine to implement it, to kind of simulate it. Whereas McCulloch and Pitts, they were just doing this kind of mathematical logical exercise in a paper. But the perceptron also is a bit different. It still has, as it's basic construction neurons that send connections to each other and those connections are kind of the heart of the computation that are being done. But the perceptron doesn't explicitly implement these logical functions that McCulloch and Pitts identified as being possible in these networks. Instead, it learns to do kind of whatever computation it's trained to do by having a learning algorithm that changes the strength of the connections between these artificial neurons based on how well the network is performing on the task, based on if it's getting things correct or incorrect when it's asked to like classify some sort of input. So in that way, it has more utility. It has more functionality, especially applied to the real world than what McCulloch and Pitts were doing because it can actually be run and simulated and actually be trained to solve more complex and real problems. And then Rosenblatt made all these grandiose claims what it could do. And then there was like this story with a book of minskinskin paper, who sort of like wrote about the perceptron and then ended up sort of almost like making what's called the first nuclear winter, no nuclear winter. Well, the first network winter. Yeah, it could have been worse. It could have been a nuclear winter. That would be quite a book if it could be that. So anyway, but so because it sort of like show that you need it's like a single layer network couldn't do all this thing. So that was our own. But that's like a different story. But what was interesting to me to learn by reading a book was that they actually found something like the perceptron in the brain in the cerebellum. Yeah, in the in the cerebellum there's kind of it the cerebellum has compared to the cortex has somewhat neater organization to it just looking at the cell structure by eye. And yeah, the few different scientists were kind of came up with this idea that the mechanism of the cerebellum kind of what was happening in the cerebellum with its different cell types could be related to how perceptron works. And so there's cell types that represent the output of the cerebellum that can go on to control behavior, the perkinji cells. And then there's cell types that represent the inputs, like sensory inputs. And so basically you have a system where sensory inputs are being transferred to behavioral outputs. And then there's a third set of cells that come in and signal error. So to say that you know something about the behavior was not what it should be. And so with those three components, you can have a learning algorithm that can update the connections from the sensory inputs to the behavioral outputs based on error. And that's kind of the whole heart of the perceptron learning algorithm. And so that was found to be happening essentially in the cerebellum. And that's how the cerebellum can support error based learning. Because I think I mean you have this this March three levels of right of modeling. And so what are those again? So you can that's one. So there's the computational level, which is kind of the goal of the system, like what is it trying to do? So in this case, it could be error based learning. Then there's the algorithm that the circuit implements. And so in that case, it could be the specifics of the perceptron learning algorithm, how the weights should update in response to different types of errors. And then there's the implementation level, which is what physical parts actually realize that. So you have these different cell types in the cerebellum that play the different parts to do the algorithm. So this cerebellum example is maybe the first first example of actually a system where we'll which was understood at all these three levels. Yeah, I'm not sure. I mean, it depends on yeah, how strict you are. You could probably find other examples earlier, but it certainly is a very nice example of it. No, I think it's always so because I think at that time, also if you look back at the modeling that did, I mean, because it was also some of these like associative networks and like memory networks that was like started in the work on that in the 60s. And they often had very simple units that didn't have anything like Hodgkin Huxley. They're just very simple neural units. And it was more about what the network structure can do and maybe like some kind of simple synaptic plasticity. So it was like, yeah, I guess it was, well, I guess it was also a practical reason. It was difficult to do network. Yeah, to simulate these big networks of detailed neurons is more recent ability. Yeah. Yeah. So and then another aspect, of course, is this if you go go back to when you started recording spikes. And I guess Adrian was like this, this Englishman who was like, was doing measuring all this this spikes. And I came up with the first suggestion for a, for I guess what it's called a neural code. So what is meant by, well, what is meant what did he do and what is meant by a neural code? Yeah. So the idea of a neural code is kind of you try to identify what about neural activity you actually think matters in terms of what's carrying information and what's driving behavior. And so you can think of, you know, as we said, you know, neurons, they're firing or they're not firing. They have a shape to their action potential and all of that. And so there could be information hidden in multiple different ways within a neurons activity. It could be that the action potential, the actual shape of the voltage changes will change depending on the stimulus that's coming into the neuron. It could be that the number of action potentials changes. It could be that the time between action potentials changes as a way of, you know, encoding, so to speak, the information that's coming into the neuron. What Adrian showed was that the action potential is constant. It's all or none. It's if the cell gets enough input to fire. It will fire, but the action potential itself will not change based on the inputs that are coming to the cell. So that kind of rules the shape of the action potential out as something that can carry information because if it responds the same way every time, then it has no ability to signal what has come into the cell. And so through Adrian's experiments by kind of putting in sensory inputs to different sensory nerve types, he showed that it seemed more convincing that the information was being carried in the number of action potentials that a neuron emitted rather than anything about the shape of the action potential itself. So he was kind of an early proponent of this rate coding theory, meaning that the rate, the firing rate of a neuron is carrying information that is, you know, relevant for the computations that are being performed. And alternative codes that, I mean, has been suggested later is sort of like there's like the details, I mean, the timing between each spike really matters and like it's correlation code or Yeah, when you're looking at Yeah, when you start looking at multiple neurons and you can also get kind of more complex codes about timing between different neurons and all of that So yeah, it's really in some ways it's it's open ended as to what you want to define or try to test as Coding in the brain because there are many dynamic parts to neurons and neural activity And you could argue that you know any any one of them is encoding information to some extent so so encoding that that can be summarizing that's essentially going from say for example a stimulus to a pattern of of spikes In like in in a set of cells a set of neurons. Yeah, and so that's sort of like encoding and then because lots of competition neuroscientists also works on decoding So so what's the what's the job there? Yeah, so that is more um fraught as a topic because um you know If you're thinking about this kind of coding as just a means of communicating information of conveying information Then the decoding process should just kind of be a reverse of the encoding process you go from some input stimulus Into a series of spikes of a neuron and then there's something on the other end that takes those spikes and reads them out and then turns them back into an input stimulus into the same stimulus which is not what we want our brains to do We don't want them to just recreate the inputs that we gifted them Um, so yeah So Really they're in some sense there kind of isn't that you know Very basic decoding that happens in the brain because there's transformation of information that happens in the brain There's computation that happens and you're supposed to take in inputs and and do something with them to create different outputs So what is decoding in the brain is it's a far broader question But it still relies on the fact that Information is encoded in neural activity in some forms such that other neurons can get input from those neurons and that can you know Create something useful Uh and behavior I guess a general problem if you see some kind of neural representation in there which in principle contains information about Something about the I mean it about the outside world It doesn't mean that the the nervous system are able is able to extract this information right that's uh Yeah, and this is something people fight about a lot now You know in papers if all you did was record neural activity and show that you as the experimenter could use some sort of Algorithm to read out the information and you can see the information is kind of in that neural activity Um is that what is that saying about the brain itself Um, it's saying the information is present in that neural activity It's not saying that there are neurons in the brain that are reading out that information from that neural activity Yeah, I guess I mean you also have this this now and this question about so like the like all there Other things on the spikes, but also like the local field potential or the EEG Yeah, and and and nobody would say that the EEG itself is used by the rest of the brain Right, so there are people who would say that the the local field potential is Yeah, that's true. Yeah, the other neurons. Yeah, so that could be that could be Like a neural signal because it's not directly coming from the neuron But it's kind of a diffuse signal of the activity of a bunch of neurons that they could be hearing it So that's the truth that that could be so that they're there. I guess the jurists are out. We don't really know Yeah, and it's not extent but them so that's good But then you had like this other other theory that came we sort of like to for quantifying information Which came from from Claude Shannon that was all like just well, I guess it was just published as after the war or something Yeah, yeah, so he developed this kind of formalization of the concept of information because it's something that like we've been using and Neuroscience to the use for a long time But without actually having a formal definition. It's hard to study it in the brain or are anywhere else But his motivation was coming from thinking about communication and thinking about You know things like communication during the war where how can you send how can you make sure that you're sending information That's reliable, but can also be sent quickly and and that kind of thing and so his notion of Information depends on actually kind of already knowing what the code is you have to be able to say what a symbol in this code is And then if you can say that then you can do a simple calculation to say this is how much information You know is carried in these symbols in this code But it doesn't solve the problem of not knowing what the code of the brain is It's just a way of talking about information quantifying information If you have a guess about what the code is Because I think they it was like when it came it was it was like a formalism you could apply So you could compute things like bits per second or bits per spike and stuff like that so But it was then I think even Shannon himself got a little bit worried about the Overapplication of his ideas Yeah, he wrote this short article a few years after he published this Definition of information and to just say like it's being applied too much being You know people are attributing to this concept more than it's capable of providing and that people should be cautious Because yeah, it was again, it's based mostly on the concept of communication And so it's just about sending a signal and then being able to recover the signal that was sent And as we're saying in the brain you're doing more than just sending a signal you're trying to transform it combine it with other things and create useful output from it and none of that is inherent to the original definition of information from Shannon Because one way to maybe to get too closer to while I write this about the Like the codes that I use is to have some kind of principle like Is that like one principle is this idea of a efficient coding that came my as late 50s or something So what was that all about? Yeah, so that comes from Horace Barlow for the most part and that the idea there is that Basically the the brain would not be redundant the brain wouldn't be sending signals that are not helpful or necessary And so if something in the environment is redundant or something the environment is happening over and over The brain would stop sending a signal associated to that and there are kind of other ways in which you can reduce redundancy in a code Which are you know, it's based on the statistics of the information that's coming in and being transmitted How you decide what's redundant and what makes a code efficient as a result of that so that was his idea that Because of you know the metabolic cost of sending spikes and all of that That the brain is going to use an efficient code and if we keep that in mind will be able to understand some of the peculiarities of how neurons respond to things are really how neurons don't respond to things as well Cool, so actually we're going to have a Podcast upcoming podcast about the neural code and with arvin Kumar which will Come be soon at the podcast closed home So yeah, so but think now if it goes sort of today If starting now we have talked about these principles and these ideas and I guess the first the system that was like Or which was really has gotten a lot of attention. I guess it's vision vision has a lot. I mean one thing we are very visual animals and and so that I guess it was this Think you mentioned this Jerome let win guy And also just after the after the war. So what did he do? Yeah, so he was part of a study on frogs that spoke to this idea of the visual system as being a hierarchy of feature extractors So if you kind of maybe just had like the most basic sense of how vision could work You might think that if you're trying to recognize something Like you know a coffee mug that you just have stored in your brain some template of what a coffee mug is and Information comes in and you compare it to that template and that's how you decide That was kind of a very basic theory that was being tossed around But it has a lot of practical challenges because Most things aren't so easily Describable that a single template would explain all of them and also if you're really thinking about a template at kind of the pixel or or Retina level Just changes in lighting changes in angle and all of that are going to you're going to need separate templates for for the same object under different conditions So it's just not a really a feasible way to solve vision But the idea of using a hierarchy of feature extractors can build in some robustness and so the the Project that let been was a part of was recording from The retinal cells in a frog and seeing the different types of light patterns that they respond to and so they found a few different cell types in the frog retina That they weren't just kind of conveying verbatim the light hit this part of the retina and that goes on to the brain They were doing some computations themselves and so one of the most striking computations was that you know You'd have neurons that would respond if a small dark dot kind of moved quickly across the visual field and The natural conclusion or assumption there is that these can help the frog detect bugs that they're trying to catch And so having part of that computation built in even at the earliest layers of the visual system means that the visual system isn't just you know The retina isn't just taking in information and doing a single calculation later. It's kind of pulling out the relevant bits Throughout the hierarchy But already this idea is quite different from the idea of my company and pits, right? Because here these neurons were doing much more than just sort of doing this binary operation, right? It was not like Boolean things they were doing. So I guess that was also quite an argument against that idea. Yeah, and it's points more in the perceptron direction in the sense that it's kind of just messier and more spread out. And so you know, you have things are getting done where they need to get done to achieve the desired behavior. And yeah, you can't put a clean label on each of the parts. And then this was taken on and while moved, well, generalized or checked, well, tested out in cats, I mean, I'm both in, well, I guess first retinol also, LGM and then the visual cortex with Yublan and Viesel. So they are probably there. Of course, their work is quite well known. So what did they do? So they discovered that, so yeah, as you said at that time, you know, people knew that there were cells in the retina and cells in the lateral geniculate nucleus in the thalamus that would respond to kind of points of contrast, like a dark point surrounded by a lot of light or the reverse. And so they kind of went into the next stage of visual processing, which is visual cortex at the back of the brain. And initially started looking for cells that also responded to those kind of contrast points of light. But what they discovered was that that's not what those cells responded to. They actually responded to oriented lines, kind of more like bars of light, sometimes that are moving and that the neurons had very specific responses. They only responded to a particular orientation at a particular location. And particularly for what they called simple cells, it really had to be in the exact precise location for complex cells. It could be in one of a few locations that were near each other. But on the whole, they all had these very particular orientation preferences. And so through that, they were able to kind of guess about this hierarchical model whereby the LGM cells have responded to these points of light. But if you align a bunch of points in a row, you get online. And so the orientation of those points leads to the orientation preference of the visual cortical cells. And then also the spatial preferences of the simple cells, if you give a few simple cells as input to a complex cell, then it responds to the line in multiple different locations, whereas the simple cells are responding just to their one location. So this was a really cool idea. And then of course, they wanted to see does this work at the higher visual areas. And there it wasn't so clean-cup, right? Yeah, they kind of tried to keep, they were looking for like hyper complex cells and kind of, you know, to keep going. But it did, it did start to fall apart. And, you know, there was, really for many decades following human measles, there was this attempt in a lot of studies in vision and other mostly sensory areas that the goal is to kind of categorize cells to record from a bunch of cells and then be able to say these are, you know, the simple cells of a complex cells are these are the curved detectors and these are the star detectors or something like that. And that did that that only had medium success in terms of actually being able to explain things in a satisfying way because the cells weren't that categorizable. They didn't form these kind of neat categories, especially once you got past the primary visual cortex. So he will and we'll then just started studying development of the visual system and particularly of how this orientation preference develops in V1. And then in Fukushima, now in Fukushima in Japan, there was this Fukushima guy. So he took this idea and and it was like a computational scientist and he took this idea to to construct a network called it what's called neo-cognitron or something. Was it? Yeah. Yeah. Yeah. Yeah. He heard about human measles work through fellow employees at the radio station that he was working at as an engineer. And yeah, he heard about and thought, okay, this is kind of the algorithm for how vision is done in the brain. You have these cells that respond to oriented edges and then you have these other cells that get input from those and you know have some more spatial invariance as a result. And so he built this very early computer vision system that was based on the principles of hubo and measle, but he kind of extended it beyond by kind of replicating this pattern of you have these simple like cells that look for patterns, very simple patterns in the image or in the inputs that they get. And then you have the complex cells that get more spatially invariant and then you repeat that pattern of looking for patterns and making it spatially invariant and looking for patterns and making it spatially invariant until you can go, you know, you can have a whole system that takes an image and puts out a label of what's in that image. Now his images were very simple. They were like binary black and white images of digits. So just like very simple lines and stuff. But the concept was there that you could build this hierarchy of features extraction essentially. I mean, another lot, I mean, at that time, I mean, in the 70s, there were also people working on this, making this firing rate models. So that was like so far we talked about like single neural models and by physical detail or more simplified leakage rate of firing neurons, but still neurons that fires spikes. But then you have these firing rate models and they were against like Wilson and Cowan was like to early pioneers, they were made is where you sort of model the probability for firing or firing, like firing rates of populations or something. So they they they become they were used in studying the the visual system also, right? And I think one really cool recent example which you highlight in the book is this ring networks of this this this head direction cells in the fly fly visual system. So that's because there they're they use yeah. So then I think that's one of the examples of oh, if you can tell them remember those. Yeah. So yeah. So the firing rate models, yeah, as you say, they're not the same as like leaky integrated fire or hutch canhuxly. The neurons and those models are represented by continuous variable that is supposed to represent something like firing rate, which is consistent with the general belief in rate coding in the brain, right? If you think the firing rate is what matters, then you can just have a model that captures that and you don't have to capture each individual spike. But yeah, those those models have been used, you know, throughout a lot of different areas of interest in computational neuroscience because again, you might my baking it a little bit simpler, you can study more complex populations of neurons if you make each individual neuron a little bit simpler to model. And you can apply like a lot of linear algebra and dynamical systems analysis to be able to make some nice statements about how these populations of neurons behave. And one of the examples where that has really been kind of quite elegant is in the head direction system. In it exists in flies and mice and I assume most animals that need to know which direction they're head is facing. But the idea there is that you have a set of neurons that are connected to each other in a spatially dependent way. So there's like nearby neurons that are connected to each other and then there's farther away neurons that don't connect to the original neuron but connect to their neighbors. And if you have this in the shape of a ring, you can think of different locations on this ring of neurons as representing different locations, different directions for the head to face because you know, it can go in 360 degrees. And so the firing rate pattern of the neurons in this ring of neurons, which neurons are firing, indicates which direction the head is facing. And these ring networks, if they're built exactly right, can kind of have memory. So if there's a way that the head is facing and a lot of times animals get this Q based on kind of visual inputs or other things in the environment, they know which direction their head is facing. Even if you turn off all the lights, they still have a memory of which direction their head is facing, which where they're facing. And that works because the neurons in this network, their connections are such that it's known as there's an attractor state, meaning that the neurons will sustain their own activity even in the absence of inputs. And that's really important for memory more broadly. And it comes out of, as I said, kind of this notion of an attractor is you can study it really elegantly with dynamical systems theory. It's a very core concept there. But yeah, in the heading direction system, you could also then give them the model inputs that update the direction of the head in the representation. And it can just really function very well with a relatively simple and elegant system. So computational neuroscientists like it. And then it was discovered, you know, in a very again elegant and beautiful finding in the flybrain that these neurons, which we think of as a ring network as an abstraction, actually formed the shape of a ring in the flybrain. That's what we call textbook material. The text must be rewritten as soon as that paper came out. Exactly. So I think it's something of the simple models, conceptual simple models that can sort of interpretation is clear. And so I just want to complete this. I guess so far we have talked about what we could call mechanistic models, which sort of like all of this has been about mechanistic models, at least the biophysical models and also these like, well, the ring networks. But you also have this descriptive models more like, well, I mean, for example, the gobbledore function, well models which I just used to capture like experimental data. I guess that's I mean often you see this and they will like a different so Gaussian model which are used for Neyretna and also the LGM and then you have these Gabore functions that is just sort of kept in the prong for the simple cells Just telling sort of giving in well. It's a way to capture information or To capture or to store information about sort of like the response of a cell to different kinds of Visual stimuli. We're not going to talk so much about that, but that's also in sort of obviously a part of of computational neuroscience Yeah, and the descriptive models actually interplay with these mechanistic models I think quite nicely because usually at least my perspective on it is that you know You need the data to be described in a nice compact form when you're trying to work on building a mechanistic model Or at least it certainly helps if you have some sense of Yeah, if you don't have to deal with kind of the messy data itself, but you have some abstracted description of it So kind of it's already put in mathematical terms and it's already Simplified in a way so that you're you're target of what the mechanistic model is trying to capture is clearer I think that's that's one way in which they can interact They don't have to like sometimes descriptive models are just on their own and that's fine But I certainly see a connection between the descriptive and the mechanistic one thing We also I mean there's also this of course data analysis. That's a whole I mean a lot lots of competition neuroscientists work on data Analysis and and so there's all this thing about which I guess is in the I mean this descriptive models Are a kind of data analysis, right? You sort of try to sort of fit the date well make the describe the data in terms of these like the receptive field models And but then you also have this all this dimensionality reduction techniques switch RL mm-hmm Yeah Yeah, that's becoming increasingly popular as the Recording methodology makes it such that more and more neurons are being recorded at the same time You know back when he will in weasel and and those kinds of people were working They could only record from one neuron at a time and so it made sense that they were trying to categorize these neurons and Describe these neurons in this very individual way about what is this neuron doing? But when you're recording from a thousand neurons at a time you're not gonna go through one by one probably and try to to give them all Little names or anything like that And so the question is what do you do with them? And so these dimensionality reduction techniques are Yeah, becoming increasingly crucial for how people Visualize and try to make sense of a big pile of of neurons that they recorded by Taking those neurons and combining them in ways that you can make this simplified plot and deal with You know instead of a thousand neurons you can deal with three dimensions that represent a lot of the variability that's happening And then you see it's like ECA perperitable components analysis is sort of like And then you and then you do this I guess you make this neural manifolds is that sort of like And you sort of plot how these components move around in Yeah, that's another one that there's a lot of debate over how those concepts should be used and then the utility that they have But certainly yeah people are trying really just trying to come up with new concepts in a way for how you understand Large populations of neural activity what what should we be trying to pull out of them and how should we describe the things that we find And relate them to things like behavior or whatever other useful Commutations you think are happening. Yeah, because now I mean with this new I mean if you just look at electrophysiology with all these like neuro pixel probes That you can put in many at the same time you can measure from like thousands of neurons and with two phone the calcium imaging It's even more so how what should you do with this data you really need some kind of Some techniques for handling them. Yeah, so this is sort of a Obvious need so but now I mean so far we talked about computations, I guess like but we haven't another important aspect of the brain is is memory and this this idea of like Hebbian learning that's like a key thing and it's just like a give a short Short short intro to the hebbian learning before we move on to the Hopfield model like that Yeah, so hebbian learning is named after Donald Hebb And it was kind of a speculative thing that he put forth to say that There's you know neurons that are active together are going to form stronger associations and the way people say it now is like neurons that fire together wire together And so but it is it's a simple idea But it has been explored and you know can lead to a lot of useful things when applied at a broad population level But yeah, it's just the idea that if you know, especially there's there's versions of it that are More temporarily dependent, but if you know one neuron spikes and then the neuronic connects to spikes after it Then it seems like that first neuron caused that second neuron to spike and Hebbian learning would say that those uh that that connection between those neurons should grow even stronger So that this first neuron will continue to cause the second neuron to spike So it's kind of simple in that way. It doesn't actually involve any feedback about what happened after those neurons spiked and was it a good thing or a bad thing or anything like that the most basic form of Hebbian learning doesn't It just says that things that happened temporarily close in time should create a greater association. Oh, because I see spike timing dependent plasticity Is what's which was I guess was discovered in the late 1990s or something that is so this that sort of like a Hebbian, yeah, that's that's really is his hebbian ID At the single neural level. Yeah, I have the hebb's original conception. I don't think spoke of temporal order necessarily But yeah, just the idea that things that were you know firing together Associations should be formed between things that are occurring at the same time. Mm-hmm And then you have that like the the Hopfield model Which is sort of like the yeah This is a really nice and popular model which Which everybody likes in sense. It's a beautiful model Yeah, it sort of is Oh, it gives a lot of insights at this qualitative and with rather simple mathematics and elegant mathematics Yeah, the Hopfield model really represents the I mean you could maybe divide kind of the history of computational neuroscience into a first wave That was really like the electrical circuit kind of models That were more on the biophysical level and then In the 80s you get this influx of physicists who want to study the brain And Hopfield himself and his model the Hopfield network really Represent that era where From what I've heard from these physicists that they found physics to like already be solved like too many of the mysteries For not mysteries anymore And so they were turning to the brain where things were a wider Many of them came from statistical physics also because that's like the branch with many units Yes, exactly. It was like cooperative properties. So it sort of has like this spin So in that way But well suited for the brain you can see why they saw that connection Yeah, that like where we were studying individual atoms and how they create Large-scale behavior from their interactions and the brain is a bunch of individual neurons that interact and create large-scale behavior And so that that's kind of what the Hopfield model, you know, is based on the idea that you have these individual neurons and by changing the connection shrinks between them You can Create these large-scale behaviors that Hopfield associated with memory states so you can create a network that can store memories and recall memories Based solely on the interactions between the individual neurons and it also had this like Associated thing or that that I can you that you can sort of complete memories that if you have like you can put in a partial pattern of a memory state So kind of just turn some of the right neurons on or off and then the connections between the neurons will reinstate the full memory pattern The full activity pattern that represents that memory actually back back in the days when I used to do semi-conductive physics And well took a PhD in semi-conductive physics and then I switched to neuroscience I went to this meeting in Sweden where where Hopfield was So I so I was really new in this field, but I knew about the Hopfield model So so I asked him sort of what what was this role? What what what did what did you think was the role of his Hopfield model? What role would it have in the end and then he said this going well, it's going to it might be a metaphor For how the how the brain were or how memory works and that was sort of yeah But at least it's sort of certainly something about models which are not certainly not In Well correct in the details in anyway, but still very useful Because it has it gives us a way to think about think about it. Yeah, there was pushback from neuroscientists of the time of like This isn't neuroscience But then you know is that that approach has has carried on in various forms You know the more abstract approach because it does seem to still highlight useful Ideas about how the brain could be working even though it's not like these biophysically detailed models that came before Yeah, no because it's it's also that like with his biofuscally that monolith is large network models You can sort of do simulations that get out results which are hard to It's hard to get your head and wrap your head around right? I mean so so at least with these simple models has this advantage that That you can sort of yeah, you can sort of understand the consequences and sort of Yeah, get some yeah get some some key ideas out maybe So But this so this attractor models that so I think you mentioned it also that that that this has been also for a working memory that some of this attractor Attractor models has been has been used Yeah, so the The tractor model is the Hotfield Network is an a tractor model and it can be used for thinking about long-term memories as well, like this idea of putting in a partial bit and recovering it. But then, yeah, tractors are also helpful for working memory because it's just a description of kind of the dynamical properties of the model that when there's a certain state that it can be in, where the neurons will sustain their own firing and even if the tractor is built the right way, even if you kind of perturb the system a little bit, it'll still go back to that state. So it'll hold on to that memory even if some inputs are coming in. If you perturb the system too much, it'll get knocked out of that state. But it has some basic properties that would help hold on to something, which is what you need in working memory. Yeah, and this is like the Ring Network model that we talked about is an example of that, right? So yeah. So that's sort of like, obviously, you need some kind of-- you need some kind of memory, both at different timescales in the brain. And this like, a tractor is an attractive, I guess. A tractor is an attractive alternative there. And when I look at sort of-- I mean, I think if you sort of want to do something like in text message to a foreign civilization about both you have learned about the brain, I would say, well, I think we understand a single neuron fairly OK. But we are really-- the networks, we are sort of really struggling. But I guess one, it's not that many specific concrete insights that has come from, I think, network studies, at least sort of like, by a physical, by like, mechanistic network studies. But I think this idea of a balanced excitation and inhibition is one of them. So that's sort of like something we can sort of put in our belt and be proud about. So what is the problem there? A more way. Yeah. So kind of one way in to understanding this notion of balance is to think about the variability of response in neurons. If you give this a neuron in a network the same input over an external current or something like that, it won't respond exactly the same way each time. And so that was a mystery for a while as to why neurons weren't behaving in a kind of clean deterministic way and why they had this noise in them. And the solution or the kind of mechanism that's been found to explain why they're a bit noisy and a bit erratic in a way is this fact that neurons get a lot of inputs. And those inputs can be excitatory or inhibitory. And they're basically getting a lot of both of those. So at any given moment they're being strongly driven to fire but also strongly shut down by the inhibition. And when you have those two heavy things leaning against each other if there's any slight imbalance kind of the whole system falls over but it could go in different directions. And so that tight balance between excitation and inhibition puts networks of neurons in this kind of precarious state where they're very subject to small fluctuations and inputs and cause big changes in the output. And so this is achieved through processes that make it such that neurons get a roughly equal amount of excitation and inhibition coming into them at any time. But it's sort of like driving you with your gas pedal and a brake pedal in at the same time. So it sounds a bit too-- seems a bit wasteful, April-Yorey. So why-- What's the advantage of this? Yeah, I guess it goes against the efficient coding in some way if we're just like creating all this input just to cancel it out. But one thing that people have found is that it does lead to faster responses in neurons. So if it was like neurons were completely off and not getting any input and when they were supposed to fire, then you just start getting them input and then you have to wait for them to kind of integrate and then fire and everything like that, that could make it slower to respond. Whereas if you have the excitation just at the ready and you just need to kind of let the inhibition go down or push the excitation a little bit more to overcome the inhibitions, then you can get this really fast response. Shooting across traffic light when it comes to being like this. Yeah. Impressed the neighbor. Just always at the ready. Yeah, no, that's sort of like a cool idea. I guess that was developed in the-- well, on the student in the '90s. Yeah, this is part of the same wave of the physicists coming into neuroscience using their physics models. And then you have, I think, one paper I really like, which is this Brunel paper on the paper by Nikola Brunel on this phase diagram. We can sort of see how you with different-- this very simple network with it to find your own spot X, Taturian, inhibitory. And by changing the weights a little bit, you can get all this kind of different firing patterns. Not only this very noisy pattern, but also the regular oscillations and so on. So I guess we are at the-- we understand some generic properties of networks. It's just very difficult to translate it to understanding one particular experiment. Well, biological network, I guess, we're not quite at least that much harder. So I mean, one piece of-- well, one part of computation neuroscience, which I never worked on myself, is this with this-- but it's important-- well, both because it's an important problem in neuroscience, but also because it has so many-- it's all linked to applications in AI, is this thing with reinforcement learning. Because that's also one of the success stories, maybe, of computation neuroscience, where you have these explanations that at Mars three levels of understanding. Yeah, so reinforcement learning refers generally to the idea of learning from rewards, rather than learning from particular feedback. So it would be like if you took a test and instead of actually getting the graded test back where you knew what you did right or wrong, you just got the grade. And you just knew, like, you overall did a good job or a bad job. So that's pretty hard because you don't know what contributed to the reward you got, if you got what reward you don't know what contributed to not getting the reward. So it's a really difficult problem. But animals can clearly do it. There's clearly a lot of reward-based learning that goes on in humans, but in animal behavior as well. And so, yeah, the story of reinforcement learning really spans a lot of different influences. It's like people who were simply studying behavior, people who studied neurons, people who study artificial intelligence, everyone was adding their angle to it. But yeah, one of the major-- so yeah, if we think about Mars three levels, the computational level is to learn from rewards. It's to learn to do well because of reward feedback. And that means learning what actions to take well in advance of when you'd actually get the reward. And so that was a problem that was of interest to Richard Bellman, who was working at the Rand Corporation, and he was an applied mathematician. And so he was trying to solve those problems for industrial application. Any business has to make decisions that will later result in reward or not reward. And so he came up with this value function idea, which is this idea that you want to learn a value function, meaning you want to learn in any given state that you're in. Is it a good state or a bad state? So you won't know what reward you get yet, but you can have a sense of, like, am I in a good state or a bad state? And this can happen in-- it's kind of intuitive, like if you play chess or something like that. Someone could just plop you down and in front of a partially played chess game, and you'd be able to have a sense of, like, ooh, this is not a good state for me to be in. This is like a bad board state for me. I'm probably not going to win this game. So you have this sense of value, even though you're not getting the reward feedback. You don't know if you want to loss yet. You have a sense of, like, from this position, how close am I to reward? How well set up am I? And so the goal is to learn that value function. If you play chess a lot, you learn it, because humans are good at reinforcement learning, to some extent, you will learn that value function for these different states. And so Richard Bellman was trying to come up with-- he kind of defined this concept of value function that that's what you're aiming for, because then you can make the decisions well in advance of when you actually get the reward. You can make decisions as you play the chess game. They get you to a better board state that has a high value where you feel like you will win. But you can make these decisions based on the value well in advance of when you get the reward. But then the question is, how do you actually learn this value function? And that's where some more influence from behavioral studies and that sort of thing also came in. Sutton and Bartow are also computer scientists, slash cognitive science. This whole realm of reinforcement learning is very mixed in terms of what kind of scientists these people are. But this idea that you can learn the value function through exploration, where the key thing that matters is that you make a prediction about what reward you'll get. And then you compare that to what you actually got. So the key computation is doing a reward prediction error calculation. And if you update your value function when you incorrectly predicted reward, then you will learn a value function that can be very helpful for getting reward in the future. And then this has been borne out in a lot of various animal experiments as well. Yeah, because then maybe the surprise, or at least for me, surprising is that you don't-- you get this at the neural level. You get this dopamine reward, or whatever, like a dopamine squirts. But it's not like you get the dopamine reward when-- And you, well, if you don't get dopamine as reward, you get the dopamine when you signal error, right? - Yeah, so people-- - Error in prediction, yeah? - Yeah, people kind of associate dopamine with reward or with pleasure or happiness or that kind of thing. But in fact, it is a signal, at least, the kind of current computational framework for understanding dopamine is that it's a signal of reward prediction error. But if you predicted that you weren't going to get a reward and then you did, that's a positive error. And so that's how it becomes associated with something pleasurable because you got a reward when you didn't think you were going to get one. But if you expect a reward, if it's like it's payday and you get your paycheck, there's no dopamine there. There's no, even though it is a reward in some way, you got money, you got something you wanted, but you expected it. So you don't get any pleasure from that. - It is like this 50 year old, so have everything, right? They're old, they don't get any pleasant surprises anymore because they have everything. - You need to be, your expectations need to be violated. So yeah, so it was found that that's a better description of what dopamine signals is this kind of reward prediction error idea. And that makes a lot of sense because dopamine also plays a role in gating synaptic class, just the way of gating changes in connections between neurons, which is how learning happens. So if dopamine is there, it means you made an error in your prediction and therefore changes need to happen in the networks so that you don't make that error again. - But where in the brain does this happen? It's not necessarily cortex, right? - I mean, it's all, so the dopamine neurons generally come from subcortical areas, but they really spread out to a lot of places. So I think it's happening. - The whole circuit. Because it's also like this straight, and it's not like this one of these areas, I just know the name and I barely know what they do. - Yeah, so there's dopamine neurons there, but I think they send their projections to a lot of places. - Oh, I see. Yeah. So that's also one of the successes we can sort of brag about. I guess this idea almost, that idea about this error signal came actually from theory, in some sense, first. And then it was sort of like-- - Yeah, kind of from computer science, wanting to build systems that could solve this difficult problem. - That's cool. - Yeah. And then, I mean, we have this new way of doing computational science, which I think is the type of neuroscience you are interested in, or computational science, you're using AI. So to sort of, to, to, to, to, well, because they, the hard, I mean, I, when you try to fit sort of, like to say, this large scale cortical models to experiments, it's very hard. You don't really have a learning rule. You have to sort of to try to fit experiments. It's not like, it's not very easy to train or to fit these models to data. But with these AI models, you have these beautiful learning rules, right? So you can train the AI models, these convolutional neural networks and other architectures to, and that is quite successful in quite, that works quite well, right? So that is sort of the, yeah, so, so that's the advantage of that type of network. So, because that's like a new branch of computation neuroscience. Well, you could say it's new, or you could say it's a, you know, revisiting of the perceptron, a revisiting of the time in the 80s, where people were doing a similar kind of approach. But yeah, the, the benefit there is, yeah, as you say, you can train these networks. But importantly, for the most part, people are not training them to capture neural data directly. They're training them to produce a behavior like being able to classify images and that kind of thing. And so it's, in that way, it's a more behavior-forward approach than I think actually a lot of computational neuroscience had been. And maybe even the kind of systems neuroscience more generally, it really matters that you're thinking about what behavior you think the network should be generating and making sure that you're studying a model that can actually do that behavior versus, you know, some of these like circuit models we're talking about, they're, they're not meant to complete a full, full input output, you know, that the organism does, they're meant to replicate a very small part of the brain that's part of a larger circuit. And you make assumptions about how this small thing that you're modeling fits into the larger system in order to create behavior. But with these artificial neural networks that we have the data and compute to train to do full tasks, then you can really be studying a model that's actually doing the behavior of interest. But then you often go in, after we're in a train network and try to make connections to like particularly in the visual system, I guess, there has been some like, when there's sort of looked at this, this, this AI network that's been trained to, to for image classification. And then when you look into them afterwards, then they have something that resembles the neural representation or a receptive fields in the visual system of mammals, right? Yeah, that's one of the cool things that, that comes out of it and what kind of further helps verify that these are good models is that then, yeah, you can go inside and you can make comparisons between the artificial neural activity and the real neural activity in response to the same inputs. You know, you can literally show a human or a monkey in image and show the same image to the neural network and compare the neural responses. And yeah, in vision in particular, that's been quite successful on the whole. And people are interested in finding out what exactly about the neural network is helping it match the real neural activity. You know, is it about how you train it, the data you train it on, the architecture of the network trying to figure out what makes the model the best match to the neural activity so that you can say something about the visual system in the brain itself. And yeah, people have kind of deployed this in other sensory systems and other computations of the brain as well. So yeah, for the most part, the setup is you don't train on neural data. You're not training the model to predict the neural data, but you're training it to do a task. And then you're able to relate the artificial neural activity to the real neural activity because they're both doing the same task. And hopefully you've given kind of the right architecture that you're mimicking how the brain is doing that. So I mean, from the view of web page, I got the impression that you are working on these things. These days? Yeah, so my research is mostly around building these artificial neural networks. Well, can it be a little bit about it or? Hey, yeah, sure. So a big part of what I do is city attention, which is a big concept. It has a lot of different definitions. But I'm mostly focused on sensory attention. So just this idea, like if you're looking for your car keys, there are changes that happen in your visual system that make you better at finding them, kind of the neurons that respond to shiny things of a certain shape. They'll have their firing rate increased so that you can help you detect the thing that you're looking for. And so I kind of use these models because they can actually do behavior. You can show them complex images and ask them what they see in the image. And then you can also add in mechanisms that mimic attention in the brain so that you can study exactly how attention changes behavior on complex visual tasks. I'm also studying auditory tasks now. So that's kind of the reason for using these models is that for me to understand something like attention, the whole point of attention is that it enhances your performance at difficult tasks. And so I need the model to be able to perform difficult tasks. And then I also need a model that has something like neurons that correspond to different brain regions so that I can put in the biological mechanisms that I think are at play. And these models have both of those. So it's really nice for me. I think it's a nice model system to study attention in particular. So how do you include attention specifically in your models? How is that? So the basic idea, again, my goal, because some people kind of work in this neuro-AI space and partly their goal is to take the biology and make AI better. But my goal is mainly to use these artificial neural networks to build models of the brain and just make them as biologically correct as possible. So I look at the literature, the neurophysiology of attention, how it changes neural activity, what kind of neurons have their activity changed by attention and all of that. And for the most part, it comes down to changing the gain of the neuron, changing the slope of the input output function for certain neurons that represent the attended objects. And so there's a few different ways you can control that in these artificial neural networks. But the point is you kind of come in and you gain modulate parts of the network, and then you see how that impacts the performance of the network. Cool. So well, are we approaching the end here? So I think we can sort of, well, put our head down, put our head down, and be a little bit more speculative. So it's fun to talk about sort of like this-- I remember I read this book, "Dreams of a Final Theory," which I had to do with-- oh, by Stephen Weinberg, you had to do it particle physics. So what's your dream of a final-- do you have a dream of a final theory for the brain, whatever-- what would that mean? See, it's funny because I think it is very common-- I don't know about other fields, but certainly in neuroscience, people look to physics as like, this is how a science is meant to progress. Physics did this, so we should do this. Physics did large-scale experiments that centralized hubs like CERN, so we should have those as neuroscientists. But I think the nature of the brain makes it unlikely that there will be a final theory. I think it's a big-- of whatever solutions evolution could get to. And so trying to follow in the path of physics and hope that we're going to get to cleaner and simpler descriptions that explain everything, I think that's not likely to happen. I think we need to kind of accept that there will be different theories that explain different abilities and different types of neural networks and everything and that that's fine. - But I guess, I mean, when you talk about physics, you think about high energy, particle physics and because I come from solid state physics and there things are more messy and it's not like one, I mean, it's, it's not, well, when I, I mean, in some sense, you can say that if you, if you're able, if you can sort of put a bunch of atoms in a lattice, for example, and then you can use solid-shurening actuation for these all these electrons in a piece of metal or piece of whatever. And that's, that's very difficult to do numerically, but we know that if we're able to do it, then in principle, that everything should come out of this like superconductivity and semiconductors and metals and all these different things. So in some sense, you could call that a theory of, but it's, but also, but that doesn't really tell us, I mean, in practice, in order to understand things like superconductivity, you need like special theories that just like highlight that phenomena, which are much simpler. So I think maybe for me, it's more about maybe like this biophysically detailed models with large networks, that's more like this, you build, that's like a large scale simulations of electrons, which are, which tells you something because it's, well, because you can get out numerical results which can be revealing, but it doesn't really, it doesn't really tell you, it's difficult to, to wrap your hand around, head around these different phenomena. So I guess you need both maybe. Yeah, I mean, I think there is this question of, what is the right level to be trying to understand the brain and what are kind of, we entitled to expect as an understanding, because there is this idea that came with this new way of people using artificial neural networks as models that the kind of traditional things people were trying to do, like put individual neurons into categories and try to understand them on their own. Like that was misguided and that's never going to be how we'll understand the brain and we need to accept that understanding is not going to look like what we thought it would. Up to the point of people saying that like, understanding the brain just means understanding kind of its basic architecture, what it's trained to do and the learning rule that trained it and then the rest is just the emergent properties of those three things. And so that's very different than how neuroscientists have been trying to understand the brain. And so, yeah, but there's no reason why the way we kind of innately at first, when we could only record from one neuron at a time, like the norms that were set up and the expectations that were set up from that time and history, there's no reason why those have to have been the correct ones. And so I'm sympathetic to the idea that we need to expect things to be described on like a higher level of abstraction than people have mostly been working at. I don't know exactly what that level is or how to define it or how to derive it from neural to the e-book. One more little or one one, we talk about this free energy principle. We have this chapter, which I think, which is sort of fun about the run unified theories, where you sort of speculate a little bit in different directions. And so this free energy principle is one of these really high level principles that maybe can. So that's one way. Yeah, one way that's one way to phrase or like a theory at some level, right? Yeah, I mean, I don't I don't have much hope that that's going to be the answer for us, but it is something that's out there. But a principle like that. I mean, something that because that's really high level. Yeah, I think even that whole kind of shape of an answer is not. I'm not expecting to find that. No. Except, one way you could see there's one version that arguably is a general principle that you could say explains everything. And that's kind of just like the idea that artificial neural networks are universal function approximators. So just whatever the brain is doing and our neural network can do. We know that neural networks are universal function approximators. And so there that's the answer that solves the brain. Cool. Of course, I mean, if you look back at the history of computational neuroscience, like, we, I mean, we're like, we have always been underdog in neuroscience. I would say like both of these quantitatively, right? I don't know what, what, what fractional neuroscientists today would sort of identify as a computational neuroscientist, maybe like a few percent. I don't really know. Something like that. Just by looking at the number of people going to computational conferences versus society of neuroscience, for example. Yeah. And like, and, and for example, Ramon Icahal, the founder of like modern model, well, it's very important. Nure's like this. He didn't. He didn't have much respect for theories that all right? Yeah. And he was more of an artist, more of a observer, documentary kind of. But also this he sort of didn't really like. So this, these people were just thinking or not doing experiments. They were some kind of lazy charlatans. Yeah. Yeah. And there's still a little bit of that around. Isn't it? I heard, even, we even read this although John Hopfield wrote a paper about his life in science and he, he told, he wrote there that in the 70s, he was taking a side at one of these conferences by an experimentally saying that, well, this is not really good style to work on other people's data. And you have to make a round it. And I also heard like similar things in the, it's sort of this, I just, yeah. So that's one thing. Yeah. It only seems like it's changing though. You can certainly find those people who, yeah, either think that the mathematical models are useless because they don't replicate every single detail. Or yeah, that somehow using other people's data is either lazy or like you'll never be able to understand it. You couldn't like only the person who collected the data can understand it well enough to use it, which is scary because it's like shouldn't you be documenting things enough that it can be conveyed to other people. But certainly I think that's changing culturally like younger generation of neuroscientists don't see that divide as strongly. There's more people who are doing their own data collection, but also doing like serious modeling work. The grant agencies are shifting incentives to make you have to share your data and are you know, willing to fund projects that use publicly available data. I mean, the Allen Institute is definitely showing this with, I mean, their whole, a lot of what they do is collecting data for the purposes of sharing it. So yeah, I think things are shifting in a better direction. Yeah. I just wanted to want to because I know, I know the physics community and they also felt a little bit annoyed by sort of like philosophers of physics because they didn't really know physics and there was sort of who are they to start philosophies on our things. It's like, maybe if it's like a little bit like the experimentalist thinking about the scholars who are they that don't really do the recording. Yeah, there's a little maybe distrust or something like that. I think you can go both ways though. I think that there are, you know, modelers who are like this experimentalist isn't understanding what my model says and what it means for their experiments and everything. So, I mean, one goal of this, this starting this podcast is to try to make contribute to making the computational or theoretical neuroscience community. And nice and generous community because one thing, I mean, one thing that I sometimes compare the computational neuroscience community to sort of like trying to settle Australia with 10 people. It's just too few people to, it's very few people. I mean, for example, we discussed this, this, this, this network that E-Mordor has been modeling, right? That's, it's, that's not, I don't think that has been picked up by many other groups. Not because it's not exciting, but it's just so many problems, so many animals, so many ways to do modeling compared to the number of computational neuroscientists in the field. So, I think it's sort of a sparse, sparse field in that sense. We are sort of often quite alone in our, sort of, on our own little turf, so that's, that's all done. So, I think we have a lot of different approaches compared to the number of people we are. And one thing I've been wondering about, do you think we are a generous community? I mean, nice to each other. I think we are a total neuroscientist. I don't think we're particularly not generous. I mean, I mean, I mean, in terms of academic things, people build like toolboxes that they maintain for other people to use and all of that. But this, this petition against the human brain project, that was a quite unique thing. That's, that's very rare that there's like petitions against projects which has been funded, right? So, that's, and that was often, I've a lot within competition neuroscience also. I think that's, that wasn't our proudest hour, I think. I think the amount of, like that funding was itself a unique thing. So I think that does, you know, and also, but that wasn't exclusively computational, right? I mean, the human brain project and everything includes a lot of experimental work and finds a lot of experimental work as well. I think it's just when one entity is getting a lot of attention and resources and people feel that they're not representative of, you know, what the field is doing. I think that that can draw out, you know, people are going to have things to say about that. But still, it's so we should try to maybe do better. be more generous because if you look at this different approaches, they are really so many different approaches. And I think it's at the, they're not so many success stories when it comes to network behavior in particular that we should just try out different things and I think at least. So, so anyway, so, but I think it was really nice to have you on this inaugural podcast. So I think, I think you had this very nice, you wrote at the end of your chapter one of your book. I think I'll just read that. You said, and the chapter one in your book, mathematical models of the mind do not make for perfect replicas of the brain, nor should be strived them to be yet in the study of the most complex object in a known universe, mathematical models are not just useful, but absolutely essential. The brain will not be understood through words alone. That was a nice sentence, not to be understood by words alone. So I think that should be like a credo for, yeah. But then it is the start of, you know, 90,000 word book. That's true. But so you need some words also, but not words alone. So thanks for coming to the podcast Grace. Yeah, thank you. I'm so happy to be invited as the inaugural guest.